%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU011+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:55:01 PM UTC 2026
% Result : Theorem 13.94s 2.61s
% Output : CNFRefutation 13.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 46
% Syntax : Number of formulae : 6048 ( 550 unt; 5 def)
% Number of atoms : 19683 (5590 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 14290 (6107 ~;8066 |; 85 &)
% ( 6 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 6 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 8461 ( 2 sgn8440 !; 21 ?;8163 :)
% 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,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f7,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f8,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f9,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f11,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f12,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f13,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f15,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f16,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f17,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f18,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f19,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(f20,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f21,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f22,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f23,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f24,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f25,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f26,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f27,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f28,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f29,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f30,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f31,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f32,axiom,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(f33,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f34,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f35,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> relation_dom(relation_composition(identity_relation(X0),X1)) = set_intersection2(relation_dom(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_1) ).
fof(f36,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f37,conjecture,
! [X0,X1] : relation_composition(identity_relation(X1),identity_relation(X0)) = identity_relation(set_intersection2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0,X1] : relation_composition(identity_relation(X1),identity_relation(X0)) = identity_relation(set_intersection2(X0,X1)),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f40,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f41,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f42,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f43,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f44,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( ! [X2] :
( in(X2,relation_dom(X0))
=> apply(X0,X2) = apply(X1,X2) )
& relation_dom(X0) = relation_dom(X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).
fof(f45,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f20]) ).
fof(f46,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f29]) ).
fof(f47,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f36]) ).
fof(f48,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f28]) ).
fof(f50,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f51,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f52,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f53,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f54,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f56,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f58,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f60,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f17]) ).
fof(f62,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f64,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f65,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f67,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f68,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f69,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f71,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f73,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| relation_dom(relation_composition(identity_relation(X0),X1)) = set_intersection2(relation_dom(X1),X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f75,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| relation_dom(relation_composition(identity_relation(X0),X1)) = set_intersection2(relation_dom(X1),X0) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f77,plain,
? [X0,X1] : relation_composition(identity_relation(X1),identity_relation(X0)) != identity_relation(set_intersection2(X0,X1)),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f39]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f81,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f41]) ).
fof(f82,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f83,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f84,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ? [X2] :
( in(X2,relation_dom(X0))
& apply(X1,X2) != apply(X0,X2) )
| relation_dom(X0) != relation_dom(X1)
| X0 = X1 ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f85,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ? [X2] :
( in(X2,relation_dom(X0))
& apply(X1,X2) != apply(X0,X2) )
| relation_dom(X0) != relation_dom(X1)
| X0 = X1 ) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(flattening,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(rectify,[],[f87]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( in(sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f88]) ).
fof(f90,plain,
! [X0] : element(sK1(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f8]) ).
fof(f91,plain,
( function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f21]) ).
fof(f92,plain,
( relation(sK3)
& empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f22]) ).
fof(f93,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK4(X0))
& element(sK4(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f66]) ).
fof(f94,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X0,sK5)],[f24]) ).
fof(f95,plain,
( relation(sK6)
& ~ empty(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f25]) ).
fof(f96,plain,
! [X0] :
( empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f26]) ).
fof(f97,plain,
~ empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f27]) ).
fof(f98,plain,
relation(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f48]) ).
fof(f99,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f100,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(rectify,[],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ( in(sK10(X0,X1),X0)
& sK10(X0,X1) != apply(X1,sK10(X0,X1)) )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f101]) ).
fof(f103,plain,
relation_composition(identity_relation(sK12),identity_relation(sK11)) != identity_relation(set_intersection2(sK11,sK12)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f77]) ).
fof(f104,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( in(sK13(X0,X1),relation_dom(X0))
& apply(X1,sK13(X0,X1)) != apply(X0,sK13(X0,X1)) )
| relation_dom(X0) != relation_dom(X1)
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X2,sK13(X0,X1))],[f85]) ).
fof(f105,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f106,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f107,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f108,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f109,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f110,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f111,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f112,plain,
! [X2,X0,X1] :
( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f89]) ).
fof(f113,plain,
! [X2,X0,X1] :
( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f89]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f89]) ).
fof(f115,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f116,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f117,plain,
! [X0] : element(sK1(X0),X0),
inference(cnf_transformation,[],[f90]) ).
fof(f118,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f119,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| empty(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f122,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f124,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f125,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f127,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f128,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f129,plain,
relation(empty_set),
inference(cnf_transformation,[],[f16]) ).
fof(f130,plain,
empty(empty_set),
inference(cnf_transformation,[],[f16]) ).
fof(f131,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f132,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_dom(X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f133,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f134,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f135,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| empty(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f136,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f45]) ).
fof(f137,plain,
function(sK2),
inference(cnf_transformation,[],[f91]) ).
fof(f138,plain,
relation(sK2),
inference(cnf_transformation,[],[f91]) ).
fof(f139,plain,
relation(sK3),
inference(cnf_transformation,[],[f92]) ).
fof(f140,plain,
empty(sK3),
inference(cnf_transformation,[],[f92]) ).
fof(f141,plain,
! [X0] :
( empty(X0)
| ~ empty(sK4(X0)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f142,plain,
! [X0] :
( empty(X0)
| element(sK4(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f143,plain,
empty(sK5),
inference(cnf_transformation,[],[f94]) ).
fof(f144,plain,
relation(sK6),
inference(cnf_transformation,[],[f95]) ).
fof(f145,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f95]) ).
fof(f146,plain,
! [X0] : empty(sK7(X0)),
inference(cnf_transformation,[],[f96]) ).
fof(f147,plain,
! [X0] : element(sK7(X0),powerset(X0)),
inference(cnf_transformation,[],[f96]) ).
fof(f148,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f97]) ).
fof(f149,plain,
relation(sK9),
inference(cnf_transformation,[],[f98]) ).
fof(f150,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f46]) ).
fof(f151,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f153,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f32]) ).
fof(f154,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f155,plain,
! [X3,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(X3,X0)
| apply(X1,X3) = X3 ),
inference(cnf_transformation,[],[f102]) ).
fof(f156,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| identity_relation(X0) != X1
| relation_dom(X1) = X0 ),
inference(cnf_transformation,[],[f102]) ).
fof(f157,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| in(sK10(X0,X1),X0)
| relation_dom(X1) != X0
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f102]) ).
fof(f158,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| sK10(X0,X1) != apply(X1,sK10(X0,X1))
| relation_dom(X1) != X0
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f102]) ).
fof(f159,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| relation_dom(relation_composition(identity_relation(X0),X1)) = set_intersection2(relation_dom(X1),X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f160,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f161,plain,
relation_composition(identity_relation(sK12),identity_relation(sK11)) != identity_relation(set_intersection2(sK11,sK12)),
inference(cnf_transformation,[],[f103]) ).
fof(f162,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f163,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f164,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f81]) ).
fof(f165,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f166,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f167,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1)
| in(sK13(X0,X1),relation_dom(X0))
| relation_dom(X0) != relation_dom(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f104]) ).
fof(f168,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1)
| apply(X1,sK13(X0,X1)) != apply(X0,sK13(X0,X1))
| relation_dom(X0) != relation_dom(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f104]) ).
fof(f169,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f111]) ).
fof(f170,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f110]) ).
fof(f171,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f109]) ).
fof(f172,plain,
! [X1] :
( ~ function(X1)
| ~ relation(X1)
| sK10(relation_dom(X1),X1) != apply(X1,sK10(relation_dom(X1),X1))
| identity_relation(relation_dom(X1)) = X1 ),
inference(equality_resolution,[],[f158]) ).
fof(f173,plain,
! [X1] :
( ~ function(X1)
| ~ relation(X1)
| in(sK10(relation_dom(X1),X1),relation_dom(X1))
| identity_relation(relation_dom(X1)) = X1 ),
inference(equality_resolution,[],[f157]) ).
fof(f174,plain,
! [X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(equality_resolution,[],[f156]) ).
fof(f175,plain,
! [X3,X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(X3,X0)
| apply(identity_relation(X0),X3) = X3 ),
inference(equality_resolution,[],[f155]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_50,plain,
! [X0: $i] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_51,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f108]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X1)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_60,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f116]) ).
tcf(c_61,plain,
! [X0: $i] : element(sK1(X0),X0),
inference(cnf_transformation,[],[f117]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_69,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f125]) ).
tcf(c_71,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f128]) ).
tcf(c_72,plain,
! [X0: $i] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f127]) ).
tcf(c_73,plain,
empty(empty_set),
inference(cnf_transformation,[],[f130]) ).
tcf(c_74,plain,
relation(empty_set),
inference(cnf_transformation,[],[f129]) ).
tcf(c_75,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_76,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_77,plain,
! [X0: $i] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_80,plain,
! [X0: $i] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f136]) ).
tcf(c_81,plain,
relation(sK2),
inference(cnf_transformation,[],[f138]) ).
tcf(c_82,plain,
function(sK2),
inference(cnf_transformation,[],[f137]) ).
tcf(c_83,plain,
empty(sK3),
inference(cnf_transformation,[],[f140]) ).
tcf(c_84,plain,
relation(sK3),
inference(cnf_transformation,[],[f139]) ).
tcf(c_85,plain,
! [X0: $i] :
( empty(X0)
| element(sK4(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_86,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK4(X0)) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_87,plain,
empty(sK5),
inference(cnf_transformation,[],[f143]) ).
tcf(c_88,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f145]) ).
tcf(c_89,plain,
relation(sK6),
inference(cnf_transformation,[],[f144]) ).
tcf(c_90,plain,
! [X0: $i] : element(sK7(X0),powerset(X0)),
inference(cnf_transformation,[],[f147]) ).
tcf(c_91,plain,
! [X0: $i] : empty(sK7(X0)),
inference(cnf_transformation,[],[f146]) ).
tcf(c_92,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f148]) ).
tcf(c_93,plain,
relation(sK9),
inference(cnf_transformation,[],[f149]) ).
tcf(c_94,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f150]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) )
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X1)
| ~ in(X0,relation_dom(relation_composition(X1,X2))) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_97,plain,
! [X0: $i] : set_intersection2(X0,empty_set) = empty_set,
inference(cnf_transformation,[],[f153]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_99,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ( apply(X0,sK10(relation_dom(X0),X0)) != sK10(relation_dom(X0),X0) ) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_100,plain,
! [X0: $i] :
( in(sK10(relation_dom(X0),X0),relation_dom(X0))
| ( identity_relation(relation_dom(X0)) = X0 )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_101,plain,
! [X0: $i] :
( ( relation_dom(identity_relation(X0)) = X0 )
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),X0)) = set_intersection2(relation_dom(X0),X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_105,negated_conjecture,
relation_composition(identity_relation(sK12),identity_relation(sK11)) != identity_relation(set_intersection2(sK11,sK12)),
inference(cnf_transformation,[],[f161]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_108,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0)
| ( relation_dom(X0) != relation_dom(X1) )
| ( apply(X0,sK13(X0,X1)) != apply(X1,sK13(X0,X1)) ) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( in(sK13(X0,X1),relation_dom(X0))
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0)
| ( relation_dom(X0) != relation_dom(X1) ) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_117,plain,
~ empty(powerset(empty_set)),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_132,plain,
( empty(relation_composition(empty_set,empty_set))
| ~ relation(empty_set)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_144,plain,
! [X0: $i] : relation_dom(identity_relation(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_101,c_72,c_71,c_101]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ function(identity_relation(X1))
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_102,c_60]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_169,c_72]) ).
tcf(c_537,plain,
relation_composition(identity_relation(sK12),identity_relation(sK11)) != identity_relation(set_intersection2(sK12,sK11)),
inference(demodulation,[status(thm)],[c_105,c_52]) ).
tcf(c_650,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X1,powerset(X2))
| ( X0 != X2 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_94,c_104]) ).
tcf(c_651,plain,
! [X0: $i] : element(X0,powerset(X0)),
inference(unflattening,[status(thm)],[c_650]) ).
tcf(c_1147,definition,
iPr_def_10 = identity_relation(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1148,definition,
iPr_def_11 = identity_relation(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1149,definition,
iPr_def_12 = relation_composition(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1150,definition,
iPr_def_13 = set_intersection2(sK12,sK11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1151,definition,
iPr_def_14 = identity_relation(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1152,plain,
iPr_def_12 != iPr_def_14,
inference(demodulation,[status(thm)],[c_537,c_1150,c_1151,c_1148,c_1147,c_1149]) ).
tcf(c_1866,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_73,c_50]) ).
tcf(c_1867,plain,
function(sK3),
inference(superposition,[status(thm)],[c_83,c_50]) ).
tcf(c_1868,plain,
function(sK5),
inference(superposition,[status(thm)],[c_87,c_50]) ).
tcf(c_1869,plain,
! [X0: $i] : function(sK7(X0)),
inference(superposition,[status(thm)],[c_91,c_50]) ).
tcf(c_1877,plain,
relation(sK5),
inference(superposition,[status(thm)],[c_87,c_51]) ).
tcf(c_1878,plain,
! [X0: $i] : relation(sK7(X0)),
inference(superposition,[status(thm)],[c_91,c_51]) ).
tcf(c_1880,plain,
function(iPr_def_10),
inference(superposition,[status(thm)],[c_1147,c_72]) ).
tcf(c_1881,plain,
relation(iPr_def_10),
inference(superposition,[status(thm)],[c_1147,c_71]) ).
tcf(c_1882,plain,
relation_dom(iPr_def_10) = sK12,
inference(superposition,[status(thm)],[c_1147,c_144]) ).
tcf(c_1883,plain,
function(iPr_def_11),
inference(superposition,[status(thm)],[c_1148,c_72]) ).
tcf(c_1884,plain,
relation(iPr_def_11),
inference(superposition,[status(thm)],[c_1148,c_71]) ).
tcf(c_1885,plain,
relation_dom(iPr_def_11) = sK11,
inference(superposition,[status(thm)],[c_1148,c_144]) ).
tcf(c_1886,plain,
function(iPr_def_14),
inference(superposition,[status(thm)],[c_1151,c_72]) ).
tcf(c_1887,plain,
relation(iPr_def_14),
inference(superposition,[status(thm)],[c_1151,c_71]) ).
tcf(c_1888,plain,
relation_dom(iPr_def_14) = iPr_def_13,
inference(superposition,[status(thm)],[c_1151,c_144]) ).
tcf(c_1893,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_144,c_76]) ).
tcf(c_1895,plain,
! [X0: $i] :
( function(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_50]) ).
tcf(c_1901,plain,
( empty(sK12)
| ~ empty(iPr_def_10) ),
inference(superposition,[status(thm)],[c_1882,c_76]) ).
tcf(c_1904,plain,
( empty(sK11)
| ~ empty(iPr_def_11) ),
inference(superposition,[status(thm)],[c_1885,c_76]) ).
tcf(c_1907,plain,
( empty(iPr_def_13)
| ~ empty(iPr_def_14) ),
inference(superposition,[status(thm)],[c_1888,c_76]) ).
tcf(c_1918,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_144,c_77]) ).
tcf(c_1919,plain,
( relation(sK12)
| ~ empty(iPr_def_10) ),
inference(superposition,[status(thm)],[c_1882,c_77]) ).
tcf(c_1920,plain,
( relation(sK11)
| ~ empty(iPr_def_11) ),
inference(superposition,[status(thm)],[c_1885,c_77]) ).
tcf(c_1921,plain,
( relation(iPr_def_13)
| ~ empty(iPr_def_14) ),
inference(superposition,[status(thm)],[c_1888,c_77]) ).
tcf(c_1965,plain,
! [X0: $i] :
( function(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_144,c_1895]) ).
tcf(c_1966,plain,
( function(sK12)
| ~ empty(iPr_def_10) ),
inference(superposition,[status(thm)],[c_1882,c_1895]) ).
tcf(c_1967,plain,
( function(sK11)
| ~ empty(iPr_def_11) ),
inference(superposition,[status(thm)],[c_1885,c_1895]) ).
tcf(c_1968,plain,
( function(iPr_def_13)
| ~ empty(iPr_def_14) ),
inference(superposition,[status(thm)],[c_1888,c_1895]) ).
tcf(c_1996,plain,
! [X0: $i] : set_intersection2(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_97,c_52]) ).
tcf(c_2013,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_108]) ).
tcf(c_2014,plain,
empty_set = sK3,
inference(superposition,[status(thm)],[c_83,c_108]) ).
tcf(c_2015,plain,
empty_set = sK5,
inference(superposition,[status(thm)],[c_87,c_108]) ).
tcf(c_2016,plain,
! [X0: $i] : sK7(X0) = empty_set,
inference(superposition,[status(thm)],[c_91,c_108]) ).
tcf(c_2026,plain,
! [X0: $i] : element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[c_90,c_2016]) ).
tcf(c_2054,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_73,c_2013]) ).
tcf(c_2055,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_2013]) ).
tcf(c_2069,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_97,c_57]) ).
tcf(c_2071,plain,
! [X0: $i] :
( in(X0,sK12)
| ~ in(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_1150,c_57]) ).
tcf(c_2102,plain,
! [X0: $i] :
( in(X0,sK11)
| ~ in(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_1150,c_58]) ).
tcf(c_2113,plain,
! [X0: $i] :
( empty(identity_relation(X0))
| ~ empty(X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_144,c_75]) ).
tcf(c_2115,plain,
( empty(iPr_def_10)
| ~ relation(iPr_def_10)
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_1882,c_75]) ).
tcf(c_2116,plain,
( empty(iPr_def_11)
| ~ relation(iPr_def_11)
| ~ empty(sK11) ),
inference(superposition,[status(thm)],[c_1885,c_75]) ).
tcf(c_2117,plain,
( empty(iPr_def_14)
| ~ relation(iPr_def_14)
| ~ empty(iPr_def_13) ),
inference(superposition,[status(thm)],[c_1888,c_75]) ).
tcf(c_2118,plain,
( empty(iPr_def_14)
| ~ empty(iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2117,c_1887]) ).
tcf(c_2121,plain,
( empty(iPr_def_11)
| ~ empty(sK11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2116,c_1884]) ).
tcf(c_2124,plain,
( empty(iPr_def_10)
| ~ empty(sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2115,c_1881]) ).
tcf(c_2127,plain,
! [X0: $i] :
( empty(identity_relation(X0))
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2113,c_71]) ).
tcf(c_2137,plain,
! [X0: $i] :
( empty(X0)
| in(sK1(X0),X0) ),
inference(superposition,[status(thm)],[c_61,c_98]) ).
tcf(c_2138,plain,
! [X0: $i] :
( empty(X0)
| empty(powerset(X0))
| in(sK4(X0),powerset(X0)) ),
inference(superposition,[status(thm)],[c_85,c_98]) ).
tcf(c_2139,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(X0,powerset(X0)) ),
inference(superposition,[status(thm)],[c_651,c_98]) ).
tcf(c_2140,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(empty_set,powerset(X0)) ),
inference(superposition,[status(thm)],[c_2026,c_98]) ).
tcf(c_2143,plain,
! [X0: $i] : in(empty_set,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2140,c_69]) ).
tcf(c_2144,plain,
! [X0: $i] : in(X0,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2139,c_69]) ).
tcf(c_2145,plain,
! [X0: $i] :
( empty(X0)
| in(sK4(X0),powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2138,c_69]) ).
tcf(c_2155,plain,
( relation(iPr_def_12)
| ~ relation(iPr_def_11)
| ~ relation(iPr_def_10) ),
inference(superposition,[status(thm)],[c_1149,c_59]) ).
tcf(c_2156,plain,
relation(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_2155,c_1884,c_1881]) ).
tcf(c_2157,plain,
! [X0: $i] : ~ in(powerset(X0),empty_set),
inference(superposition,[status(thm)],[c_2143,c_49]) ).
tcf(c_2161,plain,
! [X0: $i] : ~ in(powerset(X0),X0),
inference(superposition,[status(thm)],[c_2144,c_49]) ).
tcf(c_2183,plain,
! [X0: $i] :
( ( relation_dom(identity_relation(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_2013]) ).
tcf(c_2184,plain,
! [X0: $i] :
( ( identity_relation(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_108]) ).
tcf(c_2198,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK1(X0)) ),
inference(superposition,[status(thm)],[c_2137,c_49]) ).
tcf(c_2201,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| in(sK1(set_intersection2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_2137,c_58]) ).
tcf(c_2202,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| in(sK1(set_intersection2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_2137,c_57]) ).
tcf(c_2204,plain,
( empty(iPr_def_13)
| in(sK1(iPr_def_13),sK12) ),
inference(superposition,[status(thm)],[c_2137,c_2071]) ).
tcf(c_2218,plain,
( empty(iPr_def_13)
| ~ in(sK12,sK1(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_2204,c_49]) ).
tcf(c_2219,plain,
( empty(iPr_def_13)
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_2204,c_109]) ).
tcf(c_2220,plain,
( empty(iPr_def_13)
| element(sK1(iPr_def_13),sK12) ),
inference(superposition,[status(thm)],[c_2204,c_95]) ).
tcf(c_2237,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,X0),X1)
| ( set_intersection2(X1,X2) = X0 )
| ~ in(X0,sK0(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_54,c_49]) ).
tcf(c_2238,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,X0),X1)
| ( set_intersection2(X1,X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_109]) ).
tcf(c_2239,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_54,c_95]) ).
tcf(c_2241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK0(X0,X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_54,c_58]) ).
tcf(c_2242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK0(X0,X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_54,c_57]) ).
tcf(c_2243,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,empty_set),X2)
| in(sK0(X0,X1,empty_set),X0)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_54,c_2069]) ).
tcf(c_2244,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,iPr_def_13),sK12)
| in(sK0(X0,X1,iPr_def_13),X0)
| ( set_intersection2(X0,X1) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_54,c_2071]) ).
tcf(c_2245,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ in(X0,sK0(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_54,c_49]) ).
tcf(c_2246,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_109]) ).
tcf(c_2247,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,X1,X2),X0)
| in(sK0(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_54,c_95]) ).
tcf(c_2249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(set_intersection2(X0,X1),X2,X3),X3)
| in(sK0(set_intersection2(X0,X1),X2,X3),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_54,c_58]) ).
tcf(c_2250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(set_intersection2(X0,X1),X2,X3),X3)
| in(sK0(set_intersection2(X0,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_54,c_57]) ).
tcf(c_2251,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(empty_set,X0,X1),X2)
| in(sK0(empty_set,X0,X1),X1)
| ( set_intersection2(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_54,c_2069]) ).
tcf(c_2252,plain,
! [X0: $i,X1: $i] :
( in(sK0(iPr_def_13,X0,X1),sK12)
| in(sK0(iPr_def_13,X0,X1),X1)
| ( set_intersection2(iPr_def_13,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_54,c_2071]) ).
tcf(c_2253,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,X0),X0)
| ( set_intersection2(X0,X1) = X0 ) ),
inference(equality_factoring,[status(thm)],[c_54]) ).
tcf(c_2266,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(empty_set,X1,X0),X2)
| in(sK0(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_2251,c_1996]) ).
tcf(c_2309,plain,
( empty(iPr_def_12)
| ~ relation(iPr_def_10)
| ~ empty(iPr_def_11) ),
inference(superposition,[status(thm)],[c_1149,c_62]) ).
tcf(c_2310,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(X1,X0)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_2013]) ).
tcf(c_2311,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,X0) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_108]) ).
tcf(c_2313,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_50]) ).
tcf(c_2314,plain,
( empty(iPr_def_12)
| ~ empty(iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2309,c_1881]) ).
tcf(c_2347,plain,
( relation(iPr_def_13)
| ~ relation(sK11)
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_1150,c_68]) ).
tcf(c_2351,plain,
! [X0: $i] :
( empty(powerset(X0))
| ~ empty(sK4(powerset(X0))) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_2352,plain,
( empty(powerset(empty_set))
| ~ empty(sK4(powerset(empty_set))) ),
inference(instantiation,[status(thm)],[c_2351]) ).
tcf(c_2361,plain,
( empty(iPr_def_12)
| ~ relation(iPr_def_11)
| ~ empty(iPr_def_10) ),
inference(superposition,[status(thm)],[c_1149,c_78]) ).
tcf(c_2362,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(X0,X1)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_2013]) ).
tcf(c_2363,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,X1) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_108]) ).
tcf(c_2365,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_50]) ).
tcf(c_2366,plain,
( empty(iPr_def_12)
| ~ empty(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2361,c_1884]) ).
tcf(c_2394,plain,
( empty(iPr_def_13)
| empty(sK12)
| in(sK1(iPr_def_13),sK12) ),
inference(superposition,[status(thm)],[c_2220,c_98]) ).
tcf(c_2402,plain,
! [X0: $i,X1: $i] :
( in(sK0(iPr_def_13,X0,X1),sK11)
| in(sK0(iPr_def_13,X0,X1),X1)
| ( set_intersection2(iPr_def_13,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_54,c_2102]) ).
tcf(c_2403,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,iPr_def_13),sK11)
| in(sK0(X0,X1,iPr_def_13),X0)
| ( set_intersection2(X0,X1) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_54,c_2102]) ).
tcf(c_2404,plain,
( empty(iPr_def_13)
| in(sK1(iPr_def_13),sK11) ),
inference(superposition,[status(thm)],[c_2137,c_2102]) ).
tcf(c_2419,plain,
( empty(iPr_def_13)
| ~ in(sK11,sK1(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_2404,c_49]) ).
tcf(c_2420,plain,
( empty(iPr_def_13)
| ~ empty(sK11) ),
inference(superposition,[status(thm)],[c_2404,c_109]) ).
tcf(c_2421,plain,
( empty(iPr_def_13)
| element(sK1(iPr_def_13),sK11) ),
inference(superposition,[status(thm)],[c_2404,c_95]) ).
tcf(c_2440,plain,
( empty(iPr_def_13)
| empty(sK11)
| in(sK1(iPr_def_13),sK11) ),
inference(superposition,[status(thm)],[c_2421,c_98]) ).
tcf(c_2448,plain,
! [X0: $i] :
( empty(X0)
| ~ in(powerset(X0),sK4(X0)) ),
inference(superposition,[status(thm)],[c_2145,c_49]) ).
tcf(c_2453,plain,
( ( iPr_def_12 = iPr_def_14 )
| ~ empty(iPr_def_14)
| ~ empty(iPr_def_12) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_2470,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_composition(X0,X1)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_2184]) ).
tcf(c_2471,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_composition(X1,X0)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_2184]) ).
tcf(c_2472,plain,
identity_relation(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_73,c_2184]) ).
tcf(c_2473,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_2184]) ).
tcf(c_2474,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_2184]) ).
tcf(c_2514,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X0,X2) = X1 )
| ~ relation(X2)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_110]) ).
tcf(c_2515,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X2,X0) = X1 )
| ~ relation(X2)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_110]) ).
tcf(c_2517,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_110]) ).
tcf(c_2518,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_110]) ).
tcf(c_2542,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ( apply(identity_relation(X0),sK0(X0,X1,X2)) = sK0(X0,X1,X2) ) ),
inference(superposition,[status(thm)],[c_54,c_172]) ).
tcf(c_2543,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,X0),X1)
| ( set_intersection2(X1,X2) = X0 )
| ( apply(identity_relation(X0),sK0(X1,X2,X0)) = sK0(X1,X2,X0) ) ),
inference(superposition,[status(thm)],[c_54,c_172]) ).
tcf(c_2544,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2137,c_172]) ).
tcf(c_2545,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(powerset(X0)),sK4(X0)) = sK4(X0) ) ),
inference(superposition,[status(thm)],[c_2145,c_172]) ).
tcf(c_2546,plain,
! [X0: $i] : apply(identity_relation(powerset(X0)),X0) = X0,
inference(superposition,[status(thm)],[c_2144,c_172]) ).
tcf(c_2547,plain,
! [X0: $i] : apply(identity_relation(powerset(X0)),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_2143,c_172]) ).
tcf(c_2548,plain,
( empty(iPr_def_13)
| ( apply(identity_relation(sK12),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_2204,c_172]) ).
tcf(c_2549,plain,
( empty(iPr_def_13)
| ( apply(identity_relation(sK11),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_2404,c_172]) ).
tcf(c_2550,plain,
( empty(iPr_def_13)
| ( apply(iPr_def_11,sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(light_normalisation,[status(thm)],[c_2549,c_1148]) ).
tcf(c_2553,plain,
( empty(iPr_def_13)
| ( apply(iPr_def_10,sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(light_normalisation,[status(thm)],[c_2548,c_1147]) ).
tcf(c_2582,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK1(powerset(X1))) ),
inference(superposition,[status(thm)],[c_61,c_106]) ).
tcf(c_2583,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(X0,X1)
| ~ in(X0,sK4(X1)) ),
inference(superposition,[status(thm)],[c_85,c_106]) ).
tcf(c_2585,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_2026,c_106]) ).
tcf(c_2606,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(empty_set,X0,X1),X2)
| in(sK0(empty_set,X0,X1),X1)
| ( set_intersection2(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_54,c_2585]) ).
tcf(c_2607,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,X1,empty_set),X2)
| in(sK0(X0,X1,empty_set),X0)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_54,c_2585]) ).
tcf(c_2612,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(empty_set,X1,X0),X2)
| in(sK0(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_2606,c_1996]) ).
tcf(c_2634,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_composition(X0,X1))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_2055]) ).
tcf(c_2635,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_composition(X1,X0))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_2055]) ).
tcf(c_2636,plain,
relation_dom(relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_2055]) ).
tcf(c_2637,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_2055]) ).
tcf(c_2638,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_2055]) ).
tcf(c_2655,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_composition(X0,X1))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_2473]) ).
tcf(c_2656,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_composition(X1,X0))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_2473]) ).
tcf(c_2657,plain,
identity_relation(relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_2473]) ).
tcf(c_2658,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_2473]) ).
tcf(c_2659,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_2473]) ).
tcf(c_2683,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_composition(X0,X1))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_2474]) ).
tcf(c_2684,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_composition(X1,X0))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_2474]) ).
tcf(c_2685,plain,
identity_relation(identity_relation(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_2474]) ).
tcf(c_2686,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_2474]) ).
tcf(c_2687,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_2474]) ).
tcf(c_2706,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(sK1(powerset(X0)),X1,X2),X0)
| in(sK0(sK1(powerset(X0)),X1,X2),X2)
| ( set_intersection2(sK1(powerset(X0)),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_54,c_2582]) ).
tcf(c_2707,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,X1,sK1(powerset(X2))),X2)
| in(sK0(X0,X1,sK1(powerset(X2))),X0)
| ( set_intersection2(X0,X1) = sK1(powerset(X2)) ) ),
inference(superposition,[status(thm)],[c_54,c_2582]) ).
tcf(c_2708,plain,
! [X0: $i] :
( empty(sK1(powerset(X0)))
| element(sK1(sK1(powerset(X0))),X0) ),
inference(superposition,[status(thm)],[c_2137,c_2582]) ).
tcf(c_2732,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| in(sK1(set_intersection2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_52,c_2201]) ).
tcf(c_2734,plain,
! [X0: $i] :
( empty(set_intersection2(X0,X0))
| in(sK1(X0),X0) ),
inference(superposition,[status(thm)],[c_80,c_2201]) ).
tcf(c_2735,plain,
! [X0: $i] :
( in(sK1(empty_set),empty_set)
| empty(set_intersection2(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_97,c_2201]) ).
tcf(c_2736,plain,
! [X0: $i] :
( empty(set_intersection2(empty_set,X0))
| in(sK1(empty_set),X0) ),
inference(superposition,[status(thm)],[c_1996,c_2201]) ).
tcf(c_2737,plain,
( empty(set_intersection2(sK12,sK11))
| in(sK1(iPr_def_13),sK11) ),
inference(superposition,[status(thm)],[c_1150,c_2201]) ).
tcf(c_2738,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ( apply(identity_relation(X0),sK1(set_intersection2(X1,X0))) = sK1(set_intersection2(X1,X0)) ) ),
inference(superposition,[status(thm)],[c_2201,c_172]) ).
tcf(c_2739,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ~ in(X0,sK1(set_intersection2(X1,X0))) ),
inference(superposition,[status(thm)],[c_2201,c_49]) ).
tcf(c_2740,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2201,c_109]) ).
tcf(c_2741,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| element(sK1(set_intersection2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_2201,c_95]) ).
tcf(c_2742,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,set_intersection2(X1,X2)))
| in(sK1(set_intersection2(X0,set_intersection2(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_2201,c_58]) ).
tcf(c_2743,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,set_intersection2(X1,X2)))
| in(sK1(set_intersection2(X0,set_intersection2(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_2201,c_57]) ).
tcf(c_2744,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,empty_set))
| element(sK1(set_intersection2(X0,empty_set)),X1) ),
inference(superposition,[status(thm)],[c_2201,c_2585]) ).
tcf(c_2745,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,empty_set))
| in(sK1(set_intersection2(X0,empty_set)),X1) ),
inference(superposition,[status(thm)],[c_2201,c_2069]) ).
tcf(c_2746,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(set_intersection2(X0,iPr_def_13)),sK11) ),
inference(superposition,[status(thm)],[c_2201,c_2102]) ).
tcf(c_2747,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(set_intersection2(X0,iPr_def_13)),sK12) ),
inference(superposition,[status(thm)],[c_2201,c_2071]) ).
tcf(c_2748,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,sK1(powerset(X1))))
| element(sK1(set_intersection2(X0,sK1(powerset(X1)))),X1) ),
inference(superposition,[status(thm)],[c_2201,c_2582]) ).
tcf(c_2752,plain,
! [X0: $i] :
( empty(empty_set)
| in(sK1(empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_2736,c_1996]) ).
tcf(c_2753,plain,
( empty(empty_set)
| in(sK1(empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_2735,c_97]) ).
tcf(c_2760,plain,
! [X0: $i] :
( empty(empty_set)
| element(sK1(empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_2744,c_97]) ).
tcf(c_2796,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,X0),X2)
| ( set_intersection2(X1,X2) = X0 )
| ( apply(identity_relation(X0),sK0(X1,X2,X0)) = sK0(X1,X2,X0) ) ),
inference(superposition,[status(thm)],[c_55,c_172]) ).
tcf(c_2797,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,X0),X2)
| ( set_intersection2(X1,X2) = X0 )
| ~ in(X0,sK0(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_55,c_49]) ).
tcf(c_2798,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,X0),X2)
| ( set_intersection2(X1,X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_109]) ).
tcf(c_2799,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X1)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_55,c_95]) ).
tcf(c_2801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK0(X0,X1,set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_55,c_58]) ).
tcf(c_2802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK0(X0,X1,set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_2803,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,X1,empty_set),X2)
| in(sK0(X0,X1,empty_set),X1)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_55,c_2585]) ).
tcf(c_2804,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,empty_set),X2)
| in(sK0(X0,X1,empty_set),X1)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_55,c_2069]) ).
tcf(c_2805,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,iPr_def_13),sK11)
| in(sK0(X0,X1,iPr_def_13),X1)
| ( set_intersection2(X0,X1) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_55,c_2102]) ).
tcf(c_2806,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,iPr_def_13),sK12)
| in(sK0(X0,X1,iPr_def_13),X1)
| ( set_intersection2(X0,X1) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_55,c_2071]) ).
tcf(c_2807,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,X1,sK1(powerset(X2))),X2)
| in(sK0(X0,X1,sK1(powerset(X2))),X1)
| ( set_intersection2(X0,X1) = sK1(powerset(X2)) ) ),
inference(superposition,[status(thm)],[c_55,c_2582]) ).
tcf(c_2808,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X0,X2),X2)
| ( set_intersection2(X1,X0) = X2 )
| ( apply(identity_relation(X0),sK0(X1,X0,X2)) = sK0(X1,X0,X2) ) ),
inference(superposition,[status(thm)],[c_55,c_172]) ).
tcf(c_2809,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X0,X2),X2)
| ( set_intersection2(X1,X0) = X2 )
| ~ in(X0,sK0(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_55,c_49]) ).
tcf(c_2810,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X0,X2),X2)
| ( set_intersection2(X1,X0) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_109]) ).
tcf(c_2811,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_55,c_95]) ).
tcf(c_2813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X0,set_intersection2(X1,X2),X3),X3)
| in(sK0(X0,set_intersection2(X1,X2),X3),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_55,c_58]) ).
tcf(c_2814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X0,set_intersection2(X1,X2),X3),X3)
| in(sK0(X0,set_intersection2(X1,X2),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_2815,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,empty_set,X1),X2)
| in(sK0(X0,empty_set,X1),X1)
| ( set_intersection2(X0,empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_55,c_2585]) ).
tcf(c_2816,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,empty_set,X1),X2)
| in(sK0(X0,empty_set,X1),X1)
| ( set_intersection2(X0,empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_55,c_2069]) ).
tcf(c_2817,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,iPr_def_13,X1),sK11)
| in(sK0(X0,iPr_def_13,X1),X1)
| ( set_intersection2(X0,iPr_def_13) = X1 ) ),
inference(superposition,[status(thm)],[c_55,c_2102]) ).
tcf(c_2818,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,iPr_def_13,X1),sK12)
| in(sK0(X0,iPr_def_13,X1),X1)
| ( set_intersection2(X0,iPr_def_13) = X1 ) ),
inference(superposition,[status(thm)],[c_55,c_2071]) ).
tcf(c_2819,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,sK1(powerset(X1)),X2),X1)
| in(sK0(X0,sK1(powerset(X1)),X2),X2)
| ( set_intersection2(X0,sK1(powerset(X1))) = X2 ) ),
inference(superposition,[status(thm)],[c_55,c_2582]) ).
tcf(c_2820,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,X1),X1)
| ( set_intersection2(X0,X1) = X1 ) ),
inference(equality_factoring,[status(thm)],[c_55]) ).
tcf(c_2836,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,empty_set,X0),X2)
| in(sK0(X1,empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_2816,c_97]) ).
tcf(c_2840,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X1,empty_set,X0),X2)
| in(sK0(X1,empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_2815,c_97]) ).
tcf(c_2908,plain,
! [X0: $i,X1: $i] :
( empty(sK4(powerset(X1)))
| in(X0,sK4(powerset(X1)))
| ~ element(X0,sK4(powerset(X1))) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_2909,plain,
( empty(sK4(powerset(empty_set)))
| in(empty_set,sK4(powerset(empty_set)))
| ~ element(empty_set,sK4(powerset(empty_set))) ),
inference(instantiation,[status(thm)],[c_2908]) ).
tcf(c_2913,plain,
! [X0: $i] :
( empty(sK4(powerset(X0)))
| ~ empty(sK4(sK4(powerset(X0)))) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_2914,plain,
( empty(sK4(powerset(empty_set)))
| ~ empty(sK4(sK4(powerset(empty_set)))) ),
inference(instantiation,[status(thm)],[c_2913]) ).
tcf(c_2933,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK1(powerset(X1))) ),
inference(superposition,[status(thm)],[c_61,c_107]) ).
tcf(c_2936,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_2026,c_107]) ).
tcf(c_2962,plain,
! [X0: $i] :
( in(X0,iPr_def_13)
| ~ in(X0,sK11)
| ~ in(X0,sK12) ),
inference(superposition,[status(thm)],[c_1150,c_56]) ).
tcf(c_2963,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(set_intersection2(X2,X1)),X0) = X0 )
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_172]) ).
tcf(c_2964,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(X2,X0)
| ~ in(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_56,c_49]) ).
tcf(c_2965,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_56,c_109]) ).
tcf(c_2966,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_95]) ).
tcf(c_2967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 )
| ~ in(sK0(X0,set_intersection2(X1,X2),X3),X3)
| ~ in(sK0(X0,set_intersection2(X1,X2),X3),X2)
| ~ in(sK0(X0,set_intersection2(X1,X2),X3),X1)
| ~ in(sK0(X0,set_intersection2(X1,X2),X3),X0) ),
inference(superposition,[status(thm)],[c_56,c_53]) ).
tcf(c_2970,plain,
! [X0: $i,X1: $i] :
( ~ in(powerset(set_intersection2(X0,X1)),X1)
| ~ in(powerset(set_intersection2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_56,c_2161]) ).
tcf(c_3010,plain,
( function(iPr_def_12)
| ~ relation(iPr_def_11)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_11)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_1149,c_67]) ).
tcf(c_3011,plain,
function(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_3010,c_1884,c_1881,c_1883,c_1880]) ).
tcf(c_3018,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(identity_relation(X2),relation_composition(X0,X1))) = set_intersection2(relation_dom(relation_composition(X0,X1)),X2) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_67,c_103]) ).
tcf(c_3019,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),identity_relation(X0))) = set_intersection2(relation_dom(identity_relation(X0)),X1) )
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_72,c_103]) ).
tcf(c_3020,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),sK2)) = set_intersection2(relation_dom(sK2),X0) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_82,c_103]) ).
tcf(c_3021,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),empty_set)) = set_intersection2(relation_dom(empty_set),X0) )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_1866,c_103]) ).
tcf(c_3022,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),iPr_def_10)) = set_intersection2(relation_dom(iPr_def_10),X0) )
| ~ relation(iPr_def_10) ),
inference(superposition,[status(thm)],[c_1880,c_103]) ).
tcf(c_3023,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),iPr_def_11)) = set_intersection2(relation_dom(iPr_def_11),X0) )
| ~ relation(iPr_def_11) ),
inference(superposition,[status(thm)],[c_1883,c_103]) ).
tcf(c_3024,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),iPr_def_14)) = set_intersection2(relation_dom(iPr_def_14),X0) )
| ~ relation(iPr_def_14) ),
inference(superposition,[status(thm)],[c_1886,c_103]) ).
tcf(c_3025,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),relation_dom(X0))) = set_intersection2(relation_dom(relation_dom(X0)),X1) )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_1895,c_103]) ).
tcf(c_3026,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),iPr_def_14)) = set_intersection2(iPr_def_13,X0) )
| ~ relation(iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_3024,c_1888]) ).
tcf(c_3027,plain,
! [X0: $i] : relation_dom(relation_composition(identity_relation(X0),iPr_def_14)) = set_intersection2(iPr_def_13,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_3026,c_1887]) ).
tcf(c_3028,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),iPr_def_11)) = set_intersection2(sK11,X0) )
| ~ relation(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_3023,c_1885]) ).
tcf(c_3029,plain,
! [X0: $i] : relation_dom(relation_composition(identity_relation(X0),iPr_def_11)) = set_intersection2(sK11,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_3028,c_1884]) ).
tcf(c_3030,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),iPr_def_10)) = set_intersection2(sK12,X0) )
| ~ relation(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_3022,c_1882]) ).
tcf(c_3031,plain,
! [X0: $i] : relation_dom(relation_composition(identity_relation(X0),iPr_def_10)) = set_intersection2(sK12,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_3030,c_1881]) ).
tcf(c_3032,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),empty_set)) = empty_set )
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_3021,c_1996,c_2054]) ).
tcf(c_3033,plain,
! [X0: $i] : relation_dom(relation_composition(identity_relation(X0),empty_set)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_3032,c_74]) ).
tcf(c_3034,plain,
! [X0: $i] : relation_dom(relation_composition(identity_relation(X0),sK2)) = set_intersection2(relation_dom(sK2),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_3020,c_81]) ).
tcf(c_3035,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),identity_relation(X0))) = set_intersection2(X0,X1) )
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_3019,c_144]) ).
tcf(c_3036,plain,
! [X0: $i,X1: $i] : relation_dom(relation_composition(identity_relation(X0),identity_relation(X1))) = set_intersection2(X1,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_3035,c_71]) ).
tcf(c_3065,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),iPr_def_12)) = set_intersection2(relation_dom(iPr_def_12),X0) )
| ~ relation(iPr_def_12) ),
inference(superposition,[status(thm)],[c_3011,c_103]) ).
tcf(c_3066,plain,
! [X0: $i] : relation_dom(relation_composition(identity_relation(X0),iPr_def_12)) = set_intersection2(relation_dom(iPr_def_12),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_3065,c_2156]) ).
tcf(c_3072,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_52,c_2740]) ).
tcf(c_3078,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_110]) ).
tcf(c_3079,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_2474]) ).
tcf(c_3080,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_2473]) ).
tcf(c_3081,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_2055]) ).
tcf(c_3082,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_2184]) ).
tcf(c_3083,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_2013]) ).
tcf(c_3084,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_108]) ).
tcf(c_3085,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X1,X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_51]) ).
tcf(c_3086,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X1,X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_50]) ).
tcf(c_3133,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,empty_set,X2),X2)
| ( set_intersection2(X1,empty_set) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_2936]) ).
tcf(c_3134,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(empty_set,X1,X2),X2)
| ( set_intersection2(empty_set,X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_2936]) ).
tcf(c_3135,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,empty_set),X2)
| ( set_intersection2(X1,X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_2936]) ).
tcf(c_3136,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,empty_set),X1)
| ( set_intersection2(X1,X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_2936]) ).
tcf(c_3138,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,empty_set))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2201,c_2936]) ).
tcf(c_3174,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_110]) ).
tcf(c_3175,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_2474]) ).
tcf(c_3176,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_2473]) ).
tcf(c_3177,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_2055]) ).
tcf(c_3178,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X0,X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_2184]) ).
tcf(c_3179,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X0,X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_2013]) ).
tcf(c_3180,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_108]) ).
tcf(c_3181,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X0,X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_51]) ).
tcf(c_3182,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X0,X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_50]) ).
tcf(c_3217,plain,
( relation(iPr_def_13)
| ~ empty(sK11) ),
inference(superposition,[status(thm)],[c_1150,c_3085]) ).
tcf(c_3220,plain,
~ empty(sK11),
inference(global_subsumption_just,[status(thm)],[c_3217,c_1152,c_2121,c_2118,c_2314,c_2420,c_2453]) ).
tcf(c_3222,plain,
~ empty(iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_1904,c_3220]) ).
tcf(c_3262,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(identity_relation(X2),set_intersection2(X0,X1))) = set_intersection2(relation_dom(set_intersection2(X0,X1)),X2) )
| ~ empty(X1)
| ~ relation(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3086,c_103]) ).
tcf(c_3267,plain,
! [X0: $i] :
( empty(empty_set)
| ~ empty(X0) ),
inference(demodulation,[status(thm)],[c_3138,c_97]) ).
tcf(c_3277,plain,
( relation(iPr_def_13)
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_1150,c_3181]) ).
tcf(c_3280,plain,
~ empty(sK12),
inference(global_subsumption_just,[status(thm)],[c_3277,c_1152,c_2124,c_2118,c_2219,c_2366,c_2453]) ).
tcf(c_3282,plain,
~ empty(iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_1901,c_3280]) ).
tcf(c_3283,plain,
relation_dom(relation_composition(iPr_def_10,iPr_def_14)) = set_intersection2(iPr_def_13,sK12),
inference(superposition,[status(thm)],[c_1147,c_3027]) ).
tcf(c_3284,plain,
relation_dom(relation_composition(iPr_def_11,iPr_def_14)) = set_intersection2(iPr_def_13,sK11),
inference(superposition,[status(thm)],[c_1148,c_3027]) ).
tcf(c_3285,plain,
relation_dom(relation_composition(empty_set,iPr_def_14)) = set_intersection2(iPr_def_13,empty_set),
inference(superposition,[status(thm)],[c_2472,c_3027]) ).
tcf(c_3286,plain,
relation_dom(relation_composition(iPr_def_14,iPr_def_14)) = set_intersection2(iPr_def_13,iPr_def_13),
inference(superposition,[status(thm)],[c_1151,c_3027]) ).
tcf(c_3287,plain,
! [X0: $i] :
( empty(relation_composition(identity_relation(X0),iPr_def_14))
| ~ empty(set_intersection2(iPr_def_13,X0))
| ~ relation(relation_composition(identity_relation(X0),iPr_def_14)) ),
inference(superposition,[status(thm)],[c_3027,c_75]) ).
tcf(c_3288,plain,
! [X0: $i] :
( function(set_intersection2(iPr_def_13,X0))
| ~ empty(relation_composition(identity_relation(X0),iPr_def_14)) ),
inference(superposition,[status(thm)],[c_3027,c_1895]) ).
tcf(c_3289,plain,
! [X0: $i] :
( relation(set_intersection2(iPr_def_13,X0))
| ~ empty(relation_composition(identity_relation(X0),iPr_def_14)) ),
inference(superposition,[status(thm)],[c_3027,c_77]) ).
tcf(c_3290,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ~ empty(relation_composition(identity_relation(X0),iPr_def_14)) ),
inference(superposition,[status(thm)],[c_3027,c_76]) ).
tcf(c_3318,plain,
! [X0: $i] :
( in(sK10(X0,identity_relation(X0)),X0)
| ( identity_relation(relation_dom(identity_relation(X0))) = identity_relation(X0) )
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_144,c_100]) ).
tcf(c_3319,plain,
( in(sK10(empty_set,empty_set),empty_set)
| ( identity_relation(relation_dom(empty_set)) = empty_set )
| ~ relation(empty_set)
| ~ function(empty_set) ),
inference(superposition,[status(thm)],[c_2054,c_100]) ).
tcf(c_3320,plain,
( in(sK10(sK12,iPr_def_10),sK12)
| ( identity_relation(relation_dom(iPr_def_10)) = iPr_def_10 )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_1882,c_100]) ).
tcf(c_3321,plain,
( in(sK10(sK11,iPr_def_11),sK11)
| ( identity_relation(relation_dom(iPr_def_11)) = iPr_def_11 )
| ~ relation(iPr_def_11)
| ~ function(iPr_def_11) ),
inference(superposition,[status(thm)],[c_1885,c_100]) ).
tcf(c_3322,plain,
( in(sK10(iPr_def_13,iPr_def_14),iPr_def_13)
| ( identity_relation(relation_dom(iPr_def_14)) = iPr_def_14 )
| ~ relation(iPr_def_14)
| ~ function(iPr_def_14) ),
inference(superposition,[status(thm)],[c_1888,c_100]) ).
tcf(c_3323,plain,
! [X0: $i] :
( in(sK10(set_intersection2(iPr_def_13,X0),relation_composition(identity_relation(X0),iPr_def_14)),set_intersection2(iPr_def_13,X0))
| ( identity_relation(relation_dom(relation_composition(identity_relation(X0),iPr_def_14))) = relation_composition(identity_relation(X0),iPr_def_14) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_14))
| ~ function(relation_composition(identity_relation(X0),iPr_def_14)) ),
inference(superposition,[status(thm)],[c_3027,c_100]) ).
tcf(c_3324,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = X0 )
| ( apply(identity_relation(relation_dom(X0)),sK10(relation_dom(X0),X0)) = sK10(relation_dom(X0),X0) )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_100,c_172]) ).
tcf(c_3325,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ in(relation_dom(X0),sK10(relation_dom(X0),X0)) ),
inference(superposition,[status(thm)],[c_100,c_49]) ).
tcf(c_3326,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_100,c_109]) ).
tcf(c_3327,plain,
! [X0: $i] :
( element(sK10(relation_dom(X0),X0),relation_dom(X0))
| ( identity_relation(relation_dom(X0)) = X0 )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_100,c_95]) ).
tcf(c_3349,plain,
! [X0: $i] :
( in(sK10(set_intersection2(iPr_def_13,X0),relation_composition(identity_relation(X0),iPr_def_14)),set_intersection2(iPr_def_13,X0))
| ( relation_composition(identity_relation(X0),iPr_def_14) = identity_relation(set_intersection2(iPr_def_13,X0)) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_14))
| ~ function(relation_composition(identity_relation(X0),iPr_def_14)) ),
inference(light_normalisation,[status(thm)],[c_3323,c_3027]) ).
tcf(c_3367,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(identity_relation(X0))) = identity_relation(X0) )
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0))
| ( apply(identity_relation(X0),sK10(X0,identity_relation(X0))) != sK10(X0,identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_144,c_99]) ).
tcf(c_3368,plain,
( ( identity_relation(relation_dom(empty_set)) = empty_set )
| ~ relation(empty_set)
| ~ function(empty_set)
| ( apply(empty_set,sK10(empty_set,empty_set)) != sK10(empty_set,empty_set) ) ),
inference(superposition,[status(thm)],[c_2054,c_99]) ).
tcf(c_3369,plain,
( ( identity_relation(relation_dom(iPr_def_10)) = iPr_def_10 )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ( apply(iPr_def_10,sK10(sK12,iPr_def_10)) != sK10(sK12,iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_1882,c_99]) ).
tcf(c_3370,plain,
( ( identity_relation(relation_dom(iPr_def_11)) = iPr_def_11 )
| ~ relation(iPr_def_11)
| ~ function(iPr_def_11)
| ( apply(iPr_def_11,sK10(sK11,iPr_def_11)) != sK10(sK11,iPr_def_11) ) ),
inference(superposition,[status(thm)],[c_1885,c_99]) ).
tcf(c_3371,plain,
( ( identity_relation(relation_dom(iPr_def_14)) = iPr_def_14 )
| ~ relation(iPr_def_14)
| ~ function(iPr_def_14)
| ( apply(iPr_def_14,sK10(iPr_def_13,iPr_def_14)) != sK10(iPr_def_13,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_1888,c_99]) ).
tcf(c_3372,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_composition(identity_relation(X0),iPr_def_14))) = relation_composition(identity_relation(X0),iPr_def_14) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_14))
| ~ function(relation_composition(identity_relation(X0),iPr_def_14))
| ( apply(relation_composition(identity_relation(X0),iPr_def_14),sK10(set_intersection2(iPr_def_13,X0),relation_composition(identity_relation(X0),iPr_def_14))) != sK10(set_intersection2(iPr_def_13,X0),relation_composition(identity_relation(X0),iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_3027,c_99]) ).
tcf(c_3378,plain,
! [X0: $i] :
( ( relation_composition(identity_relation(X0),iPr_def_14) = identity_relation(set_intersection2(iPr_def_13,X0)) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_14))
| ~ function(relation_composition(identity_relation(X0),iPr_def_14))
| ( apply(relation_composition(identity_relation(X0),iPr_def_14),sK10(set_intersection2(iPr_def_13,X0),relation_composition(identity_relation(X0),iPr_def_14))) != sK10(set_intersection2(iPr_def_13,X0),relation_composition(identity_relation(X0),iPr_def_14)) ) ),
inference(light_normalisation,[status(thm)],[c_3372,c_3027]) ).
tcf(c_3398,plain,
! [X0: $i,X1: $i] :
( in(sK13(identity_relation(X1),X0),relation_dom(identity_relation(X1)))
| ( identity_relation(X1) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ( relation_dom(X0) != X1 ) ),
inference(superposition,[status(thm)],[c_144,c_112]) ).
tcf(c_3399,plain,
! [X0: $i] :
( in(sK13(empty_set,X0),relation_dom(empty_set))
| ( X0 = empty_set )
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_2054,c_112]) ).
tcf(c_3400,plain,
! [X0: $i] :
( in(sK13(iPr_def_10,X0),relation_dom(iPr_def_10))
| ( X0 = iPr_def_10 )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != sK12 ) ),
inference(superposition,[status(thm)],[c_1882,c_112]) ).
tcf(c_3401,plain,
! [X0: $i] :
( in(sK13(iPr_def_11,X0),relation_dom(iPr_def_11))
| ( X0 = iPr_def_11 )
| ~ relation(iPr_def_11)
| ~ function(iPr_def_11)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != sK11 ) ),
inference(superposition,[status(thm)],[c_1885,c_112]) ).
tcf(c_3402,plain,
! [X0: $i] :
( in(sK13(iPr_def_14,X0),relation_dom(iPr_def_14))
| ( X0 = iPr_def_14 )
| ~ relation(iPr_def_14)
| ~ function(iPr_def_14)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1888,c_112]) ).
tcf(c_3403,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(identity_relation(X0),iPr_def_14),X1),relation_dom(relation_composition(identity_relation(X0),iPr_def_14)))
| ( relation_composition(identity_relation(X0),iPr_def_14) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),iPr_def_14))
| ~ function(relation_composition(identity_relation(X0),iPr_def_14))
| ( set_intersection2(iPr_def_13,X0) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_3027,c_112]) ).
tcf(c_3404,plain,
! [X0: $i,X1: $i] :
( in(sK13(X0,identity_relation(X1)),relation_dom(X0))
| ( identity_relation(X1) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ( relation_dom(X0) != X1 ) ),
inference(superposition,[status(thm)],[c_144,c_112]) ).
tcf(c_3405,plain,
! [X0: $i] :
( in(sK13(X0,empty_set),relation_dom(X0))
| ( X0 = empty_set )
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_2054,c_112]) ).
tcf(c_3406,plain,
! [X0: $i] :
( in(sK13(X0,iPr_def_10),relation_dom(X0))
| ( X0 = iPr_def_10 )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != sK12 ) ),
inference(superposition,[status(thm)],[c_1882,c_112]) ).
tcf(c_3407,plain,
! [X0: $i] :
( in(sK13(X0,iPr_def_11),relation_dom(X0))
| ( X0 = iPr_def_11 )
| ~ relation(iPr_def_11)
| ~ function(iPr_def_11)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != sK11 ) ),
inference(superposition,[status(thm)],[c_1885,c_112]) ).
tcf(c_3408,plain,
! [X0: $i] :
( in(sK13(X0,iPr_def_14),relation_dom(X0))
| ( X0 = iPr_def_14 )
| ~ relation(iPr_def_14)
| ~ function(iPr_def_14)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1888,c_112]) ).
tcf(c_3409,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,relation_composition(identity_relation(X0),iPr_def_14)),relation_dom(X1))
| ( relation_composition(identity_relation(X0),iPr_def_14) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),iPr_def_14))
| ~ function(relation_composition(identity_relation(X0),iPr_def_14))
| ( set_intersection2(iPr_def_13,X0) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_3027,c_112]) ).
tcf(c_3411,plain,
! [X0: $i] :
( in(sK13(X0,iPr_def_14),relation_dom(X0))
| ( X0 = iPr_def_14 )
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3408,c_1887,c_1886]) ).
tcf(c_3417,plain,
! [X0: $i] :
( in(sK13(X0,iPr_def_11),relation_dom(X0))
| ( X0 = iPr_def_11 )
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != sK11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3407,c_1884,c_1883]) ).
tcf(c_3423,plain,
! [X0: $i] :
( in(sK13(X0,iPr_def_10),relation_dom(X0))
| ( X0 = iPr_def_10 )
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3406,c_1881,c_1880]) ).
tcf(c_3429,plain,
! [X0: $i] :
( in(sK13(X0,empty_set),relation_dom(X0))
| ( X0 = empty_set )
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3405,c_74,c_1866]) ).
tcf(c_3435,plain,
! [X0: $i] :
( in(sK13(iPr_def_14,X0),iPr_def_13)
| ( X0 = iPr_def_14 )
| ~ relation(iPr_def_14)
| ~ function(iPr_def_14)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_3402,c_1888]) ).
tcf(c_3436,plain,
! [X0: $i] :
( in(sK13(iPr_def_14,X0),iPr_def_13)
| ( X0 = iPr_def_14 )
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3435,c_1887,c_1886]) ).
tcf(c_3442,plain,
! [X0: $i] :
( in(sK13(iPr_def_11,X0),sK11)
| ( X0 = iPr_def_11 )
| ~ relation(iPr_def_11)
| ~ function(iPr_def_11)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != sK11 ) ),
inference(light_normalisation,[status(thm)],[c_3401,c_1885]) ).
tcf(c_3443,plain,
! [X0: $i] :
( in(sK13(iPr_def_11,X0),sK11)
| ( X0 = iPr_def_11 )
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != sK11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3442,c_1884,c_1883]) ).
tcf(c_3449,plain,
! [X0: $i] :
( in(sK13(iPr_def_10,X0),sK12)
| ( X0 = iPr_def_10 )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != sK12 ) ),
inference(light_normalisation,[status(thm)],[c_3400,c_1882]) ).
tcf(c_3450,plain,
! [X0: $i] :
( in(sK13(iPr_def_10,X0),sK12)
| ( X0 = iPr_def_10 )
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3449,c_1881,c_1880]) ).
tcf(c_3456,plain,
! [X0: $i] :
( in(sK13(empty_set,X0),empty_set)
| ( X0 = empty_set )
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_3399,c_2054]) ).
tcf(c_3457,plain,
! [X0: $i] :
( in(sK13(empty_set,X0),empty_set)
| ( X0 = empty_set )
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3456,c_74,c_1866]) ).
tcf(c_3463,plain,
! [X0: $i,X1: $i] :
( in(sK13(X0,identity_relation(X1)),relation_dom(X0))
| ( identity_relation(X1) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3404,c_71,c_72]) ).
tcf(c_3469,plain,
! [X0: $i,X1: $i] :
( in(sK13(identity_relation(X1),X0),relation_dom(identity_relation(X1)))
| ( identity_relation(X1) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3398,c_71,c_72]) ).
tcf(c_3482,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(identity_relation(X0),iPr_def_14),X1),set_intersection2(iPr_def_13,X0))
| ( relation_composition(identity_relation(X0),iPr_def_14) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),iPr_def_14))
| ~ function(relation_composition(identity_relation(X0),iPr_def_14))
| ( set_intersection2(iPr_def_13,X0) != relation_dom(X1) ) ),
inference(light_normalisation,[status(thm)],[c_3403,c_3027]) ).
tcf(c_3510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,relation_dom(relation_composition(X0,X1)),X3),X3)
| ( set_intersection2(X2,relation_dom(relation_composition(X0,X1))) = X3 )
| ( apply(relation_composition(X0,X1),sK0(X2,relation_dom(relation_composition(X0,X1)),X3)) = apply(X1,apply(X0,sK0(X2,relation_dom(relation_composition(X0,X1)),X3))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_55,c_96]) ).
tcf(c_3511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(relation_dom(relation_composition(X0,X1)),X2,X3),X3)
| ( set_intersection2(relation_dom(relation_composition(X0,X1)),X2) = X3 )
| ( apply(relation_composition(X0,X1),sK0(relation_dom(relation_composition(X0,X1)),X2,X3)) = apply(X1,apply(X0,sK0(relation_dom(relation_composition(X0,X1)),X2,X3))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_54,c_96]) ).
tcf(c_3512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,relation_dom(relation_composition(X0,X1))),X3)
| ( relation_dom(relation_composition(X0,X1)) = set_intersection2(X2,X3) )
| ( apply(relation_composition(X0,X1),sK0(X2,X3,relation_dom(relation_composition(X0,X1)))) = apply(X1,apply(X0,sK0(X2,X3,relation_dom(relation_composition(X0,X1))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_55,c_96]) ).
tcf(c_3513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,relation_dom(relation_composition(X0,X1))),X2)
| ( relation_dom(relation_composition(X0,X1)) = set_intersection2(X2,X3) )
| ( apply(relation_composition(X0,X1),sK0(X2,X3,relation_dom(relation_composition(X0,X1)))) = apply(X1,apply(X0,sK0(X2,X3,relation_dom(relation_composition(X0,X1))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_54,c_96]) ).
tcf(c_3514,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_composition(X0,X1))) = relation_composition(X0,X1) )
| ( apply(relation_composition(X0,X1),sK10(relation_dom(relation_composition(X0,X1)),relation_composition(X0,X1))) = apply(X1,apply(X0,sK10(relation_dom(relation_composition(X0,X1)),relation_composition(X0,X1)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(relation_composition(X0,X1))
| ~ function(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_100,c_96]) ).
tcf(c_3515,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom(relation_composition(X0,X1)))
| ( apply(relation_composition(X0,X1),sK1(relation_dom(relation_composition(X0,X1)))) = apply(X1,apply(X0,sK1(relation_dom(relation_composition(X0,X1))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_2137,c_96]) ).
tcf(c_3516,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,relation_dom(relation_composition(X0,X1))))
| ( apply(relation_composition(X0,X1),sK1(set_intersection2(X2,relation_dom(relation_composition(X0,X1))))) = apply(X1,apply(X0,sK1(set_intersection2(X2,relation_dom(relation_composition(X0,X1)))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_2201,c_96]) ).
tcf(c_3517,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(identity_relation(X1),iPr_def_14),X0) = apply(iPr_def_14,apply(identity_relation(X1),X0)) )
| ~ relation(iPr_def_14)
| ~ function(iPr_def_14)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,set_intersection2(iPr_def_13,X1)) ),
inference(superposition,[status(thm)],[c_3027,c_96]) ).
tcf(c_3518,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_10,iPr_def_11),X0) = apply(iPr_def_11,apply(iPr_def_10,X0)) )
| ~ relation(iPr_def_11)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_11)
| ~ function(iPr_def_10)
| ~ in(X0,relation_dom(iPr_def_12)) ),
inference(superposition,[status(thm)],[c_1149,c_96]) ).
tcf(c_3519,plain,
! [X0: $i] :
( ( apply(iPr_def_11,apply(iPr_def_10,X0)) = apply(iPr_def_12,X0) )
| ~ relation(iPr_def_11)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_11)
| ~ function(iPr_def_10)
| ~ in(X0,relation_dom(iPr_def_12)) ),
inference(light_normalisation,[status(thm)],[c_3518,c_1149]) ).
tcf(c_3520,plain,
! [X0: $i] :
( ( apply(iPr_def_11,apply(iPr_def_10,X0)) = apply(iPr_def_12,X0) )
| ~ in(X0,relation_dom(iPr_def_12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3519,c_1884,c_1881,c_1883,c_1880]) ).
tcf(c_3523,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(identity_relation(X1),iPr_def_14),X0) = apply(iPr_def_14,apply(identity_relation(X1),X0)) )
| ~ in(X0,set_intersection2(iPr_def_13,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3517,c_1887,c_1886,c_71,c_72]) ).
tcf(c_3633,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(identity_relation(X2),set_intersection2(X0,X1))) = set_intersection2(relation_dom(set_intersection2(X0,X1)),X2) )
| ~ empty(X0)
| ~ relation(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3182,c_103]) ).
tcf(c_3637,plain,
relation_dom(relation_composition(iPr_def_10,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_1147,c_3033]) ).
tcf(c_3638,plain,
relation_dom(relation_composition(iPr_def_11,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_1148,c_3033]) ).
tcf(c_3639,plain,
relation_dom(relation_composition(empty_set,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_2472,c_3033]) ).
tcf(c_3640,plain,
relation_dom(relation_composition(iPr_def_14,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_1151,c_3033]) ).
tcf(c_3641,plain,
! [X0: $i,X1: $i] :
( in(sK13(X0,relation_composition(identity_relation(X1),empty_set)),relation_dom(X0))
| ( relation_composition(identity_relation(X1),empty_set) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(identity_relation(X1),empty_set))
| ~ function(relation_composition(identity_relation(X1),empty_set))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_3033,c_112]) ).
tcf(c_3642,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(identity_relation(X1),empty_set),X0),relation_dom(relation_composition(identity_relation(X1),empty_set)))
| ( relation_composition(identity_relation(X1),empty_set) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(identity_relation(X1),empty_set))
| ~ function(relation_composition(identity_relation(X1),empty_set))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_3033,c_112]) ).
tcf(c_3643,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_composition(identity_relation(X0),empty_set))) = relation_composition(identity_relation(X0),empty_set) )
| ~ relation(relation_composition(identity_relation(X0),empty_set))
| ~ function(relation_composition(identity_relation(X0),empty_set))
| ( apply(relation_composition(identity_relation(X0),empty_set),sK10(empty_set,relation_composition(identity_relation(X0),empty_set))) != sK10(empty_set,relation_composition(identity_relation(X0),empty_set)) ) ),
inference(superposition,[status(thm)],[c_3033,c_99]) ).
tcf(c_3644,plain,
! [X0: $i] :
( in(sK10(empty_set,relation_composition(identity_relation(X0),empty_set)),empty_set)
| ( identity_relation(relation_dom(relation_composition(identity_relation(X0),empty_set))) = relation_composition(identity_relation(X0),empty_set) )
| ~ relation(relation_composition(identity_relation(X0),empty_set))
| ~ function(relation_composition(identity_relation(X0),empty_set)) ),
inference(superposition,[status(thm)],[c_3033,c_100]) ).
tcf(c_3645,plain,
! [X0: $i] :
( empty(relation_composition(identity_relation(X0),empty_set))
| ~ empty(empty_set)
| ~ relation(relation_composition(identity_relation(X0),empty_set)) ),
inference(superposition,[status(thm)],[c_3033,c_75]) ).
tcf(c_3649,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(identity_relation(X1),empty_set),X0) = apply(empty_set,apply(identity_relation(X1),X0)) )
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_3033,c_96]) ).
tcf(c_3650,plain,
! [X0: $i] :
( empty(relation_composition(identity_relation(X0),empty_set))
| ~ relation(relation_composition(identity_relation(X0),empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3645,c_73]) ).
tcf(c_3653,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(identity_relation(X1),empty_set),X0) = apply(empty_set,apply(identity_relation(X1),X0)) )
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3649,c_74,c_1866,c_71,c_72]) ).
tcf(c_3656,plain,
! [X0: $i] :
( in(sK10(empty_set,relation_composition(identity_relation(X0),empty_set)),empty_set)
| ( relation_composition(identity_relation(X0),empty_set) = empty_set )
| ~ relation(relation_composition(identity_relation(X0),empty_set))
| ~ function(relation_composition(identity_relation(X0),empty_set)) ),
inference(light_normalisation,[status(thm)],[c_3644,c_2472,c_3033]) ).
tcf(c_3675,plain,
! [X0: $i] :
( ( relation_composition(identity_relation(X0),empty_set) = empty_set )
| ~ relation(relation_composition(identity_relation(X0),empty_set))
| ~ function(relation_composition(identity_relation(X0),empty_set))
| ( apply(relation_composition(identity_relation(X0),empty_set),sK10(empty_set,relation_composition(identity_relation(X0),empty_set))) != sK10(empty_set,relation_composition(identity_relation(X0),empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_3643,c_2472,c_3033]) ).
tcf(c_3685,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(iPr_def_10,empty_set)),relation_dom(X0))
| ( relation_composition(iPr_def_10,empty_set) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_10,empty_set))
| ~ function(relation_composition(iPr_def_10,empty_set))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_3637,c_112]) ).
tcf(c_3686,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_10,empty_set),X0),relation_dom(relation_composition(iPr_def_10,empty_set)))
| ( relation_composition(iPr_def_10,empty_set) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_10,empty_set))
| ~ function(relation_composition(iPr_def_10,empty_set))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_3637,c_112]) ).
tcf(c_3687,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_10,empty_set))) = relation_composition(iPr_def_10,empty_set) )
| ~ relation(relation_composition(iPr_def_10,empty_set))
| ~ function(relation_composition(iPr_def_10,empty_set))
| ( apply(relation_composition(iPr_def_10,empty_set),sK10(empty_set,relation_composition(iPr_def_10,empty_set))) != sK10(empty_set,relation_composition(iPr_def_10,empty_set)) ) ),
inference(superposition,[status(thm)],[c_3637,c_99]) ).
tcf(c_3688,plain,
( in(sK10(empty_set,relation_composition(iPr_def_10,empty_set)),empty_set)
| ( identity_relation(relation_dom(relation_composition(iPr_def_10,empty_set))) = relation_composition(iPr_def_10,empty_set) )
| ~ relation(relation_composition(iPr_def_10,empty_set))
| ~ function(relation_composition(iPr_def_10,empty_set)) ),
inference(superposition,[status(thm)],[c_3637,c_100]) ).
tcf(c_3689,plain,
( empty(relation_composition(iPr_def_10,empty_set))
| ~ empty(empty_set)
| ~ relation(relation_composition(iPr_def_10,empty_set)) ),
inference(superposition,[status(thm)],[c_3637,c_75]) ).
tcf(c_3693,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_10,empty_set),X0) = apply(empty_set,apply(iPr_def_10,X0)) )
| ~ relation(iPr_def_10)
| ~ relation(empty_set)
| ~ function(iPr_def_10)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_3637,c_96]) ).
tcf(c_3694,plain,
( empty(relation_composition(iPr_def_10,empty_set))
| ~ relation(relation_composition(iPr_def_10,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3689,c_73]) ).
tcf(c_3697,plain,
( in(sK10(empty_set,relation_composition(iPr_def_10,empty_set)),empty_set)
| ( relation_composition(iPr_def_10,empty_set) = empty_set )
| ~ relation(relation_composition(iPr_def_10,empty_set))
| ~ function(relation_composition(iPr_def_10,empty_set)) ),
inference(light_normalisation,[status(thm)],[c_3688,c_2472,c_3637]) ).
tcf(c_3702,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_10,empty_set),X0) = apply(empty_set,apply(iPr_def_10,X0)) )
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3693,c_1881,c_74,c_1880,c_1866]) ).
tcf(c_3712,plain,
( ( relation_composition(iPr_def_10,empty_set) = empty_set )
| ~ relation(relation_composition(iPr_def_10,empty_set))
| ~ function(relation_composition(iPr_def_10,empty_set))
| ( apply(relation_composition(iPr_def_10,empty_set),sK10(empty_set,relation_composition(iPr_def_10,empty_set))) != sK10(empty_set,relation_composition(iPr_def_10,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_3687,c_2472,c_3637]) ).
tcf(c_3717,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_10,empty_set),X0),empty_set)
| ( relation_composition(iPr_def_10,empty_set) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_10,empty_set))
| ~ function(relation_composition(iPr_def_10,empty_set))
| ( relation_dom(X0) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_3686,c_3637]) ).
tcf(c_3730,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(iPr_def_11,empty_set)),relation_dom(X0))
| ( relation_composition(iPr_def_11,empty_set) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,empty_set))
| ~ function(relation_composition(iPr_def_11,empty_set))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_3638,c_112]) ).
tcf(c_3731,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_11,empty_set),X0),relation_dom(relation_composition(iPr_def_11,empty_set)))
| ( relation_composition(iPr_def_11,empty_set) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,empty_set))
| ~ function(relation_composition(iPr_def_11,empty_set))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_3638,c_112]) ).
tcf(c_3732,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_11,empty_set))) = relation_composition(iPr_def_11,empty_set) )
| ~ relation(relation_composition(iPr_def_11,empty_set))
| ~ function(relation_composition(iPr_def_11,empty_set))
| ( apply(relation_composition(iPr_def_11,empty_set),sK10(empty_set,relation_composition(iPr_def_11,empty_set))) != sK10(empty_set,relation_composition(iPr_def_11,empty_set)) ) ),
inference(superposition,[status(thm)],[c_3638,c_99]) ).
tcf(c_3733,plain,
( in(sK10(empty_set,relation_composition(iPr_def_11,empty_set)),empty_set)
| ( identity_relation(relation_dom(relation_composition(iPr_def_11,empty_set))) = relation_composition(iPr_def_11,empty_set) )
| ~ relation(relation_composition(iPr_def_11,empty_set))
| ~ function(relation_composition(iPr_def_11,empty_set)) ),
inference(superposition,[status(thm)],[c_3638,c_100]) ).
tcf(c_3734,plain,
( empty(relation_composition(iPr_def_11,empty_set))
| ~ empty(empty_set)
| ~ relation(relation_composition(iPr_def_11,empty_set)) ),
inference(superposition,[status(thm)],[c_3638,c_75]) ).
tcf(c_3738,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_11,empty_set),X0) = apply(empty_set,apply(iPr_def_11,X0)) )
| ~ relation(iPr_def_11)
| ~ relation(empty_set)
| ~ function(iPr_def_11)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_3638,c_96]) ).
tcf(c_3739,plain,
( empty(relation_composition(iPr_def_11,empty_set))
| ~ relation(relation_composition(iPr_def_11,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3734,c_73]) ).
tcf(c_3742,plain,
( in(sK10(empty_set,relation_composition(iPr_def_11,empty_set)),empty_set)
| ( relation_composition(iPr_def_11,empty_set) = empty_set )
| ~ relation(relation_composition(iPr_def_11,empty_set))
| ~ function(relation_composition(iPr_def_11,empty_set)) ),
inference(light_normalisation,[status(thm)],[c_3733,c_2472,c_3638]) ).
tcf(c_3747,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_11,empty_set),X0) = apply(empty_set,apply(iPr_def_11,X0)) )
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3738,c_1884,c_74,c_1883,c_1866]) ).
tcf(c_3757,plain,
( ( relation_composition(iPr_def_11,empty_set) = empty_set )
| ~ relation(relation_composition(iPr_def_11,empty_set))
| ~ function(relation_composition(iPr_def_11,empty_set))
| ( apply(relation_composition(iPr_def_11,empty_set),sK10(empty_set,relation_composition(iPr_def_11,empty_set))) != sK10(empty_set,relation_composition(iPr_def_11,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_3732,c_2472,c_3638]) ).
tcf(c_3762,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_11,empty_set),X0),empty_set)
| ( relation_composition(iPr_def_11,empty_set) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,empty_set))
| ~ function(relation_composition(iPr_def_11,empty_set))
| ( relation_dom(X0) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_3731,c_3638]) ).
tcf(c_3803,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(empty_set,empty_set)),relation_dom(X0))
| ( relation_composition(empty_set,empty_set) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,empty_set))
| ~ function(relation_composition(empty_set,empty_set))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_3639,c_112]) ).
tcf(c_3804,plain,
! [X0: $i] :
( in(sK13(relation_composition(empty_set,empty_set),X0),relation_dom(relation_composition(empty_set,empty_set)))
| ( relation_composition(empty_set,empty_set) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,empty_set))
| ~ function(relation_composition(empty_set,empty_set))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_3639,c_112]) ).
tcf(c_3805,plain,
( ( identity_relation(relation_dom(relation_composition(empty_set,empty_set))) = relation_composition(empty_set,empty_set) )
| ~ relation(relation_composition(empty_set,empty_set))
| ~ function(relation_composition(empty_set,empty_set))
| ( apply(relation_composition(empty_set,empty_set),sK10(empty_set,relation_composition(empty_set,empty_set))) != sK10(empty_set,relation_composition(empty_set,empty_set)) ) ),
inference(superposition,[status(thm)],[c_3639,c_99]) ).
tcf(c_3806,plain,
( in(sK10(empty_set,relation_composition(empty_set,empty_set)),empty_set)
| ( identity_relation(relation_dom(relation_composition(empty_set,empty_set))) = relation_composition(empty_set,empty_set) )
| ~ relation(relation_composition(empty_set,empty_set))
| ~ function(relation_composition(empty_set,empty_set)) ),
inference(superposition,[status(thm)],[c_3639,c_100]) ).
tcf(c_3807,plain,
( empty(relation_composition(empty_set,empty_set))
| ~ empty(empty_set)
| ~ relation(relation_composition(empty_set,empty_set)) ),
inference(superposition,[status(thm)],[c_3639,c_75]) ).
tcf(c_3811,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,empty_set),X0) = apply(empty_set,apply(empty_set,X0)) )
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_3639,c_96]) ).
tcf(c_3812,plain,
( empty(relation_composition(empty_set,empty_set))
| ~ relation(relation_composition(empty_set,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3807,c_73]) ).
tcf(c_3815,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,empty_set),X0) = apply(empty_set,apply(empty_set,X0)) )
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3811,c_74,c_1866]) ).
tcf(c_3818,plain,
( in(sK10(empty_set,relation_composition(empty_set,empty_set)),empty_set)
| ( relation_composition(empty_set,empty_set) = empty_set )
| ~ relation(relation_composition(empty_set,empty_set))
| ~ function(relation_composition(empty_set,empty_set)) ),
inference(light_normalisation,[status(thm)],[c_3806,c_2472,c_3639]) ).
tcf(c_3830,plain,
( ( relation_composition(empty_set,empty_set) = empty_set )
| ~ relation(relation_composition(empty_set,empty_set))
| ~ function(relation_composition(empty_set,empty_set))
| ( apply(relation_composition(empty_set,empty_set),sK10(empty_set,relation_composition(empty_set,empty_set))) != sK10(empty_set,relation_composition(empty_set,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_3805,c_2472,c_3639]) ).
tcf(c_3835,plain,
! [X0: $i] :
( in(sK13(relation_composition(empty_set,empty_set),X0),empty_set)
| ( relation_composition(empty_set,empty_set) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,empty_set))
| ~ function(relation_composition(empty_set,empty_set))
| ( relation_dom(X0) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_3804,c_3639]) ).
tcf(c_3845,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(iPr_def_14,empty_set)),relation_dom(X0))
| ( relation_composition(iPr_def_14,empty_set) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,empty_set))
| ~ function(relation_composition(iPr_def_14,empty_set))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_3640,c_112]) ).
tcf(c_3846,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_14,empty_set),X0),relation_dom(relation_composition(iPr_def_14,empty_set)))
| ( relation_composition(iPr_def_14,empty_set) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,empty_set))
| ~ function(relation_composition(iPr_def_14,empty_set))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_3640,c_112]) ).
tcf(c_3847,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_14,empty_set))) = relation_composition(iPr_def_14,empty_set) )
| ~ relation(relation_composition(iPr_def_14,empty_set))
| ~ function(relation_composition(iPr_def_14,empty_set))
| ( apply(relation_composition(iPr_def_14,empty_set),sK10(empty_set,relation_composition(iPr_def_14,empty_set))) != sK10(empty_set,relation_composition(iPr_def_14,empty_set)) ) ),
inference(superposition,[status(thm)],[c_3640,c_99]) ).
tcf(c_3848,plain,
( in(sK10(empty_set,relation_composition(iPr_def_14,empty_set)),empty_set)
| ( identity_relation(relation_dom(relation_composition(iPr_def_14,empty_set))) = relation_composition(iPr_def_14,empty_set) )
| ~ relation(relation_composition(iPr_def_14,empty_set))
| ~ function(relation_composition(iPr_def_14,empty_set)) ),
inference(superposition,[status(thm)],[c_3640,c_100]) ).
tcf(c_3849,plain,
( empty(relation_composition(iPr_def_14,empty_set))
| ~ empty(empty_set)
| ~ relation(relation_composition(iPr_def_14,empty_set)) ),
inference(superposition,[status(thm)],[c_3640,c_75]) ).
tcf(c_3853,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_14,empty_set),X0) = apply(empty_set,apply(iPr_def_14,X0)) )
| ~ relation(iPr_def_14)
| ~ relation(empty_set)
| ~ function(iPr_def_14)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_3640,c_96]) ).
tcf(c_3854,plain,
( empty(relation_composition(iPr_def_14,empty_set))
| ~ relation(relation_composition(iPr_def_14,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3849,c_73]) ).
tcf(c_3857,plain,
( in(sK10(empty_set,relation_composition(iPr_def_14,empty_set)),empty_set)
| ( relation_composition(iPr_def_14,empty_set) = empty_set )
| ~ relation(relation_composition(iPr_def_14,empty_set))
| ~ function(relation_composition(iPr_def_14,empty_set)) ),
inference(light_normalisation,[status(thm)],[c_3848,c_2472,c_3640]) ).
tcf(c_3862,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_14,empty_set),X0) = apply(empty_set,apply(iPr_def_14,X0)) )
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3853,c_1887,c_74,c_1886,c_1866]) ).
tcf(c_3872,plain,
( ( relation_composition(iPr_def_14,empty_set) = empty_set )
| ~ relation(relation_composition(iPr_def_14,empty_set))
| ~ function(relation_composition(iPr_def_14,empty_set))
| ( apply(relation_composition(iPr_def_14,empty_set),sK10(empty_set,relation_composition(iPr_def_14,empty_set))) != sK10(empty_set,relation_composition(iPr_def_14,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_3847,c_2472,c_3640]) ).
tcf(c_3877,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_14,empty_set),X0),empty_set)
| ( relation_composition(iPr_def_14,empty_set) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,empty_set))
| ~ function(relation_composition(iPr_def_14,empty_set))
| ( relation_dom(X0) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_3846,c_3640]) ).
tcf(c_3891,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,sK1(powerset(X0)),X2),X2)
| ( set_intersection2(X1,sK1(powerset(X0))) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_2933]) ).
tcf(c_3892,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(sK1(powerset(X0)),X1,X2),X2)
| ( set_intersection2(sK1(powerset(X0)),X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_2933]) ).
tcf(c_3893,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,sK1(powerset(X0))),X2)
| ( set_intersection2(X1,X2) = sK1(powerset(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_2933]) ).
tcf(c_3894,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,sK1(powerset(X0))),X1)
| ( set_intersection2(X1,X2) = sK1(powerset(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_2933]) ).
tcf(c_3895,plain,
! [X0: $i] :
( empty(sK1(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2137,c_2933]) ).
tcf(c_3896,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,sK1(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2201,c_2933]) ).
tcf(c_3933,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_110]) ).
tcf(c_3934,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK1(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_2474]) ).
tcf(c_3935,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK1(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_2473]) ).
tcf(c_3936,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_2055]) ).
tcf(c_3937,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_2184]) ).
tcf(c_3938,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_2013]) ).
tcf(c_3939,plain,
! [X0: $i] :
( ( sK1(powerset(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_108]) ).
tcf(c_3940,plain,
! [X0: $i] :
( relation(sK1(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_51]) ).
tcf(c_3941,plain,
! [X0: $i] :
( function(sK1(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_50]) ).
tcf(c_3998,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),sK1(powerset(X0)))) = set_intersection2(relation_dom(sK1(powerset(X0))),X1) )
| ~ empty(X0)
| ~ relation(sK1(powerset(X0))) ),
inference(superposition,[status(thm)],[c_3941,c_103]) ).
tcf(c_4007,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,relation_composition(X0,X1)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3084]) ).
tcf(c_4008,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,relation_composition(X1,X0)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3084]) ).
tcf(c_4010,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3084]) ).
tcf(c_4011,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3084]) ).
tcf(c_4012,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X0,X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3084]) ).
tcf(c_4013,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,sK1(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_3084]) ).
tcf(c_4014,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X2,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3084]) ).
tcf(c_4056,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_composition(X0,X1),X2) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3180]) ).
tcf(c_4057,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_composition(X1,X0),X2) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3180]) ).
tcf(c_4059,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(X0),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3180]) ).
tcf(c_4060,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(X0),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3180]) ).
tcf(c_4061,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3180]) ).
tcf(c_4062,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK1(powerset(X0)),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_3180]) ).
tcf(c_4063,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,X0),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3180]) ).
tcf(c_4097,plain,
relation_dom(relation_composition(iPr_def_10,iPr_def_11)) = set_intersection2(sK11,sK12),
inference(superposition,[status(thm)],[c_1147,c_3029]) ).
tcf(c_4098,plain,
relation_dom(relation_composition(iPr_def_11,iPr_def_11)) = set_intersection2(sK11,sK11),
inference(superposition,[status(thm)],[c_1148,c_3029]) ).
tcf(c_4099,plain,
relation_dom(relation_composition(empty_set,iPr_def_11)) = set_intersection2(sK11,empty_set),
inference(superposition,[status(thm)],[c_2472,c_3029]) ).
tcf(c_4100,plain,
relation_dom(relation_composition(iPr_def_14,iPr_def_11)) = set_intersection2(sK11,iPr_def_13),
inference(superposition,[status(thm)],[c_1151,c_3029]) ).
tcf(c_4101,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,relation_composition(identity_relation(X0),iPr_def_11)),relation_dom(X1))
| ( relation_composition(identity_relation(X0),iPr_def_11) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),iPr_def_11))
| ~ function(relation_composition(identity_relation(X0),iPr_def_11))
| ( set_intersection2(sK11,X0) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_3029,c_112]) ).
tcf(c_4102,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(identity_relation(X0),iPr_def_11),X1),relation_dom(relation_composition(identity_relation(X0),iPr_def_11)))
| ( relation_composition(identity_relation(X0),iPr_def_11) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),iPr_def_11))
| ~ function(relation_composition(identity_relation(X0),iPr_def_11))
| ( set_intersection2(sK11,X0) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_3029,c_112]) ).
tcf(c_4103,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_composition(identity_relation(X0),iPr_def_11))) = relation_composition(identity_relation(X0),iPr_def_11) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_11))
| ~ function(relation_composition(identity_relation(X0),iPr_def_11))
| ( apply(relation_composition(identity_relation(X0),iPr_def_11),sK10(set_intersection2(sK11,X0),relation_composition(identity_relation(X0),iPr_def_11))) != sK10(set_intersection2(sK11,X0),relation_composition(identity_relation(X0),iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_3029,c_99]) ).
tcf(c_4104,plain,
! [X0: $i] :
( in(sK10(set_intersection2(sK11,X0),relation_composition(identity_relation(X0),iPr_def_11)),set_intersection2(sK11,X0))
| ( identity_relation(relation_dom(relation_composition(identity_relation(X0),iPr_def_11))) = relation_composition(identity_relation(X0),iPr_def_11) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_11))
| ~ function(relation_composition(identity_relation(X0),iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3029,c_100]) ).
tcf(c_4105,plain,
! [X0: $i] :
( empty(relation_composition(identity_relation(X0),iPr_def_11))
| ~ empty(set_intersection2(sK11,X0))
| ~ relation(relation_composition(identity_relation(X0),iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3029,c_75]) ).
tcf(c_4106,plain,
! [X0: $i] :
( function(set_intersection2(sK11,X0))
| ~ empty(relation_composition(identity_relation(X0),iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3029,c_1895]) ).
tcf(c_4107,plain,
! [X0: $i] :
( relation(set_intersection2(sK11,X0))
| ~ empty(relation_composition(identity_relation(X0),iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3029,c_77]) ).
tcf(c_4108,plain,
! [X0: $i] :
( empty(set_intersection2(sK11,X0))
| ~ empty(relation_composition(identity_relation(X0),iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3029,c_76]) ).
tcf(c_4109,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(identity_relation(X1),iPr_def_11),X0) = apply(iPr_def_11,apply(identity_relation(X1),X0)) )
| ~ relation(iPr_def_11)
| ~ function(iPr_def_11)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,set_intersection2(sK11,X1)) ),
inference(superposition,[status(thm)],[c_3029,c_96]) ).
tcf(c_4110,plain,
set_intersection2(sK11,sK12) = relation_dom(iPr_def_12),
inference(light_normalisation,[status(thm)],[c_4097,c_1149]) ).
tcf(c_4120,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(identity_relation(X1),iPr_def_11),X0) = apply(iPr_def_11,apply(identity_relation(X1),X0)) )
| ~ in(X0,set_intersection2(sK11,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4109,c_1884,c_1883,c_71,c_72]) ).
tcf(c_4123,plain,
! [X0: $i] :
( in(sK10(set_intersection2(sK11,X0),relation_composition(identity_relation(X0),iPr_def_11)),set_intersection2(sK11,X0))
| ( relation_composition(identity_relation(X0),iPr_def_11) = identity_relation(set_intersection2(sK11,X0)) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_11))
| ~ function(relation_composition(identity_relation(X0),iPr_def_11)) ),
inference(light_normalisation,[status(thm)],[c_4104,c_3029]) ).
tcf(c_4135,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(identity_relation(X0),iPr_def_11),X1),set_intersection2(sK11,X0))
| ( relation_composition(identity_relation(X0),iPr_def_11) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),iPr_def_11))
| ~ function(relation_composition(identity_relation(X0),iPr_def_11))
| ( set_intersection2(sK11,X0) != relation_dom(X1) ) ),
inference(light_normalisation,[status(thm)],[c_4102,c_3029]) ).
tcf(c_4143,plain,
! [X0: $i] :
( ( relation_composition(identity_relation(X0),iPr_def_11) = identity_relation(set_intersection2(sK11,X0)) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_11))
| ~ function(relation_composition(identity_relation(X0),iPr_def_11))
| ( apply(relation_composition(identity_relation(X0),iPr_def_11),sK10(set_intersection2(sK11,X0),relation_composition(identity_relation(X0),iPr_def_11))) != sK10(set_intersection2(sK11,X0),relation_composition(identity_relation(X0),iPr_def_11)) ) ),
inference(light_normalisation,[status(thm)],[c_4103,c_3029]) ).
tcf(c_4354,plain,
relation_dom(iPr_def_12) = iPr_def_13,
inference(demodulation,[status(thm)],[c_4110,c_52,c_1150]) ).
tcf(c_4355,plain,
! [X0: $i] :
( in(sK13(X0,iPr_def_12),relation_dom(X0))
| ( X0 = iPr_def_12 )
| ~ relation(iPr_def_12)
| ~ function(iPr_def_12)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_4354,c_112]) ).
tcf(c_4356,plain,
! [X0: $i] :
( in(sK13(iPr_def_12,X0),relation_dom(iPr_def_12))
| ( X0 = iPr_def_12 )
| ~ relation(iPr_def_12)
| ~ function(iPr_def_12)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_4354,c_112]) ).
tcf(c_4357,plain,
( ( identity_relation(relation_dom(iPr_def_12)) = iPr_def_12 )
| ~ relation(iPr_def_12)
| ~ function(iPr_def_12)
| ( apply(iPr_def_12,sK10(iPr_def_13,iPr_def_12)) != sK10(iPr_def_13,iPr_def_12) ) ),
inference(superposition,[status(thm)],[c_4354,c_99]) ).
tcf(c_4358,plain,
( in(sK10(iPr_def_13,iPr_def_12),iPr_def_13)
| ( identity_relation(relation_dom(iPr_def_12)) = iPr_def_12 )
| ~ relation(iPr_def_12)
| ~ function(iPr_def_12) ),
inference(superposition,[status(thm)],[c_4354,c_100]) ).
tcf(c_4359,plain,
( empty(iPr_def_12)
| ~ relation(iPr_def_12)
| ~ empty(iPr_def_13) ),
inference(superposition,[status(thm)],[c_4354,c_75]) ).
tcf(c_4360,plain,
( function(iPr_def_13)
| ~ empty(iPr_def_12) ),
inference(superposition,[status(thm)],[c_4354,c_1895]) ).
tcf(c_4361,plain,
( relation(iPr_def_13)
| ~ empty(iPr_def_12) ),
inference(superposition,[status(thm)],[c_4354,c_77]) ).
tcf(c_4362,plain,
( empty(iPr_def_13)
| ~ empty(iPr_def_12) ),
inference(superposition,[status(thm)],[c_4354,c_76]) ).
tcf(c_4369,plain,
( empty(iPr_def_12)
| ~ empty(iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4359,c_2156]) ).
tcf(c_4372,plain,
( in(sK10(iPr_def_13,iPr_def_12),iPr_def_13)
| ( iPr_def_12 = iPr_def_14 )
| ~ relation(iPr_def_12)
| ~ function(iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_4358,c_1151,c_4354]) ).
tcf(c_4373,plain,
in(sK10(iPr_def_13,iPr_def_12),iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_4372,c_1152,c_2156,c_3011]) ).
tcf(c_4374,plain,
( ( iPr_def_12 = iPr_def_14 )
| ~ relation(iPr_def_12)
| ~ function(iPr_def_12)
| ( apply(iPr_def_12,sK10(iPr_def_13,iPr_def_12)) != sK10(iPr_def_13,iPr_def_12) ) ),
inference(light_normalisation,[status(thm)],[c_4357,c_1151,c_4354]) ).
tcf(c_4375,plain,
apply(iPr_def_12,sK10(iPr_def_13,iPr_def_12)) != sK10(iPr_def_13,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_4374,c_1152,c_2156,c_3011]) ).
tcf(c_4376,plain,
! [X0: $i] :
( in(sK13(iPr_def_12,X0),iPr_def_13)
| ( X0 = iPr_def_12 )
| ~ relation(iPr_def_12)
| ~ function(iPr_def_12)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_4356,c_4354]) ).
tcf(c_4377,plain,
! [X0: $i] :
( in(sK13(iPr_def_12,X0),iPr_def_13)
| ( X0 = iPr_def_12 )
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4376,c_2156,c_3011]) ).
tcf(c_4383,plain,
! [X0: $i] :
( in(sK13(X0,iPr_def_12),relation_dom(X0))
| ( X0 = iPr_def_12 )
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4355,c_2156,c_3011]) ).
tcf(c_4398,plain,
~ empty(iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_4361,c_1152,c_2118,c_2453,c_4362]) ).
tcf(c_4400,plain,
~ empty(iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_4369,c_4369,c_4398]) ).
tcf(c_4402,plain,
element(sK1(iPr_def_13),sK11),
inference(backward_subsumption_resolution,[status(thm)],[c_2421,c_4400]) ).
tcf(c_4403,plain,
~ in(sK11,sK1(iPr_def_13)),
inference(backward_subsumption_resolution,[status(thm)],[c_2419,c_4400]) ).
tcf(c_4404,plain,
in(sK1(iPr_def_13),sK11),
inference(backward_subsumption_resolution,[status(thm)],[c_2404,c_4400]) ).
tcf(c_4405,plain,
element(sK1(iPr_def_13),sK12),
inference(backward_subsumption_resolution,[status(thm)],[c_2220,c_4400]) ).
tcf(c_4406,plain,
~ in(sK12,sK1(iPr_def_13)),
inference(backward_subsumption_resolution,[status(thm)],[c_2218,c_4400]) ).
tcf(c_4407,plain,
in(sK1(iPr_def_13),sK12),
inference(backward_subsumption_resolution,[status(thm)],[c_2204,c_4400]) ).
tcf(c_4408,plain,
~ empty(iPr_def_14),
inference(backward_subsumption_resolution,[status(thm)],[c_1907,c_4400]) ).
tcf(c_4410,plain,
apply(identity_relation(iPr_def_13),sK10(iPr_def_13,iPr_def_12)) = sK10(iPr_def_13,iPr_def_12),
inference(superposition,[status(thm)],[c_4373,c_172]) ).
tcf(c_4411,plain,
~ in(iPr_def_13,sK10(iPr_def_13,iPr_def_12)),
inference(superposition,[status(thm)],[c_4373,c_49]) ).
tcf(c_4413,plain,
element(sK10(iPr_def_13,iPr_def_12),iPr_def_13),
inference(superposition,[status(thm)],[c_4373,c_95]) ).
tcf(c_4414,plain,
in(sK10(iPr_def_13,iPr_def_12),sK11),
inference(superposition,[status(thm)],[c_4373,c_2102]) ).
tcf(c_4415,plain,
in(sK10(iPr_def_13,iPr_def_12),sK12),
inference(superposition,[status(thm)],[c_4373,c_2071]) ).
tcf(c_4416,plain,
apply(iPr_def_14,sK10(iPr_def_13,iPr_def_12)) = sK10(iPr_def_13,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_4410,c_1151]) ).
tcf(c_4418,plain,
apply(identity_relation(sK11),sK10(iPr_def_13,iPr_def_12)) = sK10(iPr_def_13,iPr_def_12),
inference(superposition,[status(thm)],[c_4414,c_172]) ).
tcf(c_4419,plain,
~ in(sK11,sK10(iPr_def_13,iPr_def_12)),
inference(superposition,[status(thm)],[c_4414,c_49]) ).
tcf(c_4421,plain,
element(sK10(iPr_def_13,iPr_def_12),sK11),
inference(superposition,[status(thm)],[c_4414,c_95]) ).
tcf(c_4422,plain,
apply(iPr_def_11,sK10(iPr_def_13,iPr_def_12)) = sK10(iPr_def_13,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_4418,c_1148]) ).
tcf(c_4423,plain,
apply(identity_relation(sK12),sK10(iPr_def_13,iPr_def_12)) = sK10(iPr_def_13,iPr_def_12),
inference(superposition,[status(thm)],[c_4415,c_172]) ).
tcf(c_4424,plain,
~ in(sK12,sK10(iPr_def_13,iPr_def_12)),
inference(superposition,[status(thm)],[c_4415,c_49]) ).
tcf(c_4426,plain,
element(sK10(iPr_def_13,iPr_def_12),sK12),
inference(superposition,[status(thm)],[c_4415,c_95]) ).
tcf(c_4427,plain,
apply(iPr_def_10,sK10(iPr_def_13,iPr_def_12)) = sK10(iPr_def_13,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_4423,c_1147]) ).
tcf(c_4455,plain,
relation_dom(relation_composition(iPr_def_10,iPr_def_10)) = set_intersection2(sK12,sK12),
inference(superposition,[status(thm)],[c_1147,c_3031]) ).
tcf(c_4456,plain,
relation_dom(relation_composition(iPr_def_11,iPr_def_10)) = set_intersection2(sK12,sK11),
inference(superposition,[status(thm)],[c_1148,c_3031]) ).
tcf(c_4457,plain,
relation_dom(relation_composition(empty_set,iPr_def_10)) = set_intersection2(sK12,empty_set),
inference(superposition,[status(thm)],[c_2472,c_3031]) ).
tcf(c_4458,plain,
relation_dom(relation_composition(iPr_def_14,iPr_def_10)) = set_intersection2(sK12,iPr_def_13),
inference(superposition,[status(thm)],[c_1151,c_3031]) ).
tcf(c_4459,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,relation_composition(identity_relation(X0),iPr_def_10)),relation_dom(X1))
| ( relation_composition(identity_relation(X0),iPr_def_10) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),iPr_def_10))
| ~ function(relation_composition(identity_relation(X0),iPr_def_10))
| ( set_intersection2(sK12,X0) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_3031,c_112]) ).
tcf(c_4460,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(identity_relation(X0),iPr_def_10),X1),relation_dom(relation_composition(identity_relation(X0),iPr_def_10)))
| ( relation_composition(identity_relation(X0),iPr_def_10) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),iPr_def_10))
| ~ function(relation_composition(identity_relation(X0),iPr_def_10))
| ( set_intersection2(sK12,X0) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_3031,c_112]) ).
tcf(c_4461,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_composition(identity_relation(X0),iPr_def_10))) = relation_composition(identity_relation(X0),iPr_def_10) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_10))
| ~ function(relation_composition(identity_relation(X0),iPr_def_10))
| ( apply(relation_composition(identity_relation(X0),iPr_def_10),sK10(set_intersection2(sK12,X0),relation_composition(identity_relation(X0),iPr_def_10))) != sK10(set_intersection2(sK12,X0),relation_composition(identity_relation(X0),iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_3031,c_99]) ).
tcf(c_4462,plain,
! [X0: $i] :
( in(sK10(set_intersection2(sK12,X0),relation_composition(identity_relation(X0),iPr_def_10)),set_intersection2(sK12,X0))
| ( identity_relation(relation_dom(relation_composition(identity_relation(X0),iPr_def_10))) = relation_composition(identity_relation(X0),iPr_def_10) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_10))
| ~ function(relation_composition(identity_relation(X0),iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3031,c_100]) ).
tcf(c_4463,plain,
! [X0: $i] :
( empty(relation_composition(identity_relation(X0),iPr_def_10))
| ~ empty(set_intersection2(sK12,X0))
| ~ relation(relation_composition(identity_relation(X0),iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3031,c_75]) ).
tcf(c_4464,plain,
! [X0: $i] :
( function(set_intersection2(sK12,X0))
| ~ empty(relation_composition(identity_relation(X0),iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3031,c_1895]) ).
tcf(c_4465,plain,
! [X0: $i] :
( relation(set_intersection2(sK12,X0))
| ~ empty(relation_composition(identity_relation(X0),iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3031,c_77]) ).
tcf(c_4466,plain,
! [X0: $i] :
( empty(set_intersection2(sK12,X0))
| ~ empty(relation_composition(identity_relation(X0),iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3031,c_76]) ).
tcf(c_4467,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(identity_relation(X1),iPr_def_10),X0) = apply(iPr_def_10,apply(identity_relation(X1),X0)) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,set_intersection2(sK12,X1)) ),
inference(superposition,[status(thm)],[c_3031,c_96]) ).
tcf(c_4468,plain,
relation_dom(relation_composition(iPr_def_11,iPr_def_10)) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_4456,c_1150]) ).
tcf(c_4478,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(identity_relation(X1),iPr_def_10),X0) = apply(iPr_def_10,apply(identity_relation(X1),X0)) )
| ~ in(X0,set_intersection2(sK12,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4467,c_1881,c_1880,c_71,c_72]) ).
tcf(c_4481,plain,
! [X0: $i] :
( in(sK10(set_intersection2(sK12,X0),relation_composition(identity_relation(X0),iPr_def_10)),set_intersection2(sK12,X0))
| ( relation_composition(identity_relation(X0),iPr_def_10) = identity_relation(set_intersection2(sK12,X0)) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_10))
| ~ function(relation_composition(identity_relation(X0),iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_4462,c_3031]) ).
tcf(c_4493,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(identity_relation(X0),iPr_def_10),X1),set_intersection2(sK12,X0))
| ( relation_composition(identity_relation(X0),iPr_def_10) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),iPr_def_10))
| ~ function(relation_composition(identity_relation(X0),iPr_def_10))
| ( set_intersection2(sK12,X0) != relation_dom(X1) ) ),
inference(light_normalisation,[status(thm)],[c_4460,c_3031]) ).
tcf(c_4501,plain,
! [X0: $i] :
( ( relation_composition(identity_relation(X0),iPr_def_10) = identity_relation(set_intersection2(sK12,X0)) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_10))
| ~ function(relation_composition(identity_relation(X0),iPr_def_10))
| ( apply(relation_composition(identity_relation(X0),iPr_def_10),sK10(set_intersection2(sK12,X0),relation_composition(identity_relation(X0),iPr_def_10))) != sK10(set_intersection2(sK12,X0),relation_composition(identity_relation(X0),iPr_def_10)) ) ),
inference(light_normalisation,[status(thm)],[c_4461,c_3031]) ).
tcf(c_4539,plain,
apply(identity_relation(sK11),sK1(iPr_def_13)) = sK1(iPr_def_13),
inference(superposition,[status(thm)],[c_4404,c_172]) ).
tcf(c_4543,plain,
apply(iPr_def_11,sK1(iPr_def_13)) = sK1(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_4539,c_1148]) ).
tcf(c_4544,plain,
apply(identity_relation(sK12),sK1(iPr_def_13)) = sK1(iPr_def_13),
inference(superposition,[status(thm)],[c_4407,c_172]) ).
tcf(c_4548,plain,
apply(iPr_def_10,sK1(iPr_def_13)) = sK1(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_4544,c_1147]) ).
tcf(c_4549,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(iPr_def_11,iPr_def_10)),relation_dom(X0))
| ( relation_composition(iPr_def_11,iPr_def_10) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,iPr_def_10))
| ~ function(relation_composition(iPr_def_11,iPr_def_10))
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_4468,c_112]) ).
tcf(c_4550,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_11,iPr_def_10),X0),relation_dom(relation_composition(iPr_def_11,iPr_def_10)))
| ( relation_composition(iPr_def_11,iPr_def_10) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,iPr_def_10))
| ~ function(relation_composition(iPr_def_11,iPr_def_10))
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_4468,c_112]) ).
tcf(c_4551,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_11,iPr_def_10))) = relation_composition(iPr_def_11,iPr_def_10) )
| ~ relation(relation_composition(iPr_def_11,iPr_def_10))
| ~ function(relation_composition(iPr_def_11,iPr_def_10))
| ( apply(relation_composition(iPr_def_11,iPr_def_10),sK10(iPr_def_13,relation_composition(iPr_def_11,iPr_def_10))) != sK10(iPr_def_13,relation_composition(iPr_def_11,iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_4468,c_99]) ).
tcf(c_4552,plain,
( in(sK10(iPr_def_13,relation_composition(iPr_def_11,iPr_def_10)),iPr_def_13)
| ( identity_relation(relation_dom(relation_composition(iPr_def_11,iPr_def_10))) = relation_composition(iPr_def_11,iPr_def_10) )
| ~ relation(relation_composition(iPr_def_11,iPr_def_10))
| ~ function(relation_composition(iPr_def_11,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4468,c_100]) ).
tcf(c_4556,plain,
( empty(iPr_def_13)
| ~ empty(relation_composition(iPr_def_11,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4468,c_76]) ).
tcf(c_4557,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_11,iPr_def_10),X0) = apply(iPr_def_10,apply(iPr_def_11,X0)) )
| ~ relation(iPr_def_11)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_11)
| ~ function(iPr_def_10)
| ~ in(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_4468,c_96]) ).
tcf(c_4558,plain,
~ empty(relation_composition(iPr_def_11,iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_4556,c_4400]) ).
tcf(c_4559,plain,
( in(sK10(iPr_def_13,relation_composition(iPr_def_11,iPr_def_10)),iPr_def_13)
| ( relation_composition(iPr_def_11,iPr_def_10) = iPr_def_14 )
| ~ relation(relation_composition(iPr_def_11,iPr_def_10))
| ~ function(relation_composition(iPr_def_11,iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_4552,c_1151,c_4468]) ).
tcf(c_4564,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_11,iPr_def_10),X0) = apply(iPr_def_10,apply(iPr_def_11,X0)) )
| ~ in(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4557,c_1884,c_1881,c_1883,c_1880]) ).
tcf(c_4574,plain,
( ( relation_composition(iPr_def_11,iPr_def_10) = iPr_def_14 )
| ~ relation(relation_composition(iPr_def_11,iPr_def_10))
| ~ function(relation_composition(iPr_def_11,iPr_def_10))
| ( apply(relation_composition(iPr_def_11,iPr_def_10),sK10(iPr_def_13,relation_composition(iPr_def_11,iPr_def_10))) != sK10(iPr_def_13,relation_composition(iPr_def_11,iPr_def_10)) ) ),
inference(light_normalisation,[status(thm)],[c_4551,c_1151,c_4468]) ).
tcf(c_4579,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_11,iPr_def_10),X0),iPr_def_13)
| ( relation_composition(iPr_def_11,iPr_def_10) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,iPr_def_10))
| ~ function(relation_composition(iPr_def_11,iPr_def_10))
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_4550,c_4468]) ).
tcf(c_4632,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(iPr_def_10,iPr_def_14)),relation_dom(X0))
| ( relation_composition(iPr_def_10,iPr_def_14) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_10,iPr_def_14))
| ~ function(relation_composition(iPr_def_10,iPr_def_14))
| ( set_intersection2(iPr_def_13,sK12) != relation_dom(X0) ) ),
inference(superposition,[status(thm)],[c_3283,c_112]) ).
tcf(c_4633,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_10,iPr_def_14),X0),relation_dom(relation_composition(iPr_def_10,iPr_def_14)))
| ( relation_composition(iPr_def_10,iPr_def_14) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_10,iPr_def_14))
| ~ function(relation_composition(iPr_def_10,iPr_def_14))
| ( set_intersection2(iPr_def_13,sK12) != relation_dom(X0) ) ),
inference(superposition,[status(thm)],[c_3283,c_112]) ).
tcf(c_4634,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_10,iPr_def_14))) = relation_composition(iPr_def_10,iPr_def_14) )
| ~ relation(relation_composition(iPr_def_10,iPr_def_14))
| ~ function(relation_composition(iPr_def_10,iPr_def_14))
| ( apply(relation_composition(iPr_def_10,iPr_def_14),sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_10,iPr_def_14))) != sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_10,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_3283,c_99]) ).
tcf(c_4635,plain,
( in(sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_10,iPr_def_14)),set_intersection2(iPr_def_13,sK12))
| ( identity_relation(relation_dom(relation_composition(iPr_def_10,iPr_def_14))) = relation_composition(iPr_def_10,iPr_def_14) )
| ~ relation(relation_composition(iPr_def_10,iPr_def_14))
| ~ function(relation_composition(iPr_def_10,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_3283,c_100]) ).
tcf(c_4636,plain,
( empty(relation_composition(iPr_def_10,iPr_def_14))
| ~ relation(relation_composition(iPr_def_10,iPr_def_14))
| ~ empty(set_intersection2(iPr_def_13,sK12)) ),
inference(superposition,[status(thm)],[c_3283,c_75]) ).
tcf(c_4637,plain,
( function(set_intersection2(iPr_def_13,sK12))
| ~ empty(relation_composition(iPr_def_10,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_3283,c_1895]) ).
tcf(c_4638,plain,
( relation(set_intersection2(iPr_def_13,sK12))
| ~ empty(relation_composition(iPr_def_10,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_3283,c_77]) ).
tcf(c_4639,plain,
( empty(set_intersection2(iPr_def_13,sK12))
| ~ empty(relation_composition(iPr_def_10,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_3283,c_76]) ).
tcf(c_4640,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_10,iPr_def_14),X0) = apply(iPr_def_14,apply(iPr_def_10,X0)) )
| ~ relation(iPr_def_14)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_14)
| ~ function(iPr_def_10)
| ~ in(X0,set_intersection2(iPr_def_13,sK12)) ),
inference(superposition,[status(thm)],[c_3283,c_96]) ).
tcf(c_4650,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_10,iPr_def_14),X0) = apply(iPr_def_14,apply(iPr_def_10,X0)) )
| ~ in(X0,set_intersection2(iPr_def_13,sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4640,c_1887,c_1881,c_1886,c_1880]) ).
tcf(c_4653,plain,
( in(sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_10,iPr_def_14)),set_intersection2(iPr_def_13,sK12))
| ( identity_relation(set_intersection2(iPr_def_13,sK12)) = relation_composition(iPr_def_10,iPr_def_14) )
| ~ relation(relation_composition(iPr_def_10,iPr_def_14))
| ~ function(relation_composition(iPr_def_10,iPr_def_14)) ),
inference(light_normalisation,[status(thm)],[c_4635,c_3283]) ).
tcf(c_4665,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_10,iPr_def_14),X0),set_intersection2(iPr_def_13,sK12))
| ( relation_composition(iPr_def_10,iPr_def_14) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_10,iPr_def_14))
| ~ function(relation_composition(iPr_def_10,iPr_def_14))
| ( set_intersection2(iPr_def_13,sK12) != relation_dom(X0) ) ),
inference(light_normalisation,[status(thm)],[c_4633,c_3283]) ).
tcf(c_4673,plain,
( ( identity_relation(set_intersection2(iPr_def_13,sK12)) = relation_composition(iPr_def_10,iPr_def_14) )
| ~ relation(relation_composition(iPr_def_10,iPr_def_14))
| ~ function(relation_composition(iPr_def_10,iPr_def_14))
| ( apply(relation_composition(iPr_def_10,iPr_def_14),sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_10,iPr_def_14))) != sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_10,iPr_def_14)) ) ),
inference(light_normalisation,[status(thm)],[c_4634,c_3283]) ).
tcf(c_4686,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(iPr_def_11,iPr_def_14)),relation_dom(X0))
| ( relation_composition(iPr_def_11,iPr_def_14) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,iPr_def_14))
| ~ function(relation_composition(iPr_def_11,iPr_def_14))
| ( set_intersection2(iPr_def_13,sK11) != relation_dom(X0) ) ),
inference(superposition,[status(thm)],[c_3284,c_112]) ).
tcf(c_4687,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_11,iPr_def_14),X0),relation_dom(relation_composition(iPr_def_11,iPr_def_14)))
| ( relation_composition(iPr_def_11,iPr_def_14) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,iPr_def_14))
| ~ function(relation_composition(iPr_def_11,iPr_def_14))
| ( set_intersection2(iPr_def_13,sK11) != relation_dom(X0) ) ),
inference(superposition,[status(thm)],[c_3284,c_112]) ).
tcf(c_4688,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_11,iPr_def_14))) = relation_composition(iPr_def_11,iPr_def_14) )
| ~ relation(relation_composition(iPr_def_11,iPr_def_14))
| ~ function(relation_composition(iPr_def_11,iPr_def_14))
| ( apply(relation_composition(iPr_def_11,iPr_def_14),sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_11,iPr_def_14))) != sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_11,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_3284,c_99]) ).
tcf(c_4689,plain,
( in(sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_11,iPr_def_14)),set_intersection2(iPr_def_13,sK11))
| ( identity_relation(relation_dom(relation_composition(iPr_def_11,iPr_def_14))) = relation_composition(iPr_def_11,iPr_def_14) )
| ~ relation(relation_composition(iPr_def_11,iPr_def_14))
| ~ function(relation_composition(iPr_def_11,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_3284,c_100]) ).
tcf(c_4690,plain,
( empty(relation_composition(iPr_def_11,iPr_def_14))
| ~ relation(relation_composition(iPr_def_11,iPr_def_14))
| ~ empty(set_intersection2(iPr_def_13,sK11)) ),
inference(superposition,[status(thm)],[c_3284,c_75]) ).
tcf(c_4691,plain,
( function(set_intersection2(iPr_def_13,sK11))
| ~ empty(relation_composition(iPr_def_11,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_3284,c_1895]) ).
tcf(c_4692,plain,
( relation(set_intersection2(iPr_def_13,sK11))
| ~ empty(relation_composition(iPr_def_11,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_3284,c_77]) ).
tcf(c_4693,plain,
( empty(set_intersection2(iPr_def_13,sK11))
| ~ empty(relation_composition(iPr_def_11,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_3284,c_76]) ).
tcf(c_4694,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_11,iPr_def_14),X0) = apply(iPr_def_14,apply(iPr_def_11,X0)) )
| ~ relation(iPr_def_14)
| ~ relation(iPr_def_11)
| ~ function(iPr_def_14)
| ~ function(iPr_def_11)
| ~ in(X0,set_intersection2(iPr_def_13,sK11)) ),
inference(superposition,[status(thm)],[c_3284,c_96]) ).
tcf(c_4704,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_11,iPr_def_14),X0) = apply(iPr_def_14,apply(iPr_def_11,X0)) )
| ~ in(X0,set_intersection2(iPr_def_13,sK11)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4694,c_1887,c_1884,c_1886,c_1883]) ).
tcf(c_4707,plain,
( in(sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_11,iPr_def_14)),set_intersection2(iPr_def_13,sK11))
| ( identity_relation(set_intersection2(iPr_def_13,sK11)) = relation_composition(iPr_def_11,iPr_def_14) )
| ~ relation(relation_composition(iPr_def_11,iPr_def_14))
| ~ function(relation_composition(iPr_def_11,iPr_def_14)) ),
inference(light_normalisation,[status(thm)],[c_4689,c_3284]) ).
tcf(c_4719,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_11,iPr_def_14),X0),set_intersection2(iPr_def_13,sK11))
| ( relation_composition(iPr_def_11,iPr_def_14) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,iPr_def_14))
| ~ function(relation_composition(iPr_def_11,iPr_def_14))
| ( set_intersection2(iPr_def_13,sK11) != relation_dom(X0) ) ),
inference(light_normalisation,[status(thm)],[c_4687,c_3284]) ).
tcf(c_4727,plain,
( ( identity_relation(set_intersection2(iPr_def_13,sK11)) = relation_composition(iPr_def_11,iPr_def_14) )
| ~ relation(relation_composition(iPr_def_11,iPr_def_14))
| ~ function(relation_composition(iPr_def_11,iPr_def_14))
| ( apply(relation_composition(iPr_def_11,iPr_def_14),sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_11,iPr_def_14))) != sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_11,iPr_def_14)) ) ),
inference(light_normalisation,[status(thm)],[c_4688,c_3284]) ).
tcf(c_4756,plain,
set_intersection2(relation_dom(sK2),sK12) = relation_dom(relation_composition(iPr_def_10,sK2)),
inference(superposition,[status(thm)],[c_1147,c_3034]) ).
tcf(c_4757,plain,
set_intersection2(relation_dom(sK2),sK11) = relation_dom(relation_composition(iPr_def_11,sK2)),
inference(superposition,[status(thm)],[c_1148,c_3034]) ).
tcf(c_4758,plain,
set_intersection2(relation_dom(sK2),empty_set) = relation_dom(relation_composition(empty_set,sK2)),
inference(superposition,[status(thm)],[c_2472,c_3034]) ).
tcf(c_4759,plain,
set_intersection2(relation_dom(sK2),iPr_def_13) = relation_dom(relation_composition(iPr_def_14,sK2)),
inference(superposition,[status(thm)],[c_1151,c_3034]) ).
tcf(c_4760,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,relation_composition(identity_relation(X0),sK2)),relation_dom(X1))
| ( relation_composition(identity_relation(X0),sK2) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),sK2))
| ~ function(relation_composition(identity_relation(X0),sK2))
| ( set_intersection2(relation_dom(sK2),X0) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_3034,c_112]) ).
tcf(c_4761,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(identity_relation(X0),sK2),X1),relation_dom(relation_composition(identity_relation(X0),sK2)))
| ( relation_composition(identity_relation(X0),sK2) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),sK2))
| ~ function(relation_composition(identity_relation(X0),sK2))
| ( set_intersection2(relation_dom(sK2),X0) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_3034,c_112]) ).
tcf(c_4762,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_composition(identity_relation(X0),sK2))) = relation_composition(identity_relation(X0),sK2) )
| ~ relation(relation_composition(identity_relation(X0),sK2))
| ~ function(relation_composition(identity_relation(X0),sK2))
| ( apply(relation_composition(identity_relation(X0),sK2),sK10(set_intersection2(relation_dom(sK2),X0),relation_composition(identity_relation(X0),sK2))) != sK10(set_intersection2(relation_dom(sK2),X0),relation_composition(identity_relation(X0),sK2)) ) ),
inference(superposition,[status(thm)],[c_3034,c_99]) ).
tcf(c_4763,plain,
! [X0: $i] :
( in(sK10(set_intersection2(relation_dom(sK2),X0),relation_composition(identity_relation(X0),sK2)),set_intersection2(relation_dom(sK2),X0))
| ( identity_relation(relation_dom(relation_composition(identity_relation(X0),sK2))) = relation_composition(identity_relation(X0),sK2) )
| ~ relation(relation_composition(identity_relation(X0),sK2))
| ~ function(relation_composition(identity_relation(X0),sK2)) ),
inference(superposition,[status(thm)],[c_3034,c_100]) ).
tcf(c_4764,plain,
! [X0: $i] :
( empty(relation_composition(identity_relation(X0),sK2))
| ~ relation(relation_composition(identity_relation(X0),sK2))
| ~ empty(set_intersection2(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_3034,c_75]) ).
tcf(c_4765,plain,
! [X0: $i] :
( function(set_intersection2(relation_dom(sK2),X0))
| ~ empty(relation_composition(identity_relation(X0),sK2)) ),
inference(superposition,[status(thm)],[c_3034,c_1895]) ).
tcf(c_4766,plain,
! [X0: $i] :
( relation(set_intersection2(relation_dom(sK2),X0))
| ~ empty(relation_composition(identity_relation(X0),sK2)) ),
inference(superposition,[status(thm)],[c_3034,c_77]) ).
tcf(c_4767,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(sK2),X0))
| ~ empty(relation_composition(identity_relation(X0),sK2)) ),
inference(superposition,[status(thm)],[c_3034,c_76]) ).
tcf(c_4768,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(identity_relation(X1),sK2),X0) = apply(sK2,apply(identity_relation(X1),X0)) )
| ~ relation(sK2)
| ~ function(sK2)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,set_intersection2(relation_dom(sK2),X1)) ),
inference(superposition,[status(thm)],[c_3034,c_96]) ).
tcf(c_4778,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(identity_relation(X1),sK2),X0) = apply(sK2,apply(identity_relation(X1),X0)) )
| ~ in(X0,set_intersection2(relation_dom(sK2),X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4768,c_81,c_82,c_71,c_72]) ).
tcf(c_4781,plain,
! [X0: $i] :
( in(sK10(set_intersection2(relation_dom(sK2),X0),relation_composition(identity_relation(X0),sK2)),set_intersection2(relation_dom(sK2),X0))
| ( identity_relation(set_intersection2(relation_dom(sK2),X0)) = relation_composition(identity_relation(X0),sK2) )
| ~ relation(relation_composition(identity_relation(X0),sK2))
| ~ function(relation_composition(identity_relation(X0),sK2)) ),
inference(light_normalisation,[status(thm)],[c_4763,c_3034]) ).
tcf(c_4793,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(identity_relation(X0),sK2),X1),set_intersection2(relation_dom(sK2),X0))
| ( relation_composition(identity_relation(X0),sK2) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),sK2))
| ~ function(relation_composition(identity_relation(X0),sK2))
| ( set_intersection2(relation_dom(sK2),X0) != relation_dom(X1) ) ),
inference(light_normalisation,[status(thm)],[c_4761,c_3034]) ).
tcf(c_4801,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(sK2),X0)) = relation_composition(identity_relation(X0),sK2) )
| ~ relation(relation_composition(identity_relation(X0),sK2))
| ~ function(relation_composition(identity_relation(X0),sK2))
| ( apply(relation_composition(identity_relation(X0),sK2),sK10(set_intersection2(relation_dom(sK2),X0),relation_composition(identity_relation(X0),sK2))) != sK10(set_intersection2(relation_dom(sK2),X0),relation_composition(identity_relation(X0),sK2)) ) ),
inference(light_normalisation,[status(thm)],[c_4762,c_3034]) ).
tcf(c_4864,plain,
relation_dom(relation_composition(iPr_def_14,iPr_def_14)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_3286,c_80]) ).
tcf(c_4865,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(iPr_def_14,iPr_def_14)),relation_dom(X0))
| ( relation_composition(iPr_def_14,iPr_def_14) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,iPr_def_14))
| ~ function(relation_composition(iPr_def_14,iPr_def_14))
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_4864,c_112]) ).
tcf(c_4866,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_14,iPr_def_14),X0),relation_dom(relation_composition(iPr_def_14,iPr_def_14)))
| ( relation_composition(iPr_def_14,iPr_def_14) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,iPr_def_14))
| ~ function(relation_composition(iPr_def_14,iPr_def_14))
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_4864,c_112]) ).
tcf(c_4867,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_14,iPr_def_14))) = relation_composition(iPr_def_14,iPr_def_14) )
| ~ relation(relation_composition(iPr_def_14,iPr_def_14))
| ~ function(relation_composition(iPr_def_14,iPr_def_14))
| ( apply(relation_composition(iPr_def_14,iPr_def_14),sK10(iPr_def_13,relation_composition(iPr_def_14,iPr_def_14))) != sK10(iPr_def_13,relation_composition(iPr_def_14,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_4864,c_99]) ).
tcf(c_4868,plain,
( in(sK10(iPr_def_13,relation_composition(iPr_def_14,iPr_def_14)),iPr_def_13)
| ( identity_relation(relation_dom(relation_composition(iPr_def_14,iPr_def_14))) = relation_composition(iPr_def_14,iPr_def_14) )
| ~ relation(relation_composition(iPr_def_14,iPr_def_14))
| ~ function(relation_composition(iPr_def_14,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_4864,c_100]) ).
tcf(c_4872,plain,
( empty(iPr_def_13)
| ~ empty(relation_composition(iPr_def_14,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_4864,c_76]) ).
tcf(c_4873,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_14,iPr_def_14),X0) = apply(iPr_def_14,apply(iPr_def_14,X0)) )
| ~ relation(iPr_def_14)
| ~ function(iPr_def_14)
| ~ in(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_4864,c_96]) ).
tcf(c_4874,plain,
~ empty(relation_composition(iPr_def_14,iPr_def_14)),
inference(forward_subsumption_resolution,[status(thm)],[c_4872,c_4400]) ).
tcf(c_4875,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_14,iPr_def_14),X0) = apply(iPr_def_14,apply(iPr_def_14,X0)) )
| ~ in(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4873,c_1887,c_1886]) ).
tcf(c_4878,plain,
( in(sK10(iPr_def_13,relation_composition(iPr_def_14,iPr_def_14)),iPr_def_13)
| ( relation_composition(iPr_def_14,iPr_def_14) = iPr_def_14 )
| ~ relation(relation_composition(iPr_def_14,iPr_def_14))
| ~ function(relation_composition(iPr_def_14,iPr_def_14)) ),
inference(light_normalisation,[status(thm)],[c_4868,c_1151,c_4864]) ).
tcf(c_4890,plain,
( ( relation_composition(iPr_def_14,iPr_def_14) = iPr_def_14 )
| ~ relation(relation_composition(iPr_def_14,iPr_def_14))
| ~ function(relation_composition(iPr_def_14,iPr_def_14))
| ( apply(relation_composition(iPr_def_14,iPr_def_14),sK10(iPr_def_13,relation_composition(iPr_def_14,iPr_def_14))) != sK10(iPr_def_13,relation_composition(iPr_def_14,iPr_def_14)) ) ),
inference(light_normalisation,[status(thm)],[c_4867,c_1151,c_4864]) ).
tcf(c_4895,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_14,iPr_def_14),X0),iPr_def_13)
| ( relation_composition(iPr_def_14,iPr_def_14) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,iPr_def_14))
| ~ function(relation_composition(iPr_def_14,iPr_def_14))
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_4866,c_4864]) ).
tcf(c_4927,plain,
( empty(relation_composition(iPr_def_10,empty_set))
| ~ relation(iPr_def_10)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_59,c_3694]) ).
tcf(c_4929,plain,
empty(relation_composition(iPr_def_10,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_4927,c_1881,c_74]) ).
tcf(c_4930,plain,
! [X0: $i] :
( ( relation_composition(iPr_def_10,empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4929,c_110]) ).
tcf(c_4931,plain,
! [X0: $i] : set_intersection2(relation_composition(iPr_def_10,empty_set),X0) = empty_set,
inference(superposition,[status(thm)],[c_4929,c_3180]) ).
tcf(c_4932,plain,
! [X0: $i] : set_intersection2(X0,relation_composition(iPr_def_10,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_4929,c_3084]) ).
tcf(c_4933,plain,
identity_relation(identity_relation(relation_composition(iPr_def_10,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_4929,c_2474]) ).
tcf(c_4934,plain,
identity_relation(relation_dom(relation_composition(iPr_def_10,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_4929,c_2473]) ).
tcf(c_4935,plain,
relation_dom(relation_dom(relation_composition(iPr_def_10,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_4929,c_2055]) ).
tcf(c_4936,plain,
identity_relation(relation_composition(iPr_def_10,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_4929,c_2184]) ).
tcf(c_4938,plain,
relation_composition(iPr_def_10,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_4929,c_108]) ).
tcf(c_4939,plain,
relation(relation_composition(iPr_def_10,empty_set)),
inference(superposition,[status(thm)],[c_4929,c_51]) ).
tcf(c_4940,plain,
function(relation_composition(iPr_def_10,empty_set)),
inference(superposition,[status(thm)],[c_4929,c_50]) ).
tcf(c_4957,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_10,empty_set),X0) = apply(empty_set,apply(iPr_def_10,X0)) )
| ~ relation(iPr_def_10)
| ~ relation(empty_set)
| ~ function(iPr_def_10)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_4938,c_96]) ).
tcf(c_4958,plain,
! [X0: $i] :
( ( apply(empty_set,apply(iPr_def_10,X0)) = apply(empty_set,X0) )
| ~ relation(iPr_def_10)
| ~ relation(empty_set)
| ~ function(iPr_def_10)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_4957,c_2054,c_4938]) ).
tcf(c_4959,plain,
! [X0: $i] :
( ( apply(empty_set,apply(iPr_def_10,X0)) = apply(empty_set,X0) )
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4958,c_1881,c_74,c_1880,c_1866]) ).
tcf(c_4966,plain,
relation_dom(relation_composition(empty_set,iPr_def_14)) = empty_set,
inference(demodulation,[status(thm)],[c_3285,c_97]) ).
tcf(c_4967,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(empty_set,iPr_def_14)),relation_dom(X0))
| ( relation_composition(empty_set,iPr_def_14) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,iPr_def_14))
| ~ function(relation_composition(empty_set,iPr_def_14))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_4966,c_112]) ).
tcf(c_4968,plain,
! [X0: $i] :
( in(sK13(relation_composition(empty_set,iPr_def_14),X0),relation_dom(relation_composition(empty_set,iPr_def_14)))
| ( relation_composition(empty_set,iPr_def_14) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,iPr_def_14))
| ~ function(relation_composition(empty_set,iPr_def_14))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_4966,c_112]) ).
tcf(c_4969,plain,
( ( identity_relation(relation_dom(relation_composition(empty_set,iPr_def_14))) = relation_composition(empty_set,iPr_def_14) )
| ~ relation(relation_composition(empty_set,iPr_def_14))
| ~ function(relation_composition(empty_set,iPr_def_14))
| ( apply(relation_composition(empty_set,iPr_def_14),sK10(empty_set,relation_composition(empty_set,iPr_def_14))) != sK10(empty_set,relation_composition(empty_set,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_4966,c_99]) ).
tcf(c_4970,plain,
( in(sK10(empty_set,relation_composition(empty_set,iPr_def_14)),empty_set)
| ( identity_relation(relation_dom(relation_composition(empty_set,iPr_def_14))) = relation_composition(empty_set,iPr_def_14) )
| ~ relation(relation_composition(empty_set,iPr_def_14))
| ~ function(relation_composition(empty_set,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_4966,c_100]) ).
tcf(c_4971,plain,
( empty(relation_composition(empty_set,iPr_def_14))
| ~ empty(empty_set)
| ~ relation(relation_composition(empty_set,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_4966,c_75]) ).
tcf(c_4975,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,iPr_def_14),X0) = apply(iPr_def_14,apply(empty_set,X0)) )
| ~ relation(iPr_def_14)
| ~ relation(empty_set)
| ~ function(iPr_def_14)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_4966,c_96]) ).
tcf(c_4976,plain,
( empty(relation_composition(empty_set,iPr_def_14))
| ~ relation(relation_composition(empty_set,iPr_def_14)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4971,c_73]) ).
tcf(c_4979,plain,
( in(sK10(empty_set,relation_composition(empty_set,iPr_def_14)),empty_set)
| ( relation_composition(empty_set,iPr_def_14) = empty_set )
| ~ relation(relation_composition(empty_set,iPr_def_14))
| ~ function(relation_composition(empty_set,iPr_def_14)) ),
inference(light_normalisation,[status(thm)],[c_4970,c_2472,c_4966]) ).
tcf(c_4984,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,iPr_def_14),X0) = apply(iPr_def_14,apply(empty_set,X0)) )
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4975,c_1887,c_74,c_1886,c_1866]) ).
tcf(c_4994,plain,
( ( relation_composition(empty_set,iPr_def_14) = empty_set )
| ~ relation(relation_composition(empty_set,iPr_def_14))
| ~ function(relation_composition(empty_set,iPr_def_14))
| ( apply(relation_composition(empty_set,iPr_def_14),sK10(empty_set,relation_composition(empty_set,iPr_def_14))) != sK10(empty_set,relation_composition(empty_set,iPr_def_14)) ) ),
inference(light_normalisation,[status(thm)],[c_4969,c_2472,c_4966]) ).
tcf(c_4999,plain,
! [X0: $i] :
( in(sK13(relation_composition(empty_set,iPr_def_14),X0),empty_set)
| ( relation_composition(empty_set,iPr_def_14) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,iPr_def_14))
| ~ function(relation_composition(empty_set,iPr_def_14))
| ( relation_dom(X0) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_4968,c_4966]) ).
tcf(c_5091,plain,
( empty(relation_composition(iPr_def_11,empty_set))
| ~ relation(iPr_def_11)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_59,c_3739]) ).
tcf(c_5093,plain,
empty(relation_composition(iPr_def_11,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_5091,c_1884,c_74]) ).
tcf(c_5094,plain,
! [X0: $i] :
( ( relation_composition(iPr_def_11,empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5093,c_110]) ).
tcf(c_5095,plain,
! [X0: $i] : set_intersection2(relation_composition(iPr_def_11,empty_set),X0) = empty_set,
inference(superposition,[status(thm)],[c_5093,c_3180]) ).
tcf(c_5096,plain,
! [X0: $i] : set_intersection2(X0,relation_composition(iPr_def_11,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_5093,c_3084]) ).
tcf(c_5097,plain,
identity_relation(identity_relation(relation_composition(iPr_def_11,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_5093,c_2474]) ).
tcf(c_5098,plain,
identity_relation(relation_dom(relation_composition(iPr_def_11,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_5093,c_2473]) ).
tcf(c_5099,plain,
relation_dom(relation_dom(relation_composition(iPr_def_11,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_5093,c_2055]) ).
tcf(c_5100,plain,
identity_relation(relation_composition(iPr_def_11,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_5093,c_2184]) ).
tcf(c_5102,plain,
relation_composition(iPr_def_11,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_5093,c_108]) ).
tcf(c_5103,plain,
relation(relation_composition(iPr_def_11,empty_set)),
inference(superposition,[status(thm)],[c_5093,c_51]) ).
tcf(c_5104,plain,
function(relation_composition(iPr_def_11,empty_set)),
inference(superposition,[status(thm)],[c_5093,c_50]) ).
tcf(c_5115,plain,
! [X0: $i] : relation_dom(relation_composition(iPr_def_10,identity_relation(X0))) = set_intersection2(X0,sK12),
inference(superposition,[status(thm)],[c_1147,c_3036]) ).
tcf(c_5116,plain,
! [X0: $i] : relation_dom(relation_composition(iPr_def_11,identity_relation(X0))) = set_intersection2(X0,sK11),
inference(superposition,[status(thm)],[c_1148,c_3036]) ).
tcf(c_5117,plain,
! [X0: $i] : relation_dom(relation_composition(empty_set,identity_relation(X0))) = set_intersection2(X0,empty_set),
inference(superposition,[status(thm)],[c_2472,c_3036]) ).
tcf(c_5118,plain,
! [X0: $i] : relation_dom(relation_composition(iPr_def_14,identity_relation(X0))) = set_intersection2(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_1151,c_3036]) ).
tcf(c_5121,plain,
! [X0: $i] : relation_dom(relation_composition(identity_relation(X0),empty_set)) = set_intersection2(empty_set,X0),
inference(superposition,[status(thm)],[c_2472,c_3036]) ).
tcf(c_5123,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X2,relation_composition(identity_relation(X1),identity_relation(X0))),relation_dom(X2))
| ( relation_composition(identity_relation(X1),identity_relation(X0)) = X2 )
| ~ relation(X2)
| ~ function(X2)
| ~ relation(relation_composition(identity_relation(X1),identity_relation(X0)))
| ~ function(relation_composition(identity_relation(X1),identity_relation(X0)))
| ( set_intersection2(X0,X1) != relation_dom(X2) ) ),
inference(superposition,[status(thm)],[c_3036,c_112]) ).
tcf(c_5124,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(relation_composition(identity_relation(X1),identity_relation(X0)),X2),relation_dom(relation_composition(identity_relation(X1),identity_relation(X0))))
| ( relation_composition(identity_relation(X1),identity_relation(X0)) = X2 )
| ~ relation(X2)
| ~ function(X2)
| ~ relation(relation_composition(identity_relation(X1),identity_relation(X0)))
| ~ function(relation_composition(identity_relation(X1),identity_relation(X0)))
| ( set_intersection2(X0,X1) != relation_dom(X2) ) ),
inference(superposition,[status(thm)],[c_3036,c_112]) ).
tcf(c_5125,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_composition(identity_relation(X0),identity_relation(X1)))) = relation_composition(identity_relation(X0),identity_relation(X1)) )
| ~ relation(relation_composition(identity_relation(X0),identity_relation(X1)))
| ~ function(relation_composition(identity_relation(X0),identity_relation(X1)))
| ( apply(relation_composition(identity_relation(X0),identity_relation(X1)),sK10(set_intersection2(X1,X0),relation_composition(identity_relation(X0),identity_relation(X1)))) != sK10(set_intersection2(X1,X0),relation_composition(identity_relation(X0),identity_relation(X1))) ) ),
inference(superposition,[status(thm)],[c_3036,c_99]) ).
tcf(c_5126,plain,
! [X0: $i,X1: $i] :
( in(sK10(set_intersection2(X1,X0),relation_composition(identity_relation(X0),identity_relation(X1))),set_intersection2(X1,X0))
| ( identity_relation(relation_dom(relation_composition(identity_relation(X0),identity_relation(X1)))) = relation_composition(identity_relation(X0),identity_relation(X1)) )
| ~ relation(relation_composition(identity_relation(X0),identity_relation(X1)))
| ~ function(relation_composition(identity_relation(X0),identity_relation(X1))) ),
inference(superposition,[status(thm)],[c_3036,c_100]) ).
tcf(c_5127,plain,
! [X0: $i,X1: $i] :
( empty(relation_composition(identity_relation(X0),identity_relation(X1)))
| ~ empty(set_intersection2(X1,X0))
| ~ relation(relation_composition(identity_relation(X0),identity_relation(X1))) ),
inference(superposition,[status(thm)],[c_3036,c_75]) ).
tcf(c_5128,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X1,X0))
| ~ empty(relation_composition(identity_relation(X0),identity_relation(X1))) ),
inference(superposition,[status(thm)],[c_3036,c_1895]) ).
tcf(c_5129,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X1,X0))
| ~ empty(relation_composition(identity_relation(X0),identity_relation(X1))) ),
inference(superposition,[status(thm)],[c_3036,c_77]) ).
tcf(c_5130,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ~ empty(relation_composition(identity_relation(X0),identity_relation(X1))) ),
inference(superposition,[status(thm)],[c_3036,c_76]) ).
tcf(c_5131,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_composition(identity_relation(X2),identity_relation(X1)),X0) = apply(identity_relation(X1),apply(identity_relation(X2),X0)) )
| ~ relation(identity_relation(X2))
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X2))
| ~ function(identity_relation(X1))
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_3036,c_96]) ).
tcf(c_5133,plain,
! [X0: $i] : relation_dom(relation_composition(empty_set,identity_relation(X0))) = empty_set,
inference(light_normalisation,[status(thm)],[c_5117,c_97]) ).
tcf(c_5143,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_composition(identity_relation(X2),identity_relation(X1)),X0) = apply(identity_relation(X1),apply(identity_relation(X2),X0)) )
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5131,c_71,c_71,c_72,c_72]) ).
tcf(c_5146,plain,
! [X0: $i,X1: $i] :
( in(sK10(set_intersection2(X1,X0),relation_composition(identity_relation(X0),identity_relation(X1))),set_intersection2(X1,X0))
| ( relation_composition(identity_relation(X0),identity_relation(X1)) = identity_relation(set_intersection2(X1,X0)) )
| ~ relation(relation_composition(identity_relation(X0),identity_relation(X1)))
| ~ function(relation_composition(identity_relation(X0),identity_relation(X1))) ),
inference(light_normalisation,[status(thm)],[c_5126,c_3036]) ).
tcf(c_5165,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X0),identity_relation(X1)) = identity_relation(set_intersection2(X1,X0)) )
| ~ relation(relation_composition(identity_relation(X0),identity_relation(X1)))
| ~ function(relation_composition(identity_relation(X0),identity_relation(X1)))
| ( apply(relation_composition(identity_relation(X0),identity_relation(X1)),sK10(set_intersection2(X1,X0),relation_composition(identity_relation(X0),identity_relation(X1)))) != sK10(set_intersection2(X1,X0),relation_composition(identity_relation(X0),identity_relation(X1))) ) ),
inference(light_normalisation,[status(thm)],[c_5125,c_3036]) ).
tcf(c_5200,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_11,empty_set),X0) = apply(empty_set,apply(iPr_def_11,X0)) )
| ~ relation(iPr_def_11)
| ~ relation(empty_set)
| ~ function(iPr_def_11)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_5102,c_96]) ).
tcf(c_5201,plain,
! [X0: $i] :
( ( apply(empty_set,apply(iPr_def_11,X0)) = apply(empty_set,X0) )
| ~ relation(iPr_def_11)
| ~ relation(empty_set)
| ~ function(iPr_def_11)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_5200,c_2054,c_5102]) ).
tcf(c_5202,plain,
! [X0: $i] :
( ( apply(empty_set,apply(iPr_def_11,X0)) = apply(empty_set,X0) )
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5201,c_1884,c_74,c_1883,c_1866]) ).
tcf(c_5205,plain,
empty(relation_composition(empty_set,empty_set)),
inference(global_subsumption_just,[status(thm)],[c_3812,c_74,c_73,c_132]) ).
tcf(c_5207,plain,
! [X0: $i] :
( ( relation_composition(empty_set,empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5205,c_110]) ).
tcf(c_5208,plain,
! [X0: $i] : set_intersection2(relation_composition(empty_set,empty_set),X0) = empty_set,
inference(superposition,[status(thm)],[c_5205,c_3180]) ).
tcf(c_5209,plain,
! [X0: $i] : set_intersection2(X0,relation_composition(empty_set,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_5205,c_3084]) ).
tcf(c_5210,plain,
identity_relation(identity_relation(relation_composition(empty_set,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_5205,c_2474]) ).
tcf(c_5211,plain,
identity_relation(relation_dom(relation_composition(empty_set,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_5205,c_2473]) ).
tcf(c_5212,plain,
relation_dom(relation_dom(relation_composition(empty_set,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_5205,c_2055]) ).
tcf(c_5213,plain,
identity_relation(relation_composition(empty_set,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_5205,c_2184]) ).
tcf(c_5215,plain,
relation_composition(empty_set,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_5205,c_108]) ).
tcf(c_5216,plain,
relation(relation_composition(empty_set,empty_set)),
inference(superposition,[status(thm)],[c_5205,c_51]) ).
tcf(c_5217,plain,
function(relation_composition(empty_set,empty_set)),
inference(superposition,[status(thm)],[c_5205,c_50]) ).
tcf(c_5249,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,empty_set),X0) = apply(empty_set,apply(empty_set,X0)) )
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_5215,c_96]) ).
tcf(c_5250,plain,
! [X0: $i] :
( ( apply(empty_set,apply(empty_set,X0)) = apply(empty_set,X0) )
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_5249,c_2054,c_5215]) ).
tcf(c_5251,plain,
! [X0: $i] :
( ( apply(empty_set,apply(empty_set,X0)) = apply(empty_set,X0) )
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5250,c_74,c_1866]) ).
tcf(c_5259,plain,
relation_dom(relation_composition(empty_set,iPr_def_10)) = empty_set,
inference(superposition,[status(thm)],[c_1147,c_5133]) ).
tcf(c_5260,plain,
relation_dom(relation_composition(empty_set,iPr_def_11)) = empty_set,
inference(superposition,[status(thm)],[c_1148,c_5133]) ).
tcf(c_5263,plain,
! [X0: $i,X1: $i] :
( in(sK13(X0,relation_composition(empty_set,identity_relation(X1))),relation_dom(X0))
| ( relation_composition(empty_set,identity_relation(X1)) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,identity_relation(X1)))
| ~ function(relation_composition(empty_set,identity_relation(X1)))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_5133,c_112]) ).
tcf(c_5264,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(empty_set,identity_relation(X1)),X0),relation_dom(relation_composition(empty_set,identity_relation(X1))))
| ( relation_composition(empty_set,identity_relation(X1)) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,identity_relation(X1)))
| ~ function(relation_composition(empty_set,identity_relation(X1)))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_5133,c_112]) ).
tcf(c_5265,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_composition(empty_set,identity_relation(X0)))) = relation_composition(empty_set,identity_relation(X0)) )
| ~ relation(relation_composition(empty_set,identity_relation(X0)))
| ~ function(relation_composition(empty_set,identity_relation(X0)))
| ( apply(relation_composition(empty_set,identity_relation(X0)),sK10(empty_set,relation_composition(empty_set,identity_relation(X0)))) != sK10(empty_set,relation_composition(empty_set,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_5133,c_99]) ).
tcf(c_5266,plain,
! [X0: $i] :
( in(sK10(empty_set,relation_composition(empty_set,identity_relation(X0))),empty_set)
| ( identity_relation(relation_dom(relation_composition(empty_set,identity_relation(X0)))) = relation_composition(empty_set,identity_relation(X0)) )
| ~ relation(relation_composition(empty_set,identity_relation(X0)))
| ~ function(relation_composition(empty_set,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5133,c_100]) ).
tcf(c_5267,plain,
! [X0: $i] :
( empty(relation_composition(empty_set,identity_relation(X0)))
| ~ empty(empty_set)
| ~ relation(relation_composition(empty_set,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5133,c_75]) ).
tcf(c_5271,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(empty_set,identity_relation(X1)),X0) = apply(identity_relation(X1),apply(empty_set,X0)) )
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_5133,c_96]) ).
tcf(c_5272,plain,
! [X0: $i] :
( empty(relation_composition(empty_set,identity_relation(X0)))
| ~ relation(relation_composition(empty_set,identity_relation(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5267,c_73]) ).
tcf(c_5275,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(empty_set,identity_relation(X1)),X0) = apply(identity_relation(X1),apply(empty_set,X0)) )
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5271,c_74,c_1866,c_71,c_72]) ).
tcf(c_5278,plain,
! [X0: $i] :
( in(sK10(empty_set,relation_composition(empty_set,identity_relation(X0))),empty_set)
| ( relation_composition(empty_set,identity_relation(X0)) = empty_set )
| ~ relation(relation_composition(empty_set,identity_relation(X0)))
| ~ function(relation_composition(empty_set,identity_relation(X0))) ),
inference(light_normalisation,[status(thm)],[c_5266,c_2472,c_5133]) ).
tcf(c_5297,plain,
! [X0: $i] :
( ( relation_composition(empty_set,identity_relation(X0)) = empty_set )
| ~ relation(relation_composition(empty_set,identity_relation(X0)))
| ~ function(relation_composition(empty_set,identity_relation(X0)))
| ( apply(relation_composition(empty_set,identity_relation(X0)),sK10(empty_set,relation_composition(empty_set,identity_relation(X0)))) != sK10(empty_set,relation_composition(empty_set,identity_relation(X0))) ) ),
inference(light_normalisation,[status(thm)],[c_5265,c_2472,c_5133]) ).
tcf(c_5307,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(empty_set,iPr_def_10)),relation_dom(X0))
| ( relation_composition(empty_set,iPr_def_10) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,iPr_def_10))
| ~ function(relation_composition(empty_set,iPr_def_10))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_5259,c_112]) ).
tcf(c_5308,plain,
! [X0: $i] :
( in(sK13(relation_composition(empty_set,iPr_def_10),X0),relation_dom(relation_composition(empty_set,iPr_def_10)))
| ( relation_composition(empty_set,iPr_def_10) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,iPr_def_10))
| ~ function(relation_composition(empty_set,iPr_def_10))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_5259,c_112]) ).
tcf(c_5309,plain,
( ( identity_relation(relation_dom(relation_composition(empty_set,iPr_def_10))) = relation_composition(empty_set,iPr_def_10) )
| ~ relation(relation_composition(empty_set,iPr_def_10))
| ~ function(relation_composition(empty_set,iPr_def_10))
| ( apply(relation_composition(empty_set,iPr_def_10),sK10(empty_set,relation_composition(empty_set,iPr_def_10))) != sK10(empty_set,relation_composition(empty_set,iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_5259,c_99]) ).
tcf(c_5310,plain,
( in(sK10(empty_set,relation_composition(empty_set,iPr_def_10)),empty_set)
| ( identity_relation(relation_dom(relation_composition(empty_set,iPr_def_10))) = relation_composition(empty_set,iPr_def_10) )
| ~ relation(relation_composition(empty_set,iPr_def_10))
| ~ function(relation_composition(empty_set,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5259,c_100]) ).
tcf(c_5311,plain,
( empty(relation_composition(empty_set,iPr_def_10))
| ~ empty(empty_set)
| ~ relation(relation_composition(empty_set,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5259,c_75]) ).
tcf(c_5315,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,iPr_def_10),X0) = apply(iPr_def_10,apply(empty_set,X0)) )
| ~ relation(iPr_def_10)
| ~ relation(empty_set)
| ~ function(iPr_def_10)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_5259,c_96]) ).
tcf(c_5316,plain,
( empty(relation_composition(empty_set,iPr_def_10))
| ~ relation(relation_composition(empty_set,iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5311,c_73]) ).
tcf(c_5319,plain,
( in(sK10(empty_set,relation_composition(empty_set,iPr_def_10)),empty_set)
| ( relation_composition(empty_set,iPr_def_10) = empty_set )
| ~ relation(relation_composition(empty_set,iPr_def_10))
| ~ function(relation_composition(empty_set,iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_5310,c_2472,c_5259]) ).
tcf(c_5324,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,iPr_def_10),X0) = apply(iPr_def_10,apply(empty_set,X0)) )
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5315,c_1881,c_74,c_1880,c_1866]) ).
tcf(c_5334,plain,
( ( relation_composition(empty_set,iPr_def_10) = empty_set )
| ~ relation(relation_composition(empty_set,iPr_def_10))
| ~ function(relation_composition(empty_set,iPr_def_10))
| ( apply(relation_composition(empty_set,iPr_def_10),sK10(empty_set,relation_composition(empty_set,iPr_def_10))) != sK10(empty_set,relation_composition(empty_set,iPr_def_10)) ) ),
inference(light_normalisation,[status(thm)],[c_5309,c_2472,c_5259]) ).
tcf(c_5339,plain,
! [X0: $i] :
( in(sK13(relation_composition(empty_set,iPr_def_10),X0),empty_set)
| ( relation_composition(empty_set,iPr_def_10) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,iPr_def_10))
| ~ function(relation_composition(empty_set,iPr_def_10))
| ( relation_dom(X0) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_5308,c_5259]) ).
tcf(c_5349,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(empty_set,iPr_def_11)),relation_dom(X0))
| ( relation_composition(empty_set,iPr_def_11) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,iPr_def_11))
| ~ function(relation_composition(empty_set,iPr_def_11))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_5260,c_112]) ).
tcf(c_5350,plain,
! [X0: $i] :
( in(sK13(relation_composition(empty_set,iPr_def_11),X0),relation_dom(relation_composition(empty_set,iPr_def_11)))
| ( relation_composition(empty_set,iPr_def_11) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,iPr_def_11))
| ~ function(relation_composition(empty_set,iPr_def_11))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_5260,c_112]) ).
tcf(c_5351,plain,
( ( identity_relation(relation_dom(relation_composition(empty_set,iPr_def_11))) = relation_composition(empty_set,iPr_def_11) )
| ~ relation(relation_composition(empty_set,iPr_def_11))
| ~ function(relation_composition(empty_set,iPr_def_11))
| ( apply(relation_composition(empty_set,iPr_def_11),sK10(empty_set,relation_composition(empty_set,iPr_def_11))) != sK10(empty_set,relation_composition(empty_set,iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_5260,c_99]) ).
tcf(c_5352,plain,
( in(sK10(empty_set,relation_composition(empty_set,iPr_def_11)),empty_set)
| ( identity_relation(relation_dom(relation_composition(empty_set,iPr_def_11))) = relation_composition(empty_set,iPr_def_11) )
| ~ relation(relation_composition(empty_set,iPr_def_11))
| ~ function(relation_composition(empty_set,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_5260,c_100]) ).
tcf(c_5353,plain,
( empty(relation_composition(empty_set,iPr_def_11))
| ~ empty(empty_set)
| ~ relation(relation_composition(empty_set,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_5260,c_75]) ).
tcf(c_5357,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,iPr_def_11),X0) = apply(iPr_def_11,apply(empty_set,X0)) )
| ~ relation(iPr_def_11)
| ~ relation(empty_set)
| ~ function(iPr_def_11)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_5260,c_96]) ).
tcf(c_5358,plain,
( empty(relation_composition(empty_set,iPr_def_11))
| ~ relation(relation_composition(empty_set,iPr_def_11)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5353,c_73]) ).
tcf(c_5361,plain,
( in(sK10(empty_set,relation_composition(empty_set,iPr_def_11)),empty_set)
| ( relation_composition(empty_set,iPr_def_11) = empty_set )
| ~ relation(relation_composition(empty_set,iPr_def_11))
| ~ function(relation_composition(empty_set,iPr_def_11)) ),
inference(light_normalisation,[status(thm)],[c_5352,c_2472,c_5260]) ).
tcf(c_5366,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,iPr_def_11),X0) = apply(iPr_def_11,apply(empty_set,X0)) )
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5357,c_1884,c_74,c_1883,c_1866]) ).
tcf(c_5376,plain,
( ( relation_composition(empty_set,iPr_def_11) = empty_set )
| ~ relation(relation_composition(empty_set,iPr_def_11))
| ~ function(relation_composition(empty_set,iPr_def_11))
| ( apply(relation_composition(empty_set,iPr_def_11),sK10(empty_set,relation_composition(empty_set,iPr_def_11))) != sK10(empty_set,relation_composition(empty_set,iPr_def_11)) ) ),
inference(light_normalisation,[status(thm)],[c_5351,c_2472,c_5260]) ).
tcf(c_5381,plain,
! [X0: $i] :
( in(sK13(relation_composition(empty_set,iPr_def_11),X0),empty_set)
| ( relation_composition(empty_set,iPr_def_11) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,iPr_def_11))
| ~ function(relation_composition(empty_set,iPr_def_11))
| ( relation_dom(X0) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_5350,c_5260]) ).
tcf(c_5400,plain,
! [X0: $i,X1: $i] :
( empty(sK4(sK4(powerset(X1))))
| in(X0,sK4(sK4(powerset(X1))))
| ~ element(X0,sK4(sK4(powerset(X1)))) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_5401,plain,
( empty(sK4(sK4(powerset(empty_set))))
| in(empty_set,sK4(sK4(powerset(empty_set))))
| ~ element(empty_set,sK4(sK4(powerset(empty_set)))) ),
inference(instantiation,[status(thm)],[c_5400]) ).
tcf(c_5413,plain,
! [X0: $i] : relation_dom(relation_composition(identity_relation(X0),iPr_def_12)) = set_intersection2(iPr_def_13,X0),
inference(light_normalisation,[status(thm)],[c_3066,c_4354]) ).
tcf(c_5414,plain,
relation_dom(relation_composition(iPr_def_10,iPr_def_12)) = set_intersection2(iPr_def_13,sK12),
inference(superposition,[status(thm)],[c_1147,c_5413]) ).
tcf(c_5415,plain,
relation_dom(relation_composition(iPr_def_11,iPr_def_12)) = set_intersection2(iPr_def_13,sK11),
inference(superposition,[status(thm)],[c_1148,c_5413]) ).
tcf(c_5416,plain,
relation_dom(relation_composition(empty_set,iPr_def_12)) = set_intersection2(iPr_def_13,empty_set),
inference(superposition,[status(thm)],[c_2472,c_5413]) ).
tcf(c_5417,plain,
relation_dom(relation_composition(iPr_def_14,iPr_def_12)) = set_intersection2(iPr_def_13,iPr_def_13),
inference(superposition,[status(thm)],[c_1151,c_5413]) ).
tcf(c_5418,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,relation_composition(identity_relation(X0),iPr_def_12)),relation_dom(X1))
| ( relation_composition(identity_relation(X0),iPr_def_12) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),iPr_def_12))
| ~ function(relation_composition(identity_relation(X0),iPr_def_12))
| ( set_intersection2(iPr_def_13,X0) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_5413,c_112]) ).
tcf(c_5419,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(identity_relation(X0),iPr_def_12),X1),relation_dom(relation_composition(identity_relation(X0),iPr_def_12)))
| ( relation_composition(identity_relation(X0),iPr_def_12) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),iPr_def_12))
| ~ function(relation_composition(identity_relation(X0),iPr_def_12))
| ( set_intersection2(iPr_def_13,X0) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_5413,c_112]) ).
tcf(c_5420,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_composition(identity_relation(X0),iPr_def_12))) = relation_composition(identity_relation(X0),iPr_def_12) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_12))
| ~ function(relation_composition(identity_relation(X0),iPr_def_12))
| ( apply(relation_composition(identity_relation(X0),iPr_def_12),sK10(set_intersection2(iPr_def_13,X0),relation_composition(identity_relation(X0),iPr_def_12))) != sK10(set_intersection2(iPr_def_13,X0),relation_composition(identity_relation(X0),iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_5413,c_99]) ).
tcf(c_5421,plain,
! [X0: $i] :
( in(sK10(set_intersection2(iPr_def_13,X0),relation_composition(identity_relation(X0),iPr_def_12)),set_intersection2(iPr_def_13,X0))
| ( identity_relation(relation_dom(relation_composition(identity_relation(X0),iPr_def_12))) = relation_composition(identity_relation(X0),iPr_def_12) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_12))
| ~ function(relation_composition(identity_relation(X0),iPr_def_12)) ),
inference(superposition,[status(thm)],[c_5413,c_100]) ).
tcf(c_5422,plain,
! [X0: $i] :
( empty(relation_composition(identity_relation(X0),iPr_def_12))
| ~ empty(set_intersection2(iPr_def_13,X0))
| ~ relation(relation_composition(identity_relation(X0),iPr_def_12)) ),
inference(superposition,[status(thm)],[c_5413,c_75]) ).
tcf(c_5423,plain,
! [X0: $i] :
( function(set_intersection2(iPr_def_13,X0))
| ~ empty(relation_composition(identity_relation(X0),iPr_def_12)) ),
inference(superposition,[status(thm)],[c_5413,c_1895]) ).
tcf(c_5424,plain,
! [X0: $i] :
( relation(set_intersection2(iPr_def_13,X0))
| ~ empty(relation_composition(identity_relation(X0),iPr_def_12)) ),
inference(superposition,[status(thm)],[c_5413,c_77]) ).
tcf(c_5425,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ~ empty(relation_composition(identity_relation(X0),iPr_def_12)) ),
inference(superposition,[status(thm)],[c_5413,c_76]) ).
tcf(c_5426,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(identity_relation(X1),iPr_def_12),X0) = apply(iPr_def_12,apply(identity_relation(X1),X0)) )
| ~ relation(iPr_def_12)
| ~ function(iPr_def_12)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,set_intersection2(iPr_def_13,X1)) ),
inference(superposition,[status(thm)],[c_5413,c_96]) ).
tcf(c_5436,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(identity_relation(X1),iPr_def_12),X0) = apply(iPr_def_12,apply(identity_relation(X1),X0)) )
| ~ in(X0,set_intersection2(iPr_def_13,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5426,c_2156,c_3011,c_71,c_72]) ).
tcf(c_5439,plain,
! [X0: $i] :
( in(sK10(set_intersection2(iPr_def_13,X0),relation_composition(identity_relation(X0),iPr_def_12)),set_intersection2(iPr_def_13,X0))
| ( relation_composition(identity_relation(X0),iPr_def_12) = identity_relation(set_intersection2(iPr_def_13,X0)) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_12))
| ~ function(relation_composition(identity_relation(X0),iPr_def_12)) ),
inference(light_normalisation,[status(thm)],[c_5421,c_5413]) ).
tcf(c_5451,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(identity_relation(X0),iPr_def_12),X1),set_intersection2(iPr_def_13,X0))
| ( relation_composition(identity_relation(X0),iPr_def_12) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(identity_relation(X0),iPr_def_12))
| ~ function(relation_composition(identity_relation(X0),iPr_def_12))
| ( set_intersection2(iPr_def_13,X0) != relation_dom(X1) ) ),
inference(light_normalisation,[status(thm)],[c_5419,c_5413]) ).
tcf(c_5459,plain,
! [X0: $i] :
( ( relation_composition(identity_relation(X0),iPr_def_12) = identity_relation(set_intersection2(iPr_def_13,X0)) )
| ~ relation(relation_composition(identity_relation(X0),iPr_def_12))
| ~ function(relation_composition(identity_relation(X0),iPr_def_12))
| ( apply(relation_composition(identity_relation(X0),iPr_def_12),sK10(set_intersection2(iPr_def_13,X0),relation_composition(identity_relation(X0),iPr_def_12))) != sK10(set_intersection2(iPr_def_13,X0),relation_composition(identity_relation(X0),iPr_def_12)) ) ),
inference(light_normalisation,[status(thm)],[c_5420,c_5413]) ).
tcf(c_5493,plain,
( empty(relation_composition(iPr_def_14,empty_set))
| ~ relation(iPr_def_14)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_59,c_3854]) ).
tcf(c_5495,plain,
empty(relation_composition(iPr_def_14,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_5493,c_1887,c_74]) ).
tcf(c_5500,plain,
! [X0: $i] :
( ( relation_composition(iPr_def_14,empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5495,c_110]) ).
tcf(c_5501,plain,
! [X0: $i] : set_intersection2(relation_composition(iPr_def_14,empty_set),X0) = empty_set,
inference(superposition,[status(thm)],[c_5495,c_3180]) ).
tcf(c_5502,plain,
! [X0: $i] : set_intersection2(X0,relation_composition(iPr_def_14,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_5495,c_3084]) ).
tcf(c_5503,plain,
identity_relation(identity_relation(relation_composition(iPr_def_14,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_5495,c_2474]) ).
tcf(c_5504,plain,
identity_relation(relation_dom(relation_composition(iPr_def_14,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_5495,c_2473]) ).
tcf(c_5505,plain,
relation_dom(relation_dom(relation_composition(iPr_def_14,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_5495,c_2055]) ).
tcf(c_5506,plain,
identity_relation(relation_composition(iPr_def_14,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_5495,c_2184]) ).
tcf(c_5508,plain,
relation_composition(iPr_def_14,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_5495,c_108]) ).
tcf(c_5509,plain,
relation(relation_composition(iPr_def_14,empty_set)),
inference(superposition,[status(thm)],[c_5495,c_51]) ).
tcf(c_5510,plain,
function(relation_composition(iPr_def_14,empty_set)),
inference(superposition,[status(thm)],[c_5495,c_50]) ).
tcf(c_5561,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_14,empty_set),X0) = apply(empty_set,apply(iPr_def_14,X0)) )
| ~ relation(iPr_def_14)
| ~ relation(empty_set)
| ~ function(iPr_def_14)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_5508,c_96]) ).
tcf(c_5562,plain,
! [X0: $i] :
( ( apply(empty_set,apply(iPr_def_14,X0)) = apply(empty_set,X0) )
| ~ relation(iPr_def_14)
| ~ relation(empty_set)
| ~ function(iPr_def_14)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_5561,c_2054,c_5508]) ).
tcf(c_5563,plain,
! [X0: $i] :
( ( apply(empty_set,apply(iPr_def_14,X0)) = apply(empty_set,X0) )
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5562,c_1887,c_74,c_1886,c_1866]) ).
tcf(c_5574,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(powerset(X0)),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_52,c_3896]) ).
tcf(c_5578,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,sK1(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_110]) ).
tcf(c_5579,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,sK1(powerset(X0))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3180]) ).
tcf(c_5580,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X2,sK1(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3084]) ).
tcf(c_5581,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_2474]) ).
tcf(c_5582,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_2473]) ).
tcf(c_5583,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_2055]) ).
tcf(c_5584,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,sK1(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_2184]) ).
tcf(c_5585,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,sK1(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_2013]) ).
tcf(c_5587,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X1,sK1(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_51]) ).
tcf(c_5588,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X1,sK1(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_50]) ).
tcf(c_5626,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_composition(X0,X1))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3939]) ).
tcf(c_5627,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_composition(X1,X0))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3939]) ).
tcf(c_5628,plain,
sK1(powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3939]) ).
tcf(c_5629,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3939]) ).
tcf(c_5630,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3939]) ).
tcf(c_5631,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(X0,X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3939]) ).
tcf(c_5632,plain,
! [X0: $i] :
( ( sK1(powerset(sK1(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_3939]) ).
tcf(c_5633,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(X1,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3939]) ).
tcf(c_5634,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(X1,sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3939]) ).
tcf(c_5660,plain,
( empty(powerset(empty_set))
| in(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_5628,c_2137]) ).
tcf(c_5661,plain,
element(empty_set,powerset(empty_set)),
inference(superposition,[status(thm)],[c_5628,c_61]) ).
tcf(c_5662,plain,
! [X0: $i] :
( ~ empty(empty_set)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_5628,c_2933]) ).
tcf(c_5664,plain,
! [X0: $i] :
( empty(set_intersection2(X0,empty_set))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_5628,c_3896]) ).
tcf(c_5671,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_5662,c_73]) ).
tcf(c_5672,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,empty_set,X1),X1)
| ( set_intersection2(X0,empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_55,c_5671]) ).
tcf(c_5673,plain,
! [X0: $i,X1: $i] :
( in(sK0(empty_set,X0,X1),X1)
| ( set_intersection2(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_54,c_5671]) ).
tcf(c_5674,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,empty_set),X1)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_55,c_5671]) ).
tcf(c_5675,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,empty_set),X0)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_54,c_5671]) ).
tcf(c_5677,plain,
! [X0: $i] : empty(set_intersection2(X0,empty_set)),
inference(superposition,[status(thm)],[c_2201,c_5671]) ).
tcf(c_5683,plain,
! [X0: $i,X1: $i] :
( in(sK0(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_5673,c_1996]) ).
tcf(c_5686,plain,
! [X0: $i,X1: $i] :
( in(sK0(X1,empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_5672,c_97]) ).
tcf(c_5689,plain,
relation_dom(relation_composition(iPr_def_11,iPr_def_11)) = sK11,
inference(demodulation,[status(thm)],[c_4098,c_80]) ).
tcf(c_5690,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(iPr_def_11,iPr_def_11)),relation_dom(X0))
| ( relation_composition(iPr_def_11,iPr_def_11) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,iPr_def_11))
| ~ function(relation_composition(iPr_def_11,iPr_def_11))
| ( relation_dom(X0) != sK11 ) ),
inference(superposition,[status(thm)],[c_5689,c_112]) ).
tcf(c_5691,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_11,iPr_def_11),X0),relation_dom(relation_composition(iPr_def_11,iPr_def_11)))
| ( relation_composition(iPr_def_11,iPr_def_11) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,iPr_def_11))
| ~ function(relation_composition(iPr_def_11,iPr_def_11))
| ( relation_dom(X0) != sK11 ) ),
inference(superposition,[status(thm)],[c_5689,c_112]) ).
tcf(c_5692,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_11,iPr_def_11))) = relation_composition(iPr_def_11,iPr_def_11) )
| ~ relation(relation_composition(iPr_def_11,iPr_def_11))
| ~ function(relation_composition(iPr_def_11,iPr_def_11))
| ( apply(relation_composition(iPr_def_11,iPr_def_11),sK10(sK11,relation_composition(iPr_def_11,iPr_def_11))) != sK10(sK11,relation_composition(iPr_def_11,iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_5689,c_99]) ).
tcf(c_5693,plain,
( in(sK10(sK11,relation_composition(iPr_def_11,iPr_def_11)),sK11)
| ( identity_relation(relation_dom(relation_composition(iPr_def_11,iPr_def_11))) = relation_composition(iPr_def_11,iPr_def_11) )
| ~ relation(relation_composition(iPr_def_11,iPr_def_11))
| ~ function(relation_composition(iPr_def_11,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_5689,c_100]) ).
tcf(c_5697,plain,
( empty(sK11)
| ~ empty(relation_composition(iPr_def_11,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_5689,c_76]) ).
tcf(c_5698,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_11,iPr_def_11),X0) = apply(iPr_def_11,apply(iPr_def_11,X0)) )
| ~ relation(iPr_def_11)
| ~ function(iPr_def_11)
| ~ in(X0,sK11) ),
inference(superposition,[status(thm)],[c_5689,c_96]) ).
tcf(c_5699,plain,
~ empty(relation_composition(iPr_def_11,iPr_def_11)),
inference(forward_subsumption_resolution,[status(thm)],[c_5697,c_3220]) ).
tcf(c_5700,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_11,iPr_def_11),X0) = apply(iPr_def_11,apply(iPr_def_11,X0)) )
| ~ in(X0,sK11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5698,c_1884,c_1883]) ).
tcf(c_5703,plain,
( in(sK10(sK11,relation_composition(iPr_def_11,iPr_def_11)),sK11)
| ( relation_composition(iPr_def_11,iPr_def_11) = iPr_def_11 )
| ~ relation(relation_composition(iPr_def_11,iPr_def_11))
| ~ function(relation_composition(iPr_def_11,iPr_def_11)) ),
inference(light_normalisation,[status(thm)],[c_5693,c_1148,c_5689]) ).
tcf(c_5715,plain,
( ( relation_composition(iPr_def_11,iPr_def_11) = iPr_def_11 )
| ~ relation(relation_composition(iPr_def_11,iPr_def_11))
| ~ function(relation_composition(iPr_def_11,iPr_def_11))
| ( apply(relation_composition(iPr_def_11,iPr_def_11),sK10(sK11,relation_composition(iPr_def_11,iPr_def_11))) != sK10(sK11,relation_composition(iPr_def_11,iPr_def_11)) ) ),
inference(light_normalisation,[status(thm)],[c_5692,c_1148,c_5689]) ).
tcf(c_5720,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_11,iPr_def_11),X0),sK11)
| ( relation_composition(iPr_def_11,iPr_def_11) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,iPr_def_11))
| ~ function(relation_composition(iPr_def_11,iPr_def_11))
| ( relation_dom(X0) != sK11 ) ),
inference(light_normalisation,[status(thm)],[c_5691,c_5689]) ).
tcf(c_5733,plain,
set_intersection2(sK11,empty_set) = empty_set,
inference(light_normalisation,[status(thm)],[c_4099,c_5260]) ).
tcf(c_5734,plain,
relation_dom(relation_composition(iPr_def_14,iPr_def_11)) = set_intersection2(iPr_def_13,sK11),
inference(demodulation,[status(thm)],[c_4100,c_52]) ).
tcf(c_5735,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(iPr_def_14,iPr_def_11)),relation_dom(X0))
| ( relation_composition(iPr_def_14,iPr_def_11) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,iPr_def_11))
| ~ function(relation_composition(iPr_def_14,iPr_def_11))
| ( set_intersection2(iPr_def_13,sK11) != relation_dom(X0) ) ),
inference(superposition,[status(thm)],[c_5734,c_112]) ).
tcf(c_5736,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_14,iPr_def_11),X0),relation_dom(relation_composition(iPr_def_14,iPr_def_11)))
| ( relation_composition(iPr_def_14,iPr_def_11) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,iPr_def_11))
| ~ function(relation_composition(iPr_def_14,iPr_def_11))
| ( set_intersection2(iPr_def_13,sK11) != relation_dom(X0) ) ),
inference(superposition,[status(thm)],[c_5734,c_112]) ).
tcf(c_5737,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_14,iPr_def_11))) = relation_composition(iPr_def_14,iPr_def_11) )
| ~ relation(relation_composition(iPr_def_14,iPr_def_11))
| ~ function(relation_composition(iPr_def_14,iPr_def_11))
| ( apply(relation_composition(iPr_def_14,iPr_def_11),sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_14,iPr_def_11))) != sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_14,iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_5734,c_99]) ).
tcf(c_5738,plain,
( in(sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_14,iPr_def_11)),set_intersection2(iPr_def_13,sK11))
| ( identity_relation(relation_dom(relation_composition(iPr_def_14,iPr_def_11))) = relation_composition(iPr_def_14,iPr_def_11) )
| ~ relation(relation_composition(iPr_def_14,iPr_def_11))
| ~ function(relation_composition(iPr_def_14,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_5734,c_100]) ).
tcf(c_5739,plain,
( empty(relation_composition(iPr_def_14,iPr_def_11))
| ~ relation(relation_composition(iPr_def_14,iPr_def_11))
| ~ empty(set_intersection2(iPr_def_13,sK11)) ),
inference(superposition,[status(thm)],[c_5734,c_75]) ).
tcf(c_5740,plain,
( function(set_intersection2(iPr_def_13,sK11))
| ~ empty(relation_composition(iPr_def_14,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_5734,c_1895]) ).
tcf(c_5741,plain,
( relation(set_intersection2(iPr_def_13,sK11))
| ~ empty(relation_composition(iPr_def_14,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_5734,c_77]) ).
tcf(c_5742,plain,
( empty(set_intersection2(iPr_def_13,sK11))
| ~ empty(relation_composition(iPr_def_14,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_5734,c_76]) ).
tcf(c_5743,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_14,iPr_def_11),X0) = apply(iPr_def_11,apply(iPr_def_14,X0)) )
| ~ relation(iPr_def_14)
| ~ relation(iPr_def_11)
| ~ function(iPr_def_14)
| ~ function(iPr_def_11)
| ~ in(X0,set_intersection2(iPr_def_13,sK11)) ),
inference(superposition,[status(thm)],[c_5734,c_96]) ).
tcf(c_5753,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_14,iPr_def_11),X0) = apply(iPr_def_11,apply(iPr_def_14,X0)) )
| ~ in(X0,set_intersection2(iPr_def_13,sK11)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5743,c_1887,c_1884,c_1886,c_1883]) ).
tcf(c_5756,plain,
( in(sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_14,iPr_def_11)),set_intersection2(iPr_def_13,sK11))
| ( identity_relation(set_intersection2(iPr_def_13,sK11)) = relation_composition(iPr_def_14,iPr_def_11) )
| ~ relation(relation_composition(iPr_def_14,iPr_def_11))
| ~ function(relation_composition(iPr_def_14,iPr_def_11)) ),
inference(light_normalisation,[status(thm)],[c_5738,c_5734]) ).
tcf(c_5768,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_14,iPr_def_11),X0),set_intersection2(iPr_def_13,sK11))
| ( relation_composition(iPr_def_14,iPr_def_11) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,iPr_def_11))
| ~ function(relation_composition(iPr_def_14,iPr_def_11))
| ( set_intersection2(iPr_def_13,sK11) != relation_dom(X0) ) ),
inference(light_normalisation,[status(thm)],[c_5736,c_5734]) ).
tcf(c_5776,plain,
( ( identity_relation(set_intersection2(iPr_def_13,sK11)) = relation_composition(iPr_def_14,iPr_def_11) )
| ~ relation(relation_composition(iPr_def_14,iPr_def_11))
| ~ function(relation_composition(iPr_def_14,iPr_def_11))
| ( apply(relation_composition(iPr_def_14,iPr_def_11),sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_14,iPr_def_11))) != sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_14,iPr_def_11)) ) ),
inference(light_normalisation,[status(thm)],[c_5737,c_5734]) ).
tcf(c_5784,plain,
relation_dom(relation_composition(iPr_def_10,iPr_def_10)) = sK12,
inference(demodulation,[status(thm)],[c_4455,c_80]) ).
tcf(c_5785,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(iPr_def_10,iPr_def_10)),relation_dom(X0))
| ( relation_composition(iPr_def_10,iPr_def_10) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_10,iPr_def_10))
| ~ function(relation_composition(iPr_def_10,iPr_def_10))
| ( relation_dom(X0) != sK12 ) ),
inference(superposition,[status(thm)],[c_5784,c_112]) ).
tcf(c_5786,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_10,iPr_def_10),X0),relation_dom(relation_composition(iPr_def_10,iPr_def_10)))
| ( relation_composition(iPr_def_10,iPr_def_10) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_10,iPr_def_10))
| ~ function(relation_composition(iPr_def_10,iPr_def_10))
| ( relation_dom(X0) != sK12 ) ),
inference(superposition,[status(thm)],[c_5784,c_112]) ).
tcf(c_5787,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_10,iPr_def_10))) = relation_composition(iPr_def_10,iPr_def_10) )
| ~ relation(relation_composition(iPr_def_10,iPr_def_10))
| ~ function(relation_composition(iPr_def_10,iPr_def_10))
| ( apply(relation_composition(iPr_def_10,iPr_def_10),sK10(sK12,relation_composition(iPr_def_10,iPr_def_10))) != sK10(sK12,relation_composition(iPr_def_10,iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_5784,c_99]) ).
tcf(c_5788,plain,
( in(sK10(sK12,relation_composition(iPr_def_10,iPr_def_10)),sK12)
| ( identity_relation(relation_dom(relation_composition(iPr_def_10,iPr_def_10))) = relation_composition(iPr_def_10,iPr_def_10) )
| ~ relation(relation_composition(iPr_def_10,iPr_def_10))
| ~ function(relation_composition(iPr_def_10,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5784,c_100]) ).
tcf(c_5792,plain,
( empty(sK12)
| ~ empty(relation_composition(iPr_def_10,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5784,c_76]) ).
tcf(c_5793,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_10,iPr_def_10),X0) = apply(iPr_def_10,apply(iPr_def_10,X0)) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ~ in(X0,sK12) ),
inference(superposition,[status(thm)],[c_5784,c_96]) ).
tcf(c_5794,plain,
~ empty(relation_composition(iPr_def_10,iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_5792,c_3280]) ).
tcf(c_5795,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_10,iPr_def_10),X0) = apply(iPr_def_10,apply(iPr_def_10,X0)) )
| ~ in(X0,sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5793,c_1881,c_1880]) ).
tcf(c_5798,plain,
( in(sK10(sK12,relation_composition(iPr_def_10,iPr_def_10)),sK12)
| ( relation_composition(iPr_def_10,iPr_def_10) = iPr_def_10 )
| ~ relation(relation_composition(iPr_def_10,iPr_def_10))
| ~ function(relation_composition(iPr_def_10,iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_5788,c_1147,c_5784]) ).
tcf(c_5810,plain,
( ( relation_composition(iPr_def_10,iPr_def_10) = iPr_def_10 )
| ~ relation(relation_composition(iPr_def_10,iPr_def_10))
| ~ function(relation_composition(iPr_def_10,iPr_def_10))
| ( apply(relation_composition(iPr_def_10,iPr_def_10),sK10(sK12,relation_composition(iPr_def_10,iPr_def_10))) != sK10(sK12,relation_composition(iPr_def_10,iPr_def_10)) ) ),
inference(light_normalisation,[status(thm)],[c_5787,c_1147,c_5784]) ).
tcf(c_5815,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_10,iPr_def_10),X0),sK12)
| ( relation_composition(iPr_def_10,iPr_def_10) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_10,iPr_def_10))
| ~ function(relation_composition(iPr_def_10,iPr_def_10))
| ( relation_dom(X0) != sK12 ) ),
inference(light_normalisation,[status(thm)],[c_5786,c_5784]) ).
tcf(c_5828,plain,
relation_dom(relation_composition(iPr_def_14,iPr_def_10)) = set_intersection2(iPr_def_13,sK12),
inference(demodulation,[status(thm)],[c_4458,c_52]) ).
tcf(c_5829,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(iPr_def_14,iPr_def_10)),relation_dom(X0))
| ( relation_composition(iPr_def_14,iPr_def_10) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,iPr_def_10))
| ~ function(relation_composition(iPr_def_14,iPr_def_10))
| ( set_intersection2(iPr_def_13,sK12) != relation_dom(X0) ) ),
inference(superposition,[status(thm)],[c_5828,c_112]) ).
tcf(c_5830,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_14,iPr_def_10),X0),relation_dom(relation_composition(iPr_def_14,iPr_def_10)))
| ( relation_composition(iPr_def_14,iPr_def_10) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,iPr_def_10))
| ~ function(relation_composition(iPr_def_14,iPr_def_10))
| ( set_intersection2(iPr_def_13,sK12) != relation_dom(X0) ) ),
inference(superposition,[status(thm)],[c_5828,c_112]) ).
tcf(c_5831,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_14,iPr_def_10))) = relation_composition(iPr_def_14,iPr_def_10) )
| ~ relation(relation_composition(iPr_def_14,iPr_def_10))
| ~ function(relation_composition(iPr_def_14,iPr_def_10))
| ( apply(relation_composition(iPr_def_14,iPr_def_10),sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_14,iPr_def_10))) != sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_14,iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_5828,c_99]) ).
tcf(c_5832,plain,
( in(sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_14,iPr_def_10)),set_intersection2(iPr_def_13,sK12))
| ( identity_relation(relation_dom(relation_composition(iPr_def_14,iPr_def_10))) = relation_composition(iPr_def_14,iPr_def_10) )
| ~ relation(relation_composition(iPr_def_14,iPr_def_10))
| ~ function(relation_composition(iPr_def_14,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5828,c_100]) ).
tcf(c_5833,plain,
( empty(relation_composition(iPr_def_14,iPr_def_10))
| ~ relation(relation_composition(iPr_def_14,iPr_def_10))
| ~ empty(set_intersection2(iPr_def_13,sK12)) ),
inference(superposition,[status(thm)],[c_5828,c_75]) ).
tcf(c_5834,plain,
( function(set_intersection2(iPr_def_13,sK12))
| ~ empty(relation_composition(iPr_def_14,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5828,c_1895]) ).
tcf(c_5835,plain,
( relation(set_intersection2(iPr_def_13,sK12))
| ~ empty(relation_composition(iPr_def_14,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5828,c_77]) ).
tcf(c_5836,plain,
( empty(set_intersection2(iPr_def_13,sK12))
| ~ empty(relation_composition(iPr_def_14,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5828,c_76]) ).
tcf(c_5837,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_14,iPr_def_10),X0) = apply(iPr_def_10,apply(iPr_def_14,X0)) )
| ~ relation(iPr_def_14)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_14)
| ~ function(iPr_def_10)
| ~ in(X0,set_intersection2(iPr_def_13,sK12)) ),
inference(superposition,[status(thm)],[c_5828,c_96]) ).
tcf(c_5847,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_14,iPr_def_10),X0) = apply(iPr_def_10,apply(iPr_def_14,X0)) )
| ~ in(X0,set_intersection2(iPr_def_13,sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5837,c_1887,c_1881,c_1886,c_1880]) ).
tcf(c_5850,plain,
( in(sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_14,iPr_def_10)),set_intersection2(iPr_def_13,sK12))
| ( identity_relation(set_intersection2(iPr_def_13,sK12)) = relation_composition(iPr_def_14,iPr_def_10) )
| ~ relation(relation_composition(iPr_def_14,iPr_def_10))
| ~ function(relation_composition(iPr_def_14,iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_5832,c_5828]) ).
tcf(c_5862,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_14,iPr_def_10),X0),set_intersection2(iPr_def_13,sK12))
| ( relation_composition(iPr_def_14,iPr_def_10) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,iPr_def_10))
| ~ function(relation_composition(iPr_def_14,iPr_def_10))
| ( set_intersection2(iPr_def_13,sK12) != relation_dom(X0) ) ),
inference(light_normalisation,[status(thm)],[c_5830,c_5828]) ).
tcf(c_5870,plain,
( ( identity_relation(set_intersection2(iPr_def_13,sK12)) = relation_composition(iPr_def_14,iPr_def_10) )
| ~ relation(relation_composition(iPr_def_14,iPr_def_10))
| ~ function(relation_composition(iPr_def_14,iPr_def_10))
| ( apply(relation_composition(iPr_def_14,iPr_def_10),sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_14,iPr_def_10))) != sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_14,iPr_def_10)) ) ),
inference(light_normalisation,[status(thm)],[c_5831,c_5828]) ).
tcf(c_5948,plain,
set_intersection2(sK12,empty_set) = empty_set,
inference(light_normalisation,[status(thm)],[c_4457,c_5259]) ).
tcf(c_5986,plain,
( empty(relation_composition(empty_set,iPr_def_14))
| ~ relation(iPr_def_14)
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_79,c_4976]) ).
tcf(c_5987,plain,
empty(relation_composition(empty_set,iPr_def_14)),
inference(forward_subsumption_resolution,[status(thm)],[c_5986,c_1887,c_73]) ).
tcf(c_5988,plain,
! [X0: $i] :
( ( relation_composition(empty_set,iPr_def_14) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5987,c_110]) ).
tcf(c_5989,plain,
sK1(powerset(relation_composition(empty_set,iPr_def_14))) = empty_set,
inference(superposition,[status(thm)],[c_5987,c_3939]) ).
tcf(c_5990,plain,
! [X0: $i] : set_intersection2(relation_composition(empty_set,iPr_def_14),X0) = empty_set,
inference(superposition,[status(thm)],[c_5987,c_3180]) ).
tcf(c_5991,plain,
! [X0: $i] : set_intersection2(X0,relation_composition(empty_set,iPr_def_14)) = empty_set,
inference(superposition,[status(thm)],[c_5987,c_3084]) ).
tcf(c_5992,plain,
identity_relation(identity_relation(relation_composition(empty_set,iPr_def_14))) = empty_set,
inference(superposition,[status(thm)],[c_5987,c_2474]) ).
tcf(c_5993,plain,
identity_relation(relation_dom(relation_composition(empty_set,iPr_def_14))) = empty_set,
inference(superposition,[status(thm)],[c_5987,c_2473]) ).
tcf(c_5994,plain,
relation_dom(relation_dom(relation_composition(empty_set,iPr_def_14))) = empty_set,
inference(superposition,[status(thm)],[c_5987,c_2055]) ).
tcf(c_5995,plain,
identity_relation(relation_composition(empty_set,iPr_def_14)) = empty_set,
inference(superposition,[status(thm)],[c_5987,c_2184]) ).
tcf(c_5997,plain,
relation_composition(empty_set,iPr_def_14) = empty_set,
inference(superposition,[status(thm)],[c_5987,c_108]) ).
tcf(c_5998,plain,
relation(relation_composition(empty_set,iPr_def_14)),
inference(superposition,[status(thm)],[c_5987,c_51]) ).
tcf(c_5999,plain,
function(relation_composition(empty_set,iPr_def_14)),
inference(superposition,[status(thm)],[c_5987,c_50]) ).
tcf(c_6016,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,iPr_def_14),X0) = apply(iPr_def_14,apply(empty_set,X0)) )
| ~ relation(iPr_def_14)
| ~ relation(empty_set)
| ~ function(iPr_def_14)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_5997,c_96]) ).
tcf(c_6017,plain,
! [X0: $i] :
( ( apply(iPr_def_14,apply(empty_set,X0)) = apply(empty_set,X0) )
| ~ relation(iPr_def_14)
| ~ relation(empty_set)
| ~ function(iPr_def_14)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_6016,c_2054,c_5997]) ).
tcf(c_6018,plain,
set_intersection2(sK12,relation_dom(sK2)) = relation_dom(relation_composition(iPr_def_10,sK2)),
inference(demodulation,[status(thm)],[c_4756,c_52]) ).
tcf(c_6019,plain,
( function(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6018,c_3086]) ).
tcf(c_6020,plain,
( relation(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6018,c_3085]) ).
tcf(c_6021,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6018,c_2740]) ).
tcf(c_6022,plain,
( relation(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ relation(sK12)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6018,c_68]) ).
tcf(c_6026,plain,
( empty(set_intersection2(sK12,relation_dom(sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_10,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6018,c_2201]) ).
tcf(c_6027,plain,
! [X0: $i] :
( in(X0,relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ in(X0,sK12)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6018,c_56]) ).
tcf(c_6028,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ~ in(X0,relation_dom(relation_composition(iPr_def_10,sK2))) ),
inference(superposition,[status(thm)],[c_6018,c_58]) ).
tcf(c_6029,plain,
! [X0: $i] :
( in(X0,sK12)
| ~ in(X0,relation_dom(relation_composition(iPr_def_10,sK2))) ),
inference(superposition,[status(thm)],[c_6018,c_57]) ).
tcf(c_6043,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_10,sK2))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_6026,c_6018]) ).
tcf(c_6060,plain,
( empty(relation_composition(empty_set,iPr_def_10))
| ~ relation(iPr_def_10)
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_79,c_5316]) ).
tcf(c_6061,plain,
empty(relation_composition(empty_set,iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_6060,c_1881,c_73]) ).
tcf(c_6062,plain,
! [X0: $i] :
( ( relation_composition(empty_set,iPr_def_10) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6061,c_110]) ).
tcf(c_6063,plain,
sK1(powerset(relation_composition(empty_set,iPr_def_10))) = empty_set,
inference(superposition,[status(thm)],[c_6061,c_3939]) ).
tcf(c_6064,plain,
! [X0: $i] : set_intersection2(relation_composition(empty_set,iPr_def_10),X0) = empty_set,
inference(superposition,[status(thm)],[c_6061,c_3180]) ).
tcf(c_6065,plain,
! [X0: $i] : set_intersection2(X0,relation_composition(empty_set,iPr_def_10)) = empty_set,
inference(superposition,[status(thm)],[c_6061,c_3084]) ).
tcf(c_6066,plain,
identity_relation(identity_relation(relation_composition(empty_set,iPr_def_10))) = empty_set,
inference(superposition,[status(thm)],[c_6061,c_2474]) ).
tcf(c_6067,plain,
identity_relation(relation_dom(relation_composition(empty_set,iPr_def_10))) = empty_set,
inference(superposition,[status(thm)],[c_6061,c_2473]) ).
tcf(c_6068,plain,
relation_dom(relation_dom(relation_composition(empty_set,iPr_def_10))) = empty_set,
inference(superposition,[status(thm)],[c_6061,c_2055]) ).
tcf(c_6069,plain,
identity_relation(relation_composition(empty_set,iPr_def_10)) = empty_set,
inference(superposition,[status(thm)],[c_6061,c_2184]) ).
tcf(c_6071,plain,
relation_composition(empty_set,iPr_def_10) = empty_set,
inference(superposition,[status(thm)],[c_6061,c_108]) ).
tcf(c_6072,plain,
relation(relation_composition(empty_set,iPr_def_10)),
inference(superposition,[status(thm)],[c_6061,c_51]) ).
tcf(c_6073,plain,
function(relation_composition(empty_set,iPr_def_10)),
inference(superposition,[status(thm)],[c_6061,c_50]) ).
tcf(c_6122,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,iPr_def_10),X0) = apply(iPr_def_10,apply(empty_set,X0)) )
| ~ relation(iPr_def_10)
| ~ relation(empty_set)
| ~ function(iPr_def_10)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_6071,c_96]) ).
tcf(c_6123,plain,
! [X0: $i] :
( ( apply(iPr_def_10,apply(empty_set,X0)) = apply(empty_set,X0) )
| ~ relation(iPr_def_10)
| ~ relation(empty_set)
| ~ function(iPr_def_10)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_6122,c_2054,c_6071]) ).
tcf(c_6133,plain,
set_intersection2(sK11,relation_dom(sK2)) = relation_dom(relation_composition(iPr_def_11,sK2)),
inference(demodulation,[status(thm)],[c_4757,c_52]) ).
tcf(c_6134,plain,
( function(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6133,c_3086]) ).
tcf(c_6135,plain,
( relation(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6133,c_3085]) ).
tcf(c_6136,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6133,c_2740]) ).
tcf(c_6137,plain,
( relation(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ relation(sK11)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6133,c_68]) ).
tcf(c_6141,plain,
( empty(set_intersection2(sK11,relation_dom(sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_11,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6133,c_2201]) ).
tcf(c_6142,plain,
! [X0: $i] :
( in(X0,relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ in(X0,sK11)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6133,c_56]) ).
tcf(c_6143,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ~ in(X0,relation_dom(relation_composition(iPr_def_11,sK2))) ),
inference(superposition,[status(thm)],[c_6133,c_58]) ).
tcf(c_6144,plain,
! [X0: $i] :
( in(X0,sK11)
| ~ in(X0,relation_dom(relation_composition(iPr_def_11,sK2))) ),
inference(superposition,[status(thm)],[c_6133,c_57]) ).
tcf(c_6158,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_11,sK2))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_6141,c_6133]) ).
tcf(c_6173,plain,
( empty(relation_composition(empty_set,iPr_def_11))
| ~ relation(iPr_def_11)
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_79,c_5358]) ).
tcf(c_6174,plain,
empty(relation_composition(empty_set,iPr_def_11)),
inference(forward_subsumption_resolution,[status(thm)],[c_6173,c_1884,c_73]) ).
tcf(c_6175,plain,
! [X0: $i] :
( ( relation_composition(empty_set,iPr_def_11) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6174,c_110]) ).
tcf(c_6176,plain,
sK1(powerset(relation_composition(empty_set,iPr_def_11))) = empty_set,
inference(superposition,[status(thm)],[c_6174,c_3939]) ).
tcf(c_6177,plain,
! [X0: $i] : set_intersection2(relation_composition(empty_set,iPr_def_11),X0) = empty_set,
inference(superposition,[status(thm)],[c_6174,c_3180]) ).
tcf(c_6178,plain,
! [X0: $i] : set_intersection2(X0,relation_composition(empty_set,iPr_def_11)) = empty_set,
inference(superposition,[status(thm)],[c_6174,c_3084]) ).
tcf(c_6179,plain,
identity_relation(identity_relation(relation_composition(empty_set,iPr_def_11))) = empty_set,
inference(superposition,[status(thm)],[c_6174,c_2474]) ).
tcf(c_6180,plain,
identity_relation(relation_dom(relation_composition(empty_set,iPr_def_11))) = empty_set,
inference(superposition,[status(thm)],[c_6174,c_2473]) ).
tcf(c_6181,plain,
relation_dom(relation_dom(relation_composition(empty_set,iPr_def_11))) = empty_set,
inference(superposition,[status(thm)],[c_6174,c_2055]) ).
tcf(c_6182,plain,
identity_relation(relation_composition(empty_set,iPr_def_11)) = empty_set,
inference(superposition,[status(thm)],[c_6174,c_2184]) ).
tcf(c_6184,plain,
relation_composition(empty_set,iPr_def_11) = empty_set,
inference(superposition,[status(thm)],[c_6174,c_108]) ).
tcf(c_6185,plain,
relation(relation_composition(empty_set,iPr_def_11)),
inference(superposition,[status(thm)],[c_6174,c_51]) ).
tcf(c_6186,plain,
function(relation_composition(empty_set,iPr_def_11)),
inference(superposition,[status(thm)],[c_6174,c_50]) ).
tcf(c_6203,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,iPr_def_11),X0) = apply(iPr_def_11,apply(empty_set,X0)) )
| ~ relation(iPr_def_11)
| ~ relation(empty_set)
| ~ function(iPr_def_11)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_6184,c_96]) ).
tcf(c_6204,plain,
! [X0: $i] :
( ( apply(iPr_def_11,apply(empty_set,X0)) = apply(empty_set,X0) )
| ~ relation(iPr_def_11)
| ~ relation(empty_set)
| ~ function(iPr_def_11)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_6203,c_2054,c_6184]) ).
tcf(c_6211,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(iPr_def_10,iPr_def_12)),relation_dom(X0))
| ( relation_composition(iPr_def_10,iPr_def_12) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_10,iPr_def_12))
| ~ function(relation_composition(iPr_def_10,iPr_def_12))
| ( set_intersection2(iPr_def_13,sK12) != relation_dom(X0) ) ),
inference(superposition,[status(thm)],[c_5414,c_112]) ).
tcf(c_6212,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_10,iPr_def_12),X0),relation_dom(relation_composition(iPr_def_10,iPr_def_12)))
| ( relation_composition(iPr_def_10,iPr_def_12) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_10,iPr_def_12))
| ~ function(relation_composition(iPr_def_10,iPr_def_12))
| ( set_intersection2(iPr_def_13,sK12) != relation_dom(X0) ) ),
inference(superposition,[status(thm)],[c_5414,c_112]) ).
tcf(c_6213,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_10,iPr_def_12))) = relation_composition(iPr_def_10,iPr_def_12) )
| ~ relation(relation_composition(iPr_def_10,iPr_def_12))
| ~ function(relation_composition(iPr_def_10,iPr_def_12))
| ( apply(relation_composition(iPr_def_10,iPr_def_12),sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_10,iPr_def_12))) != sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_10,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_5414,c_99]) ).
tcf(c_6214,plain,
( in(sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_10,iPr_def_12)),set_intersection2(iPr_def_13,sK12))
| ( identity_relation(relation_dom(relation_composition(iPr_def_10,iPr_def_12))) = relation_composition(iPr_def_10,iPr_def_12) )
| ~ relation(relation_composition(iPr_def_10,iPr_def_12))
| ~ function(relation_composition(iPr_def_10,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_5414,c_100]) ).
tcf(c_6215,plain,
( empty(relation_composition(iPr_def_10,iPr_def_12))
| ~ relation(relation_composition(iPr_def_10,iPr_def_12))
| ~ empty(set_intersection2(iPr_def_13,sK12)) ),
inference(superposition,[status(thm)],[c_5414,c_75]) ).
tcf(c_6216,plain,
( function(set_intersection2(iPr_def_13,sK12))
| ~ empty(relation_composition(iPr_def_10,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_5414,c_1895]) ).
tcf(c_6217,plain,
( relation(set_intersection2(iPr_def_13,sK12))
| ~ empty(relation_composition(iPr_def_10,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_5414,c_77]) ).
tcf(c_6218,plain,
( empty(set_intersection2(iPr_def_13,sK12))
| ~ empty(relation_composition(iPr_def_10,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_5414,c_76]) ).
tcf(c_6219,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_10,iPr_def_12),X0) = apply(iPr_def_12,apply(iPr_def_10,X0)) )
| ~ relation(iPr_def_12)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_12)
| ~ function(iPr_def_10)
| ~ in(X0,set_intersection2(iPr_def_13,sK12)) ),
inference(superposition,[status(thm)],[c_5414,c_96]) ).
tcf(c_6229,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_10,iPr_def_12),X0) = apply(iPr_def_12,apply(iPr_def_10,X0)) )
| ~ in(X0,set_intersection2(iPr_def_13,sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6219,c_2156,c_1881,c_3011,c_1880]) ).
tcf(c_6232,plain,
( in(sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_10,iPr_def_12)),set_intersection2(iPr_def_13,sK12))
| ( identity_relation(set_intersection2(iPr_def_13,sK12)) = relation_composition(iPr_def_10,iPr_def_12) )
| ~ relation(relation_composition(iPr_def_10,iPr_def_12))
| ~ function(relation_composition(iPr_def_10,iPr_def_12)) ),
inference(light_normalisation,[status(thm)],[c_6214,c_5414]) ).
tcf(c_6244,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_10,iPr_def_12),X0),set_intersection2(iPr_def_13,sK12))
| ( relation_composition(iPr_def_10,iPr_def_12) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_10,iPr_def_12))
| ~ function(relation_composition(iPr_def_10,iPr_def_12))
| ( set_intersection2(iPr_def_13,sK12) != relation_dom(X0) ) ),
inference(light_normalisation,[status(thm)],[c_6212,c_5414]) ).
tcf(c_6252,plain,
( ( identity_relation(set_intersection2(iPr_def_13,sK12)) = relation_composition(iPr_def_10,iPr_def_12) )
| ~ relation(relation_composition(iPr_def_10,iPr_def_12))
| ~ function(relation_composition(iPr_def_10,iPr_def_12))
| ( apply(relation_composition(iPr_def_10,iPr_def_12),sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_10,iPr_def_12))) != sK10(set_intersection2(iPr_def_13,sK12),relation_composition(iPr_def_10,iPr_def_12)) ) ),
inference(light_normalisation,[status(thm)],[c_6213,c_5414]) ).
tcf(c_6263,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(iPr_def_11,iPr_def_12)),relation_dom(X0))
| ( relation_composition(iPr_def_11,iPr_def_12) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,iPr_def_12))
| ~ function(relation_composition(iPr_def_11,iPr_def_12))
| ( set_intersection2(iPr_def_13,sK11) != relation_dom(X0) ) ),
inference(superposition,[status(thm)],[c_5415,c_112]) ).
tcf(c_6264,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_11,iPr_def_12),X0),relation_dom(relation_composition(iPr_def_11,iPr_def_12)))
| ( relation_composition(iPr_def_11,iPr_def_12) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,iPr_def_12))
| ~ function(relation_composition(iPr_def_11,iPr_def_12))
| ( set_intersection2(iPr_def_13,sK11) != relation_dom(X0) ) ),
inference(superposition,[status(thm)],[c_5415,c_112]) ).
tcf(c_6265,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_11,iPr_def_12))) = relation_composition(iPr_def_11,iPr_def_12) )
| ~ relation(relation_composition(iPr_def_11,iPr_def_12))
| ~ function(relation_composition(iPr_def_11,iPr_def_12))
| ( apply(relation_composition(iPr_def_11,iPr_def_12),sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_11,iPr_def_12))) != sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_11,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_5415,c_99]) ).
tcf(c_6266,plain,
( in(sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_11,iPr_def_12)),set_intersection2(iPr_def_13,sK11))
| ( identity_relation(relation_dom(relation_composition(iPr_def_11,iPr_def_12))) = relation_composition(iPr_def_11,iPr_def_12) )
| ~ relation(relation_composition(iPr_def_11,iPr_def_12))
| ~ function(relation_composition(iPr_def_11,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_5415,c_100]) ).
tcf(c_6267,plain,
( empty(relation_composition(iPr_def_11,iPr_def_12))
| ~ relation(relation_composition(iPr_def_11,iPr_def_12))
| ~ empty(set_intersection2(iPr_def_13,sK11)) ),
inference(superposition,[status(thm)],[c_5415,c_75]) ).
tcf(c_6268,plain,
( function(set_intersection2(iPr_def_13,sK11))
| ~ empty(relation_composition(iPr_def_11,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_5415,c_1895]) ).
tcf(c_6269,plain,
( relation(set_intersection2(iPr_def_13,sK11))
| ~ empty(relation_composition(iPr_def_11,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_5415,c_77]) ).
tcf(c_6270,plain,
( empty(set_intersection2(iPr_def_13,sK11))
| ~ empty(relation_composition(iPr_def_11,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_5415,c_76]) ).
tcf(c_6271,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_11,iPr_def_12),X0) = apply(iPr_def_12,apply(iPr_def_11,X0)) )
| ~ relation(iPr_def_12)
| ~ relation(iPr_def_11)
| ~ function(iPr_def_12)
| ~ function(iPr_def_11)
| ~ in(X0,set_intersection2(iPr_def_13,sK11)) ),
inference(superposition,[status(thm)],[c_5415,c_96]) ).
tcf(c_6281,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_11,iPr_def_12),X0) = apply(iPr_def_12,apply(iPr_def_11,X0)) )
| ~ in(X0,set_intersection2(iPr_def_13,sK11)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6271,c_2156,c_1884,c_3011,c_1883]) ).
tcf(c_6284,plain,
( in(sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_11,iPr_def_12)),set_intersection2(iPr_def_13,sK11))
| ( identity_relation(set_intersection2(iPr_def_13,sK11)) = relation_composition(iPr_def_11,iPr_def_12) )
| ~ relation(relation_composition(iPr_def_11,iPr_def_12))
| ~ function(relation_composition(iPr_def_11,iPr_def_12)) ),
inference(light_normalisation,[status(thm)],[c_6266,c_5415]) ).
tcf(c_6296,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_11,iPr_def_12),X0),set_intersection2(iPr_def_13,sK11))
| ( relation_composition(iPr_def_11,iPr_def_12) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_11,iPr_def_12))
| ~ function(relation_composition(iPr_def_11,iPr_def_12))
| ( set_intersection2(iPr_def_13,sK11) != relation_dom(X0) ) ),
inference(light_normalisation,[status(thm)],[c_6264,c_5415]) ).
tcf(c_6304,plain,
( ( identity_relation(set_intersection2(iPr_def_13,sK11)) = relation_composition(iPr_def_11,iPr_def_12) )
| ~ relation(relation_composition(iPr_def_11,iPr_def_12))
| ~ function(relation_composition(iPr_def_11,iPr_def_12))
| ( apply(relation_composition(iPr_def_11,iPr_def_12),sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_11,iPr_def_12))) != sK10(set_intersection2(iPr_def_13,sK11),relation_composition(iPr_def_11,iPr_def_12)) ) ),
inference(light_normalisation,[status(thm)],[c_6265,c_5415]) ).
tcf(c_6323,plain,
relation_dom(relation_composition(empty_set,iPr_def_12)) = empty_set,
inference(demodulation,[status(thm)],[c_5416,c_97]) ).
tcf(c_6325,plain,
! [X0: $i] :
( in(sK13(relation_composition(empty_set,iPr_def_12),X0),relation_dom(relation_composition(empty_set,iPr_def_12)))
| ( relation_composition(empty_set,iPr_def_12) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,iPr_def_12))
| ~ function(relation_composition(empty_set,iPr_def_12))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_6323,c_112]) ).
tcf(c_6326,plain,
( ( identity_relation(relation_dom(relation_composition(empty_set,iPr_def_12))) = relation_composition(empty_set,iPr_def_12) )
| ~ relation(relation_composition(empty_set,iPr_def_12))
| ~ function(relation_composition(empty_set,iPr_def_12))
| ( apply(relation_composition(empty_set,iPr_def_12),sK10(empty_set,relation_composition(empty_set,iPr_def_12))) != sK10(empty_set,relation_composition(empty_set,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_6323,c_99]) ).
tcf(c_6327,plain,
( in(sK10(empty_set,relation_composition(empty_set,iPr_def_12)),empty_set)
| ( identity_relation(relation_dom(relation_composition(empty_set,iPr_def_12))) = relation_composition(empty_set,iPr_def_12) )
| ~ relation(relation_composition(empty_set,iPr_def_12))
| ~ function(relation_composition(empty_set,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_6323,c_100]) ).
tcf(c_6328,plain,
( empty(relation_composition(empty_set,iPr_def_12))
| ~ empty(empty_set)
| ~ relation(relation_composition(empty_set,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_6323,c_75]) ).
tcf(c_6333,plain,
( empty(relation_composition(empty_set,iPr_def_12))
| ~ relation(relation_composition(empty_set,iPr_def_12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6328,c_73]) ).
tcf(c_6336,plain,
( in(sK10(empty_set,relation_composition(empty_set,iPr_def_12)),empty_set)
| ( relation_composition(empty_set,iPr_def_12) = empty_set )
| ~ relation(relation_composition(empty_set,iPr_def_12))
| ~ function(relation_composition(empty_set,iPr_def_12)) ),
inference(light_normalisation,[status(thm)],[c_6327,c_2472,c_6323]) ).
tcf(c_6337,plain,
( ( relation_composition(empty_set,iPr_def_12) = empty_set )
| ~ relation(relation_composition(empty_set,iPr_def_12))
| ~ function(relation_composition(empty_set,iPr_def_12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6336,c_5671]) ).
tcf(c_6349,plain,
! [X0: $i] :
( in(sK13(relation_composition(empty_set,iPr_def_12),X0),empty_set)
| ( relation_composition(empty_set,iPr_def_12) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,iPr_def_12))
| ~ function(relation_composition(empty_set,iPr_def_12))
| ( relation_dom(X0) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_6325,c_6323]) ).
tcf(c_6350,plain,
! [X0: $i] :
( ( relation_composition(empty_set,iPr_def_12) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,iPr_def_12))
| ~ function(relation_composition(empty_set,iPr_def_12))
| ( relation_dom(X0) != empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6349,c_5671]) ).
tcf(c_6371,plain,
relation_dom(relation_composition(iPr_def_14,iPr_def_12)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_5417,c_80]) ).
tcf(c_6372,plain,
! [X0: $i] :
( in(sK13(X0,relation_composition(iPr_def_14,iPr_def_12)),relation_dom(X0))
| ( relation_composition(iPr_def_14,iPr_def_12) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,iPr_def_12))
| ~ function(relation_composition(iPr_def_14,iPr_def_12))
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6371,c_112]) ).
tcf(c_6373,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_14,iPr_def_12),X0),relation_dom(relation_composition(iPr_def_14,iPr_def_12)))
| ( relation_composition(iPr_def_14,iPr_def_12) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,iPr_def_12))
| ~ function(relation_composition(iPr_def_14,iPr_def_12))
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6371,c_112]) ).
tcf(c_6374,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_14,iPr_def_12))) = relation_composition(iPr_def_14,iPr_def_12) )
| ~ relation(relation_composition(iPr_def_14,iPr_def_12))
| ~ function(relation_composition(iPr_def_14,iPr_def_12))
| ( apply(relation_composition(iPr_def_14,iPr_def_12),sK10(iPr_def_13,relation_composition(iPr_def_14,iPr_def_12))) != sK10(iPr_def_13,relation_composition(iPr_def_14,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_6371,c_99]) ).
tcf(c_6375,plain,
( in(sK10(iPr_def_13,relation_composition(iPr_def_14,iPr_def_12)),iPr_def_13)
| ( identity_relation(relation_dom(relation_composition(iPr_def_14,iPr_def_12))) = relation_composition(iPr_def_14,iPr_def_12) )
| ~ relation(relation_composition(iPr_def_14,iPr_def_12))
| ~ function(relation_composition(iPr_def_14,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_6371,c_100]) ).
tcf(c_6379,plain,
( empty(iPr_def_13)
| ~ empty(relation_composition(iPr_def_14,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_6371,c_76]) ).
tcf(c_6380,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_14,iPr_def_12),X0) = apply(iPr_def_12,apply(iPr_def_14,X0)) )
| ~ relation(iPr_def_14)
| ~ relation(iPr_def_12)
| ~ function(iPr_def_14)
| ~ function(iPr_def_12)
| ~ in(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_6371,c_96]) ).
tcf(c_6381,plain,
~ empty(relation_composition(iPr_def_14,iPr_def_12)),
inference(forward_subsumption_resolution,[status(thm)],[c_6379,c_4400]) ).
tcf(c_6382,plain,
( in(sK10(iPr_def_13,relation_composition(iPr_def_14,iPr_def_12)),iPr_def_13)
| ( relation_composition(iPr_def_14,iPr_def_12) = iPr_def_14 )
| ~ relation(relation_composition(iPr_def_14,iPr_def_12))
| ~ function(relation_composition(iPr_def_14,iPr_def_12)) ),
inference(light_normalisation,[status(thm)],[c_6375,c_1151,c_6371]) ).
tcf(c_6387,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_14,iPr_def_12),X0) = apply(iPr_def_12,apply(iPr_def_14,X0)) )
| ~ in(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6380,c_1887,c_2156,c_1886,c_3011]) ).
tcf(c_6397,plain,
( ( relation_composition(iPr_def_14,iPr_def_12) = iPr_def_14 )
| ~ relation(relation_composition(iPr_def_14,iPr_def_12))
| ~ function(relation_composition(iPr_def_14,iPr_def_12))
| ( apply(relation_composition(iPr_def_14,iPr_def_12),sK10(iPr_def_13,relation_composition(iPr_def_14,iPr_def_12))) != sK10(iPr_def_13,relation_composition(iPr_def_14,iPr_def_12)) ) ),
inference(light_normalisation,[status(thm)],[c_6374,c_1151,c_6371]) ).
tcf(c_6402,plain,
! [X0: $i] :
( in(sK13(relation_composition(iPr_def_14,iPr_def_12),X0),iPr_def_13)
| ( relation_composition(iPr_def_14,iPr_def_12) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(iPr_def_14,iPr_def_12))
| ~ function(relation_composition(iPr_def_14,iPr_def_12))
| ( relation_dom(X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_6373,c_6371]) ).
tcf(c_6443,plain,
relation_dom(relation_composition(empty_set,sK2)) = empty_set,
inference(demodulation,[status(thm)],[c_4758,c_97]) ).
tcf(c_6445,plain,
! [X0: $i] :
( in(sK13(relation_composition(empty_set,sK2),X0),relation_dom(relation_composition(empty_set,sK2)))
| ( relation_composition(empty_set,sK2) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,sK2))
| ~ function(relation_composition(empty_set,sK2))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_6443,c_112]) ).
tcf(c_6446,plain,
( ( identity_relation(relation_dom(relation_composition(empty_set,sK2))) = relation_composition(empty_set,sK2) )
| ~ relation(relation_composition(empty_set,sK2))
| ~ function(relation_composition(empty_set,sK2))
| ( apply(relation_composition(empty_set,sK2),sK10(empty_set,relation_composition(empty_set,sK2))) != sK10(empty_set,relation_composition(empty_set,sK2)) ) ),
inference(superposition,[status(thm)],[c_6443,c_99]) ).
tcf(c_6447,plain,
( in(sK10(empty_set,relation_composition(empty_set,sK2)),empty_set)
| ( identity_relation(relation_dom(relation_composition(empty_set,sK2))) = relation_composition(empty_set,sK2) )
| ~ relation(relation_composition(empty_set,sK2))
| ~ function(relation_composition(empty_set,sK2)) ),
inference(superposition,[status(thm)],[c_6443,c_100]) ).
tcf(c_6448,plain,
( empty(relation_composition(empty_set,sK2))
| ~ empty(empty_set)
| ~ relation(relation_composition(empty_set,sK2)) ),
inference(superposition,[status(thm)],[c_6443,c_75]) ).
tcf(c_6453,plain,
( empty(relation_composition(empty_set,sK2))
| ~ relation(relation_composition(empty_set,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6448,c_73]) ).
tcf(c_6456,plain,
( in(sK10(empty_set,relation_composition(empty_set,sK2)),empty_set)
| ( relation_composition(empty_set,sK2) = empty_set )
| ~ relation(relation_composition(empty_set,sK2))
| ~ function(relation_composition(empty_set,sK2)) ),
inference(light_normalisation,[status(thm)],[c_6447,c_2472,c_6443]) ).
tcf(c_6457,plain,
( ( relation_composition(empty_set,sK2) = empty_set )
| ~ relation(relation_composition(empty_set,sK2))
| ~ function(relation_composition(empty_set,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6456,c_5671]) ).
tcf(c_6469,plain,
! [X0: $i] :
( in(sK13(relation_composition(empty_set,sK2),X0),empty_set)
| ( relation_composition(empty_set,sK2) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,sK2))
| ~ function(relation_composition(empty_set,sK2))
| ( relation_dom(X0) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_6445,c_6443]) ).
tcf(c_6470,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK2) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(relation_composition(empty_set,sK2))
| ~ function(relation_composition(empty_set,sK2))
| ( relation_dom(X0) != empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6469,c_5671]) ).
tcf(c_6495,plain,
! [X0: $i] :
( empty(set_intersection2(empty_set,X0))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_5628,c_5574]) ).
tcf(c_6496,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(X0)),X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_110]) ).
tcf(c_6497,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(sK1(powerset(X0)),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3939]) ).
tcf(c_6498,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(sK1(powerset(X0)),X1),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3180]) ).
tcf(c_6499,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(sK1(powerset(X0)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3084]) ).
tcf(c_6500,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(sK1(powerset(X0)),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_2474]) ).
tcf(c_6501,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(sK1(powerset(X0)),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_2473]) ).
tcf(c_6502,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(sK1(powerset(X0)),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_2055]) ).
tcf(c_6503,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(sK1(powerset(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_2184]) ).
tcf(c_6504,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(sK1(powerset(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_2013]) ).
tcf(c_6506,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(sK1(powerset(X0)),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_51]) ).
tcf(c_6507,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(sK1(powerset(X0)),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_50]) ).
tcf(c_6577,plain,
! [X0: $i] :
( relation(set_intersection2(X0,empty_set))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_5628,c_5587]) ).
tcf(c_6578,plain,
( relation(empty_set)
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_6577,c_97]) ).
tcf(c_6587,plain,
! [X0: $i] :
( function(set_intersection2(X0,empty_set))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_5628,c_5588]) ).
tcf(c_6588,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(identity_relation(X2),set_intersection2(X0,sK1(powerset(X1))))) = set_intersection2(relation_dom(set_intersection2(X0,sK1(powerset(X1)))),X2) )
| ~ empty(X1)
| ~ relation(set_intersection2(X0,sK1(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_5588,c_103]) ).
tcf(c_6589,plain,
( function(empty_set)
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_6587,c_97]) ).
tcf(c_6671,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),relation_dom(relation_composition(iPr_def_10,sK2)))) = set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(relation_composition(iPr_def_10,sK2))) ),
inference(superposition,[status(thm)],[c_6019,c_103]) ).
tcf(c_6684,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_110]) ).
tcf(c_6685,plain,
( ( sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3939]) ).
tcf(c_6686,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3180]) ).
tcf(c_6687,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3084]) ).
tcf(c_6688,plain,
( ( identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_2474]) ).
tcf(c_6689,plain,
( ( identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_2473]) ).
tcf(c_6690,plain,
( ( relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_2055]) ).
tcf(c_6691,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_2184]) ).
tcf(c_6692,plain,
( ( relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_2013]) ).
tcf(c_6693,plain,
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_108]) ).
tcf(c_6696,plain,
( empty(relation_composition(iPr_def_10,sK2))
| ~ empty(relation_dom(sK2))
| ~ relation(relation_composition(iPr_def_10,sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_75]) ).
tcf(c_6812,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),relation_dom(relation_composition(iPr_def_11,sK2)))) = set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(relation_composition(iPr_def_11,sK2))) ),
inference(superposition,[status(thm)],[c_6134,c_103]) ).
tcf(c_6817,plain,
set_intersection2(iPr_def_13,relation_dom(sK2)) = relation_dom(relation_composition(iPr_def_14,sK2)),
inference(demodulation,[status(thm)],[c_4759,c_52]) ).
tcf(c_6818,plain,
( function(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6817,c_3086]) ).
tcf(c_6819,plain,
( relation(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6817,c_3085]) ).
tcf(c_6820,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6817,c_2740]) ).
tcf(c_6821,plain,
( relation(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ relation(iPr_def_13)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6817,c_68]) ).
tcf(c_6825,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6817,c_2201]) ).
tcf(c_6826,plain,
! [X0: $i] :
( in(X0,relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ in(X0,iPr_def_13)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6817,c_56]) ).
tcf(c_6827,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ~ in(X0,relation_dom(relation_composition(iPr_def_14,sK2))) ),
inference(superposition,[status(thm)],[c_6817,c_58]) ).
tcf(c_6828,plain,
! [X0: $i] :
( in(X0,iPr_def_13)
| ~ in(X0,relation_dom(relation_composition(iPr_def_14,sK2))) ),
inference(superposition,[status(thm)],[c_6817,c_57]) ).
tcf(c_6842,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_6825,c_6817]) ).
tcf(c_6889,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_110]) ).
tcf(c_6890,plain,
( ( sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3939]) ).
tcf(c_6891,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3180]) ).
tcf(c_6892,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3084]) ).
tcf(c_6893,plain,
( ( identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_2474]) ).
tcf(c_6894,plain,
( ( identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_2473]) ).
tcf(c_6895,plain,
( ( relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_2055]) ).
tcf(c_6896,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_2184]) ).
tcf(c_6897,plain,
( ( relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_2013]) ).
tcf(c_6898,plain,
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_108]) ).
tcf(c_6901,plain,
( empty(relation_composition(iPr_def_11,sK2))
| ~ empty(relation_dom(sK2))
| ~ relation(relation_composition(iPr_def_11,sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_75]) ).
tcf(c_6980,plain,
( empty(relation_composition(empty_set,iPr_def_12))
| ~ relation(iPr_def_12)
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_79,c_6333]) ).
tcf(c_6981,plain,
empty(relation_composition(empty_set,iPr_def_12)),
inference(forward_subsumption_resolution,[status(thm)],[c_6980,c_2156,c_73]) ).
tcf(c_6982,plain,
! [X0: $i] :
( ( relation_composition(empty_set,iPr_def_12) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6981,c_110]) ).
tcf(c_6983,plain,
sK1(powerset(relation_composition(empty_set,iPr_def_12))) = empty_set,
inference(superposition,[status(thm)],[c_6981,c_3939]) ).
tcf(c_6984,plain,
! [X0: $i] : set_intersection2(relation_composition(empty_set,iPr_def_12),X0) = empty_set,
inference(superposition,[status(thm)],[c_6981,c_3180]) ).
tcf(c_6985,plain,
! [X0: $i] : set_intersection2(X0,relation_composition(empty_set,iPr_def_12)) = empty_set,
inference(superposition,[status(thm)],[c_6981,c_3084]) ).
tcf(c_6986,plain,
identity_relation(identity_relation(relation_composition(empty_set,iPr_def_12))) = empty_set,
inference(superposition,[status(thm)],[c_6981,c_2474]) ).
tcf(c_6987,plain,
identity_relation(relation_dom(relation_composition(empty_set,iPr_def_12))) = empty_set,
inference(superposition,[status(thm)],[c_6981,c_2473]) ).
tcf(c_6988,plain,
relation_dom(relation_dom(relation_composition(empty_set,iPr_def_12))) = empty_set,
inference(superposition,[status(thm)],[c_6981,c_2055]) ).
tcf(c_6989,plain,
identity_relation(relation_composition(empty_set,iPr_def_12)) = empty_set,
inference(superposition,[status(thm)],[c_6981,c_2184]) ).
tcf(c_6991,plain,
relation_composition(empty_set,iPr_def_12) = empty_set,
inference(superposition,[status(thm)],[c_6981,c_108]) ).
tcf(c_6992,plain,
relation(relation_composition(empty_set,iPr_def_12)),
inference(superposition,[status(thm)],[c_6981,c_51]) ).
tcf(c_6993,plain,
function(relation_composition(empty_set,iPr_def_12)),
inference(superposition,[status(thm)],[c_6981,c_50]) ).
tcf(c_7036,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,iPr_def_12),X0) = apply(iPr_def_12,apply(empty_set,X0)) )
| ~ relation(iPr_def_12)
| ~ relation(empty_set)
| ~ function(iPr_def_12)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_6991,c_96]) ).
tcf(c_7037,plain,
! [X0: $i] :
( ( apply(iPr_def_12,apply(empty_set,X0)) = apply(empty_set,X0) )
| ~ relation(iPr_def_12)
| ~ relation(empty_set)
| ~ function(iPr_def_12)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_7036,c_2054,c_6991]) ).
tcf(c_7042,plain,
relation_dom(relation_composition(iPr_def_10,empty_set)) = set_intersection2(empty_set,sK12),
inference(superposition,[status(thm)],[c_2472,c_5115]) ).
tcf(c_7044,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,relation_composition(iPr_def_10,identity_relation(X0))),relation_dom(X1))
| ( relation_composition(iPr_def_10,identity_relation(X0)) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(iPr_def_10,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_10,identity_relation(X0)))
| ( set_intersection2(X0,sK12) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_5115,c_112]) ).
tcf(c_7045,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(iPr_def_10,identity_relation(X0)),X1),relation_dom(relation_composition(iPr_def_10,identity_relation(X0))))
| ( relation_composition(iPr_def_10,identity_relation(X0)) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(iPr_def_10,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_10,identity_relation(X0)))
| ( set_intersection2(X0,sK12) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_5115,c_112]) ).
tcf(c_7046,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_composition(iPr_def_10,identity_relation(X0)))) = relation_composition(iPr_def_10,identity_relation(X0)) )
| ~ relation(relation_composition(iPr_def_10,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_10,identity_relation(X0)))
| ( apply(relation_composition(iPr_def_10,identity_relation(X0)),sK10(set_intersection2(X0,sK12),relation_composition(iPr_def_10,identity_relation(X0)))) != sK10(set_intersection2(X0,sK12),relation_composition(iPr_def_10,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_5115,c_99]) ).
tcf(c_7047,plain,
! [X0: $i] :
( in(sK10(set_intersection2(X0,sK12),relation_composition(iPr_def_10,identity_relation(X0))),set_intersection2(X0,sK12))
| ( identity_relation(relation_dom(relation_composition(iPr_def_10,identity_relation(X0)))) = relation_composition(iPr_def_10,identity_relation(X0)) )
| ~ relation(relation_composition(iPr_def_10,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_10,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5115,c_100]) ).
tcf(c_7048,plain,
! [X0: $i] :
( empty(relation_composition(iPr_def_10,identity_relation(X0)))
| ~ empty(set_intersection2(X0,sK12))
| ~ relation(relation_composition(iPr_def_10,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5115,c_75]) ).
tcf(c_7049,plain,
! [X0: $i] :
( function(set_intersection2(X0,sK12))
| ~ empty(relation_composition(iPr_def_10,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5115,c_1895]) ).
tcf(c_7050,plain,
! [X0: $i] :
( relation(set_intersection2(X0,sK12))
| ~ empty(relation_composition(iPr_def_10,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5115,c_77]) ).
tcf(c_7051,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK12))
| ~ empty(relation_composition(iPr_def_10,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5115,c_76]) ).
tcf(c_7052,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(iPr_def_10,identity_relation(X1)),X0) = apply(identity_relation(X1),apply(iPr_def_10,X0)) )
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,set_intersection2(X1,sK12)) ),
inference(superposition,[status(thm)],[c_5115,c_96]) ).
tcf(c_7053,plain,
set_intersection2(empty_set,sK12) = empty_set,
inference(light_normalisation,[status(thm)],[c_7042,c_2054,c_4938]) ).
tcf(c_7063,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(iPr_def_10,identity_relation(X1)),X0) = apply(identity_relation(X1),apply(iPr_def_10,X0)) )
| ~ in(X0,set_intersection2(X1,sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7052,c_1881,c_1880,c_71,c_72]) ).
tcf(c_7066,plain,
! [X0: $i] :
( in(sK10(set_intersection2(X0,sK12),relation_composition(iPr_def_10,identity_relation(X0))),set_intersection2(X0,sK12))
| ( relation_composition(iPr_def_10,identity_relation(X0)) = identity_relation(set_intersection2(X0,sK12)) )
| ~ relation(relation_composition(iPr_def_10,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_10,identity_relation(X0))) ),
inference(light_normalisation,[status(thm)],[c_7047,c_5115]) ).
tcf(c_7078,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(iPr_def_10,identity_relation(X0)),X1),set_intersection2(X0,sK12))
| ( relation_composition(iPr_def_10,identity_relation(X0)) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(iPr_def_10,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_10,identity_relation(X0)))
| ( set_intersection2(X0,sK12) != relation_dom(X1) ) ),
inference(light_normalisation,[status(thm)],[c_7045,c_5115]) ).
tcf(c_7086,plain,
! [X0: $i] :
( ( relation_composition(iPr_def_10,identity_relation(X0)) = identity_relation(set_intersection2(X0,sK12)) )
| ~ relation(relation_composition(iPr_def_10,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_10,identity_relation(X0)))
| ( apply(relation_composition(iPr_def_10,identity_relation(X0)),sK10(set_intersection2(X0,sK12),relation_composition(iPr_def_10,identity_relation(X0)))) != sK10(set_intersection2(X0,sK12),relation_composition(iPr_def_10,identity_relation(X0))) ) ),
inference(light_normalisation,[status(thm)],[c_7046,c_5115]) ).
tcf(c_7106,plain,
( empty(relation_composition(empty_set,sK2))
| ~ relation(sK2)
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_79,c_6453]) ).
tcf(c_7107,plain,
empty(relation_composition(empty_set,sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_7106,c_81,c_73]) ).
tcf(c_7108,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7107,c_110]) ).
tcf(c_7109,plain,
sK1(powerset(relation_composition(empty_set,sK2))) = empty_set,
inference(superposition,[status(thm)],[c_7107,c_3939]) ).
tcf(c_7110,plain,
! [X0: $i] : set_intersection2(relation_composition(empty_set,sK2),X0) = empty_set,
inference(superposition,[status(thm)],[c_7107,c_3180]) ).
tcf(c_7111,plain,
! [X0: $i] : set_intersection2(X0,relation_composition(empty_set,sK2)) = empty_set,
inference(superposition,[status(thm)],[c_7107,c_3084]) ).
tcf(c_7112,plain,
identity_relation(identity_relation(relation_composition(empty_set,sK2))) = empty_set,
inference(superposition,[status(thm)],[c_7107,c_2474]) ).
tcf(c_7113,plain,
identity_relation(relation_dom(relation_composition(empty_set,sK2))) = empty_set,
inference(superposition,[status(thm)],[c_7107,c_2473]) ).
tcf(c_7114,plain,
relation_dom(relation_dom(relation_composition(empty_set,sK2))) = empty_set,
inference(superposition,[status(thm)],[c_7107,c_2055]) ).
tcf(c_7115,plain,
identity_relation(relation_composition(empty_set,sK2)) = empty_set,
inference(superposition,[status(thm)],[c_7107,c_2184]) ).
tcf(c_7117,plain,
relation_composition(empty_set,sK2) = empty_set,
inference(superposition,[status(thm)],[c_7107,c_108]) ).
tcf(c_7118,plain,
relation(relation_composition(empty_set,sK2)),
inference(superposition,[status(thm)],[c_7107,c_51]) ).
tcf(c_7119,plain,
function(relation_composition(empty_set,sK2)),
inference(superposition,[status(thm)],[c_7107,c_50]) ).
tcf(c_7136,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,sK2),X0) = apply(sK2,apply(empty_set,X0)) )
| ~ relation(sK2)
| ~ relation(empty_set)
| ~ function(sK2)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_7117,c_96]) ).
tcf(c_7137,plain,
! [X0: $i] :
( ( apply(sK2,apply(empty_set,X0)) = apply(empty_set,X0) )
| ~ relation(sK2)
| ~ relation(empty_set)
| ~ function(sK2)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_7136,c_2054,c_7117]) ).
tcf(c_7158,plain,
! [X0: $i] :
( relation(set_intersection2(empty_set,X0))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_5628,c_6506]) ).
tcf(c_7168,plain,
! [X0: $i] :
( function(set_intersection2(empty_set,X0))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_5628,c_6507]) ).
tcf(c_7169,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(identity_relation(X2),set_intersection2(sK1(powerset(X0)),X1))) = set_intersection2(relation_dom(set_intersection2(sK1(powerset(X0)),X1)),X2) )
| ~ empty(X0)
| ~ relation(set_intersection2(sK1(powerset(X0)),X1)) ),
inference(superposition,[status(thm)],[c_6507,c_103]) ).
tcf(c_7179,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),relation_dom(relation_composition(iPr_def_14,sK2)))) = set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(relation_composition(iPr_def_14,sK2))) ),
inference(superposition,[status(thm)],[c_6818,c_103]) ).
tcf(c_7186,plain,
relation_dom(relation_composition(iPr_def_11,empty_set)) = set_intersection2(empty_set,sK11),
inference(superposition,[status(thm)],[c_2472,c_5116]) ).
tcf(c_7188,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,relation_composition(iPr_def_11,identity_relation(X0))),relation_dom(X1))
| ( relation_composition(iPr_def_11,identity_relation(X0)) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(iPr_def_11,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_11,identity_relation(X0)))
| ( set_intersection2(X0,sK11) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_5116,c_112]) ).
tcf(c_7189,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(iPr_def_11,identity_relation(X0)),X1),relation_dom(relation_composition(iPr_def_11,identity_relation(X0))))
| ( relation_composition(iPr_def_11,identity_relation(X0)) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(iPr_def_11,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_11,identity_relation(X0)))
| ( set_intersection2(X0,sK11) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_5116,c_112]) ).
tcf(c_7190,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_composition(iPr_def_11,identity_relation(X0)))) = relation_composition(iPr_def_11,identity_relation(X0)) )
| ~ relation(relation_composition(iPr_def_11,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_11,identity_relation(X0)))
| ( apply(relation_composition(iPr_def_11,identity_relation(X0)),sK10(set_intersection2(X0,sK11),relation_composition(iPr_def_11,identity_relation(X0)))) != sK10(set_intersection2(X0,sK11),relation_composition(iPr_def_11,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_5116,c_99]) ).
tcf(c_7191,plain,
! [X0: $i] :
( in(sK10(set_intersection2(X0,sK11),relation_composition(iPr_def_11,identity_relation(X0))),set_intersection2(X0,sK11))
| ( identity_relation(relation_dom(relation_composition(iPr_def_11,identity_relation(X0)))) = relation_composition(iPr_def_11,identity_relation(X0)) )
| ~ relation(relation_composition(iPr_def_11,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_11,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5116,c_100]) ).
tcf(c_7192,plain,
! [X0: $i] :
( empty(relation_composition(iPr_def_11,identity_relation(X0)))
| ~ empty(set_intersection2(X0,sK11))
| ~ relation(relation_composition(iPr_def_11,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5116,c_75]) ).
tcf(c_7193,plain,
! [X0: $i] :
( function(set_intersection2(X0,sK11))
| ~ empty(relation_composition(iPr_def_11,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5116,c_1895]) ).
tcf(c_7194,plain,
! [X0: $i] :
( relation(set_intersection2(X0,sK11))
| ~ empty(relation_composition(iPr_def_11,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5116,c_77]) ).
tcf(c_7195,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK11))
| ~ empty(relation_composition(iPr_def_11,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5116,c_76]) ).
tcf(c_7196,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(iPr_def_11,identity_relation(X1)),X0) = apply(identity_relation(X1),apply(iPr_def_11,X0)) )
| ~ relation(iPr_def_11)
| ~ function(iPr_def_11)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,set_intersection2(X1,sK11)) ),
inference(superposition,[status(thm)],[c_5116,c_96]) ).
tcf(c_7197,plain,
set_intersection2(empty_set,sK11) = empty_set,
inference(light_normalisation,[status(thm)],[c_7186,c_2054,c_5102]) ).
tcf(c_7207,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(iPr_def_11,identity_relation(X1)),X0) = apply(identity_relation(X1),apply(iPr_def_11,X0)) )
| ~ in(X0,set_intersection2(X1,sK11)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7196,c_1884,c_1883,c_71,c_72]) ).
tcf(c_7210,plain,
! [X0: $i] :
( in(sK10(set_intersection2(X0,sK11),relation_composition(iPr_def_11,identity_relation(X0))),set_intersection2(X0,sK11))
| ( relation_composition(iPr_def_11,identity_relation(X0)) = identity_relation(set_intersection2(X0,sK11)) )
| ~ relation(relation_composition(iPr_def_11,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_11,identity_relation(X0))) ),
inference(light_normalisation,[status(thm)],[c_7191,c_5116]) ).
tcf(c_7222,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(iPr_def_11,identity_relation(X0)),X1),set_intersection2(X0,sK11))
| ( relation_composition(iPr_def_11,identity_relation(X0)) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(iPr_def_11,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_11,identity_relation(X0)))
| ( set_intersection2(X0,sK11) != relation_dom(X1) ) ),
inference(light_normalisation,[status(thm)],[c_7189,c_5116]) ).
tcf(c_7230,plain,
! [X0: $i] :
( ( relation_composition(iPr_def_11,identity_relation(X0)) = identity_relation(set_intersection2(X0,sK11)) )
| ~ relation(relation_composition(iPr_def_11,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_11,identity_relation(X0)))
| ( apply(relation_composition(iPr_def_11,identity_relation(X0)),sK10(set_intersection2(X0,sK11),relation_composition(iPr_def_11,identity_relation(X0)))) != sK10(set_intersection2(X0,sK11),relation_composition(iPr_def_11,identity_relation(X0))) ) ),
inference(light_normalisation,[status(thm)],[c_7190,c_5116]) ).
tcf(c_7250,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| in(sK1(set_intersection2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_52,c_2202]) ).
tcf(c_7253,plain,
! [X0: $i] :
( empty(set_intersection2(X0,empty_set))
| in(sK1(empty_set),X0) ),
inference(superposition,[status(thm)],[c_97,c_2202]) ).
tcf(c_7254,plain,
! [X0: $i] :
( in(sK1(empty_set),empty_set)
| empty(set_intersection2(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_1996,c_2202]) ).
tcf(c_7256,plain,
( empty(set_intersection2(sK12,relation_dom(sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_10,sK2))),sK12) ),
inference(superposition,[status(thm)],[c_6018,c_2202]) ).
tcf(c_7257,plain,
( empty(set_intersection2(sK11,relation_dom(sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_11,sK2))),sK11) ),
inference(superposition,[status(thm)],[c_6133,c_2202]) ).
tcf(c_7258,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_6817,c_2202]) ).
tcf(c_7259,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ( apply(identity_relation(X0),sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_2202,c_172]) ).
tcf(c_7260,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ~ in(X0,sK1(set_intersection2(X0,X1))) ),
inference(superposition,[status(thm)],[c_2202,c_49]) ).
tcf(c_7262,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| element(sK1(set_intersection2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_2202,c_95]) ).
tcf(c_7263,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),X2))
| in(sK1(set_intersection2(set_intersection2(X0,X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_2202,c_58]) ).
tcf(c_7264,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),X2))
| in(sK1(set_intersection2(set_intersection2(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_2202,c_57]) ).
tcf(c_7265,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_dom(relation_composition(X0,X1)),X2))
| ( apply(relation_composition(X0,X1),sK1(set_intersection2(relation_dom(relation_composition(X0,X1)),X2))) = apply(X1,apply(X0,sK1(set_intersection2(relation_dom(relation_composition(X0,X1)),X2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_2202,c_96]) ).
tcf(c_7266,plain,
! [X0: $i] : empty(set_intersection2(empty_set,X0)),
inference(superposition,[status(thm)],[c_2202,c_5671]) ).
tcf(c_7267,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(set_intersection2(iPr_def_13,X0)),sK11) ),
inference(superposition,[status(thm)],[c_2202,c_2102]) ).
tcf(c_7268,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(set_intersection2(iPr_def_13,X0)),sK12) ),
inference(superposition,[status(thm)],[c_2202,c_2071]) ).
tcf(c_7270,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(powerset(X0)),X1))
| element(sK1(set_intersection2(sK1(powerset(X0)),X1)),X0) ),
inference(superposition,[status(thm)],[c_2202,c_2582]) ).
tcf(c_7284,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_7258,c_6817]) ).
tcf(c_7287,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_11,sK2))),sK11) ),
inference(light_normalisation,[status(thm)],[c_7257,c_6133]) ).
tcf(c_7290,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_10,sK2))),sK12) ),
inference(light_normalisation,[status(thm)],[c_7256,c_6018]) ).
tcf(c_7345,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(identity_relation(X2),relation_composition(X0,X1))) = set_intersection2(relation_dom(relation_composition(X0,X1)),X2) )
| ~ relation(X0)
| ~ empty(X1)
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_2313,c_103]) ).
tcf(c_7374,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_110]) ).
tcf(c_7375,plain,
( ( sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3939]) ).
tcf(c_7376,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3180]) ).
tcf(c_7377,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3084]) ).
tcf(c_7378,plain,
( ( identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_2474]) ).
tcf(c_7379,plain,
( ( identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_2473]) ).
tcf(c_7380,plain,
( ( relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_2055]) ).
tcf(c_7381,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_2184]) ).
tcf(c_7382,plain,
( ( relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_2013]) ).
tcf(c_7383,plain,
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_108]) ).
tcf(c_7386,plain,
( empty(relation_composition(iPr_def_14,sK2))
| ~ empty(relation_dom(sK2))
| ~ relation(relation_composition(iPr_def_14,sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_75]) ).
tcf(c_7429,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(identity_relation(X2),relation_composition(X0,X1))) = set_intersection2(relation_dom(relation_composition(X0,X1)),X2) )
| ~ relation(X1)
| ~ empty(X0)
| ~ relation(relation_composition(X0,X1)) ),
inference(superposition,[status(thm)],[c_2365,c_103]) ).
tcf(c_7440,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| element(sK0(X0,sK4(X1),X2),X1)
| in(sK0(X0,sK4(X1),X2),X2)
| ( set_intersection2(X0,sK4(X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_55,c_2583]) ).
tcf(c_7441,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| element(sK0(sK4(X0),X1,X2),X0)
| in(sK0(sK4(X0),X1,X2),X2)
| ( set_intersection2(sK4(X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_54,c_2583]) ).
tcf(c_7442,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK0(X0,X1,sK4(X2)),X2)
| in(sK0(X0,X1,sK4(X2)),X1)
| ( set_intersection2(X0,X1) = sK4(X2) ) ),
inference(superposition,[status(thm)],[c_55,c_2583]) ).
tcf(c_7443,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| element(sK0(X0,X1,sK4(X2)),X2)
| in(sK0(X0,X1,sK4(X2)),X0)
| ( set_intersection2(X0,X1) = sK4(X2) ) ),
inference(superposition,[status(thm)],[c_54,c_2583]) ).
tcf(c_7444,plain,
! [X0: $i] :
( empty(X0)
| empty(sK4(X0))
| element(sK1(sK4(X0)),X0) ),
inference(superposition,[status(thm)],[c_2137,c_2583]) ).
tcf(c_7445,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| empty(set_intersection2(X0,sK4(X1)))
| element(sK1(set_intersection2(X0,sK4(X1))),X1) ),
inference(superposition,[status(thm)],[c_2201,c_2583]) ).
tcf(c_7446,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| empty(set_intersection2(sK4(X0),X1))
| element(sK1(set_intersection2(sK4(X0),X1)),X0) ),
inference(superposition,[status(thm)],[c_2202,c_2583]) ).
tcf(c_7541,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_2637]) ).
tcf(c_7542,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_2637]) ).
tcf(c_7543,plain,
relation_dom(relation_dom(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_2637]) ).
tcf(c_7544,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_2637]) ).
tcf(c_7545,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_2637]) ).
tcf(c_7546,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_2637]) ).
tcf(c_7547,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_2637]) ).
tcf(c_7548,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_2637]) ).
tcf(c_7549,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(X1,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_2637]) ).
tcf(c_7550,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(sK1(powerset(X0)),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_2637]) ).
tcf(c_7551,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_2637]) ).
tcf(c_7552,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_2637]) ).
tcf(c_7553,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_2637]) ).
tcf(c_7590,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_2658]) ).
tcf(c_7591,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_2658]) ).
tcf(c_7592,plain,
identity_relation(relation_dom(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_2658]) ).
tcf(c_7593,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_2658]) ).
tcf(c_7594,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_2658]) ).
tcf(c_7595,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_2658]) ).
tcf(c_7596,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_2658]) ).
tcf(c_7597,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_2658]) ).
tcf(c_7598,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(X1,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_2658]) ).
tcf(c_7599,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(sK1(powerset(X0)),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_2658]) ).
tcf(c_7600,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_2658]) ).
tcf(c_7601,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_2658]) ).
tcf(c_7602,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_2658]) ).
tcf(c_7676,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_2686]) ).
tcf(c_7677,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_2686]) ).
tcf(c_7678,plain,
identity_relation(identity_relation(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_2686]) ).
tcf(c_7679,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_2686]) ).
tcf(c_7680,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_2686]) ).
tcf(c_7681,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_2686]) ).
tcf(c_7682,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_2686]) ).
tcf(c_7683,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_2686]) ).
tcf(c_7684,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(X1,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_2686]) ).
tcf(c_7685,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(sK1(powerset(X0)),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_2686]) ).
tcf(c_7686,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_2686]) ).
tcf(c_7687,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_2686]) ).
tcf(c_7688,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_2686]) ).
tcf(c_7753,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_2687]) ).
tcf(c_7754,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_2687]) ).
tcf(c_7755,plain,
identity_relation(identity_relation(identity_relation(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_2687]) ).
tcf(c_7756,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_2687]) ).
tcf(c_7757,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_2687]) ).
tcf(c_7758,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_2687]) ).
tcf(c_7759,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_2687]) ).
tcf(c_7760,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_2687]) ).
tcf(c_7761,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(X1,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_2687]) ).
tcf(c_7762,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(sK1(powerset(X0)),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_2687]) ).
tcf(c_7763,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_2687]) ).
tcf(c_7764,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_2687]) ).
tcf(c_7765,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_2687]) ).
tcf(c_7852,plain,
( element(sK1(empty_set),empty_set)
| empty(sK1(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_5628,c_2708]) ).
tcf(c_7853,plain,
! [X0: $i] :
( empty(X0)
| empty(sK1(powerset(X0)))
| in(sK1(sK1(powerset(X0))),X0) ),
inference(superposition,[status(thm)],[c_2708,c_98]) ).
tcf(c_7854,plain,
! [X0: $i,X1: $i] :
( empty(sK1(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK1(sK1(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_2708,c_107]) ).
tcf(c_7855,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK1(powerset(powerset(X1))))
| ~ in(X0,sK1(sK1(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_2708,c_106]) ).
tcf(c_7856,plain,
( empty(empty_set)
| element(sK1(empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_7852,c_5628]) ).
tcf(c_7912,plain,
( empty(set_intersection2(relation_dom(sK2),sK12))
| in(sK1(relation_dom(relation_composition(iPr_def_10,sK2))),sK12) ),
inference(superposition,[status(thm)],[c_6018,c_2732]) ).
tcf(c_7913,plain,
( empty(set_intersection2(relation_dom(sK2),sK11))
| in(sK1(relation_dom(relation_composition(iPr_def_11,sK2))),sK11) ),
inference(superposition,[status(thm)],[c_6133,c_2732]) ).
tcf(c_7914,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| in(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_6817,c_2732]) ).
tcf(c_7915,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ( apply(identity_relation(X0),sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_2732,c_172]) ).
tcf(c_7916,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ~ in(X0,sK1(set_intersection2(X0,X1))) ),
inference(superposition,[status(thm)],[c_2732,c_49]) ).
tcf(c_7918,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| element(sK1(set_intersection2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_2732,c_95]) ).
tcf(c_7919,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,set_intersection2(X0,X1)))
| in(sK1(set_intersection2(set_intersection2(X0,X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_2732,c_58]) ).
tcf(c_7920,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,set_intersection2(X0,X1)))
| in(sK1(set_intersection2(set_intersection2(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_2732,c_57]) ).
tcf(c_7921,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,relation_dom(relation_composition(X0,X1))))
| ( apply(relation_composition(X0,X1),sK1(set_intersection2(relation_dom(relation_composition(X0,X1)),X2))) = apply(X1,apply(X0,sK1(set_intersection2(relation_dom(relation_composition(X0,X1)),X2)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_2732,c_96]) ).
tcf(c_7923,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(set_intersection2(iPr_def_13,X0)),sK11) ),
inference(superposition,[status(thm)],[c_2732,c_2102]) ).
tcf(c_7924,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(set_intersection2(iPr_def_13,X0)),sK12) ),
inference(superposition,[status(thm)],[c_2732,c_2071]) ).
tcf(c_7926,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,sK1(powerset(X0))))
| element(sK1(set_intersection2(sK1(powerset(X0)),X1)),X0) ),
inference(superposition,[status(thm)],[c_2732,c_2582]) ).
tcf(c_7927,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| empty(set_intersection2(X1,sK4(X0)))
| element(sK1(set_intersection2(sK4(X0),X1)),X0) ),
inference(superposition,[status(thm)],[c_2732,c_2583]) ).
tcf(c_7980,plain,
relation_dom(relation_composition(iPr_def_14,empty_set)) = set_intersection2(empty_set,iPr_def_13),
inference(superposition,[status(thm)],[c_2472,c_5118]) ).
tcf(c_7982,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,relation_composition(iPr_def_14,identity_relation(X0))),relation_dom(X1))
| ( relation_composition(iPr_def_14,identity_relation(X0)) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(iPr_def_14,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_14,identity_relation(X0)))
| ( set_intersection2(X0,iPr_def_13) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_5118,c_112]) ).
tcf(c_7983,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(iPr_def_14,identity_relation(X0)),X1),relation_dom(relation_composition(iPr_def_14,identity_relation(X0))))
| ( relation_composition(iPr_def_14,identity_relation(X0)) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(iPr_def_14,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_14,identity_relation(X0)))
| ( set_intersection2(X0,iPr_def_13) != relation_dom(X1) ) ),
inference(superposition,[status(thm)],[c_5118,c_112]) ).
tcf(c_7984,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_composition(iPr_def_14,identity_relation(X0)))) = relation_composition(iPr_def_14,identity_relation(X0)) )
| ~ relation(relation_composition(iPr_def_14,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_14,identity_relation(X0)))
| ( apply(relation_composition(iPr_def_14,identity_relation(X0)),sK10(set_intersection2(X0,iPr_def_13),relation_composition(iPr_def_14,identity_relation(X0)))) != sK10(set_intersection2(X0,iPr_def_13),relation_composition(iPr_def_14,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_5118,c_99]) ).
tcf(c_7985,plain,
! [X0: $i] :
( in(sK10(set_intersection2(X0,iPr_def_13),relation_composition(iPr_def_14,identity_relation(X0))),set_intersection2(X0,iPr_def_13))
| ( identity_relation(relation_dom(relation_composition(iPr_def_14,identity_relation(X0)))) = relation_composition(iPr_def_14,identity_relation(X0)) )
| ~ relation(relation_composition(iPr_def_14,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_14,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5118,c_100]) ).
tcf(c_7986,plain,
! [X0: $i] :
( empty(relation_composition(iPr_def_14,identity_relation(X0)))
| ~ empty(set_intersection2(X0,iPr_def_13))
| ~ relation(relation_composition(iPr_def_14,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5118,c_75]) ).
tcf(c_7987,plain,
! [X0: $i] :
( function(set_intersection2(X0,iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5118,c_1895]) ).
tcf(c_7988,plain,
! [X0: $i] :
( relation(set_intersection2(X0,iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5118,c_77]) ).
tcf(c_7989,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_5118,c_76]) ).
tcf(c_7990,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(iPr_def_14,identity_relation(X1)),X0) = apply(identity_relation(X1),apply(iPr_def_14,X0)) )
| ~ relation(iPr_def_14)
| ~ function(iPr_def_14)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,set_intersection2(X1,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_5118,c_96]) ).
tcf(c_7991,plain,
set_intersection2(empty_set,iPr_def_13) = empty_set,
inference(light_normalisation,[status(thm)],[c_7980,c_2054,c_5508]) ).
tcf(c_8001,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(iPr_def_14,identity_relation(X1)),X0) = apply(identity_relation(X1),apply(iPr_def_14,X0)) )
| ~ in(X0,set_intersection2(X1,iPr_def_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7990,c_1887,c_1886,c_71,c_72]) ).
tcf(c_8004,plain,
! [X0: $i] :
( in(sK10(set_intersection2(X0,iPr_def_13),relation_composition(iPr_def_14,identity_relation(X0))),set_intersection2(X0,iPr_def_13))
| ( relation_composition(iPr_def_14,identity_relation(X0)) = identity_relation(set_intersection2(X0,iPr_def_13)) )
| ~ relation(relation_composition(iPr_def_14,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_14,identity_relation(X0))) ),
inference(light_normalisation,[status(thm)],[c_7985,c_5118]) ).
tcf(c_8016,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_composition(iPr_def_14,identity_relation(X0)),X1),set_intersection2(X0,iPr_def_13))
| ( relation_composition(iPr_def_14,identity_relation(X0)) = X1 )
| ~ relation(X1)
| ~ function(X1)
| ~ relation(relation_composition(iPr_def_14,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_14,identity_relation(X0)))
| ( set_intersection2(X0,iPr_def_13) != relation_dom(X1) ) ),
inference(light_normalisation,[status(thm)],[c_7983,c_5118]) ).
tcf(c_8024,plain,
! [X0: $i] :
( ( relation_composition(iPr_def_14,identity_relation(X0)) = identity_relation(set_intersection2(X0,iPr_def_13)) )
| ~ relation(relation_composition(iPr_def_14,identity_relation(X0)))
| ~ function(relation_composition(iPr_def_14,identity_relation(X0)))
| ( apply(relation_composition(iPr_def_14,identity_relation(X0)),sK10(set_intersection2(X0,iPr_def_13),relation_composition(iPr_def_14,identity_relation(X0)))) != sK10(set_intersection2(X0,iPr_def_13),relation_composition(iPr_def_14,identity_relation(X0))) ) ),
inference(light_normalisation,[status(thm)],[c_7984,c_5118]) ).
tcf(c_8087,plain,
! [X0: $i] :
( element(sK1(empty_set),empty_set)
| empty(set_intersection2(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_97,c_2741]) ).
tcf(c_8088,plain,
! [X0: $i] :
( element(sK1(empty_set),X0)
| empty(set_intersection2(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_1996,c_2741]) ).
tcf(c_8090,plain,
( empty(set_intersection2(sK12,relation_dom(sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_10,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6018,c_2741]) ).
tcf(c_8091,plain,
( empty(set_intersection2(sK11,relation_dom(sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_11,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6133,c_2741]) ).
tcf(c_8092,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6817,c_2741]) ).
tcf(c_8094,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X1,powerset(X2)))
| ~ empty(X2)
| ~ in(X0,sK1(set_intersection2(X1,powerset(X2)))) ),
inference(superposition,[status(thm)],[c_2741,c_107]) ).
tcf(c_8095,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| empty(set_intersection2(X1,powerset(X2)))
| ~ in(X0,sK1(set_intersection2(X1,powerset(X2)))) ),
inference(superposition,[status(thm)],[c_2741,c_106]) ).
tcf(c_8098,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_8092,c_6817]) ).
tcf(c_8101,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_11,sK2))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_8091,c_6133]) ).
tcf(c_8104,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_10,sK2))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_8090,c_6018]) ).
tcf(c_8141,plain,
! [X0: $i] :
( relation(set_intersection2(iPr_def_13,X0))
| ~ relation(iPr_def_14)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_3289]) ).
tcf(c_8145,plain,
( relation(set_intersection2(iPr_def_13,empty_set))
| ~ empty(relation_composition(empty_set,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_2472,c_3289]) ).
tcf(c_8147,plain,
( relation(set_intersection2(iPr_def_13,empty_set))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_8145,c_5997]) ).
tcf(c_8148,plain,
relation(set_intersection2(iPr_def_13,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_8147,c_73]) ).
tcf(c_8149,plain,
! [X0: $i] :
( relation(set_intersection2(iPr_def_13,X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8141,c_1887]) ).
tcf(c_8192,plain,
! [X0: $i] :
( relation(set_intersection2(X0,iPr_def_13))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_52,c_8149]) ).
tcf(c_8194,plain,
( relation(iPr_def_13)
| ~ empty(identity_relation(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_80,c_8149]) ).
tcf(c_8196,plain,
( relation(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_6817,c_8149]) ).
tcf(c_8219,plain,
( empty(set_intersection2(empty_set,iPr_def_13))
| in(sK1(empty_set),sK11) ),
inference(superposition,[status(thm)],[c_1996,c_2746]) ).
tcf(c_8220,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(sK11),sK1(set_intersection2(X0,iPr_def_13))) = sK1(set_intersection2(X0,iPr_def_13)) ) ),
inference(superposition,[status(thm)],[c_2746,c_172]) ).
tcf(c_8221,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ~ in(sK11,sK1(set_intersection2(X0,iPr_def_13))) ),
inference(superposition,[status(thm)],[c_2746,c_49]) ).
tcf(c_8223,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| element(sK1(set_intersection2(X0,iPr_def_13)),sK11) ),
inference(superposition,[status(thm)],[c_2746,c_95]) ).
tcf(c_8230,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(iPr_def_11,sK1(set_intersection2(X0,iPr_def_13))) = sK1(set_intersection2(X0,iPr_def_13)) ) ),
inference(light_normalisation,[status(thm)],[c_8220,c_1148]) ).
tcf(c_8236,plain,
( empty(empty_set)
| in(sK1(empty_set),sK11) ),
inference(demodulation,[status(thm)],[c_8219,c_1996]) ).
tcf(c_8244,plain,
( empty(set_intersection2(empty_set,iPr_def_13))
| in(sK1(empty_set),sK12) ),
inference(superposition,[status(thm)],[c_1996,c_2747]) ).
tcf(c_8245,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(sK12),sK1(set_intersection2(X0,iPr_def_13))) = sK1(set_intersection2(X0,iPr_def_13)) ) ),
inference(superposition,[status(thm)],[c_2747,c_172]) ).
tcf(c_8246,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ~ in(sK12,sK1(set_intersection2(X0,iPr_def_13))) ),
inference(superposition,[status(thm)],[c_2747,c_49]) ).
tcf(c_8248,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| element(sK1(set_intersection2(X0,iPr_def_13)),sK12) ),
inference(superposition,[status(thm)],[c_2747,c_95]) ).
tcf(c_8255,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(iPr_def_10,sK1(set_intersection2(X0,iPr_def_13))) = sK1(set_intersection2(X0,iPr_def_13)) ) ),
inference(light_normalisation,[status(thm)],[c_8245,c_1147]) ).
tcf(c_8261,plain,
( empty(empty_set)
| in(sK1(empty_set),sK12) ),
inference(demodulation,[status(thm)],[c_8244,c_1996]) ).
tcf(c_8266,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X2,relation_composition(X0,X1))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3082]) ).
tcf(c_8267,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X2,relation_composition(X1,X0))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3082]) ).
tcf(c_8268,plain,
! [X0: $i] : identity_relation(set_intersection2(X0,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3082]) ).
tcf(c_8269,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3082]) ).
tcf(c_8270,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3082]) ).
tcf(c_8271,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(X0,X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3082]) ).
tcf(c_8273,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(X2,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3082]) ).
tcf(c_8274,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(X2,sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3082]) ).
tcf(c_8275,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(sK1(powerset(X0)),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3082]) ).
tcf(c_8276,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3082]) ).
tcf(c_8277,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3082]) ).
tcf(c_8278,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3082]) ).
tcf(c_8373,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X2,relation_composition(X0,X1))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3083]) ).
tcf(c_8374,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X2,relation_composition(X1,X0))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3083]) ).
tcf(c_8375,plain,
! [X0: $i] : relation_dom(set_intersection2(X0,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3083]) ).
tcf(c_8376,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3083]) ).
tcf(c_8377,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3083]) ).
tcf(c_8378,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(X0,X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3083]) ).
tcf(c_8380,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(X2,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3083]) ).
tcf(c_8381,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(X2,sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3083]) ).
tcf(c_8382,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(sK1(powerset(X0)),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3083]) ).
tcf(c_8383,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3083]) ).
tcf(c_8384,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3083]) ).
tcf(c_8385,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3083]) ).
tcf(c_8453,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(relation_composition(X0,X1),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3178]) ).
tcf(c_8454,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(relation_composition(X1,X0),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3178]) ).
tcf(c_8455,plain,
! [X0: $i] : identity_relation(set_intersection2(empty_set,X0)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3178]) ).
tcf(c_8456,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(relation_dom(X0),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3178]) ).
tcf(c_8457,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(identity_relation(X0),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3178]) ).
tcf(c_8458,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3178]) ).
tcf(c_8460,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(set_intersection2(X1,X0),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3178]) ).
tcf(c_8461,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(set_intersection2(X1,sK1(powerset(X0))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3178]) ).
tcf(c_8462,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(set_intersection2(sK1(powerset(X0)),X1),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3178]) ).
tcf(c_8463,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3178]) ).
tcf(c_8464,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3178]) ).
tcf(c_8465,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3178]) ).
tcf(c_8527,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(relation_composition(X0,X1),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3179]) ).
tcf(c_8528,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(relation_composition(X1,X0),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3179]) ).
tcf(c_8529,plain,
! [X0: $i] : relation_dom(set_intersection2(empty_set,X0)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3179]) ).
tcf(c_8530,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(relation_dom(X0),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3179]) ).
tcf(c_8531,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(identity_relation(X0),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3179]) ).
tcf(c_8532,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3179]) ).
tcf(c_8534,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(set_intersection2(X1,X0),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3179]) ).
tcf(c_8535,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(set_intersection2(X1,sK1(powerset(X0))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3179]) ).
tcf(c_8536,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(set_intersection2(sK1(powerset(X0)),X1),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3179]) ).
tcf(c_8537,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3179]) ).
tcf(c_8538,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3179]) ).
tcf(c_8539,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3179]) ).
tcf(c_8626,plain,
! [X0: $i] :
( function(set_intersection2(iPr_def_13,X0))
| ~ relation(iPr_def_14)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_3288]) ).
tcf(c_8630,plain,
( function(set_intersection2(iPr_def_13,empty_set))
| ~ empty(relation_composition(empty_set,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_2472,c_3288]) ).
tcf(c_8632,plain,
( function(set_intersection2(iPr_def_13,empty_set))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_8630,c_5997]) ).
tcf(c_8633,plain,
function(set_intersection2(iPr_def_13,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_8632,c_73]) ).
tcf(c_8634,plain,
! [X0: $i] :
( function(set_intersection2(iPr_def_13,X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8626,c_1887]) ).
tcf(c_8665,plain,
! [X0: $i] :
( function(set_intersection2(X0,iPr_def_13))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_52,c_8634]) ).
tcf(c_8667,plain,
( function(iPr_def_13)
| ~ empty(identity_relation(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_80,c_8634]) ).
tcf(c_8669,plain,
( function(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_6817,c_8634]) ).
tcf(c_8670,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),set_intersection2(iPr_def_13,X0))) = set_intersection2(relation_dom(set_intersection2(iPr_def_13,X0)),X1) )
| ~ empty(identity_relation(X0))
| ~ relation(set_intersection2(iPr_def_13,X0)) ),
inference(superposition,[status(thm)],[c_8634,c_103]) ).
tcf(c_8716,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),set_intersection2(X0,iPr_def_13))) = set_intersection2(relation_dom(set_intersection2(X0,iPr_def_13)),X1) )
| ~ empty(identity_relation(X0))
| ~ relation(set_intersection2(X0,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_8665,c_103]) ).
tcf(c_8733,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ~ relation(iPr_def_14)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_3290]) ).
tcf(c_8737,plain,
( empty(set_intersection2(iPr_def_13,empty_set))
| ~ empty(relation_composition(empty_set,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_2472,c_3290]) ).
tcf(c_8739,plain,
( empty(set_intersection2(iPr_def_13,empty_set))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_8737,c_5997]) ).
tcf(c_8740,plain,
empty(set_intersection2(iPr_def_13,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_8739,c_73]) ).
tcf(c_8741,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8733,c_1887]) ).
tcf(c_8751,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_52,c_8741]) ).
tcf(c_8753,plain,
( empty(iPr_def_13)
| ~ empty(identity_relation(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_80,c_8741]) ).
tcf(c_8755,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_6817,c_8741]) ).
tcf(c_8756,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(iPr_def_13,X0) = X1 )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_110]) ).
tcf(c_8757,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(set_intersection2(iPr_def_13,X0),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_3179]) ).
tcf(c_8758,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(set_intersection2(iPr_def_13,X0),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_3178]) ).
tcf(c_8759,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(iPr_def_13,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_3083]) ).
tcf(c_8760,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(iPr_def_13,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_3082]) ).
tcf(c_8761,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(iPr_def_13,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_2687]) ).
tcf(c_8762,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(iPr_def_13,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_2686]) ).
tcf(c_8763,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(iPr_def_13,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_2658]) ).
tcf(c_8764,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(iPr_def_13,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_2637]) ).
tcf(c_8765,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(iPr_def_13,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_3939]) ).
tcf(c_8766,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(iPr_def_13,X0),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_3180]) ).
tcf(c_8767,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(iPr_def_13,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_3084]) ).
tcf(c_8768,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(iPr_def_13,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_2474]) ).
tcf(c_8769,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(iPr_def_13,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_2473]) ).
tcf(c_8770,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(iPr_def_13,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_2055]) ).
tcf(c_8771,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(iPr_def_13,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_2184]) ).
tcf(c_8772,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(iPr_def_13,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_2013]) ).
tcf(c_8773,plain,
! [X0: $i] :
( ( set_intersection2(iPr_def_13,X0) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_108]) ).
tcf(c_8910,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,iPr_def_13) = X1 )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_110]) ).
tcf(c_8911,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(set_intersection2(X0,iPr_def_13),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_3179]) ).
tcf(c_8912,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(set_intersection2(X0,iPr_def_13),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_3178]) ).
tcf(c_8913,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(X0,iPr_def_13))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_3083]) ).
tcf(c_8914,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(X0,iPr_def_13))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_3082]) ).
tcf(c_8915,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(X0,iPr_def_13)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_2687]) ).
tcf(c_8916,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(X0,iPr_def_13)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_2686]) ).
tcf(c_8917,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(X0,iPr_def_13)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_2658]) ).
tcf(c_8918,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(X0,iPr_def_13)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_2637]) ).
tcf(c_8919,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(X0,iPr_def_13))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_3939]) ).
tcf(c_8920,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,iPr_def_13),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_3180]) ).
tcf(c_8921,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(X0,iPr_def_13)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_3084]) ).
tcf(c_8922,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,iPr_def_13))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_2474]) ).
tcf(c_8923,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,iPr_def_13))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_2473]) ).
tcf(c_8924,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,iPr_def_13))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_2055]) ).
tcf(c_8925,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,iPr_def_13)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_2184]) ).
tcf(c_8926,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,iPr_def_13)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_2013]) ).
tcf(c_8927,plain,
! [X0: $i] :
( ( set_intersection2(X0,iPr_def_13) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_108]) ).
tcf(c_9048,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3937]) ).
tcf(c_9049,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3937]) ).
tcf(c_9050,plain,
identity_relation(sK1(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3937]) ).
tcf(c_9051,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3937]) ).
tcf(c_9052,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3937]) ).
tcf(c_9053,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3937]) ).
tcf(c_9054,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_3937]) ).
tcf(c_9055,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3937]) ).
tcf(c_9056,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(X0,iPr_def_13)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_3937]) ).
tcf(c_9057,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(iPr_def_13,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_3937]) ).
tcf(c_9058,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(X1,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3937]) ).
tcf(c_9059,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(sK1(powerset(X0)),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3937]) ).
tcf(c_9060,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3937]) ).
tcf(c_9061,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3937]) ).
tcf(c_9062,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3937]) ).
tcf(c_9234,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3938]) ).
tcf(c_9235,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3938]) ).
tcf(c_9236,plain,
relation_dom(sK1(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3938]) ).
tcf(c_9237,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3938]) ).
tcf(c_9238,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3938]) ).
tcf(c_9239,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3938]) ).
tcf(c_9240,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_3938]) ).
tcf(c_9241,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3938]) ).
tcf(c_9242,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(X0,iPr_def_13)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_3938]) ).
tcf(c_9243,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(iPr_def_13,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_3938]) ).
tcf(c_9244,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(X1,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3938]) ).
tcf(c_9245,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(sK1(powerset(X0)),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3938]) ).
tcf(c_9246,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3938]) ).
tcf(c_9247,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3938]) ).
tcf(c_9248,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3938]) ).
tcf(c_9316,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,relation_dom(relation_composition(X0,X1))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_4010]) ).
tcf(c_9317,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,relation_dom(relation_composition(X1,X0))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_4010]) ).
tcf(c_9318,plain,
! [X0: $i] : set_intersection2(X0,relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_4010]) ).
tcf(c_9319,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_4010]) ).
tcf(c_9320,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_4010]) ).
tcf(c_9321,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(X0,X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_4010]) ).
tcf(c_9322,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(sK1(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_4010]) ).
tcf(c_9323,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(X2,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_4010]) ).
tcf(c_9324,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(X0,iPr_def_13))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_4010]) ).
tcf(c_9325,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(iPr_def_13,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_4010]) ).
tcf(c_9326,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(X2,sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_4010]) ).
tcf(c_9327,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(sK1(powerset(X0)),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_4010]) ).
tcf(c_9328,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_4010]) ).
tcf(c_9329,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_4010]) ).
tcf(c_9330,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_4010]) ).
tcf(c_9436,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,identity_relation(relation_composition(X0,X1))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_4011]) ).
tcf(c_9437,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,identity_relation(relation_composition(X1,X0))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_4011]) ).
tcf(c_9438,plain,
! [X0: $i] : set_intersection2(X0,identity_relation(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_4011]) ).
tcf(c_9439,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_4011]) ).
tcf(c_9440,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_4011]) ).
tcf(c_9441,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(X0,X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_4011]) ).
tcf(c_9442,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(sK1(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_4011]) ).
tcf(c_9443,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(X2,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_4011]) ).
tcf(c_9444,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(X0,iPr_def_13))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_4011]) ).
tcf(c_9445,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(iPr_def_13,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_4011]) ).
tcf(c_9446,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(X2,sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_4011]) ).
tcf(c_9447,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(sK1(powerset(X0)),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_4011]) ).
tcf(c_9448,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_4011]) ).
tcf(c_9449,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_4011]) ).
tcf(c_9450,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_4011]) ).
tcf(c_9514,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_composition(X0,X1)),X2) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_4059]) ).
tcf(c_9515,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_composition(X1,X0)),X2) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_4059]) ).
tcf(c_9516,plain,
! [X0: $i] : set_intersection2(relation_dom(empty_set),X0) = empty_set,
inference(superposition,[status(thm)],[c_73,c_4059]) ).
tcf(c_9517,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(relation_dom(X0)),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_4059]) ).
tcf(c_9518,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(identity_relation(X0)),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_4059]) ).
tcf(c_9519,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X0,X1)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_4059]) ).
tcf(c_9520,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(sK1(powerset(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_4059]) ).
tcf(c_9521,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X1,X0)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_4059]) ).
tcf(c_9522,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X0,iPr_def_13)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_4059]) ).
tcf(c_9523,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(set_intersection2(iPr_def_13,X0)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_4059]) ).
tcf(c_9524,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X1,sK1(powerset(X0)))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_4059]) ).
tcf(c_9525,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(sK1(powerset(X0)),X1)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_4059]) ).
tcf(c_9526,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_4059]) ).
tcf(c_9527,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_4059]) ).
tcf(c_9528,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_4059]) ).
tcf(c_9635,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_composition(X0,X1)),X2) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_4060]) ).
tcf(c_9636,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_composition(X1,X0)),X2) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_4060]) ).
tcf(c_9637,plain,
! [X0: $i] : set_intersection2(identity_relation(empty_set),X0) = empty_set,
inference(superposition,[status(thm)],[c_73,c_4060]) ).
tcf(c_9638,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(relation_dom(X0)),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_4060]) ).
tcf(c_9639,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(identity_relation(X0)),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_4060]) ).
tcf(c_9640,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X0,X1)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_4060]) ).
tcf(c_9641,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(sK1(powerset(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_4060]) ).
tcf(c_9642,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X1,X0)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_4060]) ).
tcf(c_9643,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X0,iPr_def_13)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_4060]) ).
tcf(c_9644,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(set_intersection2(iPr_def_13,X0)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_4060]) ).
tcf(c_9645,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X1,sK1(powerset(X0)))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_4060]) ).
tcf(c_9646,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(sK1(powerset(X0)),X1)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_4060]) ).
tcf(c_9647,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_4060]) ).
tcf(c_9648,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_4060]) ).
tcf(c_9649,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_4060]) ).
tcf(c_9731,plain,
! [X0: $i] :
( function(set_intersection2(sK11,X0))
| ~ relation(iPr_def_11)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_4106]) ).
tcf(c_9733,plain,
( function(set_intersection2(sK11,sK12))
| ~ empty(relation_composition(iPr_def_10,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_1147,c_4106]) ).
tcf(c_9735,plain,
( function(set_intersection2(sK11,empty_set))
| ~ empty(relation_composition(empty_set,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_2472,c_4106]) ).
tcf(c_9736,plain,
( function(set_intersection2(sK11,iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_1151,c_4106]) ).
tcf(c_9739,plain,
( function(set_intersection2(sK11,empty_set))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_9735,c_6184]) ).
tcf(c_9740,plain,
function(set_intersection2(sK11,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_9739,c_73]) ).
tcf(c_9741,plain,
( function(set_intersection2(sK11,sK12))
| ~ empty(iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_9733,c_1149]) ).
tcf(c_9742,plain,
! [X0: $i] :
( function(set_intersection2(sK11,X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9731,c_1884]) ).
tcf(c_9750,plain,
! [X0: $i] :
( function(set_intersection2(X0,sK11))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_52,c_9742]) ).
tcf(c_9752,plain,
( function(sK11)
| ~ empty(identity_relation(sK11)) ),
inference(superposition,[status(thm)],[c_80,c_9742]) ).
tcf(c_9754,plain,
( function(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_6133,c_9742]) ).
tcf(c_9755,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),set_intersection2(sK11,X0))) = set_intersection2(relation_dom(set_intersection2(sK11,X0)),X1) )
| ~ empty(identity_relation(X0))
| ~ relation(set_intersection2(sK11,X0)) ),
inference(superposition,[status(thm)],[c_9742,c_103]) ).
tcf(c_9774,plain,
( function(iPr_def_13)
| ~ empty(identity_relation(sK12)) ),
inference(superposition,[status(thm)],[c_1150,c_9750]) ).
tcf(c_9775,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),set_intersection2(X0,sK11))) = set_intersection2(relation_dom(set_intersection2(X0,sK11)),X1) )
| ~ empty(identity_relation(X0))
| ~ relation(set_intersection2(X0,sK11)) ),
inference(superposition,[status(thm)],[c_9750,c_103]) ).
tcf(c_9776,plain,
( function(iPr_def_13)
| ~ empty(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_9774,c_1147]) ).
tcf(c_9789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X1,X2,powerset(X3)),X1)
| ( set_intersection2(X1,X2) = powerset(X3) )
| ~ empty(X3)
| ~ in(X0,sK0(X1,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_2239,c_107]) ).
tcf(c_9790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X0,X3)
| in(sK0(X1,X2,powerset(X3)),X1)
| ( set_intersection2(X1,X2) = powerset(X3) )
| ~ in(X0,sK0(X1,X2,powerset(X3))) ),
inference(superposition,[status(thm)],[c_2239,c_106]) ).
tcf(c_9791,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ( apply(identity_relation(X0),sK0(X0,X1,X2)) = sK0(X0,X1,X2) ) ),
inference(superposition,[status(thm)],[c_2239,c_172]) ).
tcf(c_9792,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ in(X0,sK0(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2239,c_49]) ).
tcf(c_9793,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2239,c_109]) ).
tcf(c_9794,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,X1,X2),X2)
| element(sK0(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_2239,c_95]) ).
tcf(c_9795,plain,
! [X0: $i,X1: $i] :
( element(sK0(X0,X0,X1),X1)
| ( set_intersection2(X0,X0) = X1 )
| ~ in(sK0(X0,X0,X1),X1)
| ~ in(sK0(X0,X0,X1),X0) ),
inference(superposition,[status(thm)],[c_2239,c_53]) ).
tcf(c_9796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK0(set_intersection2(X0,X1),X2,X3),X3)
| in(sK0(set_intersection2(X0,X1),X2,X3),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_2239,c_58]) ).
tcf(c_9797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK0(set_intersection2(X0,X1),X2,X3),X3)
| in(sK0(set_intersection2(X0,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_2239,c_57]) ).
tcf(c_9798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK0(relation_dom(relation_composition(X0,X1)),X2,X3),X3)
| ( set_intersection2(relation_dom(relation_composition(X0,X1)),X2) = X3 )
| ( apply(relation_composition(X0,X1),sK0(relation_dom(relation_composition(X0,X1)),X2,X3)) = apply(X1,apply(X0,sK0(relation_dom(relation_composition(X0,X1)),X2,X3))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_2239,c_96]) ).
tcf(c_9799,plain,
! [X0: $i,X1: $i] :
( element(sK0(empty_set,X0,X1),X1)
| ( set_intersection2(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_2239,c_5671]) ).
tcf(c_9800,plain,
! [X0: $i,X1: $i] :
( in(sK0(iPr_def_13,X0,X1),sK11)
| element(sK0(iPr_def_13,X0,X1),X1)
| ( set_intersection2(iPr_def_13,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_2239,c_2102]) ).
tcf(c_9801,plain,
! [X0: $i,X1: $i] :
( in(sK0(iPr_def_13,X0,X1),sK12)
| element(sK0(iPr_def_13,X0,X1),X1)
| ( set_intersection2(iPr_def_13,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_2239,c_2071]) ).
tcf(c_9802,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(sK1(powerset(X0)),X1,X2),X2)
| ( set_intersection2(sK1(powerset(X0)),X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2239,c_2933]) ).
tcf(c_9803,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(sK1(powerset(X0)),X1,X2),X2)
| element(sK0(sK1(powerset(X0)),X1,X2),X0)
| ( set_intersection2(sK1(powerset(X0)),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_2239,c_2582]) ).
tcf(c_9804,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| element(sK0(sK4(X0),X1,X2),X2)
| element(sK0(sK4(X0),X1,X2),X0)
| ( set_intersection2(sK4(X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_2239,c_2583]) ).
tcf(c_9805,plain,
! [X0: $i,X1: $i] :
( element(sK0(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_9799,c_1996]) ).
tcf(c_9850,plain,
! [X0: $i,X1: $i] :
( element(sK0(X0,X0,X1),X1)
| ( X0 = X1 )
| ~ in(sK0(X0,X0,X1),X1)
| ~ in(sK0(X0,X0,X1),X0) ),
inference(light_normalisation,[status(thm)],[c_9795,c_80]) ).
tcf(c_9928,plain,
! [X0: $i] :
( relation(set_intersection2(sK11,X0))
| ~ relation(iPr_def_11)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_4107]) ).
tcf(c_9930,plain,
( relation(set_intersection2(sK11,sK12))
| ~ empty(relation_composition(iPr_def_10,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_1147,c_4107]) ).
tcf(c_9932,plain,
( relation(set_intersection2(sK11,empty_set))
| ~ empty(relation_composition(empty_set,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_2472,c_4107]) ).
tcf(c_9933,plain,
( relation(set_intersection2(sK11,iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_1151,c_4107]) ).
tcf(c_9936,plain,
( relation(set_intersection2(sK11,empty_set))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_9932,c_6184]) ).
tcf(c_9937,plain,
relation(set_intersection2(sK11,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_9936,c_73]) ).
tcf(c_9938,plain,
( relation(set_intersection2(sK11,sK12))
| ~ empty(iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_9930,c_1149]) ).
tcf(c_9939,plain,
! [X0: $i] :
( relation(set_intersection2(sK11,X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9928,c_1884]) ).
tcf(c_9972,plain,
! [X0: $i] :
( relation(set_intersection2(X0,sK11))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_52,c_9939]) ).
tcf(c_9974,plain,
( relation(sK11)
| ~ empty(identity_relation(sK11)) ),
inference(superposition,[status(thm)],[c_80,c_9939]) ).
tcf(c_9976,plain,
( relation(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_6133,c_9939]) ).
tcf(c_9991,plain,
( relation(iPr_def_13)
| ~ empty(identity_relation(sK12)) ),
inference(superposition,[status(thm)],[c_1150,c_9972]) ).
tcf(c_9992,plain,
( relation(iPr_def_13)
| ~ empty(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_9991,c_1147]) ).
tcf(c_9999,plain,
! [X0: $i] :
( empty(set_intersection2(sK11,X0))
| ~ relation(iPr_def_11)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_4108]) ).
tcf(c_10001,plain,
( empty(set_intersection2(sK11,sK12))
| ~ empty(relation_composition(iPr_def_10,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_1147,c_4108]) ).
tcf(c_10003,plain,
( empty(set_intersection2(sK11,empty_set))
| ~ empty(relation_composition(empty_set,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_2472,c_4108]) ).
tcf(c_10004,plain,
( empty(set_intersection2(sK11,iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_1151,c_4108]) ).
tcf(c_10007,plain,
( empty(set_intersection2(sK11,empty_set))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_10003,c_6184]) ).
tcf(c_10008,plain,
empty(set_intersection2(sK11,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_10007,c_73]) ).
tcf(c_10009,plain,
( empty(set_intersection2(sK11,sK12))
| ~ empty(iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_10001,c_1149]) ).
tcf(c_10010,plain,
! [X0: $i] :
( empty(set_intersection2(sK11,X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9999,c_1884]) ).
tcf(c_10033,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK11))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_52,c_10010]) ).
tcf(c_10035,plain,
( empty(sK11)
| ~ empty(identity_relation(sK11)) ),
inference(superposition,[status(thm)],[c_80,c_10010]) ).
tcf(c_10037,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_6133,c_10010]) ).
tcf(c_10038,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK11,X0) = X1 )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_110]) ).
tcf(c_10039,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(set_intersection2(sK11,X0)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_4060]) ).
tcf(c_10040,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(set_intersection2(sK11,X0)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_4059]) ).
tcf(c_10041,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(sK11,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_4011]) ).
tcf(c_10042,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(sK11,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_4010]) ).
tcf(c_10043,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(sK11,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_3938]) ).
tcf(c_10044,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(sK11,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_3937]) ).
tcf(c_10045,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(set_intersection2(sK11,X0),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_3179]) ).
tcf(c_10046,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(set_intersection2(sK11,X0),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_3178]) ).
tcf(c_10047,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(sK11,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_3083]) ).
tcf(c_10048,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(sK11,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_3082]) ).
tcf(c_10049,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(sK11,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_2687]) ).
tcf(c_10050,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(sK11,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_2686]) ).
tcf(c_10051,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(sK11,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_2658]) ).
tcf(c_10052,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(sK11,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_2637]) ).
tcf(c_10053,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(sK11,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_3939]) ).
tcf(c_10054,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(sK11,X0),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_3180]) ).
tcf(c_10055,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(sK11,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_3084]) ).
tcf(c_10056,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(sK11,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_2474]) ).
tcf(c_10057,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(sK11,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_2473]) ).
tcf(c_10058,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(sK11,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_2055]) ).
tcf(c_10059,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(sK11,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_2184]) ).
tcf(c_10060,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(sK11,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_2013]) ).
tcf(c_10061,plain,
! [X0: $i] :
( ( set_intersection2(sK11,X0) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_108]) ).
tcf(c_10239,plain,
( empty(iPr_def_13)
| ~ empty(identity_relation(sK12)) ),
inference(superposition,[status(thm)],[c_1150,c_10033]) ).
tcf(c_10240,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,sK11) = X1 )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_110]) ).
tcf(c_10241,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X0,sK11)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_4060]) ).
tcf(c_10242,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X0,sK11)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_4059]) ).
tcf(c_10243,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(X0,sK11))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_4011]) ).
tcf(c_10244,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(X0,sK11))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_4010]) ).
tcf(c_10245,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(X0,sK11)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_3938]) ).
tcf(c_10246,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(X0,sK11)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_3937]) ).
tcf(c_10247,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(set_intersection2(X0,sK11),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_3179]) ).
tcf(c_10248,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(set_intersection2(X0,sK11),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_3178]) ).
tcf(c_10249,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(X0,sK11))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_3083]) ).
tcf(c_10250,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(X0,sK11))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_3082]) ).
tcf(c_10251,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(X0,sK11)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_2687]) ).
tcf(c_10252,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(X0,sK11)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_2686]) ).
tcf(c_10253,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(X0,sK11)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_2658]) ).
tcf(c_10254,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(X0,sK11)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_2637]) ).
tcf(c_10255,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(X0,sK11))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_3939]) ).
tcf(c_10256,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,sK11),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_3180]) ).
tcf(c_10257,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(X0,sK11)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_3084]) ).
tcf(c_10258,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,sK11))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_2474]) ).
tcf(c_10259,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,sK11))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_2473]) ).
tcf(c_10260,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,sK11))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_2055]) ).
tcf(c_10261,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,sK11)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_2184]) ).
tcf(c_10262,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,sK11)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_2013]) ).
tcf(c_10263,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK11) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_108]) ).
tcf(c_10266,plain,
( empty(iPr_def_13)
| ~ empty(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_10239,c_1147]) ).
tcf(c_10440,plain,
! [X0: $i] :
( function(set_intersection2(sK12,X0))
| ~ relation(iPr_def_10)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_4464]) ).
tcf(c_10444,plain,
( function(set_intersection2(sK12,empty_set))
| ~ empty(relation_composition(empty_set,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_2472,c_4464]) ).
tcf(c_10445,plain,
( function(set_intersection2(sK12,iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1151,c_4464]) ).
tcf(c_10448,plain,
( function(set_intersection2(sK12,empty_set))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_10444,c_6071]) ).
tcf(c_10449,plain,
function(set_intersection2(sK12,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_10448,c_73]) ).
tcf(c_10450,plain,
! [X0: $i] :
( function(set_intersection2(sK12,X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10440,c_1881]) ).
tcf(c_10465,plain,
! [X0: $i] :
( function(set_intersection2(X0,sK12))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_52,c_10450]) ).
tcf(c_10467,plain,
( function(sK12)
| ~ empty(identity_relation(sK12)) ),
inference(superposition,[status(thm)],[c_80,c_10450]) ).
tcf(c_10469,plain,
( function(iPr_def_13)
| ~ empty(identity_relation(sK11)) ),
inference(superposition,[status(thm)],[c_1150,c_10450]) ).
tcf(c_10470,plain,
( function(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_6018,c_10450]) ).
tcf(c_10471,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),set_intersection2(sK12,X0))) = set_intersection2(relation_dom(set_intersection2(sK12,X0)),X1) )
| ~ empty(identity_relation(X0))
| ~ relation(set_intersection2(sK12,X0)) ),
inference(superposition,[status(thm)],[c_10450,c_103]) ).
tcf(c_10472,plain,
( function(iPr_def_13)
| ~ empty(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_10469,c_1148]) ).
tcf(c_10491,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),set_intersection2(X0,sK12))) = set_intersection2(relation_dom(set_intersection2(X0,sK12)),X1) )
| ~ empty(identity_relation(X0))
| ~ relation(set_intersection2(X0,sK12)) ),
inference(superposition,[status(thm)],[c_10465,c_103]) ).
tcf(c_10501,plain,
! [X0: $i] :
( relation(set_intersection2(sK12,X0))
| ~ relation(iPr_def_10)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_4465]) ).
tcf(c_10505,plain,
( relation(set_intersection2(sK12,empty_set))
| ~ empty(relation_composition(empty_set,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_2472,c_4465]) ).
tcf(c_10506,plain,
( relation(set_intersection2(sK12,iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1151,c_4465]) ).
tcf(c_10509,plain,
( relation(set_intersection2(sK12,empty_set))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_10505,c_6071]) ).
tcf(c_10510,plain,
relation(set_intersection2(sK12,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_10509,c_73]) ).
tcf(c_10511,plain,
! [X0: $i] :
( relation(set_intersection2(sK12,X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10501,c_1881]) ).
tcf(c_10520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X0,X1,set_intersection2(X3,X2)),X3)
| in(sK0(X0,X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_52,c_2241]) ).
tcf(c_10522,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,X0),X0)
| in(sK0(X1,X2,set_intersection2(X0,X0)),X1)
| ( set_intersection2(X0,X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_80,c_2241]) ).
tcf(c_10524,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,empty_set),X2)
| in(sK0(X0,X1,set_intersection2(empty_set,X2)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_1996,c_2241]) ).
tcf(c_10525,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,iPr_def_13),sK11)
| in(sK0(X0,X1,set_intersection2(sK12,sK11)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(sK12,sK11) ) ),
inference(superposition,[status(thm)],[c_1150,c_2241]) ).
tcf(c_10526,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,set_intersection2(sK12,relation_dom(sK2))),X0)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_10,sK2))),relation_dom(sK2))
| ( set_intersection2(sK12,relation_dom(sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_6018,c_2241]) ).
tcf(c_10527,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,set_intersection2(sK11,relation_dom(sK2))),X0)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_11,sK2))),relation_dom(sK2))
| ( set_intersection2(sK11,relation_dom(sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_6133,c_2241]) ).
tcf(c_10528,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,set_intersection2(iPr_def_13,relation_dom(sK2))),X0)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_14,sK2))),relation_dom(sK2))
| ( set_intersection2(iPr_def_13,relation_dom(sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_6817,c_2241]) ).
tcf(c_10529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X0,X1,set_intersection2(X3,X2)),X0)
| in(sK0(X0,X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_52,c_2241]) ).
tcf(c_10531,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,X0),X1)
| in(sK0(X1,X2,set_intersection2(X0,X0)),X0)
| ( set_intersection2(X0,X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_80,c_2241]) ).
tcf(c_10532,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,empty_set),X0)
| in(sK0(X0,X1,set_intersection2(X2,empty_set)),empty_set)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_97,c_2241]) ).
tcf(c_10533,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,empty_set),X0)
| in(sK0(X0,X1,set_intersection2(empty_set,X2)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_1996,c_2241]) ).
tcf(c_10534,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,iPr_def_13),X0)
| in(sK0(X0,X1,set_intersection2(sK12,sK11)),sK11)
| ( set_intersection2(X0,X1) = set_intersection2(sK12,sK11) ) ),
inference(superposition,[status(thm)],[c_1150,c_2241]) ).
tcf(c_10535,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_10,sK2))),X0)
| in(sK0(X0,X1,set_intersection2(sK12,relation_dom(sK2))),relation_dom(sK2))
| ( set_intersection2(sK12,relation_dom(sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_6018,c_2241]) ).
tcf(c_10536,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_11,sK2))),X0)
| in(sK0(X0,X1,set_intersection2(sK11,relation_dom(sK2))),relation_dom(sK2))
| ( set_intersection2(sK11,relation_dom(sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_6133,c_2241]) ).
tcf(c_10537,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_14,sK2))),X0)
| in(sK0(X0,X1,set_intersection2(iPr_def_13,relation_dom(sK2))),relation_dom(sK2))
| ( set_intersection2(iPr_def_13,relation_dom(sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_6817,c_2241]) ).
tcf(c_10538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X1,X2,set_intersection2(X3,X0)),X1)
| ( set_intersection2(X1,X2) = set_intersection2(X3,X0) )
| ( apply(identity_relation(X0),sK0(X1,X2,set_intersection2(X3,X0))) = sK0(X1,X2,set_intersection2(X3,X0)) ) ),
inference(superposition,[status(thm)],[c_2241,c_172]) ).
tcf(c_10539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X1,X2,set_intersection2(X3,X0)),X1)
| ( set_intersection2(X1,X2) = set_intersection2(X3,X0) )
| ~ in(X0,sK0(X1,X2,set_intersection2(X3,X0))) ),
inference(superposition,[status(thm)],[c_2241,c_49]) ).
tcf(c_10540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,set_intersection2(X1,X0)),X2)
| ( set_intersection2(X1,X0) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2241,c_109]) ).
tcf(c_10541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK0(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK0(X0,X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_2241,c_95]) ).
tcf(c_10543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK0(X3,X4,set_intersection2(X0,set_intersection2(X1,X2))),X3)
| in(sK0(X3,X4,set_intersection2(X0,set_intersection2(X1,X2))),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_2241,c_58]) ).
tcf(c_10544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK0(X3,X4,set_intersection2(X0,set_intersection2(X1,X2))),X3)
| in(sK0(X3,X4,set_intersection2(X0,set_intersection2(X1,X2))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_2241,c_57]) ).
tcf(c_10545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK0(X2,X3,set_intersection2(X4,relation_dom(relation_composition(X0,X1)))),X2)
| ( set_intersection2(X4,relation_dom(relation_composition(X0,X1))) = set_intersection2(X2,X3) )
| ( apply(relation_composition(X0,X1),sK0(X2,X3,set_intersection2(X4,relation_dom(relation_composition(X0,X1))))) = apply(X1,apply(X0,sK0(X2,X3,set_intersection2(X4,relation_dom(relation_composition(X0,X1)))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_2241,c_96]) ).
tcf(c_10546,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,set_intersection2(X2,empty_set)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_2241,c_5671]) ).
tcf(c_10547,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,set_intersection2(X2,iPr_def_13)),sK11)
| in(sK0(X0,X1,set_intersection2(X2,iPr_def_13)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_2241,c_2102]) ).
tcf(c_10548,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,set_intersection2(X2,iPr_def_13)),sK12)
| in(sK0(X0,X1,set_intersection2(X2,iPr_def_13)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_2241,c_2071]) ).
tcf(c_10549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,set_intersection2(X1,sK1(powerset(X0)))),X2)
| ( set_intersection2(X1,sK1(powerset(X0))) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2241,c_2933]) ).
tcf(c_10550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK0(X2,X3,set_intersection2(X0,sK1(powerset(X1)))),X1)
| in(sK0(X2,X3,set_intersection2(X0,sK1(powerset(X1)))),X2)
| ( set_intersection2(X0,sK1(powerset(X1))) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_2241,c_2582]) ).
tcf(c_10551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| element(sK0(X2,X3,set_intersection2(X0,sK4(X1))),X1)
| in(sK0(X2,X3,set_intersection2(X0,sK4(X1))),X2)
| ( set_intersection2(X0,sK4(X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_2241,c_2583]) ).
tcf(c_10552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X0,X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ( apply(identity_relation(X0),sK0(X0,X1,set_intersection2(X2,X3))) = sK0(X0,X1,set_intersection2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_2241,c_172]) ).
tcf(c_10553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X0,X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ~ in(X0,sK0(X0,X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_2241,c_49]) ).
tcf(c_10554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X0,X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2241,c_109]) ).
tcf(c_10555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK0(X0,X1,set_intersection2(X2,X3)),X0)
| in(sK0(X0,X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_2241,c_95]) ).
tcf(c_10556,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X0,set_intersection2(X1,X2)),X2)
| ( set_intersection2(X0,X0) = set_intersection2(X1,X2) )
| ~ in(sK0(X0,X0,set_intersection2(X1,X2)),X0)
| ~ in(sK0(X0,X0,set_intersection2(X1,X2)),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_2241,c_53]) ).
tcf(c_10557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK0(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X4)
| in(sK0(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_2241,c_58]) ).
tcf(c_10558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK0(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X4)
| in(sK0(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_2241,c_57]) ).
tcf(c_10559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK0(relation_dom(relation_composition(X0,X1)),X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(relation_dom(relation_composition(X0,X1)),X2) = set_intersection2(X3,X4) )
| ( apply(relation_composition(X0,X1),sK0(relation_dom(relation_composition(X0,X1)),X2,set_intersection2(X3,X4))) = apply(X1,apply(X0,sK0(relation_dom(relation_composition(X0,X1)),X2,set_intersection2(X3,X4)))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_2241,c_96]) ).
tcf(c_10560,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(empty_set,X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_5671]) ).
tcf(c_10561,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(iPr_def_13,X2,set_intersection2(X0,X1)),sK11)
| in(sK0(iPr_def_13,X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(iPr_def_13,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_2102]) ).
tcf(c_10562,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(iPr_def_13,X2,set_intersection2(X0,X1)),sK12)
| in(sK0(iPr_def_13,X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(iPr_def_13,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_2071]) ).
tcf(c_10563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(sK1(powerset(X0)),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(sK1(powerset(X0)),X1) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2241,c_2933]) ).
tcf(c_10564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK0(sK1(powerset(X0)),X1,set_intersection2(X2,X3)),X0)
| in(sK0(sK1(powerset(X0)),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(sK1(powerset(X0)),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_2241,c_2582]) ).
tcf(c_10565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X0)
| element(sK0(sK4(X0),X1,set_intersection2(X2,X3)),X0)
| in(sK0(sK4(X0),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(sK4(X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_2241,c_2583]) ).
tcf(c_10566,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X1,X2) ) ),
inference(equality_factoring,[status(thm)],[c_2241]) ).
tcf(c_10584,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,empty_set),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10532,c_5671]) ).
tcf(c_10629,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_14,sK2))),X0)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_14,sK2))),relation_dom(sK2))
| ( relation_dom(relation_composition(iPr_def_14,sK2)) = set_intersection2(X0,X1) ) ),
inference(light_normalisation,[status(thm)],[c_10537,c_6817]) ).
tcf(c_10633,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_11,sK2))),X0)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_11,sK2))),relation_dom(sK2))
| ( relation_dom(relation_composition(iPr_def_11,sK2)) = set_intersection2(X0,X1) ) ),
inference(light_normalisation,[status(thm)],[c_10536,c_6133]) ).
tcf(c_10637,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_10,sK2))),X0)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_10,sK2))),relation_dom(sK2))
| ( relation_dom(relation_composition(iPr_def_10,sK2)) = set_intersection2(X0,X1) ) ),
inference(light_normalisation,[status(thm)],[c_10535,c_6018]) ).
tcf(c_10676,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X0,set_intersection2(X1,X2)),X2)
| ( set_intersection2(X1,X2) = X0 )
| ~ in(sK0(X0,X0,set_intersection2(X1,X2)),X0)
| ~ in(sK0(X0,X0,set_intersection2(X1,X2)),set_intersection2(X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_10556,c_80]) ).
tcf(c_10958,plain,
! [X0: $i] :
( relation(set_intersection2(X0,sK12))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_52,c_10511]) ).
tcf(c_10960,plain,
( relation(sK12)
| ~ empty(identity_relation(sK12)) ),
inference(superposition,[status(thm)],[c_80,c_10511]) ).
tcf(c_10962,plain,
( relation(iPr_def_13)
| ~ empty(identity_relation(sK11)) ),
inference(superposition,[status(thm)],[c_1150,c_10511]) ).
tcf(c_10963,plain,
( relation(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_6018,c_10511]) ).
tcf(c_10964,plain,
( relation(iPr_def_13)
| ~ empty(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_10962,c_1148]) ).
tcf(c_10984,plain,
! [X0: $i] :
( empty(set_intersection2(sK12,X0))
| ~ relation(iPr_def_10)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_4466]) ).
tcf(c_10988,plain,
( empty(set_intersection2(sK12,empty_set))
| ~ empty(relation_composition(empty_set,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_2472,c_4466]) ).
tcf(c_10989,plain,
( empty(set_intersection2(sK12,iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1151,c_4466]) ).
tcf(c_10992,plain,
( empty(set_intersection2(sK12,empty_set))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_10988,c_6071]) ).
tcf(c_10993,plain,
empty(set_intersection2(sK12,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_10992,c_73]) ).
tcf(c_10994,plain,
! [X0: $i] :
( empty(set_intersection2(sK12,X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10984,c_1881]) ).
tcf(c_11003,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK12))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_52,c_10994]) ).
tcf(c_11005,plain,
( empty(sK12)
| ~ empty(identity_relation(sK12)) ),
inference(superposition,[status(thm)],[c_80,c_10994]) ).
tcf(c_11007,plain,
( empty(iPr_def_13)
| ~ empty(identity_relation(sK11)) ),
inference(superposition,[status(thm)],[c_1150,c_10994]) ).
tcf(c_11008,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_6018,c_10994]) ).
tcf(c_11009,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK12,X0) = X1 )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_110]) ).
tcf(c_11010,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(set_intersection2(sK12,X0)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_4060]) ).
tcf(c_11011,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(set_intersection2(sK12,X0)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_4059]) ).
tcf(c_11012,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(sK12,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_4011]) ).
tcf(c_11013,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(sK12,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_4010]) ).
tcf(c_11014,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(sK12,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_3938]) ).
tcf(c_11015,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(sK12,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_3937]) ).
tcf(c_11016,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(set_intersection2(sK12,X0),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_3179]) ).
tcf(c_11017,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(set_intersection2(sK12,X0),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_3178]) ).
tcf(c_11018,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(sK12,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_3083]) ).
tcf(c_11019,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(sK12,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_3082]) ).
tcf(c_11020,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(sK12,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_2687]) ).
tcf(c_11021,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(sK12,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_2686]) ).
tcf(c_11022,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(sK12,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_2658]) ).
tcf(c_11023,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(sK12,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_2637]) ).
tcf(c_11024,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(sK12,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_3939]) ).
tcf(c_11025,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(sK12,X0),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_3180]) ).
tcf(c_11026,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(sK12,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_3084]) ).
tcf(c_11027,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(sK12,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_2474]) ).
tcf(c_11028,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(sK12,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_2473]) ).
tcf(c_11029,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(sK12,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_2055]) ).
tcf(c_11030,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(sK12,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_2184]) ).
tcf(c_11031,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(sK12,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_2013]) ).
tcf(c_11032,plain,
! [X0: $i] :
( ( set_intersection2(sK12,X0) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_108]) ).
tcf(c_11035,plain,
( empty(iPr_def_13)
| ~ empty(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_11007,c_1148]) ).
tcf(c_11171,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,sK12) = X1 )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_110]) ).
tcf(c_11172,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X0,sK12)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_4060]) ).
tcf(c_11173,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X0,sK12)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_4059]) ).
tcf(c_11174,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(X0,sK12))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_4011]) ).
tcf(c_11175,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(X0,sK12))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_4010]) ).
tcf(c_11176,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(X0,sK12)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_3938]) ).
tcf(c_11177,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(X0,sK12)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_3937]) ).
tcf(c_11178,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(set_intersection2(X0,sK12),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_3179]) ).
tcf(c_11179,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(set_intersection2(X0,sK12),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_3178]) ).
tcf(c_11180,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(X0,sK12))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_3083]) ).
tcf(c_11181,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(X0,sK12))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_3082]) ).
tcf(c_11182,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(X0,sK12)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_2687]) ).
tcf(c_11183,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(X0,sK12)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_2686]) ).
tcf(c_11184,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(X0,sK12)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_2658]) ).
tcf(c_11185,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(X0,sK12)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_2637]) ).
tcf(c_11186,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(X0,sK12))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_3939]) ).
tcf(c_11187,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,sK12),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_3180]) ).
tcf(c_11188,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(X0,sK12)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_3084]) ).
tcf(c_11189,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,sK12))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_2474]) ).
tcf(c_11190,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,sK12))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_2473]) ).
tcf(c_11191,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,sK12))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_2055]) ).
tcf(c_11192,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,sK12)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_2184]) ).
tcf(c_11193,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,sK12)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_2013]) ).
tcf(c_11194,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK12) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_108]) ).
tcf(c_11306,plain,
! [X0: $i] :
( function(set_intersection2(iPr_def_13,X0))
| ~ relation(iPr_def_12)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_5423]) ).
tcf(c_11310,plain,
( function(set_intersection2(iPr_def_13,empty_set))
| ~ empty(relation_composition(empty_set,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_2472,c_5423]) ).
tcf(c_11319,plain,
! [X0: $i] :
( relation(set_intersection2(iPr_def_13,X0))
| ~ relation(iPr_def_12)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_5424]) ).
tcf(c_11323,plain,
( relation(set_intersection2(iPr_def_13,empty_set))
| ~ empty(relation_composition(empty_set,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_2472,c_5424]) ).
tcf(c_11332,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ~ relation(iPr_def_12)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_5425]) ).
tcf(c_11336,plain,
( empty(set_intersection2(iPr_def_13,empty_set))
| ~ empty(relation_composition(empty_set,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_2472,c_5425]) ).
tcf(c_11345,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_5629]) ).
tcf(c_11346,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_5629]) ).
tcf(c_11347,plain,
sK1(powerset(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_5629]) ).
tcf(c_11348,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_5629]) ).
tcf(c_11349,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_5629]) ).
tcf(c_11350,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_5629]) ).
tcf(c_11351,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_5629]) ).
tcf(c_11352,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_5629]) ).
tcf(c_11353,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(X0,iPr_def_13)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_5629]) ).
tcf(c_11354,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(iPr_def_13,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_5629]) ).
tcf(c_11355,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(X1,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_5629]) ).
tcf(c_11356,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(sK11,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_5629]) ).
tcf(c_11357,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(sK12,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_5629]) ).
tcf(c_11358,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(sK1(powerset(X0)),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_5629]) ).
tcf(c_11359,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_5629]) ).
tcf(c_11360,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_5629]) ).
tcf(c_11361,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_5629]) ).
tcf(c_11362,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(X0,sK12)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_5629]) ).
tcf(c_11363,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(X0,sK11)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_5629]) ).
tcf(c_11508,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_5630]) ).
tcf(c_11509,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_5630]) ).
tcf(c_11510,plain,
sK1(powerset(identity_relation(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_5630]) ).
tcf(c_11511,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_5630]) ).
tcf(c_11512,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_5630]) ).
tcf(c_11513,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_5630]) ).
tcf(c_11514,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_5630]) ).
tcf(c_11515,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_5630]) ).
tcf(c_11516,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(X0,iPr_def_13)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_5630]) ).
tcf(c_11517,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(iPr_def_13,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_5630]) ).
tcf(c_11518,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(X1,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_5630]) ).
tcf(c_11519,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(sK11,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_5630]) ).
tcf(c_11520,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(sK12,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_5630]) ).
tcf(c_11521,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(sK1(powerset(X0)),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_5630]) ).
tcf(c_11522,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_5630]) ).
tcf(c_11523,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_5630]) ).
tcf(c_11524,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_5630]) ).
tcf(c_11525,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(X0,sK12)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_5630]) ).
tcf(c_11526,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(X0,sK11)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_5630]) ).
tcf(c_11616,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( apply(identity_relation(X0),sK0(empty_set,X1,X0)) = sK0(empty_set,X1,X0) ) ),
inference(superposition,[status(thm)],[c_5683,c_172]) ).
tcf(c_11617,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK0(empty_set,X1,X0)) ),
inference(superposition,[status(thm)],[c_5683,c_49]) ).
tcf(c_11620,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( set_intersection2(empty_set,X0) = X0 )
| ~ in(sK0(empty_set,X0,X0),empty_set)
| ~ in(sK0(empty_set,X0,X0),X0) ),
inference(superposition,[status(thm)],[c_5683,c_53]) ).
tcf(c_11621,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(empty_set,X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5683,c_58]) ).
tcf(c_11622,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(empty_set,X2,set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5683,c_57]) ).
tcf(c_11623,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(X0,X1)) = empty_set )
| ( apply(relation_composition(X0,X1),sK0(empty_set,X2,relation_dom(relation_composition(X0,X1)))) = apply(X1,apply(X0,sK0(empty_set,X2,relation_dom(relation_composition(X0,X1))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_5683,c_96]) ).
tcf(c_11625,plain,
! [X0: $i] :
( in(sK0(empty_set,X0,iPr_def_13),sK11)
| ( empty_set = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_5683,c_2102]) ).
tcf(c_11626,plain,
! [X0: $i] :
( in(sK0(empty_set,X0,iPr_def_13),sK12)
| ( empty_set = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_5683,c_2071]) ).
tcf(c_11628,plain,
! [X0: $i,X1: $i] :
( element(sK0(empty_set,X1,sK1(powerset(X0))),X0)
| ( sK1(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5683,c_2582]) ).
tcf(c_11629,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(sK0(empty_set,X1,sK4(X0)),X0)
| ( sK4(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_5683,c_2583]) ).
tcf(c_11647,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ in(sK0(empty_set,X0,X0),empty_set)
| ~ in(sK0(empty_set,X0,X0),X0) ),
inference(light_normalisation,[status(thm)],[c_11620,c_1996]) ).
tcf(c_11677,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( apply(identity_relation(X0),sK0(X1,empty_set,X0)) = sK0(X1,empty_set,X0) ) ),
inference(superposition,[status(thm)],[c_5686,c_172]) ).
tcf(c_11678,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK0(X1,empty_set,X0)) ),
inference(superposition,[status(thm)],[c_5686,c_49]) ).
tcf(c_11680,plain,
! [X0: $i,X1: $i] :
( element(sK0(X1,empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_5686,c_95]) ).
tcf(c_11682,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X2,empty_set,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5686,c_58]) ).
tcf(c_11683,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X2,empty_set,set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5686,c_57]) ).
tcf(c_11684,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(X0,X1)) = empty_set )
| ( apply(relation_composition(X0,X1),sK0(X2,empty_set,relation_dom(relation_composition(X0,X1)))) = apply(X1,apply(X0,sK0(X2,empty_set,relation_dom(relation_composition(X0,X1))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_5686,c_96]) ).
tcf(c_11686,plain,
! [X0: $i] :
( in(sK0(X0,empty_set,iPr_def_13),sK11)
| ( empty_set = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_5686,c_2102]) ).
tcf(c_11687,plain,
! [X0: $i] :
( in(sK0(X0,empty_set,iPr_def_13),sK12)
| ( empty_set = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_5686,c_2071]) ).
tcf(c_11689,plain,
! [X0: $i,X1: $i] :
( element(sK0(X1,empty_set,sK1(powerset(X0))),X0)
| ( sK1(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5686,c_2582]) ).
tcf(c_11690,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(sK0(X1,empty_set,sK4(X0)),X0)
| ( sK4(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_5686,c_2583]) ).
tcf(c_11784,plain,
! [X0: $i] :
( ( empty_set = sK12 )
| ( apply(iPr_def_10,sK0(empty_set,X0,sK12)) = sK0(empty_set,X0,sK12) ) ),
inference(superposition,[status(thm)],[c_1147,c_11616]) ).
tcf(c_11785,plain,
! [X0: $i] :
( ( empty_set = sK11 )
| ( apply(iPr_def_11,sK0(empty_set,X0,sK11)) = sK0(empty_set,X0,sK11) ) ),
inference(superposition,[status(thm)],[c_1148,c_11616]) ).
tcf(c_11787,plain,
! [X0: $i] :
( ( empty_set = iPr_def_13 )
| ( apply(iPr_def_14,sK0(empty_set,X0,iPr_def_13)) = sK0(empty_set,X0,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_1151,c_11616]) ).
tcf(c_11811,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,relation_dom(relation_composition(iPr_def_10,sK2)),X1),sK12)
| in(sK0(X0,relation_dom(relation_composition(iPr_def_10,sK2)),X1),X1)
| ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))) = X1 ) ),
inference(superposition,[status(thm)],[c_55,c_6029]) ).
tcf(c_11812,plain,
! [X0: $i,X1: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_10,sK2)),X0,X1),sK12)
| element(sK0(relation_dom(relation_composition(iPr_def_10,sK2)),X0,X1),X1)
| ( set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_2239,c_6029]) ).
tcf(c_11813,plain,
! [X0: $i,X1: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_10,sK2)),X0,X1),sK12)
| in(sK0(relation_dom(relation_composition(iPr_def_10,sK2)),X0,X1),X1)
| ( set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_54,c_6029]) ).
tcf(c_11814,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_10,sK2))),sK12)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_10,sK2))),X1)
| ( relation_dom(relation_composition(iPr_def_10,sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_55,c_6029]) ).
tcf(c_11815,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_10,sK2))),sK12)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_10,sK2))),X0)
| ( relation_dom(relation_composition(iPr_def_10,sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_54,c_6029]) ).
tcf(c_11816,plain,
( in(sK10(relation_dom(relation_composition(iPr_def_10,sK2)),relation_composition(iPr_def_10,sK2)),sK12)
| ( identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))) = relation_composition(iPr_def_10,sK2) )
| ~ relation(relation_composition(iPr_def_10,sK2))
| ~ function(relation_composition(iPr_def_10,sK2)) ),
inference(superposition,[status(thm)],[c_100,c_6029]) ).
tcf(c_11818,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))
| in(sK1(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))),sK12) ),
inference(superposition,[status(thm)],[c_2201,c_6029]) ).
tcf(c_11819,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))
| in(sK1(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0)),sK12) ),
inference(superposition,[status(thm)],[c_2732,c_6029]) ).
tcf(c_11820,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))
| in(sK1(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0)),sK12) ),
inference(superposition,[status(thm)],[c_2202,c_6029]) ).
tcf(c_11821,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_10,sK2)),X0,set_intersection2(X1,X2)),sK12)
| in(sK0(relation_dom(relation_composition(iPr_def_10,sK2)),X0,set_intersection2(X1,X2)),X2)
| ( set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_6029]) ).
tcf(c_11822,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))),sK12)
| in(sK0(X1,X2,set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))),X1)
| ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_6029]) ).
tcf(c_11823,plain,
! [X0: $i] :
( in(sK0(empty_set,X0,relation_dom(relation_composition(iPr_def_10,sK2))),sK12)
| ( relation_dom(relation_composition(iPr_def_10,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5683,c_6029]) ).
tcf(c_11824,plain,
! [X0: $i] :
( in(sK0(X0,empty_set,relation_dom(relation_composition(iPr_def_10,sK2))),sK12)
| ( relation_dom(relation_composition(iPr_def_10,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5686,c_6029]) ).
tcf(c_11967,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,relation_dom(relation_composition(iPr_def_11,sK2)),X1),sK11)
| in(sK0(X0,relation_dom(relation_composition(iPr_def_11,sK2)),X1),X1)
| ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))) = X1 ) ),
inference(superposition,[status(thm)],[c_55,c_6144]) ).
tcf(c_11968,plain,
! [X0: $i,X1: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_11,sK2)),X0,X1),sK11)
| element(sK0(relation_dom(relation_composition(iPr_def_11,sK2)),X0,X1),X1)
| ( set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_2239,c_6144]) ).
tcf(c_11969,plain,
! [X0: $i,X1: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_11,sK2)),X0,X1),sK11)
| in(sK0(relation_dom(relation_composition(iPr_def_11,sK2)),X0,X1),X1)
| ( set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_54,c_6144]) ).
tcf(c_11970,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_11,sK2))),sK11)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_11,sK2))),X1)
| ( relation_dom(relation_composition(iPr_def_11,sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_55,c_6144]) ).
tcf(c_11971,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_11,sK2))),sK11)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_11,sK2))),X0)
| ( relation_dom(relation_composition(iPr_def_11,sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_54,c_6144]) ).
tcf(c_11972,plain,
( in(sK10(relation_dom(relation_composition(iPr_def_11,sK2)),relation_composition(iPr_def_11,sK2)),sK11)
| ( identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))) = relation_composition(iPr_def_11,sK2) )
| ~ relation(relation_composition(iPr_def_11,sK2))
| ~ function(relation_composition(iPr_def_11,sK2)) ),
inference(superposition,[status(thm)],[c_100,c_6144]) ).
tcf(c_11974,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))
| in(sK1(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))),sK11) ),
inference(superposition,[status(thm)],[c_2201,c_6144]) ).
tcf(c_11975,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))
| in(sK1(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0)),sK11) ),
inference(superposition,[status(thm)],[c_2732,c_6144]) ).
tcf(c_11976,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))
| in(sK1(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0)),sK11) ),
inference(superposition,[status(thm)],[c_2202,c_6144]) ).
tcf(c_11977,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_11,sK2)),X0,set_intersection2(X1,X2)),sK11)
| in(sK0(relation_dom(relation_composition(iPr_def_11,sK2)),X0,set_intersection2(X1,X2)),X2)
| ( set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_6144]) ).
tcf(c_11978,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))),sK11)
| in(sK0(X1,X2,set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))),X1)
| ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_6144]) ).
tcf(c_11979,plain,
! [X0: $i] :
( in(sK0(empty_set,X0,relation_dom(relation_composition(iPr_def_11,sK2))),sK11)
| ( relation_dom(relation_composition(iPr_def_11,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5683,c_6144]) ).
tcf(c_11980,plain,
! [X0: $i] :
( in(sK0(X0,empty_set,relation_dom(relation_composition(iPr_def_11,sK2))),sK11)
| ( relation_dom(relation_composition(iPr_def_11,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5686,c_6144]) ).
tcf(c_12040,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,relation_dom(relation_composition(iPr_def_14,sK2)),X1),iPr_def_13)
| in(sK0(X0,relation_dom(relation_composition(iPr_def_14,sK2)),X1),X1)
| ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))) = X1 ) ),
inference(superposition,[status(thm)],[c_55,c_6828]) ).
tcf(c_12041,plain,
! [X0: $i,X1: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_14,sK2)),X0,X1),iPr_def_13)
| element(sK0(relation_dom(relation_composition(iPr_def_14,sK2)),X0,X1),X1)
| ( set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_2239,c_6828]) ).
tcf(c_12042,plain,
! [X0: $i,X1: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_14,sK2)),X0,X1),iPr_def_13)
| in(sK0(relation_dom(relation_composition(iPr_def_14,sK2)),X0,X1),X1)
| ( set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_54,c_6828]) ).
tcf(c_12043,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_14,sK2))),iPr_def_13)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_14,sK2))),X1)
| ( relation_dom(relation_composition(iPr_def_14,sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_55,c_6828]) ).
tcf(c_12044,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_14,sK2))),iPr_def_13)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_14,sK2))),X0)
| ( relation_dom(relation_composition(iPr_def_14,sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_54,c_6828]) ).
tcf(c_12045,plain,
( in(sK10(relation_dom(relation_composition(iPr_def_14,sK2)),relation_composition(iPr_def_14,sK2)),iPr_def_13)
| ( identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))) = relation_composition(iPr_def_14,sK2) )
| ~ relation(relation_composition(iPr_def_14,sK2))
| ~ function(relation_composition(iPr_def_14,sK2)) ),
inference(superposition,[status(thm)],[c_100,c_6828]) ).
tcf(c_12047,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))
| in(sK1(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_2201,c_6828]) ).
tcf(c_12048,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))
| in(sK1(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0)),iPr_def_13) ),
inference(superposition,[status(thm)],[c_2732,c_6828]) ).
tcf(c_12049,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))
| in(sK1(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0)),iPr_def_13) ),
inference(superposition,[status(thm)],[c_2202,c_6828]) ).
tcf(c_12050,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_14,sK2)),X0,set_intersection2(X1,X2)),iPr_def_13)
| in(sK0(relation_dom(relation_composition(iPr_def_14,sK2)),X0,set_intersection2(X1,X2)),X2)
| ( set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_6828]) ).
tcf(c_12051,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))),iPr_def_13)
| in(sK0(X1,X2,set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))),X1)
| ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_6828]) ).
tcf(c_12052,plain,
! [X0: $i] :
( in(sK0(empty_set,X0,relation_dom(relation_composition(iPr_def_14,sK2))),iPr_def_13)
| ( relation_dom(relation_composition(iPr_def_14,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5683,c_6828]) ).
tcf(c_12053,plain,
! [X0: $i] :
( in(sK0(X0,empty_set,relation_dom(relation_composition(iPr_def_14,sK2))),iPr_def_13)
| ( relation_dom(relation_composition(iPr_def_14,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5686,c_6828]) ).
tcf(c_12151,plain,
! [X0: $i] :
( relation(set_intersection2(X0,sK12))
| ~ relation(iPr_def_10)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_7050]) ).
tcf(c_12154,plain,
( relation(set_intersection2(empty_set,sK12))
| ~ empty(relation_composition(iPr_def_10,empty_set)) ),
inference(superposition,[status(thm)],[c_2472,c_7050]) ).
tcf(c_12156,plain,
( relation(set_intersection2(empty_set,sK12))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_12154,c_4938]) ).
tcf(c_12157,plain,
relation(set_intersection2(empty_set,sK12)),
inference(forward_subsumption_resolution,[status(thm)],[c_12156,c_73]) ).
tcf(c_12165,plain,
! [X0: $i] :
( function(set_intersection2(X0,sK12))
| ~ relation(iPr_def_10)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_7049]) ).
tcf(c_12168,plain,
( function(set_intersection2(empty_set,sK12))
| ~ empty(relation_composition(iPr_def_10,empty_set)) ),
inference(superposition,[status(thm)],[c_2472,c_7049]) ).
tcf(c_12170,plain,
( function(set_intersection2(empty_set,sK12))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_12168,c_4938]) ).
tcf(c_12171,plain,
function(set_intersection2(empty_set,sK12)),
inference(forward_subsumption_resolution,[status(thm)],[c_12170,c_73]) ).
tcf(c_12179,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK12))
| ~ relation(iPr_def_10)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_7051]) ).
tcf(c_12182,plain,
( empty(set_intersection2(empty_set,sK12))
| ~ empty(relation_composition(iPr_def_10,empty_set)) ),
inference(superposition,[status(thm)],[c_2472,c_7051]) ).
tcf(c_12184,plain,
( empty(set_intersection2(empty_set,sK12))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_12182,c_4938]) ).
tcf(c_12185,plain,
empty(set_intersection2(empty_set,sK12)),
inference(forward_subsumption_resolution,[status(thm)],[c_12184,c_73]) ).
tcf(c_12193,plain,
! [X0: $i] :
( function(set_intersection2(X0,sK11))
| ~ relation(iPr_def_11)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_7193]) ).
tcf(c_12196,plain,
( function(set_intersection2(empty_set,sK11))
| ~ empty(relation_composition(iPr_def_11,empty_set)) ),
inference(superposition,[status(thm)],[c_2472,c_7193]) ).
tcf(c_12198,plain,
( function(set_intersection2(empty_set,sK11))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_12196,c_5102]) ).
tcf(c_12199,plain,
function(set_intersection2(empty_set,sK11)),
inference(forward_subsumption_resolution,[status(thm)],[c_12198,c_73]) ).
tcf(c_12207,plain,
! [X0: $i] :
( relation(set_intersection2(X0,sK11))
| ~ relation(iPr_def_11)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_7194]) ).
tcf(c_12210,plain,
( relation(set_intersection2(empty_set,sK11))
| ~ empty(relation_composition(iPr_def_11,empty_set)) ),
inference(superposition,[status(thm)],[c_2472,c_7194]) ).
tcf(c_12212,plain,
( relation(set_intersection2(empty_set,sK11))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_12210,c_5102]) ).
tcf(c_12213,plain,
relation(set_intersection2(empty_set,sK11)),
inference(forward_subsumption_resolution,[status(thm)],[c_12212,c_73]) ).
tcf(c_12221,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK11))
| ~ relation(iPr_def_11)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_7195]) ).
tcf(c_12224,plain,
( empty(set_intersection2(empty_set,sK11))
| ~ empty(relation_composition(iPr_def_11,empty_set)) ),
inference(superposition,[status(thm)],[c_2472,c_7195]) ).
tcf(c_12226,plain,
( empty(set_intersection2(empty_set,sK11))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_12224,c_5102]) ).
tcf(c_12227,plain,
empty(set_intersection2(empty_set,sK11)),
inference(forward_subsumption_resolution,[status(thm)],[c_12226,c_73]) ).
tcf(c_12240,plain,
( empty(set_intersection2(relation_dom(sK2),sK12))
| in(sK1(relation_dom(relation_composition(iPr_def_10,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6018,c_7250]) ).
tcf(c_12241,plain,
( empty(set_intersection2(relation_dom(sK2),sK11))
| in(sK1(relation_dom(relation_composition(iPr_def_11,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6133,c_7250]) ).
tcf(c_12242,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| in(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6817,c_7250]) ).
tcf(c_12243,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ( apply(identity_relation(X0),sK1(set_intersection2(X1,X0))) = sK1(set_intersection2(X1,X0)) ) ),
inference(superposition,[status(thm)],[c_7250,c_172]) ).
tcf(c_12244,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ~ in(X0,sK1(set_intersection2(X1,X0))) ),
inference(superposition,[status(thm)],[c_7250,c_49]) ).
tcf(c_12246,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| element(sK1(set_intersection2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_7250,c_95]) ).
tcf(c_12247,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X1,X2),X0))
| in(sK1(set_intersection2(X0,set_intersection2(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_7250,c_58]) ).
tcf(c_12248,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X1,X2),X0))
| in(sK1(set_intersection2(X0,set_intersection2(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_7250,c_57]) ).
tcf(c_12249,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_dom(relation_composition(X0,X1)),X2))
| ( apply(relation_composition(X0,X1),sK1(set_intersection2(X2,relation_dom(relation_composition(X0,X1))))) = apply(X1,apply(X0,sK1(set_intersection2(X2,relation_dom(relation_composition(X0,X1)))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_7250,c_96]) ).
tcf(c_12251,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(set_intersection2(X0,iPr_def_13)),sK11) ),
inference(superposition,[status(thm)],[c_7250,c_2102]) ).
tcf(c_12252,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(set_intersection2(X0,iPr_def_13)),sK12) ),
inference(superposition,[status(thm)],[c_7250,c_2071]) ).
tcf(c_12254,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(powerset(X1)),X0))
| element(sK1(set_intersection2(X0,sK1(powerset(X1)))),X1) ),
inference(superposition,[status(thm)],[c_7250,c_2582]) ).
tcf(c_12255,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| empty(set_intersection2(sK4(X1),X0))
| element(sK1(set_intersection2(X0,sK4(X1))),X1) ),
inference(superposition,[status(thm)],[c_7250,c_2583]) ).
tcf(c_12256,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))
| in(sK1(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))),sK12) ),
inference(superposition,[status(thm)],[c_7250,c_6029]) ).
tcf(c_12257,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))
| in(sK1(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))),sK11) ),
inference(superposition,[status(thm)],[c_7250,c_6144]) ).
tcf(c_12258,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))
| in(sK1(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_7250,c_6828]) ).
tcf(c_12406,plain,
! [X0: $i] :
( ( empty_set = sK12 )
| ( apply(iPr_def_10,sK0(X0,empty_set,sK12)) = sK0(X0,empty_set,sK12) ) ),
inference(superposition,[status(thm)],[c_1147,c_11677]) ).
tcf(c_12407,plain,
! [X0: $i] :
( ( empty_set = sK11 )
| ( apply(iPr_def_11,sK0(X0,empty_set,sK11)) = sK0(X0,empty_set,sK11) ) ),
inference(superposition,[status(thm)],[c_1148,c_11677]) ).
tcf(c_12409,plain,
! [X0: $i] :
( ( empty_set = iPr_def_13 )
| ( apply(iPr_def_14,sK0(X0,empty_set,iPr_def_13)) = sK0(X0,empty_set,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_1151,c_11677]) ).
tcf(c_12469,plain,
! [X0: $i] :
( element(sK1(empty_set),X0)
| empty(set_intersection2(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_97,c_7262]) ).
tcf(c_12470,plain,
! [X0: $i] :
( element(sK1(empty_set),empty_set)
| empty(set_intersection2(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_1996,c_7262]) ).
tcf(c_12472,plain,
( empty(set_intersection2(sK12,relation_dom(sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_10,sK2))),sK12) ),
inference(superposition,[status(thm)],[c_6018,c_7262]) ).
tcf(c_12473,plain,
( empty(set_intersection2(sK11,relation_dom(sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_11,sK2))),sK11) ),
inference(superposition,[status(thm)],[c_6133,c_7262]) ).
tcf(c_12474,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_6817,c_7262]) ).
tcf(c_12476,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(powerset(X1),X2))
| ~ empty(X1)
| ~ in(X0,sK1(set_intersection2(powerset(X1),X2))) ),
inference(superposition,[status(thm)],[c_7262,c_107]) ).
tcf(c_12477,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X1)
| empty(set_intersection2(powerset(X1),X2))
| ~ in(X0,sK1(set_intersection2(powerset(X1),X2))) ),
inference(superposition,[status(thm)],[c_7262,c_106]) ).
tcf(c_12480,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_12474,c_6817]) ).
tcf(c_12483,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_11,sK2))),sK11) ),
inference(light_normalisation,[status(thm)],[c_12473,c_6133]) ).
tcf(c_12486,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_10,sK2))),sK12) ),
inference(light_normalisation,[status(thm)],[c_12472,c_6018]) ).
tcf(c_12507,plain,
( empty(set_intersection2(relation_dom(sK2),sK12))
| element(sK1(relation_dom(relation_composition(iPr_def_10,sK2))),sK12) ),
inference(superposition,[status(thm)],[c_6018,c_7918]) ).
tcf(c_12508,plain,
( empty(set_intersection2(relation_dom(sK2),sK11))
| element(sK1(relation_dom(relation_composition(iPr_def_11,sK2))),sK11) ),
inference(superposition,[status(thm)],[c_6133,c_7918]) ).
tcf(c_12509,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| element(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_6817,c_7918]) ).
tcf(c_12511,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,powerset(X1)))
| ~ empty(X1)
| ~ in(X0,sK1(set_intersection2(powerset(X1),X2))) ),
inference(superposition,[status(thm)],[c_7918,c_107]) ).
tcf(c_12512,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X1)
| empty(set_intersection2(X2,powerset(X1)))
| ~ in(X0,sK1(set_intersection2(powerset(X1),X2))) ),
inference(superposition,[status(thm)],[c_7918,c_106]) ).
tcf(c_12595,plain,
! [X0: $i] :
( relation(set_intersection2(X0,iPr_def_13))
| ~ relation(iPr_def_14)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_7988]) ).
tcf(c_12598,plain,
( relation(set_intersection2(empty_set,iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,empty_set)) ),
inference(superposition,[status(thm)],[c_2472,c_7988]) ).
tcf(c_12600,plain,
( relation(set_intersection2(empty_set,iPr_def_13))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_12598,c_5508]) ).
tcf(c_12601,plain,
relation(set_intersection2(empty_set,iPr_def_13)),
inference(forward_subsumption_resolution,[status(thm)],[c_12600,c_73]) ).
tcf(c_12608,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ~ relation(iPr_def_14)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_7989]) ).
tcf(c_12611,plain,
( empty(set_intersection2(empty_set,iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,empty_set)) ),
inference(superposition,[status(thm)],[c_2472,c_7989]) ).
tcf(c_12613,plain,
( empty(set_intersection2(empty_set,iPr_def_13))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_12611,c_5508]) ).
tcf(c_12614,plain,
empty(set_intersection2(empty_set,iPr_def_13)),
inference(forward_subsumption_resolution,[status(thm)],[c_12613,c_73]) ).
tcf(c_12625,plain,
( empty(set_intersection2(iPr_def_13,empty_set))
| in(sK1(empty_set),sK11) ),
inference(superposition,[status(thm)],[c_97,c_7267]) ).
tcf(c_12626,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),sK11) ),
inference(superposition,[status(thm)],[c_6817,c_7267]) ).
tcf(c_12627,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(sK11),sK1(set_intersection2(iPr_def_13,X0))) = sK1(set_intersection2(iPr_def_13,X0)) ) ),
inference(superposition,[status(thm)],[c_7267,c_172]) ).
tcf(c_12628,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ~ in(sK11,sK1(set_intersection2(iPr_def_13,X0))) ),
inference(superposition,[status(thm)],[c_7267,c_49]) ).
tcf(c_12630,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| element(sK1(set_intersection2(iPr_def_13,X0)),sK11) ),
inference(superposition,[status(thm)],[c_7267,c_95]) ).
tcf(c_12637,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),sK11) ),
inference(light_normalisation,[status(thm)],[c_12626,c_6817]) ).
tcf(c_12640,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(iPr_def_11,sK1(set_intersection2(iPr_def_13,X0))) = sK1(set_intersection2(iPr_def_13,X0)) ) ),
inference(light_normalisation,[status(thm)],[c_12627,c_1148]) ).
tcf(c_12659,plain,
( empty(set_intersection2(iPr_def_13,empty_set))
| in(sK1(empty_set),sK12) ),
inference(superposition,[status(thm)],[c_97,c_7268]) ).
tcf(c_12660,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),sK12) ),
inference(superposition,[status(thm)],[c_6817,c_7268]) ).
tcf(c_12661,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(sK12),sK1(set_intersection2(iPr_def_13,X0))) = sK1(set_intersection2(iPr_def_13,X0)) ) ),
inference(superposition,[status(thm)],[c_7268,c_172]) ).
tcf(c_12662,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ~ in(sK12,sK1(set_intersection2(iPr_def_13,X0))) ),
inference(superposition,[status(thm)],[c_7268,c_49]) ).
tcf(c_12664,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| element(sK1(set_intersection2(iPr_def_13,X0)),sK12) ),
inference(superposition,[status(thm)],[c_7268,c_95]) ).
tcf(c_12671,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| in(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),sK12) ),
inference(light_normalisation,[status(thm)],[c_12660,c_6817]) ).
tcf(c_12674,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(iPr_def_10,sK1(set_intersection2(iPr_def_13,X0))) = sK1(set_intersection2(iPr_def_13,X0)) ) ),
inference(light_normalisation,[status(thm)],[c_12661,c_1147]) ).
tcf(c_12685,plain,
! [X0: $i] :
( empty(X0)
| element(sK1(sK4(X0)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_7444,c_86,c_7444]) ).
tcf(c_12691,plain,
! [X0: $i] :
( empty(X0)
| in(sK1(sK4(X0)),X0) ),
inference(superposition,[status(thm)],[c_12685,c_98]) ).
tcf(c_12692,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(X0,sK1(sK4(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_12685,c_107]) ).
tcf(c_12693,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ~ in(X0,sK1(sK4(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_12685,c_106]) ).
tcf(c_12696,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK1(sK4(powerset(X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12693,c_69]) ).
tcf(c_12699,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK1(sK4(powerset(X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12692,c_69]) ).
tcf(c_12708,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(X0),sK1(sK4(X0))) = sK1(sK4(X0)) ) ),
inference(superposition,[status(thm)],[c_12691,c_172]) ).
tcf(c_12709,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK1(sK4(X0))) ),
inference(superposition,[status(thm)],[c_12691,c_49]) ).
tcf(c_12712,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| in(sK1(sK4(set_intersection2(X0,X1))),X1) ),
inference(superposition,[status(thm)],[c_12691,c_58]) ).
tcf(c_12713,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| in(sK1(sK4(set_intersection2(X0,X1))),X0) ),
inference(superposition,[status(thm)],[c_12691,c_57]) ).
tcf(c_12714,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom(relation_composition(X0,X1)))
| ( apply(relation_composition(X0,X1),sK1(sK4(relation_dom(relation_composition(X0,X1))))) = apply(X1,apply(X0,sK1(sK4(relation_dom(relation_composition(X0,X1)))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_12691,c_96]) ).
tcf(c_12716,plain,
( empty(iPr_def_13)
| in(sK1(sK4(iPr_def_13)),sK11) ),
inference(superposition,[status(thm)],[c_12691,c_2102]) ).
tcf(c_12717,plain,
( empty(iPr_def_13)
| in(sK1(sK4(iPr_def_13)),sK12) ),
inference(superposition,[status(thm)],[c_12691,c_2071]) ).
tcf(c_12719,plain,
! [X0: $i] :
( empty(sK1(powerset(X0)))
| element(sK1(sK4(sK1(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_12691,c_2582]) ).
tcf(c_12720,plain,
! [X0: $i] :
( empty(X0)
| empty(sK4(X0))
| element(sK1(sK4(sK4(X0))),X0) ),
inference(superposition,[status(thm)],[c_12691,c_2583]) ).
tcf(c_12721,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_10,sK2)))),sK12) ),
inference(superposition,[status(thm)],[c_12691,c_6029]) ).
tcf(c_12722,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_11,sK2)))),sK11) ),
inference(superposition,[status(thm)],[c_12691,c_6144]) ).
tcf(c_12723,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_12691,c_6828]) ).
tcf(c_12724,plain,
in(sK1(sK4(iPr_def_13)),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_12717,c_4400]) ).
tcf(c_12725,plain,
in(sK1(sK4(iPr_def_13)),sK11),
inference(forward_subsumption_resolution,[status(thm)],[c_12716,c_4400]) ).
tcf(c_12823,plain,
apply(identity_relation(sK12),sK1(sK4(iPr_def_13))) = sK1(sK4(iPr_def_13)),
inference(superposition,[status(thm)],[c_12724,c_172]) ).
tcf(c_12824,plain,
~ in(sK12,sK1(sK4(iPr_def_13))),
inference(superposition,[status(thm)],[c_12724,c_49]) ).
tcf(c_12826,plain,
element(sK1(sK4(iPr_def_13)),sK12),
inference(superposition,[status(thm)],[c_12724,c_95]) ).
tcf(c_12827,plain,
apply(iPr_def_10,sK1(sK4(iPr_def_13))) = sK1(sK4(iPr_def_13)),
inference(light_normalisation,[status(thm)],[c_12823,c_1147]) ).
tcf(c_12834,plain,
apply(identity_relation(sK11),sK1(sK4(iPr_def_13))) = sK1(sK4(iPr_def_13)),
inference(superposition,[status(thm)],[c_12725,c_172]) ).
tcf(c_12835,plain,
~ in(sK11,sK1(sK4(iPr_def_13))),
inference(superposition,[status(thm)],[c_12725,c_49]) ).
tcf(c_12837,plain,
element(sK1(sK4(iPr_def_13)),sK11),
inference(superposition,[status(thm)],[c_12725,c_95]) ).
tcf(c_12838,plain,
apply(iPr_def_11,sK1(sK4(iPr_def_13))) = sK1(sK4(iPr_def_13)),
inference(light_normalisation,[status(thm)],[c_12834,c_1148]) ).
tcf(c_12853,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| element(sK1(set_intersection2(iPr_def_13,X0)),sK11) ),
inference(superposition,[status(thm)],[c_52,c_8223]) ).
tcf(c_12856,plain,
( element(sK1(empty_set),sK11)
| empty(set_intersection2(empty_set,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_1996,c_8223]) ).
tcf(c_12877,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| in(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),sK11) ),
inference(superposition,[status(thm)],[c_6817,c_7923]) ).
tcf(c_12878,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(sK11),sK1(set_intersection2(iPr_def_13,X0))) = sK1(set_intersection2(iPr_def_13,X0)) ) ),
inference(superposition,[status(thm)],[c_7923,c_172]) ).
tcf(c_12879,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ~ in(sK11,sK1(set_intersection2(iPr_def_13,X0))) ),
inference(superposition,[status(thm)],[c_7923,c_49]) ).
tcf(c_12886,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(iPr_def_11,sK1(set_intersection2(iPr_def_13,X0))) = sK1(set_intersection2(iPr_def_13,X0)) ) ),
inference(light_normalisation,[status(thm)],[c_12878,c_1148]) ).
tcf(c_12897,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| in(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),sK12) ),
inference(superposition,[status(thm)],[c_6817,c_7924]) ).
tcf(c_12898,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(sK12),sK1(set_intersection2(iPr_def_13,X0))) = sK1(set_intersection2(iPr_def_13,X0)) ) ),
inference(superposition,[status(thm)],[c_7924,c_172]) ).
tcf(c_12899,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ~ in(sK12,sK1(set_intersection2(iPr_def_13,X0))) ),
inference(superposition,[status(thm)],[c_7924,c_49]) ).
tcf(c_12901,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| element(sK1(set_intersection2(iPr_def_13,X0)),sK12) ),
inference(superposition,[status(thm)],[c_7924,c_95]) ).
tcf(c_12908,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(iPr_def_10,sK1(set_intersection2(iPr_def_13,X0))) = sK1(set_intersection2(iPr_def_13,X0)) ) ),
inference(light_normalisation,[status(thm)],[c_12898,c_1147]) ).
tcf(c_12942,plain,
! [X0: $i] :
( function(set_intersection2(X0,iPr_def_13))
| ~ relation(iPr_def_14)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_7987]) ).
tcf(c_12945,plain,
( function(set_intersection2(empty_set,iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,empty_set)) ),
inference(superposition,[status(thm)],[c_2472,c_7987]) ).
tcf(c_12947,plain,
( function(set_intersection2(empty_set,iPr_def_13))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_12945,c_5508]) ).
tcf(c_12948,plain,
function(set_intersection2(empty_set,iPr_def_13)),
inference(forward_subsumption_resolution,[status(thm)],[c_12947,c_73]) ).
tcf(c_12962,plain,
( element(sK1(empty_set),sK12)
| empty(set_intersection2(empty_set,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_1996,c_8248]) ).
tcf(c_12972,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),relation_dom(relation_composition(iPr_def_14,sK2)))) = set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0) )
| ~ empty(identity_relation(relation_dom(sK2)))
| ~ relation(relation_dom(relation_composition(iPr_def_14,sK2))) ),
inference(superposition,[status(thm)],[c_8669,c_103]) ).
tcf(c_12981,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = X0 )
| ~ empty(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_110]) ).
tcf(c_12982,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_5630]) ).
tcf(c_12983,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_5629]) ).
tcf(c_12984,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_4060]) ).
tcf(c_12985,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_4059]) ).
tcf(c_12986,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_4011]) ).
tcf(c_12987,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_4010]) ).
tcf(c_12988,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3938]) ).
tcf(c_12989,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3937]) ).
tcf(c_12990,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3179]) ).
tcf(c_12991,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3178]) ).
tcf(c_12992,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3083]) ).
tcf(c_12993,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3082]) ).
tcf(c_12994,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_2687]) ).
tcf(c_12995,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_2686]) ).
tcf(c_12996,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_2658]) ).
tcf(c_12997,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_2637]) ).
tcf(c_12998,plain,
( ( sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3939]) ).
tcf(c_12999,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3180]) ).
tcf(c_13000,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3084]) ).
tcf(c_13001,plain,
( ( identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_2474]) ).
tcf(c_13002,plain,
( ( identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_2473]) ).
tcf(c_13003,plain,
( ( relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_2055]) ).
tcf(c_13004,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_2184]) ).
tcf(c_13005,plain,
( ( relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_2013]) ).
tcf(c_13006,plain,
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_108]) ).
tcf(c_13009,plain,
( empty(relation_composition(iPr_def_14,sK2))
| ~ relation(relation_composition(iPr_def_14,sK2))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_75]) ).
tcf(c_13164,plain,
! [X0: $i] :
( ( set_intersection2(iPr_def_13,X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_8773]) ).
tcf(c_13167,plain,
( ( set_intersection2(iPr_def_13,empty_set) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_8773]) ).
tcf(c_13180,plain,
! [X0: $i] :
( ( set_intersection2(X0,iPr_def_13) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_8927]) ).
tcf(c_13183,plain,
( ( set_intersection2(empty_set,iPr_def_13) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_8927]) ).
tcf(c_13192,plain,
! [X0: $i] :
( ( set_intersection2(sK11,X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_10061]) ).
tcf(c_13195,plain,
( ( set_intersection2(sK11,empty_set) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_10061]) ).
tcf(c_13204,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK11) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_10263]) ).
tcf(c_13207,plain,
( ( set_intersection2(empty_set,sK11) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_10263]) ).
tcf(c_13216,plain,
! [X0: $i] :
( ( set_intersection2(sK12,X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_11032]) ).
tcf(c_13219,plain,
( ( set_intersection2(sK12,empty_set) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_11032]) ).
tcf(c_13228,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),relation_dom(relation_composition(iPr_def_11,sK2)))) = set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0) )
| ~ empty(identity_relation(relation_dom(sK2)))
| ~ relation(relation_dom(relation_composition(iPr_def_11,sK2))) ),
inference(superposition,[status(thm)],[c_9754,c_103]) ).
tcf(c_13238,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( powerset(X2) = empty_set )
| ~ empty(X2)
| ~ in(X0,sK0(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_9805,c_107]) ).
tcf(c_13239,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( powerset(X2) = empty_set )
| ~ in(X0,sK0(empty_set,X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_9805,c_106]) ).
tcf(c_13256,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = X0 )
| ~ empty(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_110]) ).
tcf(c_13257,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_5630]) ).
tcf(c_13258,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_5629]) ).
tcf(c_13259,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_4060]) ).
tcf(c_13260,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_4059]) ).
tcf(c_13261,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_4011]) ).
tcf(c_13262,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_4010]) ).
tcf(c_13263,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3938]) ).
tcf(c_13264,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3937]) ).
tcf(c_13265,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3179]) ).
tcf(c_13266,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3178]) ).
tcf(c_13267,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3083]) ).
tcf(c_13268,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3082]) ).
tcf(c_13269,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_2687]) ).
tcf(c_13270,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_2686]) ).
tcf(c_13271,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_2658]) ).
tcf(c_13272,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_2637]) ).
tcf(c_13273,plain,
( ( sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3939]) ).
tcf(c_13274,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3180]) ).
tcf(c_13275,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3084]) ).
tcf(c_13276,plain,
( ( identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_2474]) ).
tcf(c_13277,plain,
( ( identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_2473]) ).
tcf(c_13278,plain,
( ( relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_2055]) ).
tcf(c_13279,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_2184]) ).
tcf(c_13280,plain,
( ( relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_2013]) ).
tcf(c_13281,plain,
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_108]) ).
tcf(c_13284,plain,
( empty(relation_composition(iPr_def_11,sK2))
| ~ relation(relation_composition(iPr_def_11,sK2))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_75]) ).
tcf(c_13381,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),relation_dom(relation_composition(iPr_def_10,sK2)))) = set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0) )
| ~ empty(identity_relation(relation_dom(sK2)))
| ~ relation(relation_dom(relation_composition(iPr_def_10,sK2))) ),
inference(superposition,[status(thm)],[c_10470,c_103]) ).
tcf(c_13394,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = X0 )
| ~ empty(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_110]) ).
tcf(c_13395,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_5630]) ).
tcf(c_13396,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_5629]) ).
tcf(c_13397,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_4060]) ).
tcf(c_13398,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_4059]) ).
tcf(c_13399,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_4011]) ).
tcf(c_13400,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_4010]) ).
tcf(c_13401,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3938]) ).
tcf(c_13402,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3937]) ).
tcf(c_13403,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3179]) ).
tcf(c_13404,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3178]) ).
tcf(c_13405,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3083]) ).
tcf(c_13406,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3082]) ).
tcf(c_13407,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_2687]) ).
tcf(c_13408,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_2686]) ).
tcf(c_13409,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_2658]) ).
tcf(c_13410,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_2637]) ).
tcf(c_13411,plain,
( ( sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3939]) ).
tcf(c_13412,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3180]) ).
tcf(c_13413,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3084]) ).
tcf(c_13414,plain,
( ( identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_2474]) ).
tcf(c_13415,plain,
( ( identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_2473]) ).
tcf(c_13416,plain,
( ( relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_2055]) ).
tcf(c_13417,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_2184]) ).
tcf(c_13418,plain,
( ( relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_2013]) ).
tcf(c_13419,plain,
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_108]) ).
tcf(c_13422,plain,
( empty(relation_composition(iPr_def_10,sK2))
| ~ relation(relation_composition(iPr_def_10,sK2))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_75]) ).
tcf(c_13584,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK12) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_11194]) ).
tcf(c_13587,plain,
( ( set_intersection2(empty_set,sK12) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_11194]) ).
tcf(c_13617,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( powerset(X2) = empty_set )
| ~ empty(X2)
| ~ in(X0,sK0(X1,empty_set,powerset(X2))) ),
inference(superposition,[status(thm)],[c_11680,c_107]) ).
tcf(c_13618,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ( powerset(X2) = empty_set )
| ~ in(X0,sK0(X1,empty_set,powerset(X2))) ),
inference(superposition,[status(thm)],[c_11680,c_106]) ).
tcf(c_13635,plain,
( empty(set_intersection2(relation_dom(sK2),sK12))
| element(sK1(relation_dom(relation_composition(iPr_def_10,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6018,c_12246]) ).
tcf(c_13636,plain,
( empty(set_intersection2(relation_dom(sK2),sK11))
| element(sK1(relation_dom(relation_composition(iPr_def_11,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6133,c_12246]) ).
tcf(c_13637,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| element(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6817,c_12246]) ).
tcf(c_13639,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(powerset(X2),X1))
| ~ empty(X2)
| ~ in(X0,sK1(set_intersection2(X1,powerset(X2)))) ),
inference(superposition,[status(thm)],[c_12246,c_107]) ).
tcf(c_13640,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| empty(set_intersection2(powerset(X2),X1))
| ~ in(X0,sK1(set_intersection2(X1,powerset(X2)))) ),
inference(superposition,[status(thm)],[c_12246,c_106]) ).
tcf(c_13659,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| element(sK1(set_intersection2(X0,iPr_def_13)),sK11) ),
inference(superposition,[status(thm)],[c_52,c_12630]) ).
tcf(c_13662,plain,
( element(sK1(empty_set),sK11)
| empty(set_intersection2(iPr_def_13,empty_set)) ),
inference(superposition,[status(thm)],[c_97,c_12630]) ).
tcf(c_13663,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),sK11) ),
inference(superposition,[status(thm)],[c_6817,c_12630]) ).
tcf(c_13669,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),sK11) ),
inference(light_normalisation,[status(thm)],[c_13663,c_6817]) ).
tcf(c_13678,plain,
! [X0: $i] :
( ( empty_set = iPr_def_13 )
| ( apply(identity_relation(sK11),sK0(empty_set,X0,iPr_def_13)) = sK0(empty_set,X0,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_11625,c_172]) ).
tcf(c_13679,plain,
! [X0: $i] :
( ( empty_set = iPr_def_13 )
| ~ in(sK11,sK0(empty_set,X0,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_11625,c_49]) ).
tcf(c_13681,plain,
! [X0: $i] :
( element(sK0(empty_set,X0,iPr_def_13),sK11)
| ( empty_set = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_11625,c_95]) ).
tcf(c_13682,plain,
( ( empty_set = iPr_def_13 )
| ( set_intersection2(empty_set,sK11) = iPr_def_13 )
| ~ in(sK0(empty_set,sK11,iPr_def_13),iPr_def_13)
| ~ in(sK0(empty_set,sK11,iPr_def_13),empty_set) ),
inference(superposition,[status(thm)],[c_11625,c_53]) ).
tcf(c_13687,plain,
! [X0: $i] :
( ( empty_set = iPr_def_13 )
| ( apply(iPr_def_11,sK0(empty_set,X0,iPr_def_13)) = sK0(empty_set,X0,iPr_def_13) ) ),
inference(light_normalisation,[status(thm)],[c_13678,c_1148]) ).
tcf(c_13697,plain,
! [X0: $i] :
( ( empty_set = iPr_def_13 )
| ( apply(identity_relation(sK12),sK0(empty_set,X0,iPr_def_13)) = sK0(empty_set,X0,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_11626,c_172]) ).
tcf(c_13698,plain,
! [X0: $i] :
( ( empty_set = iPr_def_13 )
| ~ in(sK12,sK0(empty_set,X0,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_11626,c_49]) ).
tcf(c_13700,plain,
! [X0: $i] :
( element(sK0(empty_set,X0,iPr_def_13),sK12)
| ( empty_set = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_11626,c_95]) ).
tcf(c_13701,plain,
( ( empty_set = iPr_def_13 )
| ( set_intersection2(empty_set,sK12) = iPr_def_13 )
| ~ in(sK0(empty_set,sK12,iPr_def_13),iPr_def_13)
| ~ in(sK0(empty_set,sK12,iPr_def_13),empty_set) ),
inference(superposition,[status(thm)],[c_11626,c_53]) ).
tcf(c_13706,plain,
! [X0: $i] :
( ( empty_set = iPr_def_13 )
| ( apply(iPr_def_10,sK0(empty_set,X0,iPr_def_13)) = sK0(empty_set,X0,iPr_def_13) ) ),
inference(light_normalisation,[status(thm)],[c_13697,c_1147]) ).
tcf(c_13733,plain,
! [X0: $i] :
( ( empty_set = iPr_def_13 )
| ( apply(identity_relation(sK11),sK0(X0,empty_set,iPr_def_13)) = sK0(X0,empty_set,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_11686,c_172]) ).
tcf(c_13734,plain,
! [X0: $i] :
( ( empty_set = iPr_def_13 )
| ~ in(sK11,sK0(X0,empty_set,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_11686,c_49]) ).
tcf(c_13736,plain,
! [X0: $i] :
( element(sK0(X0,empty_set,iPr_def_13),sK11)
| ( empty_set = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_11686,c_95]) ).
tcf(c_13741,plain,
! [X0: $i] :
( ( empty_set = iPr_def_13 )
| ( apply(iPr_def_11,sK0(X0,empty_set,iPr_def_13)) = sK0(X0,empty_set,iPr_def_13) ) ),
inference(light_normalisation,[status(thm)],[c_13733,c_1148]) ).
tcf(c_13748,plain,
! [X0: $i] :
( ( empty_set = iPr_def_13 )
| ( apply(identity_relation(sK12),sK0(X0,empty_set,iPr_def_13)) = sK0(X0,empty_set,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_11687,c_172]) ).
tcf(c_13749,plain,
! [X0: $i] :
( ( empty_set = iPr_def_13 )
| ~ in(sK12,sK0(X0,empty_set,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_11687,c_49]) ).
tcf(c_13751,plain,
! [X0: $i] :
( element(sK0(X0,empty_set,iPr_def_13),sK12)
| ( empty_set = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_11687,c_95]) ).
tcf(c_13756,plain,
! [X0: $i] :
( ( empty_set = iPr_def_13 )
| ( apply(iPr_def_10,sK0(X0,empty_set,iPr_def_13)) = sK0(X0,empty_set,iPr_def_13) ) ),
inference(light_normalisation,[status(thm)],[c_13748,c_1147]) ).
tcf(c_13777,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(sK11),sK1(set_intersection2(X0,iPr_def_13))) = sK1(set_intersection2(X0,iPr_def_13)) ) ),
inference(superposition,[status(thm)],[c_12251,c_172]) ).
tcf(c_13778,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ~ in(sK11,sK1(set_intersection2(X0,iPr_def_13))) ),
inference(superposition,[status(thm)],[c_12251,c_49]) ).
tcf(c_13783,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(iPr_def_11,sK1(set_intersection2(X0,iPr_def_13))) = sK1(set_intersection2(X0,iPr_def_13)) ) ),
inference(light_normalisation,[status(thm)],[c_13777,c_1148]) ).
tcf(c_13893,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(sK12),sK1(set_intersection2(X0,iPr_def_13))) = sK1(set_intersection2(X0,iPr_def_13)) ) ),
inference(superposition,[status(thm)],[c_12252,c_172]) ).
tcf(c_13894,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ~ in(sK12,sK1(set_intersection2(X0,iPr_def_13))) ),
inference(superposition,[status(thm)],[c_12252,c_49]) ).
tcf(c_13896,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| element(sK1(set_intersection2(X0,iPr_def_13)),sK12) ),
inference(superposition,[status(thm)],[c_12252,c_95]) ).
tcf(c_13901,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(iPr_def_10,sK1(set_intersection2(X0,iPr_def_13))) = sK1(set_intersection2(X0,iPr_def_13)) ) ),
inference(light_normalisation,[status(thm)],[c_13893,c_1147]) ).
tcf(c_13911,plain,
( element(sK1(empty_set),sK12)
| empty(set_intersection2(iPr_def_13,empty_set)) ),
inference(superposition,[status(thm)],[c_97,c_12664]) ).
tcf(c_13912,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),sK12) ),
inference(superposition,[status(thm)],[c_6817,c_12664]) ).
tcf(c_13916,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| element(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),sK12) ),
inference(light_normalisation,[status(thm)],[c_13912,c_6817]) ).
tcf(c_13925,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,sK1(sK4(powerset(X1))),X2),X1)
| in(sK0(X0,sK1(sK4(powerset(X1))),X2),X2)
| ( set_intersection2(X0,sK1(sK4(powerset(X1)))) = X2 ) ),
inference(superposition,[status(thm)],[c_55,c_12696]) ).
tcf(c_13926,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(sK1(sK4(powerset(X0))),X1,X2),X2)
| element(sK0(sK1(sK4(powerset(X0))),X1,X2),X0)
| ( set_intersection2(sK1(sK4(powerset(X0))),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_2239,c_12696]) ).
tcf(c_13927,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(sK1(sK4(powerset(X0))),X1,X2),X0)
| in(sK0(sK1(sK4(powerset(X0))),X1,X2),X2)
| ( set_intersection2(sK1(sK4(powerset(X0))),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_54,c_12696]) ).
tcf(c_13928,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X1,X2,sK1(sK4(powerset(X0)))),X0)
| in(sK0(X1,X2,sK1(sK4(powerset(X0)))),X2)
| ( sK1(sK4(powerset(X0))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_55,c_12696]) ).
tcf(c_13929,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X1,X2,sK1(sK4(powerset(X0)))),X0)
| in(sK0(X1,X2,sK1(sK4(powerset(X0)))),X1)
| ( sK1(sK4(powerset(X0))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_54,c_12696]) ).
tcf(c_13930,plain,
! [X0: $i] :
( empty(sK1(sK4(powerset(X0))))
| element(sK1(sK1(sK4(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_2137,c_12696]) ).
tcf(c_13931,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(sK4(powerset(X1))),X0))
| element(sK1(set_intersection2(X0,sK1(sK4(powerset(X1))))),X1) ),
inference(superposition,[status(thm)],[c_7250,c_12696]) ).
tcf(c_13932,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,sK1(sK4(powerset(X1)))))
| element(sK1(set_intersection2(X0,sK1(sK4(powerset(X1))))),X1) ),
inference(superposition,[status(thm)],[c_2201,c_12696]) ).
tcf(c_13933,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,sK1(sK4(powerset(X0)))))
| element(sK1(set_intersection2(sK1(sK4(powerset(X0))),X1)),X0) ),
inference(superposition,[status(thm)],[c_2732,c_12696]) ).
tcf(c_13934,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(sK4(powerset(X0))),X1))
| element(sK1(set_intersection2(sK1(sK4(powerset(X0))),X1)),X0) ),
inference(superposition,[status(thm)],[c_2202,c_12696]) ).
tcf(c_13935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK0(sK1(sK4(powerset(X0))),X1,set_intersection2(X2,X3)),X0)
| in(sK0(sK1(sK4(powerset(X0))),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(sK1(sK4(powerset(X0))),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_2241,c_12696]) ).
tcf(c_13936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK0(X2,X3,set_intersection2(X0,sK1(sK4(powerset(X1))))),X1)
| in(sK0(X2,X3,set_intersection2(X0,sK1(sK4(powerset(X1))))),X2)
| ( set_intersection2(X0,sK1(sK4(powerset(X1)))) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_2241,c_12696]) ).
tcf(c_13937,plain,
! [X0: $i,X1: $i] :
( element(sK0(empty_set,X1,sK1(sK4(powerset(X0)))),X0)
| ( sK1(sK4(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5683,c_12696]) ).
tcf(c_13938,plain,
! [X0: $i,X1: $i] :
( element(sK0(X1,empty_set,sK1(sK4(powerset(X0)))),X0)
| ( sK1(sK4(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5686,c_12696]) ).
tcf(c_13939,plain,
! [X0: $i] :
( empty(sK1(sK4(powerset(X0))))
| element(sK1(sK4(sK1(sK4(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_12691,c_12696]) ).
tcf(c_14092,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,sK1(sK4(powerset(X0))),X2),X2)
| ( set_intersection2(X1,sK1(sK4(powerset(X0)))) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_12699]) ).
tcf(c_14093,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(sK1(sK4(powerset(X0))),X1,X2),X2)
| ( set_intersection2(sK1(sK4(powerset(X0))),X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2239,c_12699]) ).
tcf(c_14094,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(sK1(sK4(powerset(X0))),X1,X2),X2)
| ( set_intersection2(sK1(sK4(powerset(X0))),X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_12699]) ).
tcf(c_14095,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,sK1(sK4(powerset(X0)))),X2)
| ( sK1(sK4(powerset(X0))) = set_intersection2(X1,X2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_12699]) ).
tcf(c_14096,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,sK1(sK4(powerset(X0)))),X1)
| ( sK1(sK4(powerset(X0))) = set_intersection2(X1,X2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_12699]) ).
tcf(c_14099,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,sK1(sK4(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2201,c_12699]) ).
tcf(c_14101,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(sK4(powerset(X0))),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2202,c_12699]) ).
tcf(c_14102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(sK1(sK4(powerset(X0))),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(sK1(sK4(powerset(X0))),X1) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2241,c_12699]) ).
tcf(c_14103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,set_intersection2(X1,sK1(sK4(powerset(X0))))),X2)
| ( set_intersection2(X1,sK1(sK4(powerset(X0)))) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2241,c_12699]) ).
tcf(c_14104,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5683,c_12699]) ).
tcf(c_14106,plain,
! [X0: $i] :
( empty(sK1(sK4(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12691,c_12699]) ).
tcf(c_14316,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_110]) ).
tcf(c_14317,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_5630]) ).
tcf(c_14318,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_5629]) ).
tcf(c_14319,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(sK1(sK4(powerset(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_4060]) ).
tcf(c_14320,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(sK1(sK4(powerset(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_4059]) ).
tcf(c_14321,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(sK1(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_4011]) ).
tcf(c_14322,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(sK1(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_4010]) ).
tcf(c_14323,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_3938]) ).
tcf(c_14324,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_3937]) ).
tcf(c_14325,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_3179]) ).
tcf(c_14326,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_3178]) ).
tcf(c_14327,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_3083]) ).
tcf(c_14328,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_3082]) ).
tcf(c_14329,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_2687]) ).
tcf(c_14330,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_2686]) ).
tcf(c_14331,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_2658]) ).
tcf(c_14332,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_2637]) ).
tcf(c_14333,plain,
! [X0: $i] :
( ( sK1(powerset(sK1(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_3939]) ).
tcf(c_14334,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK1(sK4(powerset(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_3180]) ).
tcf(c_14335,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,sK1(sK4(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_3084]) ).
tcf(c_14336,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK1(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_2474]) ).
tcf(c_14337,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK1(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_2473]) ).
tcf(c_14338,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_2055]) ).
tcf(c_14339,plain,
! [X0: $i] :
( ( identity_relation(sK1(sK4(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_2184]) ).
tcf(c_14340,plain,
! [X0: $i] :
( ( relation_dom(sK1(sK4(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_2013]) ).
tcf(c_14342,plain,
! [X0: $i] :
( relation(sK1(sK4(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_51]) ).
tcf(c_14343,plain,
! [X0: $i] :
( function(sK1(sK4(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_50]) ).
tcf(c_14467,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),sK1(sK4(powerset(X0))))) = set_intersection2(relation_dom(sK1(sK4(powerset(X0)))),X1) )
| ~ empty(X0)
| ~ relation(sK1(sK4(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_14343,c_103]) ).
tcf(c_14480,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| element(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),sK11) ),
inference(superposition,[status(thm)],[c_6817,c_12853]) ).
tcf(c_14492,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| element(sK1(relation_dom(relation_composition(iPr_def_14,sK2))),sK12) ),
inference(superposition,[status(thm)],[c_6817,c_12901]) ).
tcf(c_14572,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,sK1(sK4(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_110]) ).
tcf(c_14573,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_5630]) ).
tcf(c_14574,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_5629]) ).
tcf(c_14575,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_4060]) ).
tcf(c_14576,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_4059]) ).
tcf(c_14577,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(X2,sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_4011]) ).
tcf(c_14578,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(X2,sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_4010]) ).
tcf(c_14579,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(X1,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3938]) ).
tcf(c_14580,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(X1,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3937]) ).
tcf(c_14581,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(set_intersection2(X1,sK1(sK4(powerset(X0)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3179]) ).
tcf(c_14582,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(set_intersection2(X1,sK1(sK4(powerset(X0)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3178]) ).
tcf(c_14583,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(X2,sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3083]) ).
tcf(c_14584,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(X2,sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3082]) ).
tcf(c_14585,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_2687]) ).
tcf(c_14586,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_2686]) ).
tcf(c_14587,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_2658]) ).
tcf(c_14588,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_2637]) ).
tcf(c_14589,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(X1,sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3939]) ).
tcf(c_14590,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,sK1(sK4(powerset(X0)))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3180]) ).
tcf(c_14591,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X2,sK1(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3084]) ).
tcf(c_14592,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_2474]) ).
tcf(c_14593,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_2473]) ).
tcf(c_14594,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_2055]) ).
tcf(c_14598,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X1,sK1(sK4(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_51]) ).
tcf(c_14599,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X1,sK1(sK4(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_50]) ).
tcf(c_14722,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(sK4(powerset(X0))),X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_110]) ).
tcf(c_14723,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_5630]) ).
tcf(c_14724,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_5629]) ).
tcf(c_14725,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_4060]) ).
tcf(c_14726,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_4059]) ).
tcf(c_14727,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_4011]) ).
tcf(c_14728,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_4010]) ).
tcf(c_14729,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(sK1(sK4(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3938]) ).
tcf(c_14730,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(sK1(sK4(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3937]) ).
tcf(c_14731,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(set_intersection2(sK1(sK4(powerset(X0))),X1),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3179]) ).
tcf(c_14732,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(set_intersection2(sK1(sK4(powerset(X0))),X1),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3178]) ).
tcf(c_14733,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(sK1(sK4(powerset(X0))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3083]) ).
tcf(c_14734,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(sK1(sK4(powerset(X0))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3082]) ).
tcf(c_14735,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_2687]) ).
tcf(c_14736,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_2686]) ).
tcf(c_14737,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_2658]) ).
tcf(c_14738,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_2637]) ).
tcf(c_14739,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(sK1(sK4(powerset(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3939]) ).
tcf(c_14740,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(sK1(sK4(powerset(X0))),X1),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3180]) ).
tcf(c_14741,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(sK1(sK4(powerset(X0))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3084]) ).
tcf(c_14742,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_2474]) ).
tcf(c_14743,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_2473]) ).
tcf(c_14744,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_2055]) ).
tcf(c_14748,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(sK1(sK4(powerset(X0))),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_51]) ).
tcf(c_14749,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(sK1(sK4(powerset(X0))),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_50]) ).
tcf(c_14936,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_14104]) ).
tcf(c_14937,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_14104]) ).
tcf(c_14938,plain,
sK1(sK4(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_14104]) ).
tcf(c_14939,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_14104]) ).
tcf(c_14940,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_14104]) ).
tcf(c_14941,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_14104]) ).
tcf(c_14942,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_14104]) ).
tcf(c_14943,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_14104]) ).
tcf(c_14944,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(set_intersection2(X0,iPr_def_13)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_14104]) ).
tcf(c_14945,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(set_intersection2(iPr_def_13,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_14104]) ).
tcf(c_14946,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(set_intersection2(X1,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_14104]) ).
tcf(c_14947,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(set_intersection2(sK11,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_14104]) ).
tcf(c_14948,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(set_intersection2(sK12,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_14104]) ).
tcf(c_14949,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(set_intersection2(sK1(powerset(X0)),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_14104]) ).
tcf(c_14950,plain,
( ( sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_14104]) ).
tcf(c_14951,plain,
( ( sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_14104]) ).
tcf(c_14952,plain,
( ( sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_14104]) ).
tcf(c_14953,plain,
( ( sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_14104]) ).
tcf(c_14954,plain,
( ( sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_14104]) ).
tcf(c_14955,plain,
( ( sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_14104]) ).
tcf(c_14956,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(set_intersection2(X0,sK12)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_14104]) ).
tcf(c_14957,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(set_intersection2(X0,sK11)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_14104]) ).
tcf(c_14958,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_14104]) ).
tcf(c_14959,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(set_intersection2(sK1(sK4(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_14104]) ).
tcf(c_14960,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(set_intersection2(X1,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_14104]) ).
tcf(c_15141,plain,
( empty(sK4(powerset(empty_set)))
| ~ in(sK4(powerset(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_14938,c_2198]) ).
tcf(c_15142,plain,
( empty(sK4(powerset(empty_set)))
| in(empty_set,sK4(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_14938,c_2137]) ).
tcf(c_15143,plain,
element(empty_set,sK4(powerset(empty_set))),
inference(superposition,[status(thm)],[c_14938,c_61]) ).
tcf(c_15149,plain,
( empty(powerset(empty_set))
| ~ in(powerset(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_14938,c_12709]) ).
tcf(c_15151,plain,
( empty(powerset(empty_set))
| element(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_14938,c_12685]) ).
tcf(c_15215,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(identity_relation(X2),set_intersection2(X0,sK1(sK4(powerset(X1)))))) = set_intersection2(relation_dom(set_intersection2(X0,sK1(sK4(powerset(X1))))),X2) )
| ~ empty(X1)
| ~ relation(set_intersection2(X0,sK1(sK4(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_14599,c_103]) ).
tcf(c_15229,plain,
in(empty_set,sK4(powerset(empty_set))),
inference(global_subsumption_just,[status(thm)],[c_15142,c_117,c_2352,c_2909,c_15143]) ).
tcf(c_15231,plain,
apply(identity_relation(sK4(powerset(empty_set))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_15229,c_172]) ).
tcf(c_15232,plain,
~ in(sK4(powerset(empty_set)),empty_set),
inference(superposition,[status(thm)],[c_15229,c_49]) ).
tcf(c_15233,plain,
~ empty(sK4(powerset(empty_set))),
inference(superposition,[status(thm)],[c_15229,c_109]) ).
tcf(c_15245,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(identity_relation(X2),set_intersection2(sK1(sK4(powerset(X0))),X1))) = set_intersection2(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1)),X2) )
| ~ empty(X0)
| ~ relation(set_intersection2(sK1(sK4(powerset(X0))),X1)) ),
inference(superposition,[status(thm)],[c_14749,c_103]) ).
tcf(c_15256,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X0,X2) = relation_dom(X1) )
| ~ relation(X2)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_2517]) ).
tcf(c_15257,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X2,X0) = relation_dom(X1) )
| ~ relation(X2)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_2517]) ).
tcf(c_15259,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_2517]) ).
tcf(c_15260,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X0) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_2517]) ).
tcf(c_15261,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X2) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_2517]) ).
tcf(c_15262,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(X0)) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_2517]) ).
tcf(c_15263,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,X0) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_2517]) ).
tcf(c_15264,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,iPr_def_13) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_2517]) ).
tcf(c_15265,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(iPr_def_13,X0) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_2517]) ).
tcf(c_15266,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,sK1(powerset(X0))) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_2517]) ).
tcf(c_15267,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK11,X0) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_2517]) ).
tcf(c_15268,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK12,X0) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_2517]) ).
tcf(c_15269,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(X0)),X2) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_2517]) ).
tcf(c_15270,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = relation_dom(X0) )
| ~ empty(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_2517]) ).
tcf(c_15271,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = relation_dom(X0) )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_2517]) ).
tcf(c_15272,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = relation_dom(X0) )
| ~ empty(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_2517]) ).
tcf(c_15273,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = relation_dom(X0) )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_2517]) ).
tcf(c_15274,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = relation_dom(X0) )
| ~ empty(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_2517]) ).
tcf(c_15275,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = relation_dom(X0) )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_2517]) ).
tcf(c_15276,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,sK12) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_2517]) ).
tcf(c_15277,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,sK11) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_2517]) ).
tcf(c_15278,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(X0))) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_2517]) ).
tcf(c_15279,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(sK4(powerset(X0))),X2) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_2517]) ).
tcf(c_15280,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,sK1(sK4(powerset(X0)))) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_2517]) ).
tcf(c_15511,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X0,X2) = identity_relation(X1) )
| ~ relation(X2)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_2518]) ).
tcf(c_15512,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X2,X0) = identity_relation(X1) )
| ~ relation(X2)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_2518]) ).
tcf(c_15514,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X1) = relation_dom(X0) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_2518]) ).
tcf(c_15515,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X0) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_2518]) ).
tcf(c_15516,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X2) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_2518]) ).
tcf(c_15517,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(X0)) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_2518]) ).
tcf(c_15518,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,X0) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_2518]) ).
tcf(c_15519,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,iPr_def_13) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_2518]) ).
tcf(c_15520,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(iPr_def_13,X0) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_2518]) ).
tcf(c_15521,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,sK1(powerset(X0))) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_2518]) ).
tcf(c_15522,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK11,X0) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_2518]) ).
tcf(c_15523,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK12,X0) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_2518]) ).
tcf(c_15524,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(X0)),X2) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_2518]) ).
tcf(c_15525,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = identity_relation(X0) )
| ~ empty(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_2518]) ).
tcf(c_15526,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = identity_relation(X0) )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_2518]) ).
tcf(c_15527,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = identity_relation(X0) )
| ~ empty(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_2518]) ).
tcf(c_15528,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = identity_relation(X0) )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_2518]) ).
tcf(c_15529,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = identity_relation(X0) )
| ~ empty(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_2518]) ).
tcf(c_15530,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = identity_relation(X0) )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_2518]) ).
tcf(c_15531,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,sK12) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_2518]) ).
tcf(c_15532,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,sK11) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_2518]) ).
tcf(c_15533,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(X0))) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_2518]) ).
tcf(c_15534,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(sK4(powerset(X0))),X2) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_2518]) ).
tcf(c_15535,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,sK1(sK4(powerset(X0)))) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_2518]) ).
tcf(c_15792,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X0) = X1 )
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2544,c_2518]) ).
tcf(c_15793,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = X1 )
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2544,c_2517]) ).
tcf(c_15794,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2544,c_110]) ).
tcf(c_15795,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(X0))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_14104]) ).
tcf(c_15796,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(X0))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_5630]) ).
tcf(c_15797,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_5629]) ).
tcf(c_15798,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(X0),X1) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_4060]) ).
tcf(c_15799,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(X0),X1) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_4059]) ).
tcf(c_15800,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(X0)) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_4011]) ).
tcf(c_15801,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(X0)) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_4010]) ).
tcf(c_15802,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(X0))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_3938]) ).
tcf(c_15803,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(X0))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_3937]) ).
tcf(c_15804,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X0,X1)) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_3179]) ).
tcf(c_15805,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X0,X1)) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_3178]) ).
tcf(c_15806,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,X0)) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_3083]) ).
tcf(c_15807,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,X0)) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_3082]) ).
tcf(c_15808,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(X0))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_2687]) ).
tcf(c_15809,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_2686]) ).
tcf(c_15810,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_2658]) ).
tcf(c_15811,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_2637]) ).
tcf(c_15812,plain,
! [X0: $i] :
( ( sK1(powerset(X0)) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_3939]) ).
tcf(c_15813,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_3180]) ).
tcf(c_15814,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_3084]) ).
tcf(c_15815,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(X0)) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_2474]) ).
tcf(c_15816,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_2473]) ).
tcf(c_15817,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_2055]) ).
tcf(c_15818,plain,
! [X0: $i] :
( ( identity_relation(X0) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_2184]) ).
tcf(c_15819,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_2013]) ).
tcf(c_15820,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_108]) ).
tcf(c_15821,plain,
! [X0: $i] :
( relation(X0)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_51]) ).
tcf(c_15822,plain,
! [X0: $i] :
( function(X0)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_50]) ).
tcf(c_15823,plain,
! [X0: $i] : apply(identity_relation(powerset(X0)),sK1(powerset(X0))) = sK1(powerset(X0)),
inference(superposition,[status(thm)],[c_2544,c_69]) ).
tcf(c_15824,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(relation_dom(X0)),sK1(relation_dom(X0))) = sK1(relation_dom(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_2544,c_75]) ).
tcf(c_15825,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(sK4(X0)),sK1(sK4(X0))) = sK1(sK4(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_86]) ).
tcf(c_15826,plain,
apply(identity_relation(sK6),sK1(sK6)) = sK1(sK6),
inference(superposition,[status(thm)],[c_2544,c_88]) ).
tcf(c_15827,plain,
apply(identity_relation(sK8),sK1(sK8)) = sK1(sK8),
inference(superposition,[status(thm)],[c_2544,c_92]) ).
tcf(c_15828,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK12) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_11194]) ).
tcf(c_15829,plain,
! [X0: $i] :
( ( set_intersection2(sK12,X0) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_11032]) ).
tcf(c_15830,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK11) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_10263]) ).
tcf(c_15831,plain,
! [X0: $i] :
( ( set_intersection2(sK11,X0) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_10061]) ).
tcf(c_15832,plain,
! [X0: $i] :
( ( set_intersection2(X0,iPr_def_13) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_8927]) ).
tcf(c_15833,plain,
! [X0: $i] :
( ( set_intersection2(iPr_def_13,X0) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_8773]) ).
tcf(c_15834,plain,
! [X0: $i] :
( function(X0)
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_1965]) ).
tcf(c_15835,plain,
! [X0: $i] :
( relation(X0)
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_1918]) ).
tcf(c_15836,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_1893]) ).
tcf(c_15837,plain,
apply(identity_relation(sK12),sK1(sK12)) = sK1(sK12),
inference(superposition,[status(thm)],[c_2544,c_3280]) ).
tcf(c_15838,plain,
apply(identity_relation(iPr_def_10),sK1(iPr_def_10)) = sK1(iPr_def_10),
inference(superposition,[status(thm)],[c_2544,c_3282]) ).
tcf(c_15839,plain,
apply(identity_relation(sK11),sK1(sK11)) = sK1(sK11),
inference(superposition,[status(thm)],[c_2544,c_3220]) ).
tcf(c_15840,plain,
apply(identity_relation(iPr_def_11),sK1(iPr_def_11)) = sK1(iPr_def_11),
inference(superposition,[status(thm)],[c_2544,c_3222]) ).
tcf(c_15841,plain,
apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13),
inference(superposition,[status(thm)],[c_2544,c_4400]) ).
tcf(c_15842,plain,
apply(identity_relation(iPr_def_14),sK1(iPr_def_14)) = sK1(iPr_def_14),
inference(superposition,[status(thm)],[c_2544,c_4408]) ).
tcf(c_15843,plain,
apply(identity_relation(iPr_def_12),sK1(iPr_def_12)) = sK1(iPr_def_12),
inference(superposition,[status(thm)],[c_2544,c_4398]) ).
tcf(c_15844,plain,
apply(identity_relation(sK4(powerset(empty_set))),sK1(sK4(powerset(empty_set)))) = sK1(sK4(powerset(empty_set))),
inference(superposition,[status(thm)],[c_2544,c_15233]) ).
tcf(c_15845,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_14)),sK1(relation_composition(identity_relation(X0),iPr_def_14))) = sK1(relation_composition(identity_relation(X0),iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_2544,c_3290]) ).
tcf(c_15846,plain,
! [X0: $i] :
( function(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_14)),sK1(relation_composition(identity_relation(X0),iPr_def_14))) = sK1(relation_composition(identity_relation(X0),iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_2544,c_3288]) ).
tcf(c_15847,plain,
! [X0: $i] :
( relation(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_14)),sK1(relation_composition(identity_relation(X0),iPr_def_14))) = sK1(relation_composition(identity_relation(X0),iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_2544,c_3289]) ).
tcf(c_15848,plain,
! [X0: $i] :
( empty(set_intersection2(sK11,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_11)),sK1(relation_composition(identity_relation(X0),iPr_def_11))) = sK1(relation_composition(identity_relation(X0),iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4108]) ).
tcf(c_15849,plain,
! [X0: $i] :
( relation(set_intersection2(sK11,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_11)),sK1(relation_composition(identity_relation(X0),iPr_def_11))) = sK1(relation_composition(identity_relation(X0),iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4107]) ).
tcf(c_15850,plain,
! [X0: $i] :
( function(set_intersection2(sK11,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_11)),sK1(relation_composition(identity_relation(X0),iPr_def_11))) = sK1(relation_composition(identity_relation(X0),iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4106]) ).
tcf(c_15851,plain,
! [X0: $i] :
( empty(set_intersection2(sK12,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_10)),sK1(relation_composition(identity_relation(X0),iPr_def_10))) = sK1(relation_composition(identity_relation(X0),iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4466]) ).
tcf(c_15852,plain,
! [X0: $i] :
( relation(set_intersection2(sK12,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_10)),sK1(relation_composition(identity_relation(X0),iPr_def_10))) = sK1(relation_composition(identity_relation(X0),iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4465]) ).
tcf(c_15853,plain,
! [X0: $i] :
( function(set_intersection2(sK12,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_10)),sK1(relation_composition(identity_relation(X0),iPr_def_10))) = sK1(relation_composition(identity_relation(X0),iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4464]) ).
tcf(c_15854,plain,
apply(identity_relation(relation_composition(iPr_def_11,iPr_def_10)),sK1(relation_composition(iPr_def_11,iPr_def_10))) = sK1(relation_composition(iPr_def_11,iPr_def_10)),
inference(superposition,[status(thm)],[c_2544,c_4558]) ).
tcf(c_15855,plain,
( empty(set_intersection2(iPr_def_13,sK12))
| ( apply(identity_relation(relation_composition(iPr_def_10,iPr_def_14)),sK1(relation_composition(iPr_def_10,iPr_def_14))) = sK1(relation_composition(iPr_def_10,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4639]) ).
tcf(c_15856,plain,
( function(set_intersection2(iPr_def_13,sK12))
| ( apply(identity_relation(relation_composition(iPr_def_10,iPr_def_14)),sK1(relation_composition(iPr_def_10,iPr_def_14))) = sK1(relation_composition(iPr_def_10,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4637]) ).
tcf(c_15857,plain,
( relation(set_intersection2(iPr_def_13,sK12))
| ( apply(identity_relation(relation_composition(iPr_def_10,iPr_def_14)),sK1(relation_composition(iPr_def_10,iPr_def_14))) = sK1(relation_composition(iPr_def_10,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4638]) ).
tcf(c_15858,plain,
( empty(set_intersection2(iPr_def_13,sK11))
| ( apply(identity_relation(relation_composition(iPr_def_11,iPr_def_14)),sK1(relation_composition(iPr_def_11,iPr_def_14))) = sK1(relation_composition(iPr_def_11,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4693]) ).
tcf(c_15859,plain,
( relation(set_intersection2(iPr_def_13,sK11))
| ( apply(identity_relation(relation_composition(iPr_def_11,iPr_def_14)),sK1(relation_composition(iPr_def_11,iPr_def_14))) = sK1(relation_composition(iPr_def_11,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4692]) ).
tcf(c_15860,plain,
( function(set_intersection2(iPr_def_13,sK11))
| ( apply(identity_relation(relation_composition(iPr_def_11,iPr_def_14)),sK1(relation_composition(iPr_def_11,iPr_def_14))) = sK1(relation_composition(iPr_def_11,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4691]) ).
tcf(c_15861,plain,
apply(identity_relation(relation_composition(iPr_def_14,iPr_def_14)),sK1(relation_composition(iPr_def_14,iPr_def_14))) = sK1(relation_composition(iPr_def_14,iPr_def_14)),
inference(superposition,[status(thm)],[c_2544,c_4874]) ).
tcf(c_15862,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_12)),sK1(relation_composition(identity_relation(X0),iPr_def_12))) = sK1(relation_composition(identity_relation(X0),iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_2544,c_5425]) ).
tcf(c_15863,plain,
! [X0: $i] :
( relation(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_12)),sK1(relation_composition(identity_relation(X0),iPr_def_12))) = sK1(relation_composition(identity_relation(X0),iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_2544,c_5424]) ).
tcf(c_15864,plain,
! [X0: $i] :
( function(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_12)),sK1(relation_composition(identity_relation(X0),iPr_def_12))) = sK1(relation_composition(identity_relation(X0),iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_2544,c_5423]) ).
tcf(c_15865,plain,
apply(identity_relation(relation_composition(iPr_def_11,iPr_def_11)),sK1(relation_composition(iPr_def_11,iPr_def_11))) = sK1(relation_composition(iPr_def_11,iPr_def_11)),
inference(superposition,[status(thm)],[c_2544,c_5699]) ).
tcf(c_15866,plain,
( empty(set_intersection2(iPr_def_13,sK11))
| ( apply(identity_relation(relation_composition(iPr_def_14,iPr_def_11)),sK1(relation_composition(iPr_def_14,iPr_def_11))) = sK1(relation_composition(iPr_def_14,iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_2544,c_5742]) ).
tcf(c_15867,plain,
( relation(set_intersection2(iPr_def_13,sK11))
| ( apply(identity_relation(relation_composition(iPr_def_14,iPr_def_11)),sK1(relation_composition(iPr_def_14,iPr_def_11))) = sK1(relation_composition(iPr_def_14,iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_2544,c_5741]) ).
tcf(c_15868,plain,
( function(set_intersection2(iPr_def_13,sK11))
| ( apply(identity_relation(relation_composition(iPr_def_14,iPr_def_11)),sK1(relation_composition(iPr_def_14,iPr_def_11))) = sK1(relation_composition(iPr_def_14,iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_2544,c_5740]) ).
tcf(c_15869,plain,
apply(identity_relation(relation_composition(iPr_def_10,iPr_def_10)),sK1(relation_composition(iPr_def_10,iPr_def_10))) = sK1(relation_composition(iPr_def_10,iPr_def_10)),
inference(superposition,[status(thm)],[c_2544,c_5794]) ).
tcf(c_15870,plain,
( empty(set_intersection2(iPr_def_13,sK12))
| ( apply(identity_relation(relation_composition(iPr_def_14,iPr_def_10)),sK1(relation_composition(iPr_def_14,iPr_def_10))) = sK1(relation_composition(iPr_def_14,iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_2544,c_5836]) ).
tcf(c_15871,plain,
( relation(set_intersection2(iPr_def_13,sK12))
| ( apply(identity_relation(relation_composition(iPr_def_14,iPr_def_10)),sK1(relation_composition(iPr_def_14,iPr_def_10))) = sK1(relation_composition(iPr_def_14,iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_2544,c_5835]) ).
tcf(c_15872,plain,
( function(set_intersection2(iPr_def_13,sK12))
| ( apply(identity_relation(relation_composition(iPr_def_14,iPr_def_10)),sK1(relation_composition(iPr_def_14,iPr_def_10))) = sK1(relation_composition(iPr_def_14,iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_2544,c_5834]) ).
tcf(c_15873,plain,
( function(set_intersection2(iPr_def_13,sK12))
| ( apply(identity_relation(relation_composition(iPr_def_10,iPr_def_12)),sK1(relation_composition(iPr_def_10,iPr_def_12))) = sK1(relation_composition(iPr_def_10,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_2544,c_6216]) ).
tcf(c_15874,plain,
( empty(set_intersection2(iPr_def_13,sK12))
| ( apply(identity_relation(relation_composition(iPr_def_10,iPr_def_12)),sK1(relation_composition(iPr_def_10,iPr_def_12))) = sK1(relation_composition(iPr_def_10,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_2544,c_6218]) ).
tcf(c_15875,plain,
( relation(set_intersection2(iPr_def_13,sK12))
| ( apply(identity_relation(relation_composition(iPr_def_10,iPr_def_12)),sK1(relation_composition(iPr_def_10,iPr_def_12))) = sK1(relation_composition(iPr_def_10,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_2544,c_6217]) ).
tcf(c_15876,plain,
( empty(set_intersection2(iPr_def_13,sK11))
| ( apply(identity_relation(relation_composition(iPr_def_11,iPr_def_12)),sK1(relation_composition(iPr_def_11,iPr_def_12))) = sK1(relation_composition(iPr_def_11,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_2544,c_6270]) ).
tcf(c_15877,plain,
( function(set_intersection2(iPr_def_13,sK11))
| ( apply(identity_relation(relation_composition(iPr_def_11,iPr_def_12)),sK1(relation_composition(iPr_def_11,iPr_def_12))) = sK1(relation_composition(iPr_def_11,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_2544,c_6268]) ).
tcf(c_15878,plain,
( relation(set_intersection2(iPr_def_13,sK11))
| ( apply(identity_relation(relation_composition(iPr_def_11,iPr_def_12)),sK1(relation_composition(iPr_def_11,iPr_def_12))) = sK1(relation_composition(iPr_def_11,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_2544,c_6269]) ).
tcf(c_15879,plain,
apply(identity_relation(relation_composition(iPr_def_14,iPr_def_12)),sK1(relation_composition(iPr_def_14,iPr_def_12))) = sK1(relation_composition(iPr_def_14,iPr_def_12)),
inference(superposition,[status(thm)],[c_2544,c_6381]) ).
tcf(c_15880,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK12))
| ( apply(identity_relation(relation_composition(iPr_def_10,identity_relation(X0))),sK1(relation_composition(iPr_def_10,identity_relation(X0)))) = sK1(relation_composition(iPr_def_10,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_2544,c_7051]) ).
tcf(c_15881,plain,
! [X0: $i] :
( function(set_intersection2(X0,sK12))
| ( apply(identity_relation(relation_composition(iPr_def_10,identity_relation(X0))),sK1(relation_composition(iPr_def_10,identity_relation(X0)))) = sK1(relation_composition(iPr_def_10,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_2544,c_7049]) ).
tcf(c_15882,plain,
! [X0: $i] :
( relation(set_intersection2(X0,sK12))
| ( apply(identity_relation(relation_composition(iPr_def_10,identity_relation(X0))),sK1(relation_composition(iPr_def_10,identity_relation(X0)))) = sK1(relation_composition(iPr_def_10,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_2544,c_7050]) ).
tcf(c_15883,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK11))
| ( apply(identity_relation(relation_composition(iPr_def_11,identity_relation(X0))),sK1(relation_composition(iPr_def_11,identity_relation(X0)))) = sK1(relation_composition(iPr_def_11,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_2544,c_7195]) ).
tcf(c_15884,plain,
! [X0: $i] :
( relation(set_intersection2(X0,sK11))
| ( apply(identity_relation(relation_composition(iPr_def_11,identity_relation(X0))),sK1(relation_composition(iPr_def_11,identity_relation(X0)))) = sK1(relation_composition(iPr_def_11,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_2544,c_7194]) ).
tcf(c_15885,plain,
! [X0: $i] :
( function(set_intersection2(X0,sK11))
| ( apply(identity_relation(relation_composition(iPr_def_11,identity_relation(X0))),sK1(relation_composition(iPr_def_11,identity_relation(X0)))) = sK1(relation_composition(iPr_def_11,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_2544,c_7193]) ).
tcf(c_15886,plain,
! [X0: $i] :
( function(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(relation_composition(iPr_def_14,identity_relation(X0))),sK1(relation_composition(iPr_def_14,identity_relation(X0)))) = sK1(relation_composition(iPr_def_14,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_2544,c_7987]) ).
tcf(c_15887,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(relation_composition(iPr_def_14,identity_relation(X0))),sK1(relation_composition(iPr_def_14,identity_relation(X0)))) = sK1(relation_composition(iPr_def_14,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_2544,c_7989]) ).
tcf(c_15888,plain,
! [X0: $i] :
( relation(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(relation_composition(iPr_def_14,identity_relation(X0))),sK1(relation_composition(iPr_def_14,identity_relation(X0)))) = sK1(relation_composition(iPr_def_14,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_2544,c_7988]) ).
tcf(c_15889,plain,
apply(iPr_def_14,sK1(iPr_def_13)) = sK1(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_15841,c_1151]) ).
tcf(c_15890,plain,
apply(iPr_def_11,sK1(sK11)) = sK1(sK11),
inference(light_normalisation,[status(thm)],[c_15839,c_1148]) ).
tcf(c_15891,plain,
apply(iPr_def_10,sK1(sK12)) = sK1(sK12),
inference(light_normalisation,[status(thm)],[c_15837,c_1147]) ).
tcf(c_16700,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( sK1(sK4(powerset(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15795]) ).
tcf(c_16708,plain,
! [X0: $i] :
( empty(set_intersection2(X0,X0))
| ~ in(X0,sK1(X0)) ),
inference(superposition,[status(thm)],[c_80,c_2739]) ).
tcf(c_16709,plain,
! [X0: $i] :
( empty(set_intersection2(X0,empty_set))
| ~ in(empty_set,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_97,c_2739]) ).
tcf(c_16710,plain,
! [X0: $i] :
( empty(set_intersection2(empty_set,X0))
| ~ in(X0,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_1996,c_2739]) ).
tcf(c_16712,plain,
( empty(set_intersection2(sK12,relation_dom(sK2)))
| ~ in(relation_dom(sK2),sK1(relation_dom(relation_composition(iPr_def_10,sK2)))) ),
inference(superposition,[status(thm)],[c_6018,c_2739]) ).
tcf(c_16713,plain,
( empty(set_intersection2(sK11,relation_dom(sK2)))
| ~ in(relation_dom(sK2),sK1(relation_dom(relation_composition(iPr_def_11,sK2)))) ),
inference(superposition,[status(thm)],[c_6133,c_2739]) ).
tcf(c_16714,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| ~ in(relation_dom(sK2),sK1(relation_dom(relation_composition(iPr_def_14,sK2)))) ),
inference(superposition,[status(thm)],[c_6817,c_2739]) ).
tcf(c_16715,plain,
! [X0: $i] :
( empty(empty_set)
| ~ in(X0,sK1(empty_set)) ),
inference(light_normalisation,[status(thm)],[c_16710,c_1996]) ).
tcf(c_16716,plain,
( empty(empty_set)
| ~ in(empty_set,sK1(empty_set)) ),
inference(light_normalisation,[status(thm)],[c_16709,c_97]) ).
tcf(c_16718,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ in(relation_dom(sK2),sK1(relation_dom(relation_composition(iPr_def_14,sK2)))) ),
inference(light_normalisation,[status(thm)],[c_16714,c_6817]) ).
tcf(c_16721,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ in(relation_dom(sK2),sK1(relation_dom(relation_composition(iPr_def_11,sK2)))) ),
inference(light_normalisation,[status(thm)],[c_16713,c_6133]) ).
tcf(c_16724,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ in(relation_dom(sK2),sK1(relation_dom(relation_composition(iPr_def_10,sK2)))) ),
inference(light_normalisation,[status(thm)],[c_16712,c_6018]) ).
tcf(c_16749,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,sK12,X1),iPr_def_13)
| in(sK0(X0,sK12,X1),X1)
| ( set_intersection2(X0,sK12) = X1 )
| ~ in(sK0(X0,sK12,X1),sK11) ),
inference(superposition,[status(thm)],[c_55,c_2962]) ).
tcf(c_16750,plain,
! [X0: $i,X1: $i] :
( in(sK0(sK12,X0,X1),iPr_def_13)
| element(sK0(sK12,X0,X1),X1)
| ( set_intersection2(sK12,X0) = X1 )
| ~ in(sK0(sK12,X0,X1),sK11) ),
inference(superposition,[status(thm)],[c_2239,c_2962]) ).
tcf(c_16751,plain,
! [X0: $i,X1: $i] :
( in(sK0(sK12,X0,X1),iPr_def_13)
| in(sK0(sK12,X0,X1),X1)
| ( set_intersection2(sK12,X0) = X1 )
| ~ in(sK0(sK12,X0,X1),sK11) ),
inference(superposition,[status(thm)],[c_54,c_2962]) ).
tcf(c_16752,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,sK12),iPr_def_13)
| in(sK0(X0,X1,sK12),X1)
| ( set_intersection2(X0,X1) = sK12 )
| ~ in(sK0(X0,X1,sK12),sK11) ),
inference(superposition,[status(thm)],[c_55,c_2962]) ).
tcf(c_16753,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,sK12),iPr_def_13)
| in(sK0(X0,X1,sK12),X0)
| ( set_intersection2(X0,X1) = sK12 )
| ~ in(sK0(X0,X1,sK12),sK11) ),
inference(superposition,[status(thm)],[c_54,c_2962]) ).
tcf(c_16754,plain,
( empty(sK12)
| in(sK1(sK12),iPr_def_13)
| ~ in(sK1(sK12),sK11) ),
inference(superposition,[status(thm)],[c_2137,c_2962]) ).
tcf(c_16755,plain,
! [X0: $i] :
( empty(set_intersection2(sK12,X0))
| in(sK1(set_intersection2(X0,sK12)),iPr_def_13)
| ~ in(sK1(set_intersection2(X0,sK12)),sK11) ),
inference(superposition,[status(thm)],[c_7250,c_2962]) ).
tcf(c_16756,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK12))
| in(sK1(set_intersection2(X0,sK12)),iPr_def_13)
| ~ in(sK1(set_intersection2(X0,sK12)),sK11) ),
inference(superposition,[status(thm)],[c_2201,c_2962]) ).
tcf(c_16757,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK12))
| in(sK1(set_intersection2(sK12,X0)),iPr_def_13)
| ~ in(sK1(set_intersection2(sK12,X0)),sK11) ),
inference(superposition,[status(thm)],[c_2732,c_2962]) ).
tcf(c_16758,plain,
! [X0: $i] :
( empty(set_intersection2(sK12,X0))
| in(sK1(set_intersection2(sK12,X0)),iPr_def_13)
| ~ in(sK1(set_intersection2(sK12,X0)),sK11) ),
inference(superposition,[status(thm)],[c_2202,c_2962]) ).
tcf(c_16759,plain,
( in(sK1(iPr_def_13),iPr_def_13)
| ~ in(sK1(iPr_def_13),sK11) ),
inference(superposition,[status(thm)],[c_4407,c_2962]) ).
tcf(c_16760,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(sK12,X0,set_intersection2(X1,X2)),iPr_def_13)
| in(sK0(sK12,X0,set_intersection2(X1,X2)),X2)
| ( set_intersection2(X1,X2) = set_intersection2(sK12,X0) )
| ~ in(sK0(sK12,X0,set_intersection2(X1,X2)),sK11) ),
inference(superposition,[status(thm)],[c_2241,c_2962]) ).
tcf(c_16761,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,set_intersection2(X2,sK12)),iPr_def_13)
| in(sK0(X0,X1,set_intersection2(X2,sK12)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,sK12) )
| ~ in(sK0(X0,X1,set_intersection2(X2,sK12)),sK11) ),
inference(superposition,[status(thm)],[c_2241,c_2962]) ).
tcf(c_16762,plain,
! [X0: $i] :
( in(sK0(empty_set,X0,sK12),iPr_def_13)
| ( empty_set = sK12 )
| ~ in(sK0(empty_set,X0,sK12),sK11) ),
inference(superposition,[status(thm)],[c_5683,c_2962]) ).
tcf(c_16763,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(set_intersection2(X0,iPr_def_13)),iPr_def_13)
| ~ in(sK1(set_intersection2(X0,iPr_def_13)),sK11) ),
inference(superposition,[status(thm)],[c_12252,c_2962]) ).
tcf(c_16764,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(set_intersection2(X0,iPr_def_13)),iPr_def_13)
| ~ in(sK1(set_intersection2(X0,iPr_def_13)),sK11) ),
inference(superposition,[status(thm)],[c_2747,c_2962]) ).
tcf(c_16765,plain,
! [X0: $i] :
( in(sK0(X0,empty_set,sK12),iPr_def_13)
| ( empty_set = sK12 )
| ~ in(sK0(X0,empty_set,sK12),sK11) ),
inference(superposition,[status(thm)],[c_5686,c_2962]) ).
tcf(c_16767,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(set_intersection2(iPr_def_13,X0)),iPr_def_13)
| ~ in(sK1(set_intersection2(iPr_def_13,X0)),sK11) ),
inference(superposition,[status(thm)],[c_7924,c_2962]) ).
tcf(c_16768,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(set_intersection2(iPr_def_13,X0)),iPr_def_13)
| ~ in(sK1(set_intersection2(iPr_def_13,X0)),sK11) ),
inference(superposition,[status(thm)],[c_7268,c_2962]) ).
tcf(c_16769,plain,
! [X0: $i] :
( in(sK0(empty_set,X0,iPr_def_13),iPr_def_13)
| ( empty_set = iPr_def_13 )
| ~ in(sK0(empty_set,X0,iPr_def_13),sK11) ),
inference(superposition,[status(thm)],[c_11626,c_2962]) ).
tcf(c_16770,plain,
! [X0: $i] :
( in(sK0(X0,empty_set,iPr_def_13),iPr_def_13)
| ( empty_set = iPr_def_13 )
| ~ in(sK0(X0,empty_set,iPr_def_13),sK11) ),
inference(superposition,[status(thm)],[c_11687,c_2962]) ).
tcf(c_16771,plain,
( empty(sK12)
| in(sK1(sK4(sK12)),iPr_def_13)
| ~ in(sK1(sK4(sK12)),sK11) ),
inference(superposition,[status(thm)],[c_12691,c_2962]) ).
tcf(c_16772,plain,
( in(sK1(sK4(iPr_def_13)),iPr_def_13)
| ~ in(sK1(sK4(iPr_def_13)),sK11) ),
inference(superposition,[status(thm)],[c_12724,c_2962]) ).
tcf(c_16773,plain,
in(sK1(iPr_def_13),iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_16759,c_4404]) ).
tcf(c_16774,plain,
in(sK1(sK4(iPr_def_13)),iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_16772,c_12725]) ).
tcf(c_16775,plain,
( in(sK1(sK12),iPr_def_13)
| ~ in(sK1(sK12),sK11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16754,c_3280]) ).
tcf(c_16778,plain,
( in(sK1(sK4(sK12)),iPr_def_13)
| ~ in(sK1(sK4(sK12)),sK11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16771,c_3280]) ).
tcf(c_16956,plain,
! [X0: $i] :
( empty(relation_composition(identity_relation(X0),empty_set))
| ~ relation(empty_set)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_59,c_3650]) ).
tcf(c_16957,plain,
! [X0: $i] :
( empty(relation_composition(identity_relation(X0),empty_set))
| ~ relation(empty_set)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_79,c_3650]) ).
tcf(c_16958,plain,
( empty(relation_composition(identity_relation(sK12),empty_set))
| ~ relation(relation_composition(iPr_def_10,empty_set)) ),
inference(superposition,[status(thm)],[c_1147,c_3650]) ).
tcf(c_16959,plain,
( empty(relation_composition(identity_relation(sK11),empty_set))
| ~ relation(relation_composition(iPr_def_11,empty_set)) ),
inference(superposition,[status(thm)],[c_1148,c_3650]) ).
tcf(c_16960,plain,
( empty(relation_composition(identity_relation(empty_set),empty_set))
| ~ relation(relation_composition(empty_set,empty_set)) ),
inference(superposition,[status(thm)],[c_2472,c_3650]) ).
tcf(c_16961,plain,
( empty(relation_composition(identity_relation(iPr_def_13),empty_set))
| ~ relation(relation_composition(iPr_def_14,empty_set)) ),
inference(superposition,[status(thm)],[c_1151,c_3650]) ).
tcf(c_16962,plain,
( empty(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_16961,c_1151,c_5508]) ).
tcf(c_16969,plain,
! [X0: $i] : empty(relation_composition(identity_relation(X0),empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_16956,c_74,c_71]) ).
tcf(c_16975,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X1),empty_set) = identity_relation(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16969,c_2518]) ).
tcf(c_16976,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X1),empty_set) = relation_dom(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16969,c_2517]) ).
tcf(c_16977,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X1),empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_16969,c_110]) ).
tcf(c_16978,plain,
! [X0: $i] : sK1(sK4(powerset(relation_composition(identity_relation(X0),empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_14104]) ).
tcf(c_16979,plain,
! [X0: $i] : sK1(powerset(identity_relation(relation_composition(identity_relation(X0),empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_5630]) ).
tcf(c_16980,plain,
! [X0: $i] : sK1(powerset(relation_dom(relation_composition(identity_relation(X0),empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_5629]) ).
tcf(c_16981,plain,
! [X0: $i,X1: $i] : set_intersection2(identity_relation(relation_composition(identity_relation(X0),empty_set)),X1) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_4060]) ).
tcf(c_16982,plain,
! [X0: $i,X1: $i] : set_intersection2(relation_dom(relation_composition(identity_relation(X0),empty_set)),X1) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_4059]) ).
tcf(c_16983,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,identity_relation(relation_composition(identity_relation(X1),empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_4011]) ).
tcf(c_16984,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,relation_dom(relation_composition(identity_relation(X1),empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_4010]) ).
tcf(c_16985,plain,
! [X0: $i] : relation_dom(sK1(powerset(relation_composition(identity_relation(X0),empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_3938]) ).
tcf(c_16986,plain,
! [X0: $i] : identity_relation(sK1(powerset(relation_composition(identity_relation(X0),empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_3937]) ).
tcf(c_16987,plain,
! [X0: $i,X1: $i] : relation_dom(set_intersection2(relation_composition(identity_relation(X0),empty_set),X1)) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_3179]) ).
tcf(c_16988,plain,
! [X0: $i,X1: $i] : identity_relation(set_intersection2(relation_composition(identity_relation(X0),empty_set),X1)) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_3178]) ).
tcf(c_16989,plain,
! [X0: $i,X1: $i] : relation_dom(set_intersection2(X0,relation_composition(identity_relation(X1),empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_3083]) ).
tcf(c_16990,plain,
! [X0: $i,X1: $i] : identity_relation(set_intersection2(X0,relation_composition(identity_relation(X1),empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_3082]) ).
tcf(c_16991,plain,
! [X0: $i] : identity_relation(identity_relation(identity_relation(relation_composition(identity_relation(X0),empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_2687]) ).
tcf(c_16992,plain,
! [X0: $i] : identity_relation(identity_relation(relation_dom(relation_composition(identity_relation(X0),empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_2686]) ).
tcf(c_16993,plain,
! [X0: $i] : identity_relation(relation_dom(relation_dom(relation_composition(identity_relation(X0),empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_2658]) ).
tcf(c_16994,plain,
! [X0: $i] : relation_dom(relation_dom(relation_dom(relation_composition(identity_relation(X0),empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_2637]) ).
tcf(c_16995,plain,
! [X0: $i] : sK1(powerset(relation_composition(identity_relation(X0),empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_3939]) ).
tcf(c_16996,plain,
! [X0: $i,X1: $i] : set_intersection2(relation_composition(identity_relation(X0),empty_set),X1) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_3180]) ).
tcf(c_16997,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,relation_composition(identity_relation(X1),empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_3084]) ).
tcf(c_16998,plain,
! [X0: $i] : identity_relation(identity_relation(relation_composition(identity_relation(X0),empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_2474]) ).
tcf(c_16999,plain,
! [X0: $i] : identity_relation(relation_dom(relation_composition(identity_relation(X0),empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_2473]) ).
tcf(c_17000,plain,
! [X0: $i] : relation_dom(relation_dom(relation_composition(identity_relation(X0),empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_2055]) ).
tcf(c_17001,plain,
! [X0: $i] : identity_relation(relation_composition(identity_relation(X0),empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_2184]) ).
tcf(c_17003,plain,
! [X0: $i] : relation_composition(identity_relation(X0),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_16969,c_108]) ).
tcf(c_17004,plain,
! [X0: $i] : relation(relation_composition(identity_relation(X0),empty_set)),
inference(superposition,[status(thm)],[c_16969,c_51]) ).
tcf(c_17005,plain,
! [X0: $i] : function(relation_composition(identity_relation(X0),empty_set)),
inference(superposition,[status(thm)],[c_16969,c_50]) ).
tcf(c_17294,plain,
~ in(iPr_def_13,sK1(iPr_def_13)),
inference(superposition,[status(thm)],[c_16773,c_49]) ).
tcf(c_17296,plain,
element(sK1(iPr_def_13),iPr_def_13),
inference(superposition,[status(thm)],[c_16773,c_95]) ).
tcf(c_17306,plain,
apply(identity_relation(iPr_def_13),sK1(sK4(iPr_def_13))) = sK1(sK4(iPr_def_13)),
inference(superposition,[status(thm)],[c_16774,c_172]) ).
tcf(c_17307,plain,
~ in(iPr_def_13,sK1(sK4(iPr_def_13))),
inference(superposition,[status(thm)],[c_16774,c_49]) ).
tcf(c_17309,plain,
element(sK1(sK4(iPr_def_13)),iPr_def_13),
inference(superposition,[status(thm)],[c_16774,c_95]) ).
tcf(c_17312,plain,
apply(iPr_def_14,sK1(sK4(iPr_def_13))) = sK1(sK4(iPr_def_13)),
inference(light_normalisation,[status(thm)],[c_17306,c_1151]) ).
tcf(c_17362,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(identity_relation(X1),empty_set),X0) = apply(empty_set,apply(identity_relation(X1),X0)) )
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_17003,c_96]) ).
tcf(c_17371,plain,
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( sK1(powerset(identity_relation(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15796]) ).
tcf(c_17373,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( sK1(powerset(identity_relation(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15796]) ).
tcf(c_17381,plain,
! [X0: $i] :
( relation(set_intersection2(relation_dom(sK2),X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),sK2)),sK1(relation_composition(identity_relation(X0),sK2))) = sK1(relation_composition(identity_relation(X0),sK2)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4766]) ).
tcf(c_17382,plain,
! [X0: $i] :
( relation(set_intersection2(relation_dom(sK2),X0))
| ~ relation(sK2)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_4766]) ).
tcf(c_17383,plain,
! [X0: $i] :
( relation(set_intersection2(relation_dom(sK2),X0))
| ~ empty(sK2)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_4766]) ).
tcf(c_17384,plain,
( relation(set_intersection2(relation_dom(sK2),sK12))
| ~ empty(relation_composition(iPr_def_10,sK2)) ),
inference(superposition,[status(thm)],[c_1147,c_4766]) ).
tcf(c_17385,plain,
( relation(set_intersection2(relation_dom(sK2),sK11))
| ~ empty(relation_composition(iPr_def_11,sK2)) ),
inference(superposition,[status(thm)],[c_1148,c_4766]) ).
tcf(c_17386,plain,
( relation(set_intersection2(relation_dom(sK2),empty_set))
| ~ empty(relation_composition(empty_set,sK2)) ),
inference(superposition,[status(thm)],[c_2472,c_4766]) ).
tcf(c_17387,plain,
( relation(set_intersection2(relation_dom(sK2),iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,sK2)) ),
inference(superposition,[status(thm)],[c_1151,c_4766]) ).
tcf(c_17390,plain,
( relation(set_intersection2(relation_dom(sK2),empty_set))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_17386,c_7117]) ).
tcf(c_17391,plain,
relation(set_intersection2(relation_dom(sK2),empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_17390,c_73]) ).
tcf(c_17396,plain,
! [X0: $i] :
( relation(set_intersection2(relation_dom(sK2),X0))
| ~ empty(sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17383,c_71]) ).
tcf(c_17399,plain,
! [X0: $i] :
( relation(set_intersection2(relation_dom(sK2),X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17382,c_81]) ).
tcf(c_17408,plain,
! [X0: $i] :
( relation(set_intersection2(X0,relation_dom(sK2)))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_52,c_17396]) ).
tcf(c_17410,plain,
( relation(relation_dom(sK2))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_80,c_17396]) ).
tcf(c_17426,plain,
( relation(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_6018,c_17408]) ).
tcf(c_17427,plain,
( relation(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_6133,c_17408]) ).
tcf(c_17428,plain,
( relation(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_6817,c_17408]) ).
tcf(c_17460,plain,
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( sK1(powerset(relation_dom(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15797]) ).
tcf(c_17462,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( sK1(powerset(relation_dom(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15797]) ).
tcf(c_17469,plain,
! [X0: $i] :
( relation(set_intersection2(X0,relation_dom(sK2)))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_52,c_17399]) ).
tcf(c_17471,plain,
( relation(relation_dom(sK2))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_80,c_17399]) ).
tcf(c_17486,plain,
( relation(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(identity_relation(sK12)) ),
inference(superposition,[status(thm)],[c_6018,c_17469]) ).
tcf(c_17487,plain,
( relation(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(identity_relation(sK11)) ),
inference(superposition,[status(thm)],[c_6133,c_17469]) ).
tcf(c_17488,plain,
( relation(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(identity_relation(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_6817,c_17469]) ).
tcf(c_17489,plain,
( relation(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_17488,c_1151]) ).
tcf(c_17490,plain,
( relation(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_17487,c_1148]) ).
tcf(c_17491,plain,
( relation(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_17486,c_1147]) ).
tcf(c_17492,plain,
( relation(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(relation_composition(iPr_def_10,sK2)) ),
inference(demodulation,[status(thm)],[c_17384,c_52,c_6018]) ).
tcf(c_17510,plain,
! [X0: $i] :
( ( set_intersection2(iPr_def_10,X0) = empty_set )
| ( apply(identity_relation(sK12),sK1(sK12)) = sK1(sK12) ) ),
inference(superposition,[status(thm)],[c_1147,c_15798]) ).
tcf(c_17511,plain,
! [X0: $i] :
( ( set_intersection2(iPr_def_11,X0) = empty_set )
| ( apply(identity_relation(sK11),sK1(sK11)) = sK1(sK11) ) ),
inference(superposition,[status(thm)],[c_1148,c_15798]) ).
tcf(c_17513,plain,
! [X0: $i] :
( ( set_intersection2(iPr_def_14,X0) = empty_set )
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_1151,c_15798]) ).
tcf(c_17516,plain,
! [X0: $i] :
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( set_intersection2(identity_relation(empty_set),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15798]) ).
tcf(c_17518,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( set_intersection2(identity_relation(powerset(empty_set)),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15798]) ).
tcf(c_17520,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(identity_relation(X1),X0))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ in(X0,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15798,c_2739]) ).
tcf(c_17526,plain,
! [X0: $i,X1: $i] :
( element(sK1(empty_set),X1)
| empty(set_intersection2(X1,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_12246]) ).
tcf(c_17527,plain,
! [X0: $i,X1: $i] :
( element(sK1(empty_set),identity_relation(X0))
| empty(set_intersection2(X1,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_7918]) ).
tcf(c_17528,plain,
! [X0: $i,X1: $i] :
( element(sK1(empty_set),identity_relation(X0))
| empty(set_intersection2(identity_relation(X0),X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_7262]) ).
tcf(c_17529,plain,
! [X0: $i,X1: $i] :
( in(sK1(empty_set),X1)
| empty(set_intersection2(X1,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_7250]) ).
tcf(c_17530,plain,
! [X0: $i,X1: $i] :
( element(sK1(empty_set),X1)
| empty(set_intersection2(identity_relation(X0),X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_2741]) ).
tcf(c_17531,plain,
! [X0: $i,X1: $i] :
( in(sK1(empty_set),identity_relation(X0))
| empty(set_intersection2(X1,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_2732]) ).
tcf(c_17532,plain,
! [X0: $i,X1: $i] :
( in(sK1(empty_set),identity_relation(X0))
| empty(set_intersection2(identity_relation(X0),X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_2202]) ).
tcf(c_17536,plain,
! [X0: $i,X1: $i] :
( in(sK1(empty_set),X1)
| empty(set_intersection2(identity_relation(X0),X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_2201]) ).
tcf(c_17538,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,empty_set)
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ in(X0,X2)
| ~ in(X0,identity_relation(X1)) ),
inference(superposition,[status(thm)],[c_15798,c_56]) ).
tcf(c_17542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,empty_set),X2)
| in(sK0(X2,X3,set_intersection2(identity_relation(X0),X1)),X1)
| ( set_intersection2(identity_relation(X0),X1) = set_intersection2(X2,X3) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_2241]) ).
tcf(c_17543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,empty_set),X1)
| in(sK0(X2,X3,set_intersection2(identity_relation(X0),X1)),X2)
| ( set_intersection2(identity_relation(X0),X1) = set_intersection2(X2,X3) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_2241]) ).
tcf(c_17544,plain,
! [X0: $i] :
( element(sK1(empty_set),sK12)
| empty(set_intersection2(iPr_def_13,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_13896]) ).
tcf(c_17545,plain,
! [X0: $i] :
( element(sK1(empty_set),sK11)
| empty(set_intersection2(iPr_def_13,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_13659]) ).
tcf(c_17546,plain,
! [X0: $i] :
( in(sK1(empty_set),sK12)
| empty(set_intersection2(iPr_def_13,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_12252]) ).
tcf(c_17547,plain,
! [X0: $i] :
( in(sK1(empty_set),sK11)
| empty(set_intersection2(iPr_def_13,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_12251]) ).
tcf(c_17548,plain,
! [X0: $i] :
( element(sK1(empty_set),sK12)
| empty(set_intersection2(identity_relation(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_8248]) ).
tcf(c_17549,plain,
! [X0: $i] :
( element(sK1(empty_set),sK11)
| empty(set_intersection2(identity_relation(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_8223]) ).
tcf(c_17552,plain,
! [X0: $i] :
( in(sK1(empty_set),sK12)
| empty(set_intersection2(identity_relation(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_2747]) ).
tcf(c_17553,plain,
! [X0: $i] :
( in(sK1(empty_set),sK11)
| empty(set_intersection2(identity_relation(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_2746]) ).
tcf(c_17624,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ in(X0,X2)
| ~ in(X0,identity_relation(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17538,c_5671]) ).
tcf(c_17652,plain,
( relation(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(relation_composition(iPr_def_11,sK2)) ),
inference(demodulation,[status(thm)],[c_17385,c_52,c_6133]) ).
tcf(c_17653,plain,
( relation(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(relation_composition(iPr_def_14,sK2)) ),
inference(demodulation,[status(thm)],[c_17387,c_52,c_6817]) ).
tcf(c_17658,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(sK2),X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),sK2)),sK1(relation_composition(identity_relation(X0),sK2))) = sK1(relation_composition(identity_relation(X0),sK2)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4767]) ).
tcf(c_17659,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(sK2),X0))
| ~ relation(sK2)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_4767]) ).
tcf(c_17660,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(sK2),X0))
| ~ empty(sK2)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_4767]) ).
tcf(c_17661,plain,
( empty(set_intersection2(relation_dom(sK2),sK12))
| ~ empty(relation_composition(iPr_def_10,sK2)) ),
inference(superposition,[status(thm)],[c_1147,c_4767]) ).
tcf(c_17662,plain,
( empty(set_intersection2(relation_dom(sK2),sK11))
| ~ empty(relation_composition(iPr_def_11,sK2)) ),
inference(superposition,[status(thm)],[c_1148,c_4767]) ).
tcf(c_17663,plain,
( empty(set_intersection2(relation_dom(sK2),empty_set))
| ~ empty(relation_composition(empty_set,sK2)) ),
inference(superposition,[status(thm)],[c_2472,c_4767]) ).
tcf(c_17664,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,sK2)) ),
inference(superposition,[status(thm)],[c_1151,c_4767]) ).
tcf(c_17667,plain,
( empty(set_intersection2(relation_dom(sK2),empty_set))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_17663,c_7117]) ).
tcf(c_17668,plain,
empty(set_intersection2(relation_dom(sK2),empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_17667,c_73]) ).
tcf(c_17673,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(sK2),X0))
| ~ empty(sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17660,c_71]) ).
tcf(c_17676,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(sK2),X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17659,c_81]) ).
tcf(c_17695,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(sK2)))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_52,c_17673]) ).
tcf(c_17697,plain,
( empty(relation_dom(sK2))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_80,c_17673]) ).
tcf(c_17699,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(sK2),X1) = identity_relation(X0) )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17673,c_2518]) ).
tcf(c_17700,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(sK2),X1) = relation_dom(X0) )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17673,c_2517]) ).
tcf(c_17701,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(sK2),X1) = X0 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17673,c_110]) ).
tcf(c_17702,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_14104]) ).
tcf(c_17703,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_5630]) ).
tcf(c_17704,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_5629]) ).
tcf(c_17705,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(set_intersection2(relation_dom(sK2),X0)),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_4060]) ).
tcf(c_17706,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(set_intersection2(relation_dom(sK2),X0)),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_4059]) ).
tcf(c_17707,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,identity_relation(set_intersection2(relation_dom(sK2),X1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_4011]) ).
tcf(c_17708,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,relation_dom(set_intersection2(relation_dom(sK2),X1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_4010]) ).
tcf(c_17709,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3938]) ).
tcf(c_17710,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3937]) ).
tcf(c_17711,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(set_intersection2(relation_dom(sK2),X0),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3179]) ).
tcf(c_17712,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(set_intersection2(relation_dom(sK2),X0),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3178]) ).
tcf(c_17713,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X0,set_intersection2(relation_dom(sK2),X1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3083]) ).
tcf(c_17714,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X0,set_intersection2(relation_dom(sK2),X1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3082]) ).
tcf(c_17715,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_2687]) ).
tcf(c_17716,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_2686]) ).
tcf(c_17717,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_2658]) ).
tcf(c_17718,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_2637]) ).
tcf(c_17719,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(relation_dom(sK2),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3939]) ).
tcf(c_17720,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(relation_dom(sK2),X0),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3180]) ).
tcf(c_17721,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(sK2),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3084]) ).
tcf(c_17722,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(relation_dom(sK2),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_2474]) ).
tcf(c_17723,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(relation_dom(sK2),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_2473]) ).
tcf(c_17724,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(relation_dom(sK2),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_2055]) ).
tcf(c_17725,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(sK2),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_2184]) ).
tcf(c_17726,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(sK2),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_2013]) ).
tcf(c_17727,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(sK2),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_108]) ).
tcf(c_17729,plain,
! [X0: $i] :
( function(set_intersection2(relation_dom(sK2),X0))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_50]) ).
tcf(c_17955,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_6018,c_17695]) ).
tcf(c_17956,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_6133,c_17695]) ).
tcf(c_17957,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_6817,c_17695]) ).
tcf(c_17958,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(sK2)) = identity_relation(X0) )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17695,c_2518]) ).
tcf(c_17959,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(sK2)) = relation_dom(X0) )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17695,c_2517]) ).
tcf(c_17960,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(sK2)) = X0 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17695,c_110]) ).
tcf(c_17961,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_14104]) ).
tcf(c_17962,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_5630]) ).
tcf(c_17963,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_5629]) ).
tcf(c_17964,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X0,relation_dom(sK2))),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_4060]) ).
tcf(c_17965,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X0,relation_dom(sK2))),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_4059]) ).
tcf(c_17966,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,identity_relation(set_intersection2(X1,relation_dom(sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_4011]) ).
tcf(c_17967,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,relation_dom(set_intersection2(X1,relation_dom(sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_4010]) ).
tcf(c_17968,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3938]) ).
tcf(c_17969,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3937]) ).
tcf(c_17970,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(set_intersection2(X0,relation_dom(sK2)),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3179]) ).
tcf(c_17971,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(set_intersection2(X0,relation_dom(sK2)),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3178]) ).
tcf(c_17972,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X0,set_intersection2(X1,relation_dom(sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3083]) ).
tcf(c_17973,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X0,set_intersection2(X1,relation_dom(sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3082]) ).
tcf(c_17974,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_2687]) ).
tcf(c_17975,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_2686]) ).
tcf(c_17976,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_2658]) ).
tcf(c_17977,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_2637]) ).
tcf(c_17978,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(X0,relation_dom(sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3939]) ).
tcf(c_17979,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,relation_dom(sK2)),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3180]) ).
tcf(c_17980,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(X1,relation_dom(sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3084]) ).
tcf(c_17981,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,relation_dom(sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_2474]) ).
tcf(c_17982,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,relation_dom(sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_2473]) ).
tcf(c_17983,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,relation_dom(sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_2055]) ).
tcf(c_17984,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_2184]) ).
tcf(c_17985,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_2013]) ).
tcf(c_17986,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(sK2)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_108]) ).
tcf(c_17988,plain,
! [X0: $i] :
( function(set_intersection2(X0,relation_dom(sK2)))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_50]) ).
tcf(c_18167,plain,
( function(relation_dom(sK2))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_80,c_17729]) ).
tcf(c_18169,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),set_intersection2(relation_dom(sK2),X0))) = set_intersection2(relation_dom(set_intersection2(relation_dom(sK2),X0)),X1) )
| ~ empty(sK2)
| ~ relation(set_intersection2(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_17729,c_103]) ).
tcf(c_18273,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = identity_relation(X0) )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17955,c_2518]) ).
tcf(c_18274,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = relation_dom(X0) )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17955,c_2517]) ).
tcf(c_18275,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = X0 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17955,c_110]) ).
tcf(c_18276,plain,
( ( sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_14104]) ).
tcf(c_18277,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_5630]) ).
tcf(c_18278,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_5629]) ).
tcf(c_18279,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_4060]) ).
tcf(c_18280,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_4059]) ).
tcf(c_18281,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_4011]) ).
tcf(c_18282,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_4010]) ).
tcf(c_18283,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3938]) ).
tcf(c_18284,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3937]) ).
tcf(c_18285,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3179]) ).
tcf(c_18286,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3178]) ).
tcf(c_18287,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3083]) ).
tcf(c_18288,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3082]) ).
tcf(c_18289,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_2687]) ).
tcf(c_18290,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_2686]) ).
tcf(c_18291,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_2658]) ).
tcf(c_18292,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_2637]) ).
tcf(c_18293,plain,
( ( sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3939]) ).
tcf(c_18294,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3180]) ).
tcf(c_18295,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3084]) ).
tcf(c_18296,plain,
( ( identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_2474]) ).
tcf(c_18297,plain,
( ( identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_2473]) ).
tcf(c_18298,plain,
( ( relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_2055]) ).
tcf(c_18299,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_2184]) ).
tcf(c_18300,plain,
( ( relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_2013]) ).
tcf(c_18301,plain,
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_108]) ).
tcf(c_18303,plain,
( function(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_50]) ).
tcf(c_18304,plain,
( empty(relation_composition(iPr_def_10,sK2))
| ~ empty(sK2)
| ~ relation(relation_composition(iPr_def_10,sK2)) ),
inference(superposition,[status(thm)],[c_17955,c_75]) ).
tcf(c_18537,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = identity_relation(X0) )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17956,c_2518]) ).
tcf(c_18538,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = relation_dom(X0) )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17956,c_2517]) ).
tcf(c_18539,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = X0 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17956,c_110]) ).
tcf(c_18540,plain,
( ( sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_14104]) ).
tcf(c_18541,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_5630]) ).
tcf(c_18542,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_5629]) ).
tcf(c_18543,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_4060]) ).
tcf(c_18544,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_4059]) ).
tcf(c_18545,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_4011]) ).
tcf(c_18546,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_4010]) ).
tcf(c_18547,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3938]) ).
tcf(c_18548,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3937]) ).
tcf(c_18549,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3179]) ).
tcf(c_18550,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3178]) ).
tcf(c_18551,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3083]) ).
tcf(c_18552,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3082]) ).
tcf(c_18553,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_2687]) ).
tcf(c_18554,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_2686]) ).
tcf(c_18555,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_2658]) ).
tcf(c_18556,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_2637]) ).
tcf(c_18557,plain,
( ( sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3939]) ).
tcf(c_18558,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3180]) ).
tcf(c_18559,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3084]) ).
tcf(c_18560,plain,
( ( identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_2474]) ).
tcf(c_18561,plain,
( ( identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_2473]) ).
tcf(c_18562,plain,
( ( relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_2055]) ).
tcf(c_18563,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_2184]) ).
tcf(c_18564,plain,
( ( relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_2013]) ).
tcf(c_18565,plain,
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_108]) ).
tcf(c_18567,plain,
( function(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_50]) ).
tcf(c_18568,plain,
( empty(relation_composition(iPr_def_11,sK2))
| ~ empty(sK2)
| ~ relation(relation_composition(iPr_def_11,sK2)) ),
inference(superposition,[status(thm)],[c_17956,c_75]) ).
tcf(c_18759,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = identity_relation(X0) )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17957,c_2518]) ).
tcf(c_18760,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = relation_dom(X0) )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17957,c_2517]) ).
tcf(c_18761,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = X0 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_17957,c_110]) ).
tcf(c_18762,plain,
( ( sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_14104]) ).
tcf(c_18763,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_5630]) ).
tcf(c_18764,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_5629]) ).
tcf(c_18765,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_4060]) ).
tcf(c_18766,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_4059]) ).
tcf(c_18767,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_4011]) ).
tcf(c_18768,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_4010]) ).
tcf(c_18769,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3938]) ).
tcf(c_18770,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3937]) ).
tcf(c_18771,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3179]) ).
tcf(c_18772,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3178]) ).
tcf(c_18773,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3083]) ).
tcf(c_18774,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3082]) ).
tcf(c_18775,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_2687]) ).
tcf(c_18776,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_2686]) ).
tcf(c_18777,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_2658]) ).
tcf(c_18778,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_2637]) ).
tcf(c_18779,plain,
( ( sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3939]) ).
tcf(c_18780,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3180]) ).
tcf(c_18781,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3084]) ).
tcf(c_18782,plain,
( ( identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_2474]) ).
tcf(c_18783,plain,
( ( identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_2473]) ).
tcf(c_18784,plain,
( ( relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_2055]) ).
tcf(c_18785,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_2184]) ).
tcf(c_18786,plain,
( ( relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_2013]) ).
tcf(c_18787,plain,
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_108]) ).
tcf(c_18789,plain,
( function(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_50]) ).
tcf(c_18790,plain,
( empty(relation_composition(iPr_def_14,sK2))
| ~ empty(sK2)
| ~ relation(relation_composition(iPr_def_14,sK2)) ),
inference(superposition,[status(thm)],[c_17957,c_75]) ).
tcf(c_19050,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),set_intersection2(X0,relation_dom(sK2)))) = set_intersection2(relation_dom(set_intersection2(X0,relation_dom(sK2))),X1) )
| ~ empty(sK2)
| ~ relation(set_intersection2(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_17988,c_103]) ).
tcf(c_19059,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),relation_dom(relation_composition(iPr_def_10,sK2)))) = set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0) )
| ~ empty(sK2)
| ~ relation(relation_dom(relation_composition(iPr_def_10,sK2))) ),
inference(superposition,[status(thm)],[c_18303,c_103]) ).
tcf(c_19068,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),relation_dom(relation_composition(iPr_def_11,sK2)))) = set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0) )
| ~ empty(sK2)
| ~ relation(relation_dom(relation_composition(iPr_def_11,sK2))) ),
inference(superposition,[status(thm)],[c_18567,c_103]) ).
tcf(c_19077,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(identity_relation(X0),relation_dom(relation_composition(iPr_def_14,sK2)))) = set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0) )
| ~ empty(sK2)
| ~ relation(relation_dom(relation_composition(iPr_def_14,sK2))) ),
inference(superposition,[status(thm)],[c_18789,c_103]) ).
tcf(c_19089,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_144,c_15799]) ).
tcf(c_19095,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(relation_dom(sK2),X0),X1) = empty_set )
| ( apply(identity_relation(relation_composition(identity_relation(X0),sK2)),sK1(relation_composition(identity_relation(X0),sK2))) = sK1(relation_composition(identity_relation(X0),sK2)) ) ),
inference(superposition,[status(thm)],[c_3034,c_15799]) ).
tcf(c_19096,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(sK12,X0),X1) = empty_set )
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_10)),sK1(relation_composition(identity_relation(X0),iPr_def_10))) = sK1(relation_composition(identity_relation(X0),iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_3031,c_15799]) ).
tcf(c_19097,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(sK11,X0),X1) = empty_set )
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_11)),sK1(relation_composition(identity_relation(X0),iPr_def_11))) = sK1(relation_composition(identity_relation(X0),iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_3029,c_15799]) ).
tcf(c_19098,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(iPr_def_13,X0),X1) = empty_set )
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_14)),sK1(relation_composition(identity_relation(X0),iPr_def_14))) = sK1(relation_composition(identity_relation(X0),iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_3027,c_15799]) ).
tcf(c_19099,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,X0),X2) = empty_set )
| ( apply(identity_relation(relation_composition(identity_relation(X0),identity_relation(X1))),sK1(relation_composition(identity_relation(X0),identity_relation(X1)))) = sK1(relation_composition(identity_relation(X0),identity_relation(X1))) ) ),
inference(superposition,[status(thm)],[c_3036,c_15799]) ).
tcf(c_19100,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(iPr_def_13,X0),X1) = empty_set )
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_12)),sK1(relation_composition(identity_relation(X0),iPr_def_12))) = sK1(relation_composition(identity_relation(X0),iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_5413,c_15799]) ).
tcf(c_19101,plain,
! [X0: $i] :
( ( set_intersection2(set_intersection2(iPr_def_13,sK12),X0) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_10,iPr_def_14)),sK1(relation_composition(iPr_def_10,iPr_def_14))) = sK1(relation_composition(iPr_def_10,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_3283,c_15799]) ).
tcf(c_19102,plain,
! [X0: $i] :
( ( set_intersection2(set_intersection2(iPr_def_13,sK11),X0) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_11,iPr_def_14)),sK1(relation_composition(iPr_def_11,iPr_def_14))) = sK1(relation_composition(iPr_def_11,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_3284,c_15799]) ).
tcf(c_19105,plain,
! [X0: $i] :
( ( set_intersection2(set_intersection2(iPr_def_13,sK11),X0) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_14,iPr_def_11)),sK1(relation_composition(iPr_def_14,iPr_def_11))) = sK1(relation_composition(iPr_def_14,iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_5734,c_15799]) ).
tcf(c_19108,plain,
! [X0: $i] :
( ( set_intersection2(set_intersection2(iPr_def_13,sK12),X0) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_14,iPr_def_10)),sK1(relation_composition(iPr_def_14,iPr_def_10))) = sK1(relation_composition(iPr_def_14,iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_5828,c_15799]) ).
tcf(c_19109,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,sK12),X1) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_10,identity_relation(X0))),sK1(relation_composition(iPr_def_10,identity_relation(X0)))) = sK1(relation_composition(iPr_def_10,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_5115,c_15799]) ).
tcf(c_19110,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,sK11),X1) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_11,identity_relation(X0))),sK1(relation_composition(iPr_def_11,identity_relation(X0)))) = sK1(relation_composition(iPr_def_11,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_5116,c_15799]) ).
tcf(c_19111,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(empty_set,X1) = empty_set )
| ( apply(identity_relation(relation_composition(empty_set,identity_relation(X0))),sK1(relation_composition(empty_set,identity_relation(X0)))) = sK1(relation_composition(empty_set,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_5133,c_15799]) ).
tcf(c_19112,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,iPr_def_13),X1) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_14,identity_relation(X0))),sK1(relation_composition(iPr_def_14,identity_relation(X0)))) = sK1(relation_composition(iPr_def_14,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_5118,c_15799]) ).
tcf(c_19113,plain,
! [X0: $i] :
( ( set_intersection2(set_intersection2(iPr_def_13,sK12),X0) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_10,iPr_def_12)),sK1(relation_composition(iPr_def_10,iPr_def_12))) = sK1(relation_composition(iPr_def_10,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_5414,c_15799]) ).
tcf(c_19114,plain,
! [X0: $i] :
( ( set_intersection2(set_intersection2(iPr_def_13,sK11),X0) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_11,iPr_def_12)),sK1(relation_composition(iPr_def_11,iPr_def_12))) = sK1(relation_composition(iPr_def_11,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_5415,c_15799]) ).
tcf(c_19118,plain,
! [X0: $i] :
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( set_intersection2(relation_dom(empty_set),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15799]) ).
tcf(c_19120,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( set_intersection2(relation_dom(powerset(empty_set)),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15799]) ).
tcf(c_19122,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(relation_dom(X1),X0))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ in(X0,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15799,c_2739]) ).
tcf(c_19128,plain,
! [X0: $i,X1: $i] :
( element(sK1(empty_set),X1)
| empty(set_intersection2(X1,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_12246]) ).
tcf(c_19129,plain,
! [X0: $i,X1: $i] :
( element(sK1(empty_set),relation_dom(X0))
| empty(set_intersection2(X1,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_7918]) ).
tcf(c_19130,plain,
! [X0: $i,X1: $i] :
( element(sK1(empty_set),relation_dom(X0))
| empty(set_intersection2(relation_dom(X0),X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_7262]) ).
tcf(c_19131,plain,
! [X0: $i,X1: $i] :
( in(sK1(empty_set),X1)
| empty(set_intersection2(X1,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_7250]) ).
tcf(c_19132,plain,
! [X0: $i,X1: $i] :
( element(sK1(empty_set),X1)
| empty(set_intersection2(relation_dom(X0),X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_2741]) ).
tcf(c_19133,plain,
! [X0: $i,X1: $i] :
( in(sK1(empty_set),relation_dom(X0))
| empty(set_intersection2(X1,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_2732]) ).
tcf(c_19134,plain,
! [X0: $i,X1: $i] :
( in(sK1(empty_set),relation_dom(X0))
| empty(set_intersection2(relation_dom(X0),X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_2202]) ).
tcf(c_19138,plain,
! [X0: $i,X1: $i] :
( in(sK1(empty_set),X1)
| empty(set_intersection2(relation_dom(X0),X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_2201]) ).
tcf(c_19140,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,empty_set)
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_15799,c_56]) ).
tcf(c_19144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,empty_set),X2)
| in(sK0(X2,X3,set_intersection2(relation_dom(X0),X1)),X1)
| ( set_intersection2(relation_dom(X0),X1) = set_intersection2(X2,X3) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_2241]) ).
tcf(c_19145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,empty_set),X1)
| in(sK0(X2,X3,set_intersection2(relation_dom(X0),X1)),X2)
| ( set_intersection2(relation_dom(X0),X1) = set_intersection2(X2,X3) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_2241]) ).
tcf(c_19146,plain,
! [X0: $i] :
( element(sK1(empty_set),sK12)
| empty(set_intersection2(iPr_def_13,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_13896]) ).
tcf(c_19147,plain,
! [X0: $i] :
( element(sK1(empty_set),sK11)
| empty(set_intersection2(iPr_def_13,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_13659]) ).
tcf(c_19148,plain,
! [X0: $i] :
( in(sK1(empty_set),sK12)
| empty(set_intersection2(iPr_def_13,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_12252]) ).
tcf(c_19149,plain,
! [X0: $i] :
( in(sK1(empty_set),sK11)
| empty(set_intersection2(iPr_def_13,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_12251]) ).
tcf(c_19150,plain,
! [X0: $i] :
( element(sK1(empty_set),sK12)
| empty(set_intersection2(relation_dom(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_8248]) ).
tcf(c_19151,plain,
! [X0: $i] :
( element(sK1(empty_set),sK11)
| empty(set_intersection2(relation_dom(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_8223]) ).
tcf(c_19154,plain,
! [X0: $i] :
( in(sK1(empty_set),sK12)
| empty(set_intersection2(relation_dom(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_2747]) ).
tcf(c_19155,plain,
! [X0: $i] :
( in(sK1(empty_set),sK11)
| empty(set_intersection2(relation_dom(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_2746]) ).
tcf(c_19231,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19140,c_5671]) ).
tcf(c_19623,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(sK2)))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_52,c_17676]) ).
tcf(c_19625,plain,
( empty(relation_dom(sK2))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_80,c_17676]) ).
tcf(c_19628,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(sK2),X0) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_2518]) ).
tcf(c_19629,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(sK2),X0) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_2517]) ).
tcf(c_19630,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(sK2),X0) = X1 )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_110]) ).
tcf(c_19631,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_14104]) ).
tcf(c_19632,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_5630]) ).
tcf(c_19633,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_5629]) ).
tcf(c_19634,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(set_intersection2(relation_dom(sK2),X0)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_4060]) ).
tcf(c_19635,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(set_intersection2(relation_dom(sK2),X0)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_4059]) ).
tcf(c_19636,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(relation_dom(sK2),X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_4011]) ).
tcf(c_19637,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(relation_dom(sK2),X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_4010]) ).
tcf(c_19638,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_3938]) ).
tcf(c_19639,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_3937]) ).
tcf(c_19640,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(set_intersection2(relation_dom(sK2),X0),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_3179]) ).
tcf(c_19641,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(set_intersection2(relation_dom(sK2),X0),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_3178]) ).
tcf(c_19642,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(relation_dom(sK2),X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_3083]) ).
tcf(c_19643,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(relation_dom(sK2),X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_3082]) ).
tcf(c_19644,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_2687]) ).
tcf(c_19645,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_2686]) ).
tcf(c_19646,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_2658]) ).
tcf(c_19647,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_2637]) ).
tcf(c_19648,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(relation_dom(sK2),X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_3939]) ).
tcf(c_19649,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(relation_dom(sK2),X0),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_3180]) ).
tcf(c_19650,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(relation_dom(sK2),X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_3084]) ).
tcf(c_19651,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(relation_dom(sK2),X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_2474]) ).
tcf(c_19652,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(relation_dom(sK2),X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_2473]) ).
tcf(c_19653,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(relation_dom(sK2),X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_2055]) ).
tcf(c_19654,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(sK2),X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_2184]) ).
tcf(c_19655,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(sK2),X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_2013]) ).
tcf(c_19656,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(sK2),X0) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_108]) ).
tcf(c_19658,plain,
! [X0: $i] :
( function(set_intersection2(relation_dom(sK2),X0))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_50]) ).
tcf(c_19957,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(identity_relation(sK12)) ),
inference(superposition,[status(thm)],[c_6018,c_19623]) ).
tcf(c_19958,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(identity_relation(sK11)) ),
inference(superposition,[status(thm)],[c_6133,c_19623]) ).
tcf(c_19959,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(identity_relation(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_6817,c_19623]) ).
tcf(c_19960,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,relation_dom(sK2)) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_2518]) ).
tcf(c_19961,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,relation_dom(sK2)) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_2517]) ).
tcf(c_19962,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,relation_dom(sK2)) = X1 )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_110]) ).
tcf(c_19963,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_14104]) ).
tcf(c_19964,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_5630]) ).
tcf(c_19965,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_5629]) ).
tcf(c_19966,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X0,relation_dom(sK2))),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_4060]) ).
tcf(c_19967,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X0,relation_dom(sK2))),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_4059]) ).
tcf(c_19968,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(X0,relation_dom(sK2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_4011]) ).
tcf(c_19969,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(X0,relation_dom(sK2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_4010]) ).
tcf(c_19970,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_3938]) ).
tcf(c_19971,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_3937]) ).
tcf(c_19972,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(set_intersection2(X0,relation_dom(sK2)),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_3179]) ).
tcf(c_19973,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(set_intersection2(X0,relation_dom(sK2)),X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_3178]) ).
tcf(c_19974,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(X0,relation_dom(sK2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_3083]) ).
tcf(c_19975,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(X0,relation_dom(sK2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_3082]) ).
tcf(c_19976,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_2687]) ).
tcf(c_19977,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_2686]) ).
tcf(c_19978,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_2658]) ).
tcf(c_19979,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_2637]) ).
tcf(c_19980,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(X0,relation_dom(sK2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_3939]) ).
tcf(c_19981,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,relation_dom(sK2)),X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_3180]) ).
tcf(c_19982,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(X0,relation_dom(sK2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_3084]) ).
tcf(c_19983,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,relation_dom(sK2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_2474]) ).
tcf(c_19984,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,relation_dom(sK2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_2473]) ).
tcf(c_19985,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,relation_dom(sK2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_2055]) ).
tcf(c_19986,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(sK2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_2184]) ).
tcf(c_19987,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(sK2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_2013]) ).
tcf(c_19988,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(sK2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_108]) ).
tcf(c_19990,plain,
! [X0: $i] :
( function(set_intersection2(X0,relation_dom(sK2)))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_50]) ).
tcf(c_19993,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_19959,c_1151]) ).
tcf(c_19994,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_19958,c_1148]) ).
tcf(c_19995,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_19957,c_1147]) ).
tcf(c_20141,plain,
( function(relation_dom(sK2))
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_80,c_19658]) ).
tcf(c_20144,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),set_intersection2(relation_dom(sK2),X0))) = set_intersection2(relation_dom(set_intersection2(relation_dom(sK2),X0)),X1) )
| ~ empty(identity_relation(X0))
| ~ relation(set_intersection2(relation_dom(sK2),X0)) ),
inference(superposition,[status(thm)],[c_19658,c_103]) ).
tcf(c_20161,plain,
( function(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(identity_relation(sK12)) ),
inference(superposition,[status(thm)],[c_6018,c_19990]) ).
tcf(c_20162,plain,
( function(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(identity_relation(sK11)) ),
inference(superposition,[status(thm)],[c_6133,c_19990]) ).
tcf(c_20163,plain,
( function(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(identity_relation(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_6817,c_19990]) ).
tcf(c_20164,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),set_intersection2(X0,relation_dom(sK2)))) = set_intersection2(relation_dom(set_intersection2(X0,relation_dom(sK2))),X1) )
| ~ empty(identity_relation(X0))
| ~ relation(set_intersection2(X0,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_19990,c_103]) ).
tcf(c_20165,plain,
( function(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_20163,c_1151]) ).
tcf(c_20166,plain,
( function(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_20162,c_1148]) ).
tcf(c_20167,plain,
( function(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_20161,c_1147]) ).
tcf(c_20172,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(relation_composition(iPr_def_10,sK2)) ),
inference(demodulation,[status(thm)],[c_17661,c_52,c_6018]) ).
tcf(c_20173,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(relation_composition(iPr_def_11,sK2)) ),
inference(demodulation,[status(thm)],[c_17662,c_52,c_6133]) ).
tcf(c_20174,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(relation_composition(iPr_def_14,sK2)) ),
inference(demodulation,[status(thm)],[c_17664,c_52,c_6817]) ).
tcf(c_20179,plain,
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = empty_set )
| ( apply(identity_relation(sK2),sK1(sK2)) = sK1(sK2) ) ),
inference(superposition,[status(thm)],[c_2544,c_18301]) ).
tcf(c_20186,plain,
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = empty_set )
| ( apply(identity_relation(sK2),sK1(sK2)) = sK1(sK2) ) ),
inference(superposition,[status(thm)],[c_2544,c_18565]) ).
tcf(c_20193,plain,
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = empty_set )
| ( apply(identity_relation(sK2),sK1(sK2)) = sK1(sK2) ) ),
inference(superposition,[status(thm)],[c_2544,c_18787]) ).
tcf(c_20200,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(identity_relation(set_intersection2(X0,X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_3079]) ).
tcf(c_20201,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(X2,relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3079]) ).
tcf(c_20202,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(X2,relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3079]) ).
tcf(c_20203,plain,
! [X0: $i] : identity_relation(identity_relation(set_intersection2(X0,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3079]) ).
tcf(c_20204,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3079]) ).
tcf(c_20205,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3079]) ).
tcf(c_20206,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(X0,X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3079]) ).
tcf(c_20208,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(X2,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3079]) ).
tcf(c_20209,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(X0,iPr_def_13)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_3079]) ).
tcf(c_20210,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(iPr_def_13,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_3079]) ).
tcf(c_20211,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(X2,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3079]) ).
tcf(c_20212,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(sK11,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_3079]) ).
tcf(c_20213,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(sK12,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_3079]) ).
tcf(c_20214,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_3079]) ).
tcf(c_20215,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,set_intersection2(relation_dom(sK2),X1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3079]) ).
tcf(c_20216,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(sK1(powerset(X0)),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3079]) ).
tcf(c_20217,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3079]) ).
tcf(c_20218,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3079]) ).
tcf(c_20219,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3079]) ).
tcf(c_20220,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3079]) ).
tcf(c_20221,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3079]) ).
tcf(c_20222,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3079]) ).
tcf(c_20223,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3079]) ).
tcf(c_20224,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3079]) ).
tcf(c_20225,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3079]) ).
tcf(c_20226,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(X0,sK12)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_3079]) ).
tcf(c_20227,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(X0,sK11)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_3079]) ).
tcf(c_20229,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(sK1(sK4(powerset(X0))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3079]) ).
tcf(c_20230,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(X2,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3079]) ).
tcf(c_20231,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_3079]) ).
tcf(c_20232,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,set_intersection2(X1,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3079]) ).
tcf(c_20406,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(relation_dom(set_intersection2(X0,X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_3080]) ).
tcf(c_20407,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(X2,relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3080]) ).
tcf(c_20408,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(X2,relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3080]) ).
tcf(c_20409,plain,
! [X0: $i] : identity_relation(relation_dom(set_intersection2(X0,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3080]) ).
tcf(c_20410,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3080]) ).
tcf(c_20411,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3080]) ).
tcf(c_20412,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(X0,X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3080]) ).
tcf(c_20414,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(X2,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3080]) ).
tcf(c_20415,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(X0,iPr_def_13)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8751,c_3080]) ).
tcf(c_20416,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(iPr_def_13,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_8741,c_3080]) ).
tcf(c_20417,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(X2,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3080]) ).
tcf(c_20418,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(sK11,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10010,c_3080]) ).
tcf(c_20419,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(sK12,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10994,c_3080]) ).
tcf(c_20420,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_17676,c_3080]) ).
tcf(c_20421,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,set_intersection2(relation_dom(sK2),X1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3080]) ).
tcf(c_20422,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(sK1(powerset(X0)),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3080]) ).
tcf(c_20423,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3080]) ).
tcf(c_20424,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3080]) ).
tcf(c_20425,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3080]) ).
tcf(c_20426,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3080]) ).
tcf(c_20427,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3080]) ).
tcf(c_20428,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3080]) ).
tcf(c_20429,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3080]) ).
tcf(c_20430,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3080]) ).
tcf(c_20431,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3080]) ).
tcf(c_20432,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(X0,sK12)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_11003,c_3080]) ).
tcf(c_20433,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(X0,sK11)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_3080]) ).
tcf(c_20435,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(sK1(sK4(powerset(X0))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3080]) ).
tcf(c_20436,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(X2,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3080]) ).
tcf(c_20437,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_19623,c_3080]) ).
tcf(c_20438,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,set_intersection2(X1,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3080]) ).
tcf(c_20646,plain,
! [X0: $i] :
( ( set_intersection2(X0,iPr_def_10) = empty_set )
| ( apply(identity_relation(sK12),sK1(sK12)) = sK1(sK12) ) ),
inference(superposition,[status(thm)],[c_1147,c_15800]) ).
tcf(c_20647,plain,
! [X0: $i] :
( ( set_intersection2(X0,iPr_def_11) = empty_set )
| ( apply(identity_relation(sK11),sK1(sK11)) = sK1(sK11) ) ),
inference(superposition,[status(thm)],[c_1148,c_15800]) ).
tcf(c_20649,plain,
! [X0: $i] :
( ( set_intersection2(X0,iPr_def_14) = empty_set )
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_1151,c_15800]) ).
tcf(c_20652,plain,
! [X0: $i] :
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( set_intersection2(X0,identity_relation(empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15800]) ).
tcf(c_20654,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( set_intersection2(X0,identity_relation(powerset(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15800]) ).
tcf(c_20656,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(identity_relation(X0),sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15800,c_2739]) ).
tcf(c_20678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,empty_set),X2)
| in(sK0(X2,X3,set_intersection2(X1,identity_relation(X0))),identity_relation(X0))
| ( set_intersection2(X1,identity_relation(X0)) = set_intersection2(X2,X3) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15800,c_2241]) ).
tcf(c_20679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,empty_set),identity_relation(X0))
| in(sK0(X2,X3,set_intersection2(X1,identity_relation(X0))),X2)
| ( set_intersection2(X1,identity_relation(X0)) = set_intersection2(X2,X3) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15800,c_2241]) ).
tcf(c_20735,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X1,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),identity_relation(X1))),sK1(relation_composition(identity_relation(X0),identity_relation(X1)))) = sK1(relation_composition(identity_relation(X0),identity_relation(X1))) ) ),
inference(superposition,[status(thm)],[c_2544,c_5129]) ).
tcf(c_20736,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X1,X0))
| ~ relation(identity_relation(X1))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_5129]) ).
tcf(c_20737,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X0,X1))
| ~ relation(identity_relation(X1))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_5129]) ).
tcf(c_20740,plain,
! [X0: $i] :
( relation(set_intersection2(X0,empty_set))
| ~ empty(relation_composition(empty_set,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_2472,c_5129]) ).
tcf(c_20744,plain,
! [X0: $i] :
( relation(set_intersection2(empty_set,X0))
| ~ empty(relation_composition(identity_relation(X0),empty_set)) ),
inference(superposition,[status(thm)],[c_2472,c_5129]) ).
tcf(c_20747,plain,
! [X0: $i] :
( relation(empty_set)
| ~ empty(relation_composition(empty_set,identity_relation(X0))) ),
inference(light_normalisation,[status(thm)],[c_20740,c_97]) ).
tcf(c_20748,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X0,X1))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20737,c_71]) ).
tcf(c_20751,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X1,X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20736,c_71]) ).
tcf(c_20803,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),identity_relation(X1))),sK1(relation_composition(identity_relation(X0),identity_relation(X1)))) = sK1(relation_composition(identity_relation(X0),identity_relation(X1))) ) ),
inference(superposition,[status(thm)],[c_2544,c_5130]) ).
tcf(c_20804,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ~ relation(identity_relation(X1))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_5130]) ).
tcf(c_20805,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ~ relation(identity_relation(X1))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_5130]) ).
tcf(c_20808,plain,
! [X0: $i] :
( empty(set_intersection2(X0,empty_set))
| ~ empty(relation_composition(empty_set,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_2472,c_5130]) ).
tcf(c_20812,plain,
! [X0: $i] :
( empty(set_intersection2(empty_set,X0))
| ~ empty(relation_composition(identity_relation(X0),empty_set)) ),
inference(superposition,[status(thm)],[c_2472,c_5130]) ).
tcf(c_20815,plain,
! [X0: $i] :
( empty(empty_set)
| ~ empty(relation_composition(empty_set,identity_relation(X0))) ),
inference(light_normalisation,[status(thm)],[c_20808,c_97]) ).
tcf(c_20816,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20805,c_71]) ).
tcf(c_20819,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20804,c_71]) ).
tcf(c_20842,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X2) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_2518]) ).
tcf(c_20843,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X2) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_2517]) ).
tcf(c_20844,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X2) = X1 )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_110]) ).
tcf(c_20845,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(X0,X2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3080]) ).
tcf(c_20846,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(X0,X2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3079]) ).
tcf(c_20847,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_14104]) ).
tcf(c_20848,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_5630]) ).
tcf(c_20849,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_5629]) ).
tcf(c_20850,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X0,X1)),X2) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_4060]) ).
tcf(c_20851,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X0,X1)),X2) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_4059]) ).
tcf(c_20852,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(X0,X2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_4011]) ).
tcf(c_20853,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(X0,X2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_4010]) ).
tcf(c_20854,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3938]) ).
tcf(c_20855,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3937]) ).
tcf(c_20856,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3179]) ).
tcf(c_20857,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3178]) ).
tcf(c_20858,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(X0,X2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3083]) ).
tcf(c_20859,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(X0,X2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3082]) ).
tcf(c_20860,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_2687]) ).
tcf(c_20861,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_2686]) ).
tcf(c_20862,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_2658]) ).
tcf(c_20863,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_2637]) ).
tcf(c_20864,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(X0,X1))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3939]) ).
tcf(c_20865,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3180]) ).
tcf(c_20866,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X0,X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3084]) ).
tcf(c_20867,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X0,X1))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_2474]) ).
tcf(c_20868,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X0,X1))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_2473]) ).
tcf(c_20869,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,X1))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_2055]) ).
tcf(c_20870,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X0,X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_2184]) ).
tcf(c_20871,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X0,X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_2013]) ).
tcf(c_20872,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_108]) ).
tcf(c_20874,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X0,X1))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_50]) ).
tcf(c_21113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,X0) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_2518]) ).
tcf(c_21114,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,X0) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_2517]) ).
tcf(c_21115,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,X0) = X1 )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_110]) ).
tcf(c_21116,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(X2,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3080]) ).
tcf(c_21117,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(X2,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3079]) ).
tcf(c_21118,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_14104]) ).
tcf(c_21119,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_5630]) ).
tcf(c_21120,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_5629]) ).
tcf(c_21121,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X1,X0)),X2) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_4060]) ).
tcf(c_21122,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X1,X0)),X2) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_4059]) ).
tcf(c_21123,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(X2,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_4011]) ).
tcf(c_21124,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(X2,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_4010]) ).
tcf(c_21125,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3938]) ).
tcf(c_21126,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3937]) ).
tcf(c_21127,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(set_intersection2(X1,X0),X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3179]) ).
tcf(c_21128,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(set_intersection2(X1,X0),X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3178]) ).
tcf(c_21129,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(X2,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3083]) ).
tcf(c_21130,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(X2,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3082]) ).
tcf(c_21131,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_2687]) ).
tcf(c_21132,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_2686]) ).
tcf(c_21133,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_2658]) ).
tcf(c_21134,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_2637]) ).
tcf(c_21135,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(X1,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3939]) ).
tcf(c_21136,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,X0),X2) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3180]) ).
tcf(c_21137,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X2,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3084]) ).
tcf(c_21138,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_2474]) ).
tcf(c_21139,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_2473]) ).
tcf(c_21140,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_2055]) ).
tcf(c_21141,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_2184]) ).
tcf(c_21142,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_2013]) ).
tcf(c_21143,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_108]) ).
tcf(c_21145,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X1,X0))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_50]) ).
tcf(c_21293,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(identity_relation(X2),set_intersection2(X0,X1))) = set_intersection2(relation_dom(set_intersection2(X0,X1)),X2) )
| ~ empty(identity_relation(X0))
| ~ relation(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_20874,c_103]) ).
tcf(c_21314,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(identity_relation(X2),set_intersection2(X0,X1))) = set_intersection2(relation_dom(set_intersection2(X0,X1)),X2) )
| ~ empty(identity_relation(X1))
| ~ relation(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_21145,c_103]) ).
tcf(c_21332,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_21143]) ).
tcf(c_21344,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(relation_dom(set_intersection2(X0,X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_3081]) ).
tcf(c_21345,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(X2,relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3081]) ).
tcf(c_21346,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(X2,relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3081]) ).
tcf(c_21347,plain,
! [X0: $i] : relation_dom(relation_dom(set_intersection2(X0,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3081]) ).
tcf(c_21348,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3081]) ).
tcf(c_21349,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3081]) ).
tcf(c_21350,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,set_intersection2(X0,X2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3081]) ).
tcf(c_21351,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,set_intersection2(X0,X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3081]) ).
tcf(c_21353,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,set_intersection2(X2,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3081]) ).
tcf(c_21354,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,set_intersection2(X2,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3081]) ).
tcf(c_21355,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,set_intersection2(X2,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3081]) ).
tcf(c_21356,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,set_intersection2(relation_dom(sK2),X1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3081]) ).
tcf(c_21357,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,set_intersection2(sK1(powerset(X0)),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3081]) ).
tcf(c_21358,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3081]) ).
tcf(c_21359,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3081]) ).
tcf(c_21360,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3081]) ).
tcf(c_21361,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3081]) ).
tcf(c_21362,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3081]) ).
tcf(c_21363,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3081]) ).
tcf(c_21364,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3081]) ).
tcf(c_21365,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3081]) ).
tcf(c_21366,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3081]) ).
tcf(c_21368,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,set_intersection2(sK1(sK4(powerset(X0))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3081]) ).
tcf(c_21369,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,set_intersection2(X2,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3081]) ).
tcf(c_21370,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,set_intersection2(X1,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3081]) ).
tcf(c_21489,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(identity_relation(set_intersection2(X0,X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_3175]) ).
tcf(c_21490,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(relation_composition(X0,X1),X2))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3175]) ).
tcf(c_21491,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(relation_composition(X1,X0),X2))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3175]) ).
tcf(c_21492,plain,
! [X0: $i] : identity_relation(identity_relation(set_intersection2(empty_set,X0))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3175]) ).
tcf(c_21493,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(relation_dom(X0),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3175]) ).
tcf(c_21494,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(identity_relation(X0),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3175]) ).
tcf(c_21495,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(set_intersection2(X0,X1),X2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3175]) ).
tcf(c_21496,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(set_intersection2(X0,X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3175]) ).
tcf(c_21498,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(set_intersection2(X1,X0),X2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3175]) ).
tcf(c_21499,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(set_intersection2(X1,X0),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3175]) ).
tcf(c_21500,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(set_intersection2(X1,sK1(powerset(X0))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3175]) ).
tcf(c_21501,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(set_intersection2(relation_dom(sK2),X0),X1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3175]) ).
tcf(c_21502,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(set_intersection2(sK1(powerset(X0)),X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3175]) ).
tcf(c_21503,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3175]) ).
tcf(c_21504,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3175]) ).
tcf(c_21505,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3175]) ).
tcf(c_21506,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3175]) ).
tcf(c_21507,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3175]) ).
tcf(c_21508,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3175]) ).
tcf(c_21509,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3175]) ).
tcf(c_21510,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3175]) ).
tcf(c_21511,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3175]) ).
tcf(c_21513,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(set_intersection2(sK1(sK4(powerset(X0))),X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3175]) ).
tcf(c_21514,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(set_intersection2(X1,sK1(sK4(powerset(X0)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3175]) ).
tcf(c_21515,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(set_intersection2(X0,relation_dom(sK2)),X1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3175]) ).
tcf(c_21665,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(relation_dom(set_intersection2(X0,X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_3176]) ).
tcf(c_21666,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(relation_composition(X0,X1),X2))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3176]) ).
tcf(c_21667,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(relation_composition(X1,X0),X2))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3176]) ).
tcf(c_21668,plain,
! [X0: $i] : identity_relation(relation_dom(set_intersection2(empty_set,X0))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3176]) ).
tcf(c_21669,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(relation_dom(X0),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3176]) ).
tcf(c_21670,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(identity_relation(X0),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3176]) ).
tcf(c_21671,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(set_intersection2(X0,X1),X2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3176]) ).
tcf(c_21672,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(set_intersection2(X0,X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3176]) ).
tcf(c_21674,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(set_intersection2(X1,X0),X2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3176]) ).
tcf(c_21675,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(set_intersection2(X1,X0),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3176]) ).
tcf(c_21676,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(set_intersection2(X1,sK1(powerset(X0))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3176]) ).
tcf(c_21677,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(set_intersection2(relation_dom(sK2),X0),X1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3176]) ).
tcf(c_21678,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(set_intersection2(sK1(powerset(X0)),X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3176]) ).
tcf(c_21679,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3176]) ).
tcf(c_21680,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3176]) ).
tcf(c_21681,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3176]) ).
tcf(c_21682,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3176]) ).
tcf(c_21683,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3176]) ).
tcf(c_21684,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3176]) ).
tcf(c_21685,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3176]) ).
tcf(c_21686,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3176]) ).
tcf(c_21687,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3176]) ).
tcf(c_21689,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(set_intersection2(sK1(sK4(powerset(X0))),X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3176]) ).
tcf(c_21690,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(set_intersection2(X1,sK1(sK4(powerset(X0)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3176]) ).
tcf(c_21691,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(set_intersection2(X0,relation_dom(sK2)),X1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3176]) ).
tcf(c_21864,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(relation_dom(set_intersection2(X0,X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_3177]) ).
tcf(c_21865,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(relation_composition(X0,X1),X2))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3177]) ).
tcf(c_21866,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(relation_composition(X1,X0),X2))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3177]) ).
tcf(c_21867,plain,
! [X0: $i] : relation_dom(relation_dom(set_intersection2(empty_set,X0))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3177]) ).
tcf(c_21868,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(relation_dom(X0),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3177]) ).
tcf(c_21869,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(identity_relation(X0),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3177]) ).
tcf(c_21870,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(set_intersection2(X0,X1),X2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3177]) ).
tcf(c_21871,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(set_intersection2(X0,X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3177]) ).
tcf(c_21873,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(set_intersection2(X1,X0),X2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3177]) ).
tcf(c_21874,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(set_intersection2(X1,X0),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3177]) ).
tcf(c_21875,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(set_intersection2(X1,sK1(powerset(X0))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3177]) ).
tcf(c_21876,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(set_intersection2(relation_dom(sK2),X0),X1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3177]) ).
tcf(c_21877,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(set_intersection2(sK1(powerset(X0)),X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3177]) ).
tcf(c_21878,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3177]) ).
tcf(c_21879,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3177]) ).
tcf(c_21880,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3177]) ).
tcf(c_21881,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3177]) ).
tcf(c_21882,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3177]) ).
tcf(c_21883,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3177]) ).
tcf(c_21884,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3177]) ).
tcf(c_21885,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3177]) ).
tcf(c_21886,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3177]) ).
tcf(c_21888,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(set_intersection2(sK1(sK4(powerset(X0))),X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3177]) ).
tcf(c_21889,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(set_intersection2(X1,sK1(sK4(powerset(X0)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3177]) ).
tcf(c_21890,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(set_intersection2(X0,relation_dom(sK2)),X1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3177]) ).
tcf(c_22017,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK1(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_3934]) ).
tcf(c_22018,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK1(powerset(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3934]) ).
tcf(c_22019,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK1(powerset(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3934]) ).
tcf(c_22020,plain,
identity_relation(identity_relation(sK1(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3934]) ).
tcf(c_22021,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK1(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3934]) ).
tcf(c_22022,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK1(powerset(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3934]) ).
tcf(c_22023,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK1(powerset(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3934]) ).
tcf(c_22024,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK1(powerset(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3934]) ).
tcf(c_22025,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK1(powerset(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_3934]) ).
tcf(c_22026,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK1(powerset(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3934]) ).
tcf(c_22027,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK1(powerset(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3934]) ).
tcf(c_22028,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK1(powerset(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3934]) ).
tcf(c_22029,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK1(powerset(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3934]) ).
tcf(c_22030,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK1(powerset(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3934]) ).
tcf(c_22031,plain,
( ( identity_relation(identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3934]) ).
tcf(c_22032,plain,
( ( identity_relation(identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3934]) ).
tcf(c_22033,plain,
( ( identity_relation(identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3934]) ).
tcf(c_22034,plain,
( ( identity_relation(identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3934]) ).
tcf(c_22035,plain,
( ( identity_relation(identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3934]) ).
tcf(c_22036,plain,
( ( identity_relation(identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3934]) ).
tcf(c_22037,plain,
( ( identity_relation(identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3934]) ).
tcf(c_22038,plain,
( ( identity_relation(identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3934]) ).
tcf(c_22039,plain,
( ( identity_relation(identity_relation(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3934]) ).
tcf(c_22040,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK1(powerset(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_3934]) ).
tcf(c_22041,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK1(powerset(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3934]) ).
tcf(c_22042,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK1(powerset(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3934]) ).
tcf(c_22043,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK1(powerset(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3934]) ).
tcf(c_22155,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK1(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_3935]) ).
tcf(c_22156,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK1(powerset(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3935]) ).
tcf(c_22157,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK1(powerset(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3935]) ).
tcf(c_22158,plain,
identity_relation(relation_dom(sK1(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3935]) ).
tcf(c_22159,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK1(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3935]) ).
tcf(c_22160,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK1(powerset(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3935]) ).
tcf(c_22161,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK1(powerset(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3935]) ).
tcf(c_22162,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK1(powerset(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3935]) ).
tcf(c_22163,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK1(powerset(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_3935]) ).
tcf(c_22164,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK1(powerset(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3935]) ).
tcf(c_22165,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK1(powerset(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3935]) ).
tcf(c_22166,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK1(powerset(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3935]) ).
tcf(c_22167,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK1(powerset(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3935]) ).
tcf(c_22168,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK1(powerset(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3935]) ).
tcf(c_22169,plain,
( ( identity_relation(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3935]) ).
tcf(c_22170,plain,
( ( identity_relation(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3935]) ).
tcf(c_22171,plain,
( ( identity_relation(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3935]) ).
tcf(c_22172,plain,
( ( identity_relation(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3935]) ).
tcf(c_22173,plain,
( ( identity_relation(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3935]) ).
tcf(c_22174,plain,
( ( identity_relation(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3935]) ).
tcf(c_22175,plain,
( ( identity_relation(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3935]) ).
tcf(c_22176,plain,
( ( identity_relation(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3935]) ).
tcf(c_22177,plain,
( ( identity_relation(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3935]) ).
tcf(c_22178,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK1(powerset(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_3935]) ).
tcf(c_22179,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK1(powerset(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3935]) ).
tcf(c_22180,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK1(powerset(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3935]) ).
tcf(c_22181,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK1(powerset(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3935]) ).
tcf(c_22368,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(relation_dom(sK2),X0)) = empty_set )
| ( apply(identity_relation(relation_composition(identity_relation(X0),sK2)),sK1(relation_composition(identity_relation(X0),sK2))) = sK1(relation_composition(identity_relation(X0),sK2)) ) ),
inference(superposition,[status(thm)],[c_3034,c_15801]) ).
tcf(c_22369,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(sK12,X0)) = empty_set )
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_10)),sK1(relation_composition(identity_relation(X0),iPr_def_10))) = sK1(relation_composition(identity_relation(X0),iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_3031,c_15801]) ).
tcf(c_22370,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(sK11,X0)) = empty_set )
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_11)),sK1(relation_composition(identity_relation(X0),iPr_def_11))) = sK1(relation_composition(identity_relation(X0),iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_3029,c_15801]) ).
tcf(c_22371,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(iPr_def_13,X0)) = empty_set )
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_14)),sK1(relation_composition(identity_relation(X0),iPr_def_14))) = sK1(relation_composition(identity_relation(X0),iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_3027,c_15801]) ).
tcf(c_22372,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,set_intersection2(X1,X0)) = empty_set )
| ( apply(identity_relation(relation_composition(identity_relation(X0),identity_relation(X1))),sK1(relation_composition(identity_relation(X0),identity_relation(X1)))) = sK1(relation_composition(identity_relation(X0),identity_relation(X1))) ) ),
inference(superposition,[status(thm)],[c_3036,c_15801]) ).
tcf(c_22373,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(iPr_def_13,X0)) = empty_set )
| ( apply(identity_relation(relation_composition(identity_relation(X0),iPr_def_12)),sK1(relation_composition(identity_relation(X0),iPr_def_12))) = sK1(relation_composition(identity_relation(X0),iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_5413,c_15801]) ).
tcf(c_22374,plain,
! [X0: $i] :
( ( set_intersection2(X0,set_intersection2(iPr_def_13,sK12)) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_10,iPr_def_14)),sK1(relation_composition(iPr_def_10,iPr_def_14))) = sK1(relation_composition(iPr_def_10,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_3283,c_15801]) ).
tcf(c_22375,plain,
! [X0: $i] :
( ( set_intersection2(X0,set_intersection2(iPr_def_13,sK11)) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_11,iPr_def_14)),sK1(relation_composition(iPr_def_11,iPr_def_14))) = sK1(relation_composition(iPr_def_11,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_3284,c_15801]) ).
tcf(c_22378,plain,
! [X0: $i] :
( ( set_intersection2(X0,set_intersection2(iPr_def_13,sK11)) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_14,iPr_def_11)),sK1(relation_composition(iPr_def_14,iPr_def_11))) = sK1(relation_composition(iPr_def_14,iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_5734,c_15801]) ).
tcf(c_22381,plain,
! [X0: $i] :
( ( set_intersection2(X0,set_intersection2(iPr_def_13,sK12)) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_14,iPr_def_10)),sK1(relation_composition(iPr_def_14,iPr_def_10))) = sK1(relation_composition(iPr_def_14,iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_5828,c_15801]) ).
tcf(c_22382,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(X0,sK12)) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_10,identity_relation(X0))),sK1(relation_composition(iPr_def_10,identity_relation(X0)))) = sK1(relation_composition(iPr_def_10,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_5115,c_15801]) ).
tcf(c_22383,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(X0,sK11)) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_11,identity_relation(X0))),sK1(relation_composition(iPr_def_11,identity_relation(X0)))) = sK1(relation_composition(iPr_def_11,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_5116,c_15801]) ).
tcf(c_22384,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,empty_set) = empty_set )
| ( apply(identity_relation(relation_composition(empty_set,identity_relation(X0))),sK1(relation_composition(empty_set,identity_relation(X0)))) = sK1(relation_composition(empty_set,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_5133,c_15801]) ).
tcf(c_22385,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,set_intersection2(X0,iPr_def_13)) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_14,identity_relation(X0))),sK1(relation_composition(iPr_def_14,identity_relation(X0)))) = sK1(relation_composition(iPr_def_14,identity_relation(X0))) ) ),
inference(superposition,[status(thm)],[c_5118,c_15801]) ).
tcf(c_22386,plain,
! [X0: $i] :
( ( set_intersection2(X0,set_intersection2(iPr_def_13,sK12)) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_10,iPr_def_12)),sK1(relation_composition(iPr_def_10,iPr_def_12))) = sK1(relation_composition(iPr_def_10,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_5414,c_15801]) ).
tcf(c_22387,plain,
! [X0: $i] :
( ( set_intersection2(X0,set_intersection2(iPr_def_13,sK11)) = empty_set )
| ( apply(identity_relation(relation_composition(iPr_def_11,iPr_def_12)),sK1(relation_composition(iPr_def_11,iPr_def_12))) = sK1(relation_composition(iPr_def_11,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_5415,c_15801]) ).
tcf(c_22391,plain,
! [X0: $i] :
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( set_intersection2(X0,relation_dom(empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15801]) ).
tcf(c_22393,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( set_intersection2(X0,relation_dom(powerset(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15801]) ).
tcf(c_22398,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(relation_dom(X0),sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15801,c_2739]) ).
tcf(c_22423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,empty_set),X2)
| in(sK0(X2,X3,set_intersection2(X1,relation_dom(X0))),relation_dom(X0))
| ( set_intersection2(X1,relation_dom(X0)) = set_intersection2(X2,X3) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15801,c_2241]) ).
tcf(c_22424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,empty_set),relation_dom(X0))
| in(sK0(X2,X3,set_intersection2(X1,relation_dom(X0))),X2)
| ( set_intersection2(X1,relation_dom(X0)) = set_intersection2(X2,X3) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15801,c_2241]) ).
tcf(c_22593,plain,
! [X0: $i] :
( empty(relation_composition(empty_set,identity_relation(X0)))
| ~ empty(empty_set)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_79,c_5272]) ).
tcf(c_22594,plain,
( empty(relation_composition(empty_set,identity_relation(sK12)))
| ~ relation(relation_composition(empty_set,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_1147,c_5272]) ).
tcf(c_22595,plain,
( empty(relation_composition(empty_set,identity_relation(sK11)))
| ~ relation(relation_composition(empty_set,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_1148,c_5272]) ).
tcf(c_22596,plain,
( empty(relation_composition(empty_set,identity_relation(empty_set)))
| ~ relation(relation_composition(empty_set,empty_set)) ),
inference(superposition,[status(thm)],[c_2472,c_5272]) ).
tcf(c_22597,plain,
( empty(relation_composition(empty_set,identity_relation(iPr_def_13)))
| ~ relation(relation_composition(empty_set,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_1151,c_5272]) ).
tcf(c_22602,plain,
! [X0: $i] : empty(relation_composition(empty_set,identity_relation(X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_22593,c_73,c_71]) ).
tcf(c_22608,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,identity_relation(X1)) = identity_relation(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_22602,c_2518]) ).
tcf(c_22609,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,identity_relation(X1)) = relation_dom(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_22602,c_2517]) ).
tcf(c_22610,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,identity_relation(X1)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_22602,c_110]) ).
tcf(c_22611,plain,
! [X0: $i] : identity_relation(relation_dom(sK1(powerset(relation_composition(empty_set,identity_relation(X0)))))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3935]) ).
tcf(c_22612,plain,
! [X0: $i] : identity_relation(identity_relation(sK1(powerset(relation_composition(empty_set,identity_relation(X0)))))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3934]) ).
tcf(c_22613,plain,
! [X0: $i,X1: $i] : relation_dom(relation_dom(set_intersection2(relation_composition(empty_set,identity_relation(X0)),X1))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3177]) ).
tcf(c_22614,plain,
! [X0: $i,X1: $i] : identity_relation(relation_dom(set_intersection2(relation_composition(empty_set,identity_relation(X0)),X1))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3176]) ).
tcf(c_22615,plain,
! [X0: $i,X1: $i] : identity_relation(identity_relation(set_intersection2(relation_composition(empty_set,identity_relation(X0)),X1))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3175]) ).
tcf(c_22616,plain,
! [X0: $i,X1: $i] : relation_dom(relation_dom(set_intersection2(X0,relation_composition(empty_set,identity_relation(X1))))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3081]) ).
tcf(c_22617,plain,
! [X0: $i,X1: $i] : identity_relation(relation_dom(set_intersection2(X0,relation_composition(empty_set,identity_relation(X1))))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3080]) ).
tcf(c_22618,plain,
! [X0: $i,X1: $i] : identity_relation(identity_relation(set_intersection2(X0,relation_composition(empty_set,identity_relation(X1))))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3079]) ).
tcf(c_22619,plain,
! [X0: $i] : sK1(sK4(powerset(relation_composition(empty_set,identity_relation(X0))))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_14104]) ).
tcf(c_22620,plain,
! [X0: $i] : sK1(powerset(identity_relation(relation_composition(empty_set,identity_relation(X0))))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_5630]) ).
tcf(c_22621,plain,
! [X0: $i] : sK1(powerset(relation_dom(relation_composition(empty_set,identity_relation(X0))))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_5629]) ).
tcf(c_22622,plain,
! [X0: $i,X1: $i] : set_intersection2(identity_relation(relation_composition(empty_set,identity_relation(X0))),X1) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_4060]) ).
tcf(c_22623,plain,
! [X0: $i,X1: $i] : set_intersection2(relation_dom(relation_composition(empty_set,identity_relation(X0))),X1) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_4059]) ).
tcf(c_22624,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,identity_relation(relation_composition(empty_set,identity_relation(X1)))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_4011]) ).
tcf(c_22625,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,relation_dom(relation_composition(empty_set,identity_relation(X1)))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_4010]) ).
tcf(c_22626,plain,
! [X0: $i] : relation_dom(sK1(powerset(relation_composition(empty_set,identity_relation(X0))))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3938]) ).
tcf(c_22627,plain,
! [X0: $i] : identity_relation(sK1(powerset(relation_composition(empty_set,identity_relation(X0))))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3937]) ).
tcf(c_22628,plain,
! [X0: $i,X1: $i] : relation_dom(set_intersection2(relation_composition(empty_set,identity_relation(X0)),X1)) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3179]) ).
tcf(c_22629,plain,
! [X0: $i,X1: $i] : identity_relation(set_intersection2(relation_composition(empty_set,identity_relation(X0)),X1)) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3178]) ).
tcf(c_22630,plain,
! [X0: $i,X1: $i] : relation_dom(set_intersection2(X0,relation_composition(empty_set,identity_relation(X1)))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3083]) ).
tcf(c_22631,plain,
! [X0: $i,X1: $i] : identity_relation(set_intersection2(X0,relation_composition(empty_set,identity_relation(X1)))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3082]) ).
tcf(c_22632,plain,
! [X0: $i] : identity_relation(identity_relation(identity_relation(relation_composition(empty_set,identity_relation(X0))))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_2687]) ).
tcf(c_22633,plain,
! [X0: $i] : identity_relation(identity_relation(relation_dom(relation_composition(empty_set,identity_relation(X0))))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_2686]) ).
tcf(c_22634,plain,
! [X0: $i] : identity_relation(relation_dom(relation_dom(relation_composition(empty_set,identity_relation(X0))))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_2658]) ).
tcf(c_22635,plain,
! [X0: $i] : relation_dom(relation_dom(relation_dom(relation_composition(empty_set,identity_relation(X0))))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_2637]) ).
tcf(c_22636,plain,
! [X0: $i] : sK1(powerset(relation_composition(empty_set,identity_relation(X0)))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3939]) ).
tcf(c_22637,plain,
! [X0: $i,X1: $i] : set_intersection2(relation_composition(empty_set,identity_relation(X0)),X1) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3180]) ).
tcf(c_22638,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,relation_composition(empty_set,identity_relation(X1))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_3084]) ).
tcf(c_22639,plain,
! [X0: $i] : identity_relation(identity_relation(relation_composition(empty_set,identity_relation(X0)))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_2474]) ).
tcf(c_22640,plain,
! [X0: $i] : identity_relation(relation_dom(relation_composition(empty_set,identity_relation(X0)))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_2473]) ).
tcf(c_22641,plain,
! [X0: $i] : relation_dom(relation_dom(relation_composition(empty_set,identity_relation(X0)))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_2055]) ).
tcf(c_22642,plain,
! [X0: $i] : identity_relation(relation_composition(empty_set,identity_relation(X0))) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_2184]) ).
tcf(c_22644,plain,
! [X0: $i] : relation_composition(empty_set,identity_relation(X0)) = empty_set,
inference(superposition,[status(thm)],[c_22602,c_108]) ).
tcf(c_22645,plain,
! [X0: $i] : relation(relation_composition(empty_set,identity_relation(X0))),
inference(superposition,[status(thm)],[c_22602,c_51]) ).
tcf(c_22646,plain,
! [X0: $i] : function(relation_composition(empty_set,identity_relation(X0))),
inference(superposition,[status(thm)],[c_22602,c_50]) ).
tcf(c_22842,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(empty_set,identity_relation(X1)),X0) = apply(identity_relation(X1),apply(empty_set,X0)) )
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_22644,c_96]) ).
tcf(c_22858,plain,
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( relation_dom(sK1(powerset(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15802]) ).
tcf(c_22860,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( relation_dom(sK1(powerset(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15802]) ).
tcf(c_22867,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,relation_dom(relation_composition(iPr_def_10,sK2)),X1),X1)
| in(sK0(X0,relation_dom(relation_composition(iPr_def_10,sK2)),X1),relation_dom(sK2))
| ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))) = X1 ) ),
inference(superposition,[status(thm)],[c_55,c_6028]) ).
tcf(c_22868,plain,
! [X0: $i,X1: $i] :
( element(sK0(relation_dom(relation_composition(iPr_def_10,sK2)),X0,X1),X1)
| in(sK0(relation_dom(relation_composition(iPr_def_10,sK2)),X0,X1),relation_dom(sK2))
| ( set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_2239,c_6028]) ).
tcf(c_22869,plain,
! [X0: $i,X1: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_10,sK2)),X0,X1),X1)
| in(sK0(relation_dom(relation_composition(iPr_def_10,sK2)),X0,X1),relation_dom(sK2))
| ( set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_54,c_6028]) ).
tcf(c_22870,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_10,sK2))),X1)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_10,sK2))),relation_dom(sK2))
| ( relation_dom(relation_composition(iPr_def_10,sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_55,c_6028]) ).
tcf(c_22872,plain,
( in(sK10(relation_dom(relation_composition(iPr_def_10,sK2)),relation_composition(iPr_def_10,sK2)),relation_dom(sK2))
| ( identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))) = relation_composition(iPr_def_10,sK2) )
| ~ relation(relation_composition(iPr_def_10,sK2))
| ~ function(relation_composition(iPr_def_10,sK2)) ),
inference(superposition,[status(thm)],[c_100,c_6028]) ).
tcf(c_22874,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))
| in(sK1(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_7250,c_6028]) ).
tcf(c_22875,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))
| in(sK1(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_2201,c_6028]) ).
tcf(c_22876,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))
| in(sK1(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_2732,c_6028]) ).
tcf(c_22877,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))
| in(sK1(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_2202,c_6028]) ).
tcf(c_22878,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_10,sK2)),X0,set_intersection2(X1,X2)),X2)
| in(sK0(relation_dom(relation_composition(iPr_def_10,sK2)),X0,set_intersection2(X1,X2)),relation_dom(sK2))
| ( set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_6028]) ).
tcf(c_22879,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))),X1)
| in(sK0(X1,X2,set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))),relation_dom(sK2))
| ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_6028]) ).
tcf(c_22880,plain,
! [X0: $i] :
( in(sK0(empty_set,X0,relation_dom(relation_composition(iPr_def_10,sK2))),relation_dom(sK2))
| ( relation_dom(relation_composition(iPr_def_10,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5683,c_6028]) ).
tcf(c_22881,plain,
! [X0: $i] :
( in(sK0(X0,empty_set,relation_dom(relation_composition(iPr_def_10,sK2))),relation_dom(sK2))
| ( relation_dom(relation_composition(iPr_def_10,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5686,c_6028]) ).
tcf(c_22882,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_10,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12691,c_6028]) ).
tcf(c_22933,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,relation_dom(relation_composition(iPr_def_11,sK2)),X1),X1)
| in(sK0(X0,relation_dom(relation_composition(iPr_def_11,sK2)),X1),relation_dom(sK2))
| ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))) = X1 ) ),
inference(superposition,[status(thm)],[c_55,c_6143]) ).
tcf(c_22934,plain,
! [X0: $i,X1: $i] :
( element(sK0(relation_dom(relation_composition(iPr_def_11,sK2)),X0,X1),X1)
| in(sK0(relation_dom(relation_composition(iPr_def_11,sK2)),X0,X1),relation_dom(sK2))
| ( set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_2239,c_6143]) ).
tcf(c_22935,plain,
! [X0: $i,X1: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_11,sK2)),X0,X1),X1)
| in(sK0(relation_dom(relation_composition(iPr_def_11,sK2)),X0,X1),relation_dom(sK2))
| ( set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_54,c_6143]) ).
tcf(c_22936,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_11,sK2))),X1)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_11,sK2))),relation_dom(sK2))
| ( relation_dom(relation_composition(iPr_def_11,sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_55,c_6143]) ).
tcf(c_22938,plain,
( in(sK10(relation_dom(relation_composition(iPr_def_11,sK2)),relation_composition(iPr_def_11,sK2)),relation_dom(sK2))
| ( identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))) = relation_composition(iPr_def_11,sK2) )
| ~ relation(relation_composition(iPr_def_11,sK2))
| ~ function(relation_composition(iPr_def_11,sK2)) ),
inference(superposition,[status(thm)],[c_100,c_6143]) ).
tcf(c_22940,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))
| in(sK1(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_7250,c_6143]) ).
tcf(c_22941,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))
| in(sK1(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_2201,c_6143]) ).
tcf(c_22942,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))
| in(sK1(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_2732,c_6143]) ).
tcf(c_22943,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))
| in(sK1(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_2202,c_6143]) ).
tcf(c_22944,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_11,sK2)),X0,set_intersection2(X1,X2)),X2)
| in(sK0(relation_dom(relation_composition(iPr_def_11,sK2)),X0,set_intersection2(X1,X2)),relation_dom(sK2))
| ( set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_6143]) ).
tcf(c_22945,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))),X1)
| in(sK0(X1,X2,set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))),relation_dom(sK2))
| ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_6143]) ).
tcf(c_22946,plain,
! [X0: $i] :
( in(sK0(empty_set,X0,relation_dom(relation_composition(iPr_def_11,sK2))),relation_dom(sK2))
| ( relation_dom(relation_composition(iPr_def_11,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5683,c_6143]) ).
tcf(c_22947,plain,
! [X0: $i] :
( in(sK0(X0,empty_set,relation_dom(relation_composition(iPr_def_11,sK2))),relation_dom(sK2))
| ( relation_dom(relation_composition(iPr_def_11,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5686,c_6143]) ).
tcf(c_22948,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_11,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12691,c_6143]) ).
tcf(c_22999,plain,
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = empty_set )
| ( apply(identity_relation(relation_dom(sK2)),sK1(relation_dom(sK2))) = sK1(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_2544,c_6693]) ).
tcf(c_23007,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,relation_dom(relation_composition(iPr_def_14,sK2)),X1),X1)
| in(sK0(X0,relation_dom(relation_composition(iPr_def_14,sK2)),X1),relation_dom(sK2))
| ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))) = X1 ) ),
inference(superposition,[status(thm)],[c_55,c_6827]) ).
tcf(c_23008,plain,
! [X0: $i,X1: $i] :
( element(sK0(relation_dom(relation_composition(iPr_def_14,sK2)),X0,X1),X1)
| in(sK0(relation_dom(relation_composition(iPr_def_14,sK2)),X0,X1),relation_dom(sK2))
| ( set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_2239,c_6827]) ).
tcf(c_23009,plain,
! [X0: $i,X1: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_14,sK2)),X0,X1),X1)
| in(sK0(relation_dom(relation_composition(iPr_def_14,sK2)),X0,X1),relation_dom(sK2))
| ( set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_54,c_6827]) ).
tcf(c_23010,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_14,sK2))),X1)
| in(sK0(X0,X1,relation_dom(relation_composition(iPr_def_14,sK2))),relation_dom(sK2))
| ( relation_dom(relation_composition(iPr_def_14,sK2)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_55,c_6827]) ).
tcf(c_23012,plain,
( in(sK10(relation_dom(relation_composition(iPr_def_14,sK2)),relation_composition(iPr_def_14,sK2)),relation_dom(sK2))
| ( identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))) = relation_composition(iPr_def_14,sK2) )
| ~ relation(relation_composition(iPr_def_14,sK2))
| ~ function(relation_composition(iPr_def_14,sK2)) ),
inference(superposition,[status(thm)],[c_100,c_6827]) ).
tcf(c_23014,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))
| in(sK1(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_7250,c_6827]) ).
tcf(c_23015,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))
| in(sK1(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_2201,c_6827]) ).
tcf(c_23016,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))
| in(sK1(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_2732,c_6827]) ).
tcf(c_23017,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))
| in(sK1(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_2202,c_6827]) ).
tcf(c_23018,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_14,sK2)),X0,set_intersection2(X1,X2)),X2)
| in(sK0(relation_dom(relation_composition(iPr_def_14,sK2)),X0,set_intersection2(X1,X2)),relation_dom(sK2))
| ( set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_6827]) ).
tcf(c_23019,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))),X1)
| in(sK0(X1,X2,set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))),relation_dom(sK2))
| ( set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_2241,c_6827]) ).
tcf(c_23020,plain,
! [X0: $i] :
( in(sK0(empty_set,X0,relation_dom(relation_composition(iPr_def_14,sK2))),relation_dom(sK2))
| ( relation_dom(relation_composition(iPr_def_14,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5683,c_6827]) ).
tcf(c_23021,plain,
! [X0: $i] :
( in(sK0(X0,empty_set,relation_dom(relation_composition(iPr_def_14,sK2))),relation_dom(sK2))
| ( relation_dom(relation_composition(iPr_def_14,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5686,c_6827]) ).
tcf(c_23022,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12691,c_6827]) ).
tcf(c_23108,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_3936]) ).
tcf(c_23109,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1(powerset(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_3936]) ).
tcf(c_23110,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1(powerset(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_3936]) ).
tcf(c_23111,plain,
relation_dom(relation_dom(sK1(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_3936]) ).
tcf(c_23112,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_3936]) ).
tcf(c_23113,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1(powerset(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_3936]) ).
tcf(c_23114,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1(powerset(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_3936]) ).
tcf(c_23115,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1(powerset(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_3936]) ).
tcf(c_23116,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1(powerset(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_3936]) ).
tcf(c_23117,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1(powerset(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_3936]) ).
tcf(c_23118,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1(powerset(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_3936]) ).
tcf(c_23119,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1(powerset(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_3936]) ).
tcf(c_23120,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1(powerset(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_3936]) ).
tcf(c_23121,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1(powerset(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_3936]) ).
tcf(c_23122,plain,
( ( relation_dom(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_3936]) ).
tcf(c_23123,plain,
( ( relation_dom(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_3936]) ).
tcf(c_23124,plain,
( ( relation_dom(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_3936]) ).
tcf(c_23125,plain,
( ( relation_dom(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_3936]) ).
tcf(c_23126,plain,
( ( relation_dom(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_3936]) ).
tcf(c_23127,plain,
( ( relation_dom(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_3936]) ).
tcf(c_23128,plain,
( ( relation_dom(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_3936]) ).
tcf(c_23129,plain,
( ( relation_dom(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_3936]) ).
tcf(c_23130,plain,
( ( relation_dom(relation_dom(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_3936]) ).
tcf(c_23131,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1(powerset(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_3936]) ).
tcf(c_23132,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1(powerset(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_3936]) ).
tcf(c_23133,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1(powerset(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_3936]) ).
tcf(c_23134,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1(powerset(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_3936]) ).
tcf(c_23265,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( set_intersection2(X0,set_intersection2(X1,X2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_4012]) ).
tcf(c_23266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,set_intersection2(relation_composition(X0,X1),X3)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_4012]) ).
tcf(c_23267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,set_intersection2(relation_composition(X1,X0),X3)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_4012]) ).
tcf(c_23268,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,set_intersection2(empty_set,X1)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_4012]) ).
tcf(c_23269,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(relation_dom(X0),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_4012]) ).
tcf(c_23270,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(identity_relation(X0),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_4012]) ).
tcf(c_23271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(set_intersection2(X0,X2),X3)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_4012]) ).
tcf(c_23272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(set_intersection2(X0,X2),X3)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_4012]) ).
tcf(c_23274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(set_intersection2(X2,X0),X3)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_4012]) ).
tcf(c_23275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(set_intersection2(X2,X0),X3)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_4012]) ).
tcf(c_23276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(set_intersection2(X2,sK1(powerset(X0))),X3)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_4012]) ).
tcf(c_23277,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,set_intersection2(set_intersection2(relation_dom(sK2),X1),X2)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_4012]) ).
tcf(c_23278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(set_intersection2(sK1(powerset(X0)),X2),X3)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_4012]) ).
tcf(c_23279,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_4012]) ).
tcf(c_23280,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X1)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_4012]) ).
tcf(c_23281,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X1)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_4012]) ).
tcf(c_23282,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_4012]) ).
tcf(c_23283,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X1)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_4012]) ).
tcf(c_23284,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X1)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_4012]) ).
tcf(c_23285,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_4012]) ).
tcf(c_23286,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X1)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_4012]) ).
tcf(c_23287,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X1)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_4012]) ).
tcf(c_23289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(set_intersection2(sK1(sK4(powerset(X0))),X2),X3)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_4012]) ).
tcf(c_23290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(set_intersection2(X2,sK1(sK4(powerset(X0)))),X3)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_4012]) ).
tcf(c_23291,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,set_intersection2(set_intersection2(X1,relation_dom(sK2)),X2)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_4012]) ).
tcf(c_23435,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( set_intersection2(X0,sK1(powerset(X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_4013]) ).
tcf(c_23436,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,sK1(powerset(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_4013]) ).
tcf(c_23437,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,sK1(powerset(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_4013]) ).
tcf(c_23438,plain,
! [X0: $i] : set_intersection2(X0,sK1(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_4013]) ).
tcf(c_23439,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,sK1(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_4013]) ).
tcf(c_23440,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,sK1(powerset(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_4013]) ).
tcf(c_23441,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,sK1(powerset(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_4013]) ).
tcf(c_23442,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,sK1(powerset(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_4013]) ).
tcf(c_23443,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,sK1(powerset(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_4013]) ).
tcf(c_23444,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,sK1(powerset(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_4013]) ).
tcf(c_23445,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,sK1(powerset(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_4013]) ).
tcf(c_23446,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,sK1(powerset(set_intersection2(X2,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_4013]) ).
tcf(c_23447,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,sK1(powerset(set_intersection2(relation_dom(sK2),X1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_4013]) ).
tcf(c_23448,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,sK1(powerset(set_intersection2(sK1(powerset(X0)),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_4013]) ).
tcf(c_23449,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_4013]) ).
tcf(c_23450,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_4013]) ).
tcf(c_23451,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_4013]) ).
tcf(c_23452,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_4013]) ).
tcf(c_23453,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_4013]) ).
tcf(c_23454,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_4013]) ).
tcf(c_23455,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_4013]) ).
tcf(c_23456,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_4013]) ).
tcf(c_23457,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_4013]) ).
tcf(c_23458,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,sK1(powerset(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_4013]) ).
tcf(c_23459,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,sK1(powerset(set_intersection2(sK1(sK4(powerset(X0))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_4013]) ).
tcf(c_23460,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,sK1(powerset(set_intersection2(X2,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_4013]) ).
tcf(c_23461,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,sK1(powerset(set_intersection2(X1,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_4013]) ).
tcf(c_23655,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ( set_intersection2(X0,set_intersection2(X1,X2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_4014]) ).
tcf(c_23656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,set_intersection2(X3,relation_composition(X0,X1))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_4014]) ).
tcf(c_23657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,set_intersection2(X3,relation_composition(X1,X0))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_4014]) ).
tcf(c_23658,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,set_intersection2(X1,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_4014]) ).
tcf(c_23659,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X2,relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_4014]) ).
tcf(c_23660,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X2,identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_4014]) ).
tcf(c_23661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X0,X3))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_4014]) ).
tcf(c_23662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X0,X3))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_4014]) ).
tcf(c_23664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X3,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_4014]) ).
tcf(c_23665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X3,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_4014]) ).
tcf(c_23666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X3,sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_4014]) ).
tcf(c_23667,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,set_intersection2(X1,set_intersection2(relation_dom(sK2),X2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_4014]) ).
tcf(c_23668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(X2,set_intersection2(sK1(powerset(X0)),X3))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_4014]) ).
tcf(c_23669,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(X1,relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_4014]) ).
tcf(c_23670,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(X1,relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_4014]) ).
tcf(c_23671,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(X1,relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_4014]) ).
tcf(c_23672,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(X1,relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_4014]) ).
tcf(c_23673,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(X1,relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_4014]) ).
tcf(c_23674,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(X1,relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_4014]) ).
tcf(c_23675,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(X1,relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_4014]) ).
tcf(c_23676,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(X1,relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_4014]) ).
tcf(c_23677,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,set_intersection2(X1,relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_4014]) ).
tcf(c_23679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(X2,set_intersection2(sK1(sK4(powerset(X0))),X3))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_4014]) ).
tcf(c_23680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X3,sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_4014]) ).
tcf(c_23681,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,relation_dom(sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_4014]) ).
tcf(c_23788,plain,
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( identity_relation(sK1(powerset(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15803]) ).
tcf(c_23790,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( identity_relation(sK1(powerset(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15803]) ).
tcf(c_23797,plain,
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = empty_set )
| ( apply(identity_relation(relation_dom(sK2)),sK1(relation_dom(sK2))) = sK1(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_2544,c_6898]) ).
tcf(c_23808,plain,
! [X0: $i] :
( empty(set_intersection2(X0,empty_set))
| ~ in(X0,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_97,c_7260]) ).
tcf(c_23809,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(relation_dom(X0),X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(relation_dom(X0),sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15799,c_7260]) ).
tcf(c_23810,plain,
! [X0: $i] :
( empty(set_intersection2(empty_set,X0))
| ~ in(empty_set,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_1996,c_7260]) ).
tcf(c_23812,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,relation_dom(X1)))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ in(X0,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15801,c_7260]) ).
tcf(c_23813,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,identity_relation(X1)))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ in(X0,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15800,c_7260]) ).
tcf(c_23814,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(identity_relation(X0),X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(identity_relation(X0),sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15798,c_7260]) ).
tcf(c_23815,plain,
( empty(set_intersection2(sK12,relation_dom(sK2)))
| ~ in(sK12,sK1(relation_dom(relation_composition(iPr_def_10,sK2)))) ),
inference(superposition,[status(thm)],[c_6018,c_7260]) ).
tcf(c_23816,plain,
( empty(set_intersection2(sK11,relation_dom(sK2)))
| ~ in(sK11,sK1(relation_dom(relation_composition(iPr_def_11,sK2)))) ),
inference(superposition,[status(thm)],[c_6133,c_7260]) ).
tcf(c_23817,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| ~ in(iPr_def_13,sK1(relation_dom(relation_composition(iPr_def_14,sK2)))) ),
inference(superposition,[status(thm)],[c_6817,c_7260]) ).
tcf(c_23820,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ in(iPr_def_13,sK1(relation_dom(relation_composition(iPr_def_14,sK2)))) ),
inference(light_normalisation,[status(thm)],[c_23817,c_6817]) ).
tcf(c_23823,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ in(sK11,sK1(relation_dom(relation_composition(iPr_def_11,sK2)))) ),
inference(light_normalisation,[status(thm)],[c_23816,c_6133]) ).
tcf(c_23826,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ in(sK12,sK1(relation_dom(relation_composition(iPr_def_10,sK2)))) ),
inference(light_normalisation,[status(thm)],[c_23815,c_6018]) ).
tcf(c_23869,plain,
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = empty_set )
| ( apply(identity_relation(relation_dom(sK2)),sK1(relation_dom(sK2))) = sK1(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_2544,c_7383]) ).
tcf(c_23877,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(set_intersection2(X0,X1),X2) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_4061]) ).
tcf(c_23878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(relation_composition(X0,X1),X2),X3) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_4061]) ).
tcf(c_23879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(relation_composition(X1,X0),X2),X3) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_4061]) ).
tcf(c_23880,plain,
! [X0: $i,X1: $i] : set_intersection2(set_intersection2(empty_set,X0),X1) = empty_set,
inference(superposition,[status(thm)],[c_73,c_4061]) ).
tcf(c_23881,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_4061]) ).
tcf(c_23882,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(identity_relation(X0),X1),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_4061]) ).
tcf(c_23883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_4061]) ).
tcf(c_23884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_4061]) ).
tcf(c_23886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X1,X0),X2),X3) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_4061]) ).
tcf(c_23887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X1,X0),X2),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_4061]) ).
tcf(c_23888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X1,sK1(powerset(X0))),X2),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_4061]) ).
tcf(c_23889,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(relation_dom(sK2),X0),X1),X2) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_4061]) ).
tcf(c_23890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(sK1(powerset(X0)),X1),X2),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_4061]) ).
tcf(c_23891,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_4061]) ).
tcf(c_23892,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0),X1) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_4061]) ).
tcf(c_23893,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0),X1) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_4061]) ).
tcf(c_23894,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_4061]) ).
tcf(c_23895,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0),X1) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_4061]) ).
tcf(c_23896,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0),X1) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_4061]) ).
tcf(c_23897,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_4061]) ).
tcf(c_23898,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0),X1) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_4061]) ).
tcf(c_23899,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0),X1) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_4061]) ).
tcf(c_23901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(sK1(sK4(powerset(X0))),X1),X2),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_4061]) ).
tcf(c_23902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X1,sK1(sK4(powerset(X0)))),X2),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_4061]) ).
tcf(c_23903,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,relation_dom(sK2)),X1),X2) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_4061]) ).
tcf(c_24085,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(sK1(powerset(X0)),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_4062]) ).
tcf(c_24086,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(relation_composition(X0,X1))),X2) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_4062]) ).
tcf(c_24087,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(relation_composition(X1,X0))),X2) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_4062]) ).
tcf(c_24088,plain,
! [X0: $i] : set_intersection2(sK1(powerset(empty_set)),X0) = empty_set,
inference(superposition,[status(thm)],[c_73,c_4062]) ).
tcf(c_24089,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK1(powerset(relation_dom(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_4062]) ).
tcf(c_24090,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK1(powerset(identity_relation(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_4062]) ).
tcf(c_24091,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(set_intersection2(X0,X1))),X2) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_4062]) ).
tcf(c_24092,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(set_intersection2(X0,X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_4062]) ).
tcf(c_24093,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK1(powerset(sK1(powerset(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_4062]) ).
tcf(c_24094,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(set_intersection2(X1,X0))),X2) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_4062]) ).
tcf(c_24095,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(set_intersection2(X1,X0))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_4062]) ).
tcf(c_24096,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(set_intersection2(X1,sK1(powerset(X0))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_4062]) ).
tcf(c_24097,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK1(powerset(set_intersection2(relation_dom(sK2),X0))),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_4062]) ).
tcf(c_24098,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(set_intersection2(sK1(powerset(X0)),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_4062]) ).
tcf(c_24099,plain,
! [X0: $i] :
( ( set_intersection2(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_4062]) ).
tcf(c_24100,plain,
! [X0: $i] :
( ( set_intersection2(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_4062]) ).
tcf(c_24101,plain,
! [X0: $i] :
( ( set_intersection2(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_4062]) ).
tcf(c_24102,plain,
! [X0: $i] :
( ( set_intersection2(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_4062]) ).
tcf(c_24103,plain,
! [X0: $i] :
( ( set_intersection2(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_4062]) ).
tcf(c_24104,plain,
! [X0: $i] :
( ( set_intersection2(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_4062]) ).
tcf(c_24105,plain,
! [X0: $i] :
( ( set_intersection2(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_4062]) ).
tcf(c_24106,plain,
! [X0: $i] :
( ( set_intersection2(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_4062]) ).
tcf(c_24107,plain,
! [X0: $i] :
( ( set_intersection2(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_4062]) ).
tcf(c_24108,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK1(powerset(sK1(sK4(powerset(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_4062]) ).
tcf(c_24109,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(set_intersection2(sK1(sK4(powerset(X0))),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_4062]) ).
tcf(c_24110,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(set_intersection2(X1,sK1(sK4(powerset(X0)))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_4062]) ).
tcf(c_24111,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK1(powerset(set_intersection2(X0,relation_dom(sK2)))),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_4062]) ).
tcf(c_24317,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( set_intersection2(set_intersection2(X0,X1),X2) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_4063]) ).
tcf(c_24318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X2,relation_composition(X0,X1)),X3) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_4063]) ).
tcf(c_24319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X2,relation_composition(X1,X0)),X3) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_4063]) ).
tcf(c_24320,plain,
! [X0: $i,X1: $i] : set_intersection2(set_intersection2(X0,empty_set),X1) = empty_set,
inference(superposition,[status(thm)],[c_73,c_4063]) ).
tcf(c_24321,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,relation_dom(X0)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_4063]) ).
tcf(c_24322,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,identity_relation(X0)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_4063]) ).
tcf(c_24323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X1,set_intersection2(X0,X2)),X3) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_4063]) ).
tcf(c_24324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X1,set_intersection2(X0,X2)),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_4063]) ).
tcf(c_24326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X1,set_intersection2(X2,X0)),X3) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_4063]) ).
tcf(c_24327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X1,set_intersection2(X2,X0)),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_4063]) ).
tcf(c_24328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X1,set_intersection2(X2,sK1(powerset(X0)))),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_4063]) ).
tcf(c_24329,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,set_intersection2(relation_dom(sK2),X1)),X2) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_4063]) ).
tcf(c_24330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X1,set_intersection2(sK1(powerset(X0)),X2)),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_4063]) ).
tcf(c_24331,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_4063]) ).
tcf(c_24332,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))),X1) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_4063]) ).
tcf(c_24333,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))),X1) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_4063]) ).
tcf(c_24334,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_4063]) ).
tcf(c_24335,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))),X1) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_4063]) ).
tcf(c_24336,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))),X1) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_4063]) ).
tcf(c_24337,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_4063]) ).
tcf(c_24338,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))),X1) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_4063]) ).
tcf(c_24339,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))),X1) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_4063]) ).
tcf(c_24341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X1,set_intersection2(sK1(sK4(powerset(X0))),X2)),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_4063]) ).
tcf(c_24342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X1,set_intersection2(X2,sK1(sK4(powerset(X0))))),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_4063]) ).
tcf(c_24343,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,set_intersection2(X1,relation_dom(sK2))),X2) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_4063]) ).
tcf(c_24468,plain,
! [X0: $i] :
( function(set_intersection2(relation_dom(sK2),X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),sK2)),sK1(relation_composition(identity_relation(X0),sK2))) = sK1(relation_composition(identity_relation(X0),sK2)) ) ),
inference(superposition,[status(thm)],[c_2544,c_4765]) ).
tcf(c_24469,plain,
! [X0: $i] :
( function(set_intersection2(relation_dom(sK2),X0))
| ~ relation(sK2)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_4765]) ).
tcf(c_24471,plain,
( function(set_intersection2(relation_dom(sK2),sK12))
| ~ empty(relation_composition(iPr_def_10,sK2)) ),
inference(superposition,[status(thm)],[c_1147,c_4765]) ).
tcf(c_24472,plain,
( function(set_intersection2(relation_dom(sK2),sK11))
| ~ empty(relation_composition(iPr_def_11,sK2)) ),
inference(superposition,[status(thm)],[c_1148,c_4765]) ).
tcf(c_24473,plain,
( function(set_intersection2(relation_dom(sK2),empty_set))
| ~ empty(relation_composition(empty_set,sK2)) ),
inference(superposition,[status(thm)],[c_2472,c_4765]) ).
tcf(c_24474,plain,
( function(set_intersection2(relation_dom(sK2),iPr_def_13))
| ~ empty(relation_composition(iPr_def_14,sK2)) ),
inference(superposition,[status(thm)],[c_1151,c_4765]) ).
tcf(c_24477,plain,
( function(set_intersection2(relation_dom(sK2),empty_set))
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_24473,c_7117]) ).
tcf(c_24478,plain,
function(set_intersection2(relation_dom(sK2),empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_24477,c_73]) ).
tcf(c_24504,plain,
( function(relation_dom(relation_composition(iPr_def_10,sK2)))
| ~ empty(relation_composition(iPr_def_10,sK2)) ),
inference(demodulation,[status(thm)],[c_24471,c_52,c_6018]) ).
tcf(c_24505,plain,
( function(relation_dom(relation_composition(iPr_def_11,sK2)))
| ~ empty(relation_composition(iPr_def_11,sK2)) ),
inference(demodulation,[status(thm)],[c_24472,c_52,c_6133]) ).
tcf(c_24506,plain,
( function(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ empty(relation_composition(iPr_def_14,sK2)) ),
inference(demodulation,[status(thm)],[c_24474,c_52,c_6817]) ).
tcf(c_24511,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X1,X0))
| ( apply(identity_relation(relation_composition(identity_relation(X0),identity_relation(X1))),sK1(relation_composition(identity_relation(X0),identity_relation(X1)))) = sK1(relation_composition(identity_relation(X0),identity_relation(X1))) ) ),
inference(superposition,[status(thm)],[c_2544,c_5128]) ).
tcf(c_24512,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X1,X0))
| ~ relation(identity_relation(X1))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_78,c_5128]) ).
tcf(c_24513,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X0,X1))
| ~ relation(identity_relation(X1))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_62,c_5128]) ).
tcf(c_24516,plain,
! [X0: $i] :
( function(set_intersection2(X0,empty_set))
| ~ empty(relation_composition(empty_set,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_2472,c_5128]) ).
tcf(c_24520,plain,
! [X0: $i] :
( function(set_intersection2(empty_set,X0))
| ~ empty(relation_composition(identity_relation(X0),empty_set)) ),
inference(superposition,[status(thm)],[c_2472,c_5128]) ).
tcf(c_24533,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( sK1(powerset(set_intersection2(X0,X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_5631]) ).
tcf(c_24534,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(relation_composition(X0,X1),X2))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_5631]) ).
tcf(c_24535,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(relation_composition(X1,X0),X2))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_5631]) ).
tcf(c_24536,plain,
! [X0: $i] : sK1(powerset(set_intersection2(empty_set,X0))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_5631]) ).
tcf(c_24537,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(relation_dom(X0),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_5631]) ).
tcf(c_24538,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(identity_relation(X0),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_5631]) ).
tcf(c_24539,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(set_intersection2(X0,X1),X2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_5631]) ).
tcf(c_24540,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(set_intersection2(X0,X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_5631]) ).
tcf(c_24542,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(set_intersection2(X1,X0),X2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_5631]) ).
tcf(c_24543,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(set_intersection2(X1,X0),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_5631]) ).
tcf(c_24544,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(set_intersection2(X1,sK1(powerset(X0))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_5631]) ).
tcf(c_24545,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(set_intersection2(relation_dom(sK2),X0),X1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_5631]) ).
tcf(c_24546,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(set_intersection2(sK1(powerset(X0)),X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_5631]) ).
tcf(c_24547,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_5631]) ).
tcf(c_24548,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_5631]) ).
tcf(c_24549,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_5631]) ).
tcf(c_24550,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_5631]) ).
tcf(c_24551,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_5631]) ).
tcf(c_24552,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_5631]) ).
tcf(c_24553,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_5631]) ).
tcf(c_24554,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_5631]) ).
tcf(c_24555,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_5631]) ).
tcf(c_24557,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(set_intersection2(sK1(sK4(powerset(X0))),X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_5631]) ).
tcf(c_24558,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(set_intersection2(X1,sK1(sK4(powerset(X0)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_5631]) ).
tcf(c_24559,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(set_intersection2(X0,relation_dom(sK2)),X1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_5631]) ).
tcf(c_24711,plain,
! [X0: $i] :
( ( sK1(powerset(sK1(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_5632]) ).
tcf(c_24712,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(sK1(powerset(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_5632]) ).
tcf(c_24713,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(sK1(powerset(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_5632]) ).
tcf(c_24714,plain,
sK1(powerset(sK1(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_5632]) ).
tcf(c_24715,plain,
! [X0: $i] :
( ( sK1(powerset(sK1(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_5632]) ).
tcf(c_24716,plain,
! [X0: $i] :
( ( sK1(powerset(sK1(powerset(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_5632]) ).
tcf(c_24717,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(sK1(powerset(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_5632]) ).
tcf(c_24718,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(sK1(powerset(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_5632]) ).
tcf(c_24719,plain,
! [X0: $i] :
( ( sK1(powerset(sK1(powerset(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_5632]) ).
tcf(c_24720,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(sK1(powerset(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_5632]) ).
tcf(c_24721,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(sK1(powerset(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_5632]) ).
tcf(c_24722,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(sK1(powerset(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_5632]) ).
tcf(c_24723,plain,
! [X0: $i] :
( ( sK1(powerset(sK1(powerset(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_5632]) ).
tcf(c_24724,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(sK1(powerset(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_5632]) ).
tcf(c_24725,plain,
( ( sK1(powerset(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_5632]) ).
tcf(c_24726,plain,
( ( sK1(powerset(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_5632]) ).
tcf(c_24727,plain,
( ( sK1(powerset(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_5632]) ).
tcf(c_24728,plain,
( ( sK1(powerset(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_5632]) ).
tcf(c_24729,plain,
( ( sK1(powerset(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_5632]) ).
tcf(c_24730,plain,
( ( sK1(powerset(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_5632]) ).
tcf(c_24731,plain,
( ( sK1(powerset(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_5632]) ).
tcf(c_24732,plain,
( ( sK1(powerset(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_5632]) ).
tcf(c_24733,plain,
( ( sK1(powerset(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_5632]) ).
tcf(c_24734,plain,
! [X0: $i] :
( ( sK1(powerset(sK1(powerset(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_5632]) ).
tcf(c_24735,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(sK1(powerset(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_5632]) ).
tcf(c_24736,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(sK1(powerset(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_5632]) ).
tcf(c_24737,plain,
! [X0: $i] :
( ( sK1(powerset(sK1(powerset(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_5632]) ).
tcf(c_24898,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( sK1(powerset(set_intersection2(X0,X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_5633]) ).
tcf(c_24899,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(X2,relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_5633]) ).
tcf(c_24900,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(X2,relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_5633]) ).
tcf(c_24901,plain,
! [X0: $i] : sK1(powerset(set_intersection2(X0,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_5633]) ).
tcf(c_24902,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(X1,relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_5633]) ).
tcf(c_24903,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(X1,identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_5633]) ).
tcf(c_24904,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(X1,set_intersection2(X0,X2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_5633]) ).
tcf(c_24905,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(X1,set_intersection2(X0,X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_5633]) ).
tcf(c_24907,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(X1,set_intersection2(X2,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_5633]) ).
tcf(c_24908,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(X1,set_intersection2(X2,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_5633]) ).
tcf(c_24909,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(X1,set_intersection2(X2,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_5633]) ).
tcf(c_24910,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(X0,set_intersection2(relation_dom(sK2),X1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_5633]) ).
tcf(c_24911,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(X1,set_intersection2(sK1(powerset(X0)),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_5633]) ).
tcf(c_24912,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_5633]) ).
tcf(c_24913,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_5633]) ).
tcf(c_24914,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_5633]) ).
tcf(c_24915,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_5633]) ).
tcf(c_24916,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_5633]) ).
tcf(c_24917,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_5633]) ).
tcf(c_24918,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_5633]) ).
tcf(c_24919,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_5633]) ).
tcf(c_24920,plain,
! [X0: $i] :
( ( sK1(powerset(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_5633]) ).
tcf(c_24922,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(X1,set_intersection2(sK1(sK4(powerset(X0))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_5633]) ).
tcf(c_24923,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(X1,set_intersection2(X2,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_5633]) ).
tcf(c_24924,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(X0,set_intersection2(X1,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_5633]) ).
tcf(c_25060,plain,
( ( relation_dom(iPr_def_13) = empty_set )
| ( apply(identity_relation(sK12),sK1(sK12)) = sK1(sK12) ) ),
inference(superposition,[status(thm)],[c_1150,c_15804]) ).
tcf(c_25064,plain,
( ( apply(identity_relation(sK12),sK1(sK12)) = sK1(sK12) )
| ( relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6018,c_15804]) ).
tcf(c_25065,plain,
( ( apply(identity_relation(sK11),sK1(sK11)) = sK1(sK11) )
| ( relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6133,c_15804]) ).
tcf(c_25066,plain,
( ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) )
| ( relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6817,c_15804]) ).
tcf(c_25069,plain,
! [X0: $i] :
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( relation_dom(set_intersection2(empty_set,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15804]) ).
tcf(c_25071,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( relation_dom(set_intersection2(powerset(empty_set),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15804]) ).
tcf(c_25073,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X0,set_intersection2(X1,X2)),relation_dom(X0))
| ( set_intersection2(X1,X2) = X0 )
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(set_intersection2(X1,X2))
| ~ function(set_intersection2(X1,X2))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_15804,c_112]) ).
tcf(c_25074,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,empty_set) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(identity_relation(set_intersection2(X0,X1)),sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_15804,c_15801]) ).
tcf(c_25075,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(empty_set,X2) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(identity_relation(set_intersection2(X0,X1)),sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_15804,c_15799]) ).
tcf(c_25076,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(set_intersection2(X1,X2),X0),relation_dom(set_intersection2(X1,X2)))
| ( set_intersection2(X1,X2) = X0 )
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(set_intersection2(X1,X2))
| ~ function(set_intersection2(X1,X2))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_15804,c_112]) ).
tcf(c_25078,plain,
! [X0: $i,X1: $i] :
( in(sK10(empty_set,set_intersection2(X0,X1)),empty_set)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(relation_dom(set_intersection2(X0,X1))) = set_intersection2(X0,X1) )
| ~ relation(set_intersection2(X0,X1))
| ~ function(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_15804,c_100]) ).
tcf(c_25079,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set)
| ~ relation(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_15804,c_75]) ).
tcf(c_25088,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ relation(set_intersection2(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25079,c_73]) ).
tcf(c_25092,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(relation_dom(set_intersection2(X0,X1))) = set_intersection2(X0,X1) )
| ~ relation(set_intersection2(X0,X1))
| ~ function(set_intersection2(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25078,c_5671]) ).
tcf(c_25119,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_7544]) ).
tcf(c_25120,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_7544]) ).
tcf(c_25121,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_7544]) ).
tcf(c_25122,plain,
relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_7544]) ).
tcf(c_25123,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_7544]) ).
tcf(c_25124,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_7544]) ).
tcf(c_25125,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_7544]) ).
tcf(c_25126,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_7544]) ).
tcf(c_25127,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_7544]) ).
tcf(c_25128,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_7544]) ).
tcf(c_25129,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_7544]) ).
tcf(c_25130,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_7544]) ).
tcf(c_25131,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_7544]) ).
tcf(c_25132,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_7544]) ).
tcf(c_25133,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_7544]) ).
tcf(c_25134,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_7544]) ).
tcf(c_25135,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_7544]) ).
tcf(c_25136,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_7544]) ).
tcf(c_25137,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_7544]) ).
tcf(c_25138,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_7544]) ).
tcf(c_25139,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_7544]) ).
tcf(c_25140,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_7544]) ).
tcf(c_25141,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_7544]) ).
tcf(c_25142,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_7544]) ).
tcf(c_25143,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_7544]) ).
tcf(c_25144,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_7544]) ).
tcf(c_25145,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_7544]) ).
tcf(c_25357,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_7593]) ).
tcf(c_25358,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_7593]) ).
tcf(c_25359,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_7593]) ).
tcf(c_25360,plain,
identity_relation(relation_dom(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_7593]) ).
tcf(c_25361,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_7593]) ).
tcf(c_25362,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_7593]) ).
tcf(c_25363,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_7593]) ).
tcf(c_25364,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_7593]) ).
tcf(c_25365,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_7593]) ).
tcf(c_25366,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_7593]) ).
tcf(c_25367,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_7593]) ).
tcf(c_25368,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_7593]) ).
tcf(c_25369,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_7593]) ).
tcf(c_25370,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_7593]) ).
tcf(c_25371,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_7593]) ).
tcf(c_25372,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_7593]) ).
tcf(c_25373,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_7593]) ).
tcf(c_25374,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_7593]) ).
tcf(c_25375,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_7593]) ).
tcf(c_25376,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_7593]) ).
tcf(c_25377,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_7593]) ).
tcf(c_25378,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_7593]) ).
tcf(c_25379,plain,
( ( identity_relation(relation_dom(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_7593]) ).
tcf(c_25380,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_7593]) ).
tcf(c_25381,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_7593]) ).
tcf(c_25382,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_7593]) ).
tcf(c_25383,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_7593]) ).
tcf(c_25535,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_7679]) ).
tcf(c_25536,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_7679]) ).
tcf(c_25537,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_7679]) ).
tcf(c_25538,plain,
identity_relation(identity_relation(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_7679]) ).
tcf(c_25539,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_7679]) ).
tcf(c_25540,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_7679]) ).
tcf(c_25541,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_7679]) ).
tcf(c_25542,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_7679]) ).
tcf(c_25543,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_7679]) ).
tcf(c_25544,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_7679]) ).
tcf(c_25545,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_7679]) ).
tcf(c_25546,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_7679]) ).
tcf(c_25547,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_7679]) ).
tcf(c_25548,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_7679]) ).
tcf(c_25549,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_7679]) ).
tcf(c_25550,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_7679]) ).
tcf(c_25551,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_7679]) ).
tcf(c_25552,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_7679]) ).
tcf(c_25553,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_7679]) ).
tcf(c_25554,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_7679]) ).
tcf(c_25555,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_7679]) ).
tcf(c_25556,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_7679]) ).
tcf(c_25557,plain,
( ( identity_relation(identity_relation(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_7679]) ).
tcf(c_25558,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_7679]) ).
tcf(c_25559,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_7679]) ).
tcf(c_25560,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_7679]) ).
tcf(c_25561,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_7679]) ).
tcf(c_25683,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_7756]) ).
tcf(c_25684,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_7756]) ).
tcf(c_25685,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_7756]) ).
tcf(c_25686,plain,
identity_relation(identity_relation(identity_relation(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_7756]) ).
tcf(c_25687,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_7756]) ).
tcf(c_25688,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_7756]) ).
tcf(c_25689,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_7756]) ).
tcf(c_25690,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_7756]) ).
tcf(c_25691,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_7756]) ).
tcf(c_25692,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_7756]) ).
tcf(c_25693,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_7756]) ).
tcf(c_25694,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_7756]) ).
tcf(c_25695,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_7756]) ).
tcf(c_25696,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_7756]) ).
tcf(c_25697,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_7756]) ).
tcf(c_25698,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_7756]) ).
tcf(c_25699,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_7756]) ).
tcf(c_25700,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_7756]) ).
tcf(c_25701,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_7756]) ).
tcf(c_25702,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_7756]) ).
tcf(c_25703,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_7756]) ).
tcf(c_25704,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_7756]) ).
tcf(c_25705,plain,
( ( identity_relation(identity_relation(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_7756]) ).
tcf(c_25706,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_7756]) ).
tcf(c_25707,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_7756]) ).
tcf(c_25708,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_7756]) ).
tcf(c_25709,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_7756]) ).
tcf(c_25923,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_7757]) ).
tcf(c_25924,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_7757]) ).
tcf(c_25925,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_7757]) ).
tcf(c_25926,plain,
identity_relation(identity_relation(identity_relation(identity_relation(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_7757]) ).
tcf(c_25927,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_7757]) ).
tcf(c_25928,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_7757]) ).
tcf(c_25929,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_7757]) ).
tcf(c_25930,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_7757]) ).
tcf(c_25931,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_7757]) ).
tcf(c_25932,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_7757]) ).
tcf(c_25933,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_7757]) ).
tcf(c_25934,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_7757]) ).
tcf(c_25935,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_7757]) ).
tcf(c_25936,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_7757]) ).
tcf(c_25937,plain,
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_7757]) ).
tcf(c_25938,plain,
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_7757]) ).
tcf(c_25939,plain,
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_7757]) ).
tcf(c_25940,plain,
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_7757]) ).
tcf(c_25941,plain,
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_7757]) ).
tcf(c_25942,plain,
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_7757]) ).
tcf(c_25943,plain,
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_7757]) ).
tcf(c_25944,plain,
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_7757]) ).
tcf(c_25945,plain,
( ( identity_relation(identity_relation(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_7757]) ).
tcf(c_25946,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_7757]) ).
tcf(c_25947,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_7757]) ).
tcf(c_25948,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_7757]) ).
tcf(c_25949,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_7757]) ).
tcf(c_26109,plain,
( empty(set_intersection2(relation_dom(sK2),sK12))
| ~ in(sK12,sK1(relation_dom(relation_composition(iPr_def_10,sK2)))) ),
inference(superposition,[status(thm)],[c_6018,c_7916]) ).
tcf(c_26110,plain,
( empty(set_intersection2(relation_dom(sK2),sK11))
| ~ in(sK11,sK1(relation_dom(relation_composition(iPr_def_11,sK2)))) ),
inference(superposition,[status(thm)],[c_6133,c_7916]) ).
tcf(c_26111,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| ~ in(iPr_def_13,sK1(relation_dom(relation_composition(iPr_def_14,sK2)))) ),
inference(superposition,[status(thm)],[c_6817,c_7916]) ).
tcf(c_26146,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(sK11,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15799,c_8221]) ).
tcf(c_26147,plain,
( empty(set_intersection2(empty_set,iPr_def_13))
| ~ in(sK11,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_1996,c_8221]) ).
tcf(c_26148,plain,
! [X0: $i] :
( empty(set_intersection2(identity_relation(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(sK11,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15798,c_8221]) ).
tcf(c_26168,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(sK12,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15799,c_8246]) ).
tcf(c_26169,plain,
( empty(set_intersection2(empty_set,iPr_def_13))
| ~ in(sK12,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_1996,c_8246]) ).
tcf(c_26170,plain,
! [X0: $i] :
( empty(set_intersection2(identity_relation(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(sK12,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15798,c_8246]) ).
tcf(c_26187,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(X0,relation_dom(X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_8269]) ).
tcf(c_26188,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X2,relation_dom(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_8269]) ).
tcf(c_26189,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X2,relation_dom(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_8269]) ).
tcf(c_26190,plain,
! [X0: $i] : identity_relation(set_intersection2(X0,relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_8269]) ).
tcf(c_26191,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_8269]) ).
tcf(c_26192,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_8269]) ).
tcf(c_26193,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_8269]) ).
tcf(c_26194,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_8269]) ).
tcf(c_26195,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_8269]) ).
tcf(c_26196,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_8269]) ).
tcf(c_26197,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_8269]) ).
tcf(c_26198,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(set_intersection2(X2,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_8269]) ).
tcf(c_26199,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(set_intersection2(relation_dom(sK2),X1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_8269]) ).
tcf(c_26200,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(set_intersection2(sK1(powerset(X0)),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_8269]) ).
tcf(c_26201,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_8269]) ).
tcf(c_26202,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_8269]) ).
tcf(c_26203,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_8269]) ).
tcf(c_26204,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_8269]) ).
tcf(c_26205,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_8269]) ).
tcf(c_26206,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_8269]) ).
tcf(c_26207,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_8269]) ).
tcf(c_26208,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_8269]) ).
tcf(c_26209,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_8269]) ).
tcf(c_26210,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_8269]) ).
tcf(c_26211,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_8269]) ).
tcf(c_26212,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(set_intersection2(X2,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_8269]) ).
tcf(c_26213,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X0,relation_dom(set_intersection2(X1,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_8269]) ).
tcf(c_26326,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(X0,identity_relation(X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_8270]) ).
tcf(c_26327,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X2,identity_relation(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_8270]) ).
tcf(c_26328,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X2,identity_relation(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_8270]) ).
tcf(c_26329,plain,
! [X0: $i] : identity_relation(set_intersection2(X0,identity_relation(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_8270]) ).
tcf(c_26330,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_8270]) ).
tcf(c_26331,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_8270]) ).
tcf(c_26332,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_8270]) ).
tcf(c_26333,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_8270]) ).
tcf(c_26334,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_8270]) ).
tcf(c_26335,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_8270]) ).
tcf(c_26336,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_8270]) ).
tcf(c_26337,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(set_intersection2(X2,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_8270]) ).
tcf(c_26338,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X0,identity_relation(set_intersection2(relation_dom(sK2),X1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_8270]) ).
tcf(c_26339,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(set_intersection2(sK1(powerset(X0)),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_8270]) ).
tcf(c_26340,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_8270]) ).
tcf(c_26341,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_8270]) ).
tcf(c_26342,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_8270]) ).
tcf(c_26343,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_8270]) ).
tcf(c_26344,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_8270]) ).
tcf(c_26345,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_8270]) ).
tcf(c_26346,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_8270]) ).
tcf(c_26347,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_8270]) ).
tcf(c_26348,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_8270]) ).
tcf(c_26349,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_8270]) ).
tcf(c_26350,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_8270]) ).
tcf(c_26351,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(set_intersection2(X2,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_8270]) ).
tcf(c_26352,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X0,identity_relation(set_intersection2(X1,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_8270]) ).
tcf(c_26519,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(X0,relation_dom(X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_8376]) ).
tcf(c_26520,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X2,relation_dom(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_8376]) ).
tcf(c_26521,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X2,relation_dom(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_8376]) ).
tcf(c_26522,plain,
! [X0: $i] : relation_dom(set_intersection2(X0,relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_8376]) ).
tcf(c_26523,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_8376]) ).
tcf(c_26524,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_8376]) ).
tcf(c_26525,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_8376]) ).
tcf(c_26526,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_8376]) ).
tcf(c_26527,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_8376]) ).
tcf(c_26528,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_8376]) ).
tcf(c_26529,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_8376]) ).
tcf(c_26530,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(set_intersection2(X2,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_8376]) ).
tcf(c_26531,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(set_intersection2(relation_dom(sK2),X1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_8376]) ).
tcf(c_26532,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(set_intersection2(sK1(powerset(X0)),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_8376]) ).
tcf(c_26533,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_8376]) ).
tcf(c_26534,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_8376]) ).
tcf(c_26535,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_8376]) ).
tcf(c_26536,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_8376]) ).
tcf(c_26537,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_8376]) ).
tcf(c_26538,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_8376]) ).
tcf(c_26539,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_8376]) ).
tcf(c_26540,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_8376]) ).
tcf(c_26541,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_8376]) ).
tcf(c_26542,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_8376]) ).
tcf(c_26543,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_8376]) ).
tcf(c_26544,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(set_intersection2(X2,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_8376]) ).
tcf(c_26545,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X0,relation_dom(set_intersection2(X1,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_8376]) ).
tcf(c_26690,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(X0,identity_relation(X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_8377]) ).
tcf(c_26691,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X2,identity_relation(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_8377]) ).
tcf(c_26692,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X2,identity_relation(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_8377]) ).
tcf(c_26693,plain,
! [X0: $i] : relation_dom(set_intersection2(X0,identity_relation(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_8377]) ).
tcf(c_26694,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_8377]) ).
tcf(c_26695,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_8377]) ).
tcf(c_26696,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_8377]) ).
tcf(c_26697,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_8377]) ).
tcf(c_26698,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_8377]) ).
tcf(c_26699,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_8377]) ).
tcf(c_26700,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_8377]) ).
tcf(c_26701,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(set_intersection2(X2,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_8377]) ).
tcf(c_26702,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X0,identity_relation(set_intersection2(relation_dom(sK2),X1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_8377]) ).
tcf(c_26703,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(set_intersection2(sK1(powerset(X0)),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_8377]) ).
tcf(c_26704,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_8377]) ).
tcf(c_26705,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_8377]) ).
tcf(c_26706,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_8377]) ).
tcf(c_26707,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_8377]) ).
tcf(c_26708,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_8377]) ).
tcf(c_26709,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_8377]) ).
tcf(c_26710,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_8377]) ).
tcf(c_26711,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_8377]) ).
tcf(c_26712,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_8377]) ).
tcf(c_26713,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_8377]) ).
tcf(c_26714,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_8377]) ).
tcf(c_26715,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(set_intersection2(X2,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_8377]) ).
tcf(c_26716,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X0,identity_relation(set_intersection2(X1,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_8377]) ).
tcf(c_26939,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(relation_dom(X0),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_8456]) ).
tcf(c_26940,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_composition(X0,X1)),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_8456]) ).
tcf(c_26941,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_composition(X1,X0)),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_8456]) ).
tcf(c_26942,plain,
! [X0: $i] : identity_relation(set_intersection2(relation_dom(empty_set),X0)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_8456]) ).
tcf(c_26943,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_dom(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_8456]) ).
tcf(c_26944,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(relation_dom(identity_relation(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_8456]) ).
tcf(c_26945,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(relation_dom(set_intersection2(X0,X1)),X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_8456]) ).
tcf(c_26946,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(relation_dom(set_intersection2(X0,X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_8456]) ).
tcf(c_26947,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(relation_dom(sK1(powerset(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_8456]) ).
tcf(c_26948,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(relation_dom(set_intersection2(X1,X0)),X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_8456]) ).
tcf(c_26949,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(relation_dom(set_intersection2(X1,X0)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_8456]) ).
tcf(c_26950,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(relation_dom(set_intersection2(X1,sK1(powerset(X0)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_8456]) ).
tcf(c_26951,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(relation_dom(set_intersection2(relation_dom(sK2),X0)),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_8456]) ).
tcf(c_26952,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(relation_dom(set_intersection2(sK1(powerset(X0)),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_8456]) ).
tcf(c_26953,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_8456]) ).
tcf(c_26954,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_8456]) ).
tcf(c_26955,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_8456]) ).
tcf(c_26956,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_8456]) ).
tcf(c_26957,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_8456]) ).
tcf(c_26958,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_8456]) ).
tcf(c_26959,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_8456]) ).
tcf(c_26960,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_8456]) ).
tcf(c_26961,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_8456]) ).
tcf(c_26962,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(relation_dom(sK1(sK4(powerset(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_8456]) ).
tcf(c_26963,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_8456]) ).
tcf(c_26964,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_8456]) ).
tcf(c_26965,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(relation_dom(set_intersection2(X0,relation_dom(sK2))),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_8456]) ).
tcf(c_27088,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(identity_relation(X0),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_8457]) ).
tcf(c_27089,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(identity_relation(relation_composition(X0,X1)),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_8457]) ).
tcf(c_27090,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(identity_relation(relation_composition(X1,X0)),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_8457]) ).
tcf(c_27091,plain,
! [X0: $i] : identity_relation(set_intersection2(identity_relation(empty_set),X0)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_8457]) ).
tcf(c_27092,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(identity_relation(relation_dom(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_8457]) ).
tcf(c_27093,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(identity_relation(identity_relation(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_8457]) ).
tcf(c_27094,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(identity_relation(set_intersection2(X0,X1)),X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_8457]) ).
tcf(c_27095,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(identity_relation(set_intersection2(X0,X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_8457]) ).
tcf(c_27096,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(identity_relation(sK1(powerset(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_8457]) ).
tcf(c_27097,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(identity_relation(set_intersection2(X1,X0)),X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_8457]) ).
tcf(c_27098,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(identity_relation(set_intersection2(X1,X0)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_8457]) ).
tcf(c_27099,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(identity_relation(set_intersection2(X1,sK1(powerset(X0)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_8457]) ).
tcf(c_27100,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(identity_relation(set_intersection2(relation_dom(sK2),X0)),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_8457]) ).
tcf(c_27101,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(identity_relation(set_intersection2(sK1(powerset(X0)),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_8457]) ).
tcf(c_27102,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_8457]) ).
tcf(c_27103,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_8457]) ).
tcf(c_27104,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_8457]) ).
tcf(c_27105,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_8457]) ).
tcf(c_27106,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_8457]) ).
tcf(c_27107,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_8457]) ).
tcf(c_27108,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_8457]) ).
tcf(c_27109,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_8457]) ).
tcf(c_27110,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_8457]) ).
tcf(c_27111,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(identity_relation(sK1(sK4(powerset(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_8457]) ).
tcf(c_27112,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_8457]) ).
tcf(c_27113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_8457]) ).
tcf(c_27114,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(identity_relation(set_intersection2(X0,relation_dom(sK2))),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_8457]) ).
tcf(c_27355,plain,
( ( identity_relation(iPr_def_13) = empty_set )
| ( apply(identity_relation(sK12),sK1(sK12)) = sK1(sK12) ) ),
inference(superposition,[status(thm)],[c_1150,c_15805]) ).
tcf(c_27359,plain,
( ( apply(identity_relation(sK12),sK1(sK12)) = sK1(sK12) )
| ( identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6018,c_15805]) ).
tcf(c_27360,plain,
( ( apply(identity_relation(sK11),sK1(sK11)) = sK1(sK11) )
| ( identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6133,c_15805]) ).
tcf(c_27361,plain,
( ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) )
| ( identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6817,c_15805]) ).
tcf(c_27364,plain,
! [X0: $i] :
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( identity_relation(set_intersection2(empty_set,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15805]) ).
tcf(c_27367,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( identity_relation(set_intersection2(powerset(empty_set),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15805]) ).
tcf(c_27369,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(set_intersection2(set_intersection2(X1,X2),X0))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(relation_composition(identity_relation(X0),empty_set)) ),
inference(superposition,[status(thm)],[c_15805,c_5128]) ).
tcf(c_27370,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X1,X2),X0))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(relation_composition(identity_relation(X0),empty_set)) ),
inference(superposition,[status(thm)],[c_15805,c_5130]) ).
tcf(c_27371,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(set_intersection2(set_intersection2(X1,X2),X0))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(relation_composition(identity_relation(X0),empty_set)) ),
inference(superposition,[status(thm)],[c_15805,c_5129]) ).
tcf(c_27372,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_dom(relation_composition(identity_relation(X2),empty_set)) ) ),
inference(superposition,[status(thm)],[c_15805,c_3036]) ).
tcf(c_27373,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15805]) ).
tcf(c_27374,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15804]) ).
tcf(c_27375,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(set_intersection2(X0,set_intersection2(X1,X2)))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(relation_composition(empty_set,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_15805,c_5128]) ).
tcf(c_27376,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(relation_dom(sK2),set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,sK2)) ),
inference(superposition,[status(thm)],[c_15805,c_4765]) ).
tcf(c_27377,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( identity_relation(sK1(powerset(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15803]) ).
tcf(c_27378,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( relation_dom(sK1(powerset(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15802]) ).
tcf(c_27380,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X1,X2))) = sK1(set_intersection2(X1,X2)) )
| ( set_intersection2(X0,relation_dom(set_intersection2(X1,X2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15801]) ).
tcf(c_27383,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,set_intersection2(X1,X2)))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(relation_composition(empty_set,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_15805,c_5130]) ).
tcf(c_27384,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(set_intersection2(X0,set_intersection2(X1,X2)))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(relation_composition(empty_set,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_15805,c_5129]) ).
tcf(c_27385,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X1,X2))) = sK1(set_intersection2(X1,X2)) )
| ( set_intersection2(X0,identity_relation(set_intersection2(X1,X2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15800]) ).
tcf(c_27387,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( set_intersection2(relation_dom(set_intersection2(X0,X1)),X2) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15799]) ).
tcf(c_27388,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(relation_dom(sK2),set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,sK2)) ),
inference(superposition,[status(thm)],[c_15805,c_4767]) ).
tcf(c_27389,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( set_intersection2(identity_relation(set_intersection2(X0,X1)),X2) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15798]) ).
tcf(c_27391,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( sK1(powerset(relation_dom(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15797]) ).
tcf(c_27392,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(relation_dom(sK2),set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,sK2)) ),
inference(superposition,[status(thm)],[c_15805,c_4766]) ).
tcf(c_27393,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( sK1(powerset(identity_relation(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15796]) ).
tcf(c_27395,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( sK1(sK4(powerset(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15795]) ).
tcf(c_27396,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(set_intersection2(X0,X1),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_14,empty_set)) ),
inference(superposition,[status(thm)],[c_15805,c_7987]) ).
tcf(c_27397,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_14,empty_set)) ),
inference(superposition,[status(thm)],[c_15805,c_7989]) ).
tcf(c_27398,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(set_intersection2(X0,X1),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_14,empty_set)) ),
inference(superposition,[status(thm)],[c_15805,c_7988]) ).
tcf(c_27399,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X2) = empty_set )
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK0(X0,empty_set,set_intersection2(X1,X2))) = sK0(X0,empty_set,set_intersection2(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_15805,c_11677]) ).
tcf(c_27400,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),sK11))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_11,empty_set)) ),
inference(superposition,[status(thm)],[c_15805,c_7195]) ).
tcf(c_27401,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(set_intersection2(X0,X1),sK11))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_11,empty_set)) ),
inference(superposition,[status(thm)],[c_15805,c_7194]) ).
tcf(c_27402,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(set_intersection2(X0,X1),sK11))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_11,empty_set)) ),
inference(superposition,[status(thm)],[c_15805,c_7193]) ).
tcf(c_27403,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),sK12))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_10,empty_set)) ),
inference(superposition,[status(thm)],[c_15805,c_7051]) ).
tcf(c_27404,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(set_intersection2(X0,X1),sK12))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_10,empty_set)) ),
inference(superposition,[status(thm)],[c_15805,c_7049]) ).
tcf(c_27405,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(set_intersection2(X0,X1),sK12))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_10,empty_set)) ),
inference(superposition,[status(thm)],[c_15805,c_7050]) ).
tcf(c_27406,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X2) = empty_set )
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK0(empty_set,X0,set_intersection2(X1,X2))) = sK0(empty_set,X0,set_intersection2(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_15805,c_11616]) ).
tcf(c_27410,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK12,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_15805,c_4466]) ).
tcf(c_27411,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(sK12,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_15805,c_4465]) ).
tcf(c_27412,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(sK12,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_15805,c_4464]) ).
tcf(c_27413,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK11,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15805,c_4108]) ).
tcf(c_27414,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(sK11,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15805,c_4107]) ).
tcf(c_27415,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(sK11,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15805,c_4106]) ).
tcf(c_27416,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(iPr_def_13,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_15805,c_3290]) ).
tcf(c_27417,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(iPr_def_13,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_15805,c_3288]) ).
tcf(c_27418,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(iPr_def_13,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_15805,c_3289]) ).
tcf(c_27419,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(set_intersection2(X0,X1),iPr_def_13) = relation_dom(relation_composition(iPr_def_14,empty_set)) ) ),
inference(superposition,[status(thm)],[c_15805,c_5118]) ).
tcf(c_27420,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(set_intersection2(X0,X1),sK11) = relation_dom(relation_composition(iPr_def_11,empty_set)) ) ),
inference(superposition,[status(thm)],[c_15805,c_5116]) ).
tcf(c_27421,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(set_intersection2(X0,X1),sK12) = relation_dom(relation_composition(iPr_def_10,empty_set)) ) ),
inference(superposition,[status(thm)],[c_15805,c_5115]) ).
tcf(c_27422,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(iPr_def_13,set_intersection2(X0,X1)) = relation_dom(relation_composition(empty_set,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_15805,c_5413]) ).
tcf(c_27423,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(X1,set_intersection2(X0,X2)) = relation_dom(relation_composition(empty_set,identity_relation(X1))) ) ),
inference(superposition,[status(thm)],[c_15805,c_3036]) ).
tcf(c_27424,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(relation_dom(sK2),set_intersection2(X0,X1)) = relation_dom(relation_composition(empty_set,sK2)) ) ),
inference(superposition,[status(thm)],[c_15805,c_3034]) ).
tcf(c_27425,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(sK12,set_intersection2(X0,X1)) = relation_dom(relation_composition(empty_set,iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_15805,c_3031]) ).
tcf(c_27426,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(sK11,set_intersection2(X0,X1)) = relation_dom(relation_composition(empty_set,iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_15805,c_3029]) ).
tcf(c_27427,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(iPr_def_13,set_intersection2(X0,X1)) = relation_dom(relation_composition(empty_set,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_15805,c_3027]) ).
tcf(c_27429,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X0,X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_1965]) ).
tcf(c_27430,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X0,X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_1918]) ).
tcf(c_27431,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_1893]) ).
tcf(c_27434,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = relation_dom(empty_set) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15805,c_144]) ).
tcf(c_27438,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27431,c_73]) ).
tcf(c_27441,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X0,X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27430,c_73]) ).
tcf(c_27444,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X0,X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27429,c_73]) ).
tcf(c_27450,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(iPr_def_13,set_intersection2(X0,X1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_27427,c_2054,c_5997]) ).
tcf(c_27453,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(sK11,set_intersection2(X0,X1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_27426,c_2054,c_6184]) ).
tcf(c_27456,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(sK12,set_intersection2(X0,X1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_27425,c_2054,c_6071]) ).
tcf(c_27460,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(set_intersection2(X0,X1),sK12) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_27421,c_2054,c_4938]) ).
tcf(c_27463,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(set_intersection2(X0,X1),sK11) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_27420,c_2054,c_5102]) ).
tcf(c_27466,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(set_intersection2(X0,X1),iPr_def_13) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_27419,c_2054,c_5508]) ).
tcf(c_27469,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(iPr_def_13,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27418,c_5997]) ).
tcf(c_27473,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(iPr_def_13,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27417,c_5997]) ).
tcf(c_27477,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(iPr_def_13,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27416,c_5997]) ).
tcf(c_27481,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(sK11,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27415,c_6184]) ).
tcf(c_27485,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(sK11,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27414,c_6184]) ).
tcf(c_27489,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK11,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27413,c_6184]) ).
tcf(c_27493,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(sK12,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27412,c_6071]) ).
tcf(c_27497,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(sK12,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27411,c_6071]) ).
tcf(c_27501,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK12,set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27410,c_6071]) ).
tcf(c_27505,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(set_intersection2(X0,X1),sK12))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27405,c_4938]) ).
tcf(c_27509,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(set_intersection2(X0,X1),sK12))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27404,c_4938]) ).
tcf(c_27513,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),sK12))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27403,c_4938]) ).
tcf(c_27517,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(set_intersection2(X0,X1),sK11))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27402,c_5102]) ).
tcf(c_27521,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(set_intersection2(X0,X1),sK11))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27401,c_5102]) ).
tcf(c_27525,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),sK11))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27400,c_5102]) ).
tcf(c_27529,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(set_intersection2(X0,X1),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27398,c_5508]) ).
tcf(c_27533,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27397,c_5508]) ).
tcf(c_27537,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(set_intersection2(X0,X1),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27396,c_5508]) ).
tcf(c_27541,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(relation_dom(sK2),set_intersection2(X0,X1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_27424,c_2054,c_7117]) ).
tcf(c_27546,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(relation_dom(sK2),set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27392,c_7117]) ).
tcf(c_27550,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(relation_dom(sK2),set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27388,c_7117]) ).
tcf(c_27554,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(set_intersection2(X1,set_intersection2(X0,X2)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27384,c_22644]) ).
tcf(c_27555,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(set_intersection2(X1,set_intersection2(X0,X2)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27554,c_73]) ).
tcf(c_27558,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X1,set_intersection2(X0,X2)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27383,c_22644]) ).
tcf(c_27559,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X1,set_intersection2(X0,X2)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27558,c_73]) ).
tcf(c_27562,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(relation_dom(sK2),set_intersection2(X0,X1)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27376,c_7117]) ).
tcf(c_27566,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(set_intersection2(X1,set_intersection2(X0,X2)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27375,c_22644]) ).
tcf(c_27567,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(set_intersection2(X1,set_intersection2(X0,X2)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27566,c_73]) ).
tcf(c_27572,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(set_intersection2(set_intersection2(X0,X1),X2))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27371,c_17003]) ).
tcf(c_27573,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(set_intersection2(set_intersection2(X0,X1),X2))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27572,c_73]) ).
tcf(c_27576,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),X2))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27370,c_17003]) ).
tcf(c_27577,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),X2))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27576,c_73]) ).
tcf(c_27580,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(set_intersection2(set_intersection2(X0,X1),X2))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_27369,c_17003]) ).
tcf(c_27581,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(set_intersection2(set_intersection2(X0,X1),X2))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27580,c_73]) ).
tcf(c_27845,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(relation_dom(X0),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_8530]) ).
tcf(c_27846,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_composition(X0,X1)),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_8530]) ).
tcf(c_27847,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_composition(X1,X0)),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_8530]) ).
tcf(c_27848,plain,
! [X0: $i] : relation_dom(set_intersection2(relation_dom(empty_set),X0)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_8530]) ).
tcf(c_27849,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_dom(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_8530]) ).
tcf(c_27850,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(relation_dom(identity_relation(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_8530]) ).
tcf(c_27851,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(relation_dom(set_intersection2(X0,X1)),X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_8530]) ).
tcf(c_27852,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(relation_dom(set_intersection2(X0,X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_8530]) ).
tcf(c_27853,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(relation_dom(sK1(powerset(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_8530]) ).
tcf(c_27854,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(relation_dom(set_intersection2(X1,X0)),X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_8530]) ).
tcf(c_27855,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(relation_dom(set_intersection2(X1,X0)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_8530]) ).
tcf(c_27856,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(relation_dom(set_intersection2(X1,sK1(powerset(X0)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_8530]) ).
tcf(c_27857,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(relation_dom(set_intersection2(relation_dom(sK2),X0)),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_8530]) ).
tcf(c_27858,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(relation_dom(set_intersection2(sK1(powerset(X0)),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_8530]) ).
tcf(c_27859,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_8530]) ).
tcf(c_27860,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_8530]) ).
tcf(c_27861,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_8530]) ).
tcf(c_27862,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_8530]) ).
tcf(c_27863,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_8530]) ).
tcf(c_27864,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_8530]) ).
tcf(c_27865,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_8530]) ).
tcf(c_27866,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_8530]) ).
tcf(c_27867,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_8530]) ).
tcf(c_27868,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(relation_dom(sK1(sK4(powerset(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_8530]) ).
tcf(c_27869,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_8530]) ).
tcf(c_27870,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_8530]) ).
tcf(c_27871,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(relation_dom(set_intersection2(X0,relation_dom(sK2))),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_8530]) ).
tcf(c_28120,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_9051]) ).
tcf(c_28121,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(relation_dom(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_9051]) ).
tcf(c_28122,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(relation_dom(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_9051]) ).
tcf(c_28123,plain,
identity_relation(sK1(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_9051]) ).
tcf(c_28124,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_9051]) ).
tcf(c_28125,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_9051]) ).
tcf(c_28126,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_9051]) ).
tcf(c_28127,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_9051]) ).
tcf(c_28128,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(relation_dom(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_9051]) ).
tcf(c_28129,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_9051]) ).
tcf(c_28130,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_9051]) ).
tcf(c_28131,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(relation_dom(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_9051]) ).
tcf(c_28132,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(relation_dom(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_9051]) ).
tcf(c_28133,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(relation_dom(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_9051]) ).
tcf(c_28134,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_9051]) ).
tcf(c_28135,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_9051]) ).
tcf(c_28136,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_9051]) ).
tcf(c_28137,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_9051]) ).
tcf(c_28138,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_9051]) ).
tcf(c_28139,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_9051]) ).
tcf(c_28140,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_9051]) ).
tcf(c_28141,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_9051]) ).
tcf(c_28142,plain,
( ( identity_relation(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_9051]) ).
tcf(c_28143,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(relation_dom(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_9051]) ).
tcf(c_28144,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_9051]) ).
tcf(c_28145,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_9051]) ).
tcf(c_28146,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(relation_dom(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_9051]) ).
tcf(c_28332,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_9237]) ).
tcf(c_28333,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(relation_dom(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_9237]) ).
tcf(c_28334,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(relation_dom(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_9237]) ).
tcf(c_28335,plain,
relation_dom(sK1(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_9237]) ).
tcf(c_28336,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_9237]) ).
tcf(c_28337,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_9237]) ).
tcf(c_28338,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_9237]) ).
tcf(c_28339,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_9237]) ).
tcf(c_28340,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(relation_dom(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_9237]) ).
tcf(c_28341,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_9237]) ).
tcf(c_28342,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_9237]) ).
tcf(c_28343,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(relation_dom(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_9237]) ).
tcf(c_28344,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(relation_dom(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_9237]) ).
tcf(c_28345,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(relation_dom(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_9237]) ).
tcf(c_28346,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_9237]) ).
tcf(c_28347,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_9237]) ).
tcf(c_28348,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_9237]) ).
tcf(c_28349,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_9237]) ).
tcf(c_28350,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_9237]) ).
tcf(c_28351,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_9237]) ).
tcf(c_28352,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_9237]) ).
tcf(c_28353,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_9237]) ).
tcf(c_28354,plain,
( ( relation_dom(sK1(powerset(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_9237]) ).
tcf(c_28355,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(relation_dom(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_9237]) ).
tcf(c_28356,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_9237]) ).
tcf(c_28357,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_9237]) ).
tcf(c_28358,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(relation_dom(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_9237]) ).
tcf(c_28549,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( set_intersection2(X0,relation_dom(relation_dom(X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_9319]) ).
tcf(c_28550,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,relation_dom(relation_dom(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_9319]) ).
tcf(c_28551,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,relation_dom(relation_dom(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_9319]) ).
tcf(c_28552,plain,
! [X0: $i] : set_intersection2(X0,relation_dom(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_9319]) ).
tcf(c_28553,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_9319]) ).
tcf(c_28554,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_9319]) ).
tcf(c_28555,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_9319]) ).
tcf(c_28556,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_9319]) ).
tcf(c_28557,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_9319]) ).
tcf(c_28558,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_9319]) ).
tcf(c_28559,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_9319]) ).
tcf(c_28560,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(set_intersection2(X2,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_9319]) ).
tcf(c_28561,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(set_intersection2(relation_dom(sK2),X1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_9319]) ).
tcf(c_28562,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(set_intersection2(sK1(powerset(X0)),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_9319]) ).
tcf(c_28563,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_9319]) ).
tcf(c_28564,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_9319]) ).
tcf(c_28565,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_9319]) ).
tcf(c_28566,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_9319]) ).
tcf(c_28567,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_9319]) ).
tcf(c_28568,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_9319]) ).
tcf(c_28569,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_9319]) ).
tcf(c_28570,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_9319]) ).
tcf(c_28571,plain,
! [X0: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_9319]) ).
tcf(c_28572,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_9319]) ).
tcf(c_28573,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_9319]) ).
tcf(c_28574,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(set_intersection2(X2,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_9319]) ).
tcf(c_28575,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,relation_dom(relation_dom(set_intersection2(X1,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_9319]) ).
tcf(c_28697,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(identity_relation(X0),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_8531]) ).
tcf(c_28698,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(identity_relation(relation_composition(X0,X1)),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_8531]) ).
tcf(c_28699,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(identity_relation(relation_composition(X1,X0)),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_8531]) ).
tcf(c_28700,plain,
! [X0: $i] : relation_dom(set_intersection2(identity_relation(empty_set),X0)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_8531]) ).
tcf(c_28701,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(identity_relation(relation_dom(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_8531]) ).
tcf(c_28702,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(identity_relation(identity_relation(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_8531]) ).
tcf(c_28703,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(identity_relation(set_intersection2(X0,X1)),X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_8531]) ).
tcf(c_28704,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(identity_relation(set_intersection2(X0,X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_8531]) ).
tcf(c_28705,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(identity_relation(sK1(powerset(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_8531]) ).
tcf(c_28706,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(identity_relation(set_intersection2(X1,X0)),X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_8531]) ).
tcf(c_28707,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(identity_relation(set_intersection2(X1,X0)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_8531]) ).
tcf(c_28708,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(identity_relation(set_intersection2(X1,sK1(powerset(X0)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_8531]) ).
tcf(c_28709,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(identity_relation(set_intersection2(relation_dom(sK2),X0)),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_8531]) ).
tcf(c_28710,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(identity_relation(set_intersection2(sK1(powerset(X0)),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_8531]) ).
tcf(c_28711,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_8531]) ).
tcf(c_28712,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_8531]) ).
tcf(c_28713,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_8531]) ).
tcf(c_28714,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_8531]) ).
tcf(c_28715,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_8531]) ).
tcf(c_28716,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_8531]) ).
tcf(c_28717,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_8531]) ).
tcf(c_28718,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_8531]) ).
tcf(c_28719,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_8531]) ).
tcf(c_28720,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(identity_relation(sK1(sK4(powerset(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_8531]) ).
tcf(c_28721,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_8531]) ).
tcf(c_28722,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_8531]) ).
tcf(c_28723,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(identity_relation(set_intersection2(X0,relation_dom(sK2))),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_8531]) ).
tcf(c_29030,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(iPr_def_13,X0)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_8771]) ).
tcf(c_29031,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(iPr_def_13,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_8771]) ).
tcf(c_29034,plain,
( ( identity_relation(set_intersection2(iPr_def_13,empty_set)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_8771]) ).
tcf(c_29036,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(iPr_def_13,set_intersection2(X0,X1))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_8771]) ).
tcf(c_29037,plain,
identity_relation(set_intersection2(iPr_def_13,empty_set)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_29034,c_73]) ).
tcf(c_29042,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(iPr_def_13,set_intersection2(X0,X1))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29036,c_73]) ).
tcf(c_29064,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(iPr_def_13,X0)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_8772]) ).
tcf(c_29065,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(iPr_def_13,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_8772]) ).
tcf(c_29068,plain,
( ( relation_dom(set_intersection2(iPr_def_13,empty_set)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_8772]) ).
tcf(c_29070,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(iPr_def_13,set_intersection2(X0,X1))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_8772]) ).
tcf(c_29071,plain,
relation_dom(set_intersection2(iPr_def_13,empty_set)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_29068,c_73]) ).
tcf(c_29076,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(iPr_def_13,set_intersection2(X0,X1))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29070,c_73]) ).
tcf(c_29084,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,iPr_def_13)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_8925]) ).
tcf(c_29085,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,iPr_def_13)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_8925]) ).
tcf(c_29088,plain,
( ( identity_relation(set_intersection2(empty_set,iPr_def_13)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_8925]) ).
tcf(c_29090,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),iPr_def_13)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_8925]) ).
tcf(c_29091,plain,
identity_relation(set_intersection2(empty_set,iPr_def_13)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_29088,c_73]) ).
tcf(c_29096,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),iPr_def_13)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29090,c_73]) ).
tcf(c_29104,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,iPr_def_13)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_8926]) ).
tcf(c_29105,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,iPr_def_13)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_8926]) ).
tcf(c_29108,plain,
( ( relation_dom(set_intersection2(empty_set,iPr_def_13)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_8926]) ).
tcf(c_29110,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),iPr_def_13)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_8926]) ).
tcf(c_29111,plain,
relation_dom(set_intersection2(empty_set,iPr_def_13)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_29108,c_73]) ).
tcf(c_29116,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),iPr_def_13)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29110,c_73]) ).
tcf(c_29181,plain,
( ( relation_dom(iPr_def_13) = empty_set )
| ( apply(identity_relation(sK11),sK1(sK11)) = sK1(sK11) ) ),
inference(superposition,[status(thm)],[c_1150,c_15806]) ).
tcf(c_29185,plain,
( ( relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ( apply(identity_relation(relation_dom(sK2)),sK1(relation_dom(sK2))) = sK1(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_6018,c_15806]) ).
tcf(c_29186,plain,
( ( relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ( apply(identity_relation(relation_dom(sK2)),sK1(relation_dom(sK2))) = sK1(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_6133,c_15806]) ).
tcf(c_29187,plain,
( ( relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ( apply(identity_relation(relation_dom(sK2)),sK1(relation_dom(sK2))) = sK1(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_6817,c_15806]) ).
tcf(c_29190,plain,
! [X0: $i] :
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( relation_dom(set_intersection2(X0,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15806]) ).
tcf(c_29192,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X1,X2))) = sK1(set_intersection2(X1,X2)) )
| ( relation_dom(set_intersection2(X0,set_intersection2(X1,X2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15806]) ).
tcf(c_29193,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( relation_dom(set_intersection2(X0,powerset(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15806]) ).
tcf(c_29195,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X0,set_intersection2(X1,X2)),relation_dom(X0))
| ( set_intersection2(X1,X2) = X0 )
| ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(set_intersection2(X1,X2))
| ~ function(set_intersection2(X1,X2))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_15806,c_112]) ).
tcf(c_29196,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,empty_set) = empty_set )
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(identity_relation(set_intersection2(X0,X1)),sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_15806,c_15801]) ).
tcf(c_29197,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(empty_set,X2) = empty_set )
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(identity_relation(set_intersection2(X0,X1)),sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_15806,c_15799]) ).
tcf(c_29198,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(set_intersection2(X1,X2),X0),relation_dom(set_intersection2(X1,X2)))
| ( set_intersection2(X1,X2) = X0 )
| ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(set_intersection2(X1,X2))
| ~ function(set_intersection2(X1,X2))
| ( relation_dom(X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_15806,c_112]) ).
tcf(c_29200,plain,
! [X0: $i,X1: $i] :
( in(sK10(empty_set,set_intersection2(X0,X1)),empty_set)
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(relation_dom(set_intersection2(X0,X1))) = set_intersection2(X0,X1) )
| ~ relation(set_intersection2(X0,X1))
| ~ function(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_15806,c_100]) ).
tcf(c_29201,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(empty_set)
| ~ relation(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_15806,c_75]) ).
tcf(c_29213,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ relation(set_intersection2(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29201,c_73]) ).
tcf(c_29220,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(relation_dom(set_intersection2(X0,X1))) = set_intersection2(X0,X1) )
| ~ relation(set_intersection2(X0,X1))
| ~ function(set_intersection2(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29200,c_5671]) ).
tcf(c_29250,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( set_intersection2(X0,identity_relation(relation_dom(X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_9439]) ).
tcf(c_29251,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,identity_relation(relation_dom(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_9439]) ).
tcf(c_29252,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,identity_relation(relation_dom(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_9439]) ).
tcf(c_29253,plain,
! [X0: $i] : set_intersection2(X0,identity_relation(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_9439]) ).
tcf(c_29254,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_9439]) ).
tcf(c_29255,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_9439]) ).
tcf(c_29256,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_9439]) ).
tcf(c_29257,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_9439]) ).
tcf(c_29258,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_9439]) ).
tcf(c_29259,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_9439]) ).
tcf(c_29260,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_9439]) ).
tcf(c_29261,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(set_intersection2(X2,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_9439]) ).
tcf(c_29262,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(set_intersection2(relation_dom(sK2),X1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_9439]) ).
tcf(c_29263,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(set_intersection2(sK1(powerset(X0)),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_9439]) ).
tcf(c_29264,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_9439]) ).
tcf(c_29265,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_9439]) ).
tcf(c_29266,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_9439]) ).
tcf(c_29267,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_9439]) ).
tcf(c_29268,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_9439]) ).
tcf(c_29269,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_9439]) ).
tcf(c_29270,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_9439]) ).
tcf(c_29271,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_9439]) ).
tcf(c_29272,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_9439]) ).
tcf(c_29273,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_9439]) ).
tcf(c_29274,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_9439]) ).
tcf(c_29275,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(set_intersection2(X2,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_9439]) ).
tcf(c_29276,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,identity_relation(relation_dom(set_intersection2(X1,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_9439]) ).
tcf(c_29420,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(relation_dom(relation_dom(X0)),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_9517]) ).
tcf(c_29421,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(X0,X1))),X2) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_9517]) ).
tcf(c_29422,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(X1,X0))),X2) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_9517]) ).
tcf(c_29423,plain,
! [X0: $i] : set_intersection2(relation_dom(relation_dom(empty_set)),X0) = empty_set,
inference(superposition,[status(thm)],[c_73,c_9517]) ).
tcf(c_29424,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_dom(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_9517]) ).
tcf(c_29425,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(relation_dom(identity_relation(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_9517]) ).
tcf(c_29426,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_dom(set_intersection2(X0,X1))),X2) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_9517]) ).
tcf(c_29427,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_dom(set_intersection2(X0,X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_9517]) ).
tcf(c_29428,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(relation_dom(sK1(powerset(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_9517]) ).
tcf(c_29429,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_dom(set_intersection2(X1,X0))),X2) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_9517]) ).
tcf(c_29430,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_dom(set_intersection2(X1,X0))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_9517]) ).
tcf(c_29431,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_dom(set_intersection2(X1,sK1(powerset(X0))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_9517]) ).
tcf(c_29432,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(relation_dom(set_intersection2(relation_dom(sK2),X0))),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_9517]) ).
tcf(c_29433,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_dom(set_intersection2(sK1(powerset(X0)),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_9517]) ).
tcf(c_29434,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_9517]) ).
tcf(c_29435,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_9517]) ).
tcf(c_29436,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_9517]) ).
tcf(c_29437,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_9517]) ).
tcf(c_29438,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_9517]) ).
tcf(c_29439,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_9517]) ).
tcf(c_29440,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_9517]) ).
tcf(c_29441,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_9517]) ).
tcf(c_29442,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_9517]) ).
tcf(c_29443,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(relation_dom(sK1(sK4(powerset(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_9517]) ).
tcf(c_29444,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_9517]) ).
tcf(c_29445,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_9517]) ).
tcf(c_29446,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(relation_dom(set_intersection2(X0,relation_dom(sK2)))),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_9517]) ).
tcf(c_33293,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(identity_relation(relation_dom(X0)),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_9638]) ).
tcf(c_33294,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(X0,X1))),X2) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_9638]) ).
tcf(c_33295,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(X1,X0))),X2) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_9638]) ).
tcf(c_33296,plain,
! [X0: $i] : set_intersection2(identity_relation(relation_dom(empty_set)),X0) = empty_set,
inference(superposition,[status(thm)],[c_73,c_9638]) ).
tcf(c_33297,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_dom(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_9638]) ).
tcf(c_33298,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(relation_dom(identity_relation(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_9638]) ).
tcf(c_33299,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_dom(set_intersection2(X0,X1))),X2) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_9638]) ).
tcf(c_33300,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_dom(set_intersection2(X0,X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_9638]) ).
tcf(c_33301,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(relation_dom(sK1(powerset(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_9638]) ).
tcf(c_33302,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_dom(set_intersection2(X1,X0))),X2) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_9638]) ).
tcf(c_33303,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_dom(set_intersection2(X1,X0))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_9638]) ).
tcf(c_33304,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_dom(set_intersection2(X1,sK1(powerset(X0))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_9638]) ).
tcf(c_33305,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(relation_dom(set_intersection2(relation_dom(sK2),X0))),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_9638]) ).
tcf(c_33306,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_dom(set_intersection2(sK1(powerset(X0)),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_9638]) ).
tcf(c_33307,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_9638]) ).
tcf(c_33308,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_9638]) ).
tcf(c_33309,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_9638]) ).
tcf(c_33310,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_9638]) ).
tcf(c_33311,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_9638]) ).
tcf(c_33312,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_9638]) ).
tcf(c_33313,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_9638]) ).
tcf(c_33314,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_9638]) ).
tcf(c_33315,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_9638]) ).
tcf(c_33316,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(relation_dom(sK1(sK4(powerset(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_9638]) ).
tcf(c_33317,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_9638]) ).
tcf(c_33318,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_9638]) ).
tcf(c_33319,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(relation_dom(set_intersection2(X0,relation_dom(sK2)))),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_9638]) ).
tcf(c_33537,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_11348]) ).
tcf(c_33538,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(relation_dom(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_11348]) ).
tcf(c_33539,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(relation_dom(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_11348]) ).
tcf(c_33540,plain,
sK1(powerset(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_11348]) ).
tcf(c_33541,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_11348]) ).
tcf(c_33542,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_11348]) ).
tcf(c_33543,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_11348]) ).
tcf(c_33544,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_11348]) ).
tcf(c_33545,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(relation_dom(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_11348]) ).
tcf(c_33546,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_11348]) ).
tcf(c_33547,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_11348]) ).
tcf(c_33548,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(relation_dom(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_11348]) ).
tcf(c_33549,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(relation_dom(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_11348]) ).
tcf(c_33550,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(relation_dom(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_11348]) ).
tcf(c_33551,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_11348]) ).
tcf(c_33552,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_11348]) ).
tcf(c_33553,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_11348]) ).
tcf(c_33554,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_11348]) ).
tcf(c_33555,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_11348]) ).
tcf(c_33556,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_11348]) ).
tcf(c_33557,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_11348]) ).
tcf(c_33558,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_11348]) ).
tcf(c_33559,plain,
( ( sK1(powerset(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_11348]) ).
tcf(c_33560,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(relation_dom(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_11348]) ).
tcf(c_33561,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_11348]) ).
tcf(c_33562,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_11348]) ).
tcf(c_33563,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(relation_dom(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_11348]) ).
tcf(c_33670,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_9052]) ).
tcf(c_33671,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(identity_relation(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_9052]) ).
tcf(c_33672,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(identity_relation(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_9052]) ).
tcf(c_33673,plain,
identity_relation(sK1(powerset(identity_relation(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_9052]) ).
tcf(c_33674,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_9052]) ).
tcf(c_33675,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_9052]) ).
tcf(c_33676,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(identity_relation(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_9052]) ).
tcf(c_33677,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(identity_relation(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_9052]) ).
tcf(c_33678,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(identity_relation(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_9052]) ).
tcf(c_33679,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(identity_relation(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_9052]) ).
tcf(c_33680,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(identity_relation(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_9052]) ).
tcf(c_33681,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(identity_relation(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_9052]) ).
tcf(c_33682,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(identity_relation(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_9052]) ).
tcf(c_33683,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(identity_relation(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_9052]) ).
tcf(c_33684,plain,
( ( identity_relation(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_9052]) ).
tcf(c_33685,plain,
( ( identity_relation(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_9052]) ).
tcf(c_33686,plain,
( ( identity_relation(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_9052]) ).
tcf(c_33687,plain,
( ( identity_relation(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_9052]) ).
tcf(c_33688,plain,
( ( identity_relation(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_9052]) ).
tcf(c_33689,plain,
( ( identity_relation(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_9052]) ).
tcf(c_33690,plain,
( ( identity_relation(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_9052]) ).
tcf(c_33691,plain,
( ( identity_relation(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_9052]) ).
tcf(c_33692,plain,
( ( identity_relation(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_9052]) ).
tcf(c_33693,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(identity_relation(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_9052]) ).
tcf(c_33694,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_9052]) ).
tcf(c_33695,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_9052]) ).
tcf(c_33696,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(identity_relation(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_9052]) ).
tcf(c_33884,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_9238]) ).
tcf(c_33885,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(identity_relation(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_9238]) ).
tcf(c_33886,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(identity_relation(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_9238]) ).
tcf(c_33887,plain,
relation_dom(sK1(powerset(identity_relation(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_9238]) ).
tcf(c_33888,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_9238]) ).
tcf(c_33889,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_9238]) ).
tcf(c_33890,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(identity_relation(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_9238]) ).
tcf(c_33891,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(identity_relation(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_9238]) ).
tcf(c_33892,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(identity_relation(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_9238]) ).
tcf(c_33893,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(identity_relation(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_9238]) ).
tcf(c_33894,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(identity_relation(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_9238]) ).
tcf(c_33895,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(identity_relation(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_9238]) ).
tcf(c_33896,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(identity_relation(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_9238]) ).
tcf(c_33897,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(identity_relation(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_9238]) ).
tcf(c_33898,plain,
( ( relation_dom(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_9238]) ).
tcf(c_33899,plain,
( ( relation_dom(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_9238]) ).
tcf(c_33900,plain,
( ( relation_dom(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_9238]) ).
tcf(c_33901,plain,
( ( relation_dom(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_9238]) ).
tcf(c_33902,plain,
( ( relation_dom(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_9238]) ).
tcf(c_33903,plain,
( ( relation_dom(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_9238]) ).
tcf(c_33904,plain,
( ( relation_dom(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_9238]) ).
tcf(c_33905,plain,
( ( relation_dom(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_9238]) ).
tcf(c_33906,plain,
( ( relation_dom(sK1(powerset(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_9238]) ).
tcf(c_33907,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(identity_relation(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_9238]) ).
tcf(c_33908,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_9238]) ).
tcf(c_33909,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_9238]) ).
tcf(c_33910,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(identity_relation(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_9238]) ).
tcf(c_34036,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( set_intersection2(X0,identity_relation(identity_relation(X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_9440]) ).
tcf(c_34037,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,identity_relation(identity_relation(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_9440]) ).
tcf(c_34038,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,identity_relation(identity_relation(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_9440]) ).
tcf(c_34039,plain,
! [X0: $i] : set_intersection2(X0,identity_relation(identity_relation(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_9440]) ).
tcf(c_34040,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_9440]) ).
tcf(c_34041,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_9440]) ).
tcf(c_34042,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_9440]) ).
tcf(c_34043,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(set_intersection2(X0,X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_9440]) ).
tcf(c_34044,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_9440]) ).
tcf(c_34045,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_9440]) ).
tcf(c_34046,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(set_intersection2(X2,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_9440]) ).
tcf(c_34047,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(set_intersection2(X2,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_9440]) ).
tcf(c_34048,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,identity_relation(identity_relation(set_intersection2(relation_dom(sK2),X1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_9440]) ).
tcf(c_34049,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(set_intersection2(sK1(powerset(X0)),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_9440]) ).
tcf(c_34050,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_9440]) ).
tcf(c_34051,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_9440]) ).
tcf(c_34052,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_9440]) ).
tcf(c_34053,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_9440]) ).
tcf(c_34054,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_9440]) ).
tcf(c_34055,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_9440]) ).
tcf(c_34056,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_9440]) ).
tcf(c_34057,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_9440]) ).
tcf(c_34058,plain,
! [X0: $i] :
( ( set_intersection2(X0,identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_9440]) ).
tcf(c_34059,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_9440]) ).
tcf(c_34060,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_9440]) ).
tcf(c_34061,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(set_intersection2(X2,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_9440]) ).
tcf(c_34062,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,identity_relation(identity_relation(set_intersection2(X1,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_9440]) ).
tcf(c_34248,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(identity_relation(identity_relation(X0)),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_9639]) ).
tcf(c_34249,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(identity_relation(relation_composition(X0,X1))),X2) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_9639]) ).
tcf(c_34250,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(identity_relation(relation_composition(X1,X0))),X2) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_9639]) ).
tcf(c_34251,plain,
! [X0: $i] : set_intersection2(identity_relation(identity_relation(empty_set)),X0) = empty_set,
inference(superposition,[status(thm)],[c_73,c_9639]) ).
tcf(c_34252,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(identity_relation(relation_dom(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_9639]) ).
tcf(c_34253,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(identity_relation(identity_relation(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_9639]) ).
tcf(c_34254,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(identity_relation(set_intersection2(X0,X1))),X2) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_9639]) ).
tcf(c_34255,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(identity_relation(set_intersection2(X0,X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_9639]) ).
tcf(c_34256,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(identity_relation(sK1(powerset(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_9639]) ).
tcf(c_34257,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(identity_relation(set_intersection2(X1,X0))),X2) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_9639]) ).
tcf(c_34258,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(identity_relation(set_intersection2(X1,X0))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_9639]) ).
tcf(c_34259,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(identity_relation(set_intersection2(X1,sK1(powerset(X0))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_9639]) ).
tcf(c_34260,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(identity_relation(set_intersection2(relation_dom(sK2),X0))),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_9639]) ).
tcf(c_34261,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(identity_relation(set_intersection2(sK1(powerset(X0)),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_9639]) ).
tcf(c_34262,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_9639]) ).
tcf(c_34263,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_9639]) ).
tcf(c_34264,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_9639]) ).
tcf(c_34265,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_9639]) ).
tcf(c_34266,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_9639]) ).
tcf(c_34267,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_9639]) ).
tcf(c_34268,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_9639]) ).
tcf(c_34269,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))),X0) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_9639]) ).
tcf(c_34270,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_9639]) ).
tcf(c_34271,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(identity_relation(sK1(sK4(powerset(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_9639]) ).
tcf(c_34272,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_9639]) ).
tcf(c_34273,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0)))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_9639]) ).
tcf(c_34274,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(identity_relation(set_intersection2(X0,relation_dom(sK2)))),X1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_9639]) ).
tcf(c_34512,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(sK11,X0)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_10059]) ).
tcf(c_34513,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(sK11,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_10059]) ).
tcf(c_34516,plain,
( ( identity_relation(set_intersection2(sK11,empty_set)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_10059]) ).
tcf(c_34518,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(sK11,set_intersection2(X0,X1))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_10059]) ).
tcf(c_34519,plain,
identity_relation(set_intersection2(sK11,empty_set)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_34516,c_73]) ).
tcf(c_34524,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(sK11,set_intersection2(X0,X1))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34518,c_73]) ).
tcf(c_34771,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(sK11,X0)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_10060]) ).
tcf(c_34772,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(sK11,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_10060]) ).
tcf(c_34775,plain,
( ( relation_dom(set_intersection2(sK11,empty_set)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_10060]) ).
tcf(c_34777,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(sK11,set_intersection2(X0,X1))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_10060]) ).
tcf(c_34778,plain,
relation_dom(set_intersection2(sK11,empty_set)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_34775,c_73]) ).
tcf(c_34783,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(sK11,set_intersection2(X0,X1))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34777,c_73]) ).
tcf(c_34791,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,sK11)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_10261]) ).
tcf(c_34792,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,sK11)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_10261]) ).
tcf(c_34795,plain,
( ( identity_relation(set_intersection2(empty_set,sK11)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_10261]) ).
tcf(c_34797,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),sK11)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_10261]) ).
tcf(c_34798,plain,
identity_relation(set_intersection2(empty_set,sK11)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_34795,c_73]) ).
tcf(c_34803,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),sK11)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34797,c_73]) ).
tcf(c_34817,plain,
( ( identity_relation(iPr_def_13) = empty_set )
| ( apply(identity_relation(sK11),sK1(sK11)) = sK1(sK11) ) ),
inference(superposition,[status(thm)],[c_1150,c_15807]) ).
tcf(c_34821,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ( apply(identity_relation(relation_dom(sK2)),sK1(relation_dom(sK2))) = sK1(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_6018,c_15807]) ).
tcf(c_34822,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ( apply(identity_relation(relation_dom(sK2)),sK1(relation_dom(sK2))) = sK1(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_6133,c_15807]) ).
tcf(c_34823,plain,
( ( identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ( apply(identity_relation(relation_dom(sK2)),sK1(relation_dom(sK2))) = sK1(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_6817,c_15807]) ).
tcf(c_34826,plain,
! [X0: $i] :
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( identity_relation(set_intersection2(X0,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15807]) ).
tcf(c_34829,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X1,X2))) = sK1(set_intersection2(X1,X2)) )
| ( identity_relation(set_intersection2(X0,set_intersection2(X1,X2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15807]) ).
tcf(c_34830,plain,
! [X0: $i] :
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( identity_relation(set_intersection2(X0,powerset(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15807]) ).
tcf(c_34832,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(set_intersection2(set_intersection2(X2,X1),X0))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(relation_composition(identity_relation(X0),empty_set)) ),
inference(superposition,[status(thm)],[c_15807,c_5128]) ).
tcf(c_34833,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X2,X1),X0))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(relation_composition(identity_relation(X0),empty_set)) ),
inference(superposition,[status(thm)],[c_15807,c_5130]) ).
tcf(c_34834,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(set_intersection2(set_intersection2(X2,X1),X0))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(relation_composition(identity_relation(X0),empty_set)) ),
inference(superposition,[status(thm)],[c_15807,c_5129]) ).
tcf(c_34835,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(set_intersection2(X1,X0),X2) = relation_dom(relation_composition(identity_relation(X2),empty_set)) ) ),
inference(superposition,[status(thm)],[c_15807,c_3036]) ).
tcf(c_34836,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ( apply(empty_set,sK1(set_intersection2(X1,X2))) = sK1(set_intersection2(X1,X2)) )
| ( identity_relation(set_intersection2(X0,set_intersection2(X1,X2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15807]) ).
tcf(c_34837,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),sK11)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_10261]) ).
tcf(c_34838,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(sK11,set_intersection2(X0,X1))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_10060]) ).
tcf(c_34839,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(sK11,set_intersection2(X0,X1))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_10059]) ).
tcf(c_34840,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ( apply(empty_set,sK1(set_intersection2(X1,X2))) = sK1(set_intersection2(X1,X2)) )
| ( relation_dom(set_intersection2(X0,set_intersection2(X1,X2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15806]) ).
tcf(c_34841,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),iPr_def_13)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_8926]) ).
tcf(c_34842,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),iPr_def_13)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_8925]) ).
tcf(c_34843,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(iPr_def_13,set_intersection2(X0,X1))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_8772]) ).
tcf(c_34844,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(iPr_def_13,set_intersection2(X0,X1))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_8771]) ).
tcf(c_34845,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15805]) ).
tcf(c_34846,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15804]) ).
tcf(c_34847,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(set_intersection2(X0,set_intersection2(X2,X1)))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(relation_composition(empty_set,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_15807,c_5128]) ).
tcf(c_34848,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(relation_dom(sK2),set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,sK2)) ),
inference(superposition,[status(thm)],[c_15807,c_4765]) ).
tcf(c_34849,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( identity_relation(sK1(powerset(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15803]) ).
tcf(c_34850,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( relation_dom(sK1(powerset(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15802]) ).
tcf(c_34852,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ( apply(empty_set,sK1(set_intersection2(X1,X2))) = sK1(set_intersection2(X1,X2)) )
| ( set_intersection2(X0,relation_dom(set_intersection2(X1,X2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15801]) ).
tcf(c_34855,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,set_intersection2(X2,X1)))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(relation_composition(empty_set,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_15807,c_5130]) ).
tcf(c_34856,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(set_intersection2(X0,set_intersection2(X2,X1)))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ empty(relation_composition(empty_set,identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_15807,c_5129]) ).
tcf(c_34857,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ( apply(empty_set,sK1(set_intersection2(X1,X2))) = sK1(set_intersection2(X1,X2)) )
| ( set_intersection2(X0,identity_relation(set_intersection2(X1,X2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15800]) ).
tcf(c_34859,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( set_intersection2(relation_dom(set_intersection2(X0,X1)),X2) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15799]) ).
tcf(c_34860,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(relation_dom(sK2),set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,sK2)) ),
inference(superposition,[status(thm)],[c_15807,c_4767]) ).
tcf(c_34861,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( set_intersection2(identity_relation(set_intersection2(X0,X1)),X2) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15798]) ).
tcf(c_34863,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( sK1(powerset(relation_dom(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15797]) ).
tcf(c_34864,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(relation_dom(sK2),set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,sK2)) ),
inference(superposition,[status(thm)],[c_15807,c_4766]) ).
tcf(c_34865,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( sK1(powerset(identity_relation(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15796]) ).
tcf(c_34867,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( sK1(sK4(powerset(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15795]) ).
tcf(c_34868,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(set_intersection2(X1,X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_14,empty_set)) ),
inference(superposition,[status(thm)],[c_15807,c_7987]) ).
tcf(c_34869,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X1,X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_14,empty_set)) ),
inference(superposition,[status(thm)],[c_15807,c_7989]) ).
tcf(c_34870,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(set_intersection2(X1,X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_14,empty_set)) ),
inference(superposition,[status(thm)],[c_15807,c_7988]) ).
tcf(c_34871,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X2) = empty_set )
| ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ( apply(empty_set,sK0(X0,empty_set,set_intersection2(X1,X2))) = sK0(X0,empty_set,set_intersection2(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_15807,c_11677]) ).
tcf(c_34872,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X1,X0),sK11))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_11,empty_set)) ),
inference(superposition,[status(thm)],[c_15807,c_7195]) ).
tcf(c_34873,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(set_intersection2(X1,X0),sK11))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_11,empty_set)) ),
inference(superposition,[status(thm)],[c_15807,c_7194]) ).
tcf(c_34874,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(set_intersection2(X1,X0),sK11))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_11,empty_set)) ),
inference(superposition,[status(thm)],[c_15807,c_7193]) ).
tcf(c_34875,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X1,X0),sK12))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_10,empty_set)) ),
inference(superposition,[status(thm)],[c_15807,c_7051]) ).
tcf(c_34876,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(set_intersection2(X1,X0),sK12))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_10,empty_set)) ),
inference(superposition,[status(thm)],[c_15807,c_7049]) ).
tcf(c_34877,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(set_intersection2(X1,X0),sK12))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(iPr_def_10,empty_set)) ),
inference(superposition,[status(thm)],[c_15807,c_7050]) ).
tcf(c_34878,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X2) = empty_set )
| ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ( apply(empty_set,sK0(empty_set,X0,set_intersection2(X1,X2))) = sK0(empty_set,X0,set_intersection2(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_15807,c_11616]) ).
tcf(c_34882,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK12,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_15807,c_4466]) ).
tcf(c_34883,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(sK12,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_15807,c_4465]) ).
tcf(c_34884,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(sK12,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_15807,c_4464]) ).
tcf(c_34885,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK11,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15807,c_4108]) ).
tcf(c_34886,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(sK11,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15807,c_4107]) ).
tcf(c_34887,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(sK11,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15807,c_4106]) ).
tcf(c_34888,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(iPr_def_13,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_15807,c_3290]) ).
tcf(c_34889,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(iPr_def_13,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_15807,c_3288]) ).
tcf(c_34890,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(iPr_def_13,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(relation_composition(empty_set,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_15807,c_3289]) ).
tcf(c_34891,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(set_intersection2(X1,X0),iPr_def_13) = relation_dom(relation_composition(iPr_def_14,empty_set)) ) ),
inference(superposition,[status(thm)],[c_15807,c_5118]) ).
tcf(c_34892,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(set_intersection2(X1,X0),sK11) = relation_dom(relation_composition(iPr_def_11,empty_set)) ) ),
inference(superposition,[status(thm)],[c_15807,c_5116]) ).
tcf(c_34893,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(set_intersection2(X1,X0),sK12) = relation_dom(relation_composition(iPr_def_10,empty_set)) ) ),
inference(superposition,[status(thm)],[c_15807,c_5115]) ).
tcf(c_34894,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(iPr_def_13,set_intersection2(X1,X0)) = relation_dom(relation_composition(empty_set,iPr_def_12)) ) ),
inference(superposition,[status(thm)],[c_15807,c_5413]) ).
tcf(c_34895,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(X1,set_intersection2(X2,X0)) = relation_dom(relation_composition(empty_set,identity_relation(X1))) ) ),
inference(superposition,[status(thm)],[c_15807,c_3036]) ).
tcf(c_34896,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(relation_dom(sK2),set_intersection2(X1,X0)) = relation_dom(relation_composition(empty_set,sK2)) ) ),
inference(superposition,[status(thm)],[c_15807,c_3034]) ).
tcf(c_34897,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(sK12,set_intersection2(X1,X0)) = relation_dom(relation_composition(empty_set,iPr_def_10)) ) ),
inference(superposition,[status(thm)],[c_15807,c_3031]) ).
tcf(c_34898,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(sK11,set_intersection2(X1,X0)) = relation_dom(relation_composition(empty_set,iPr_def_11)) ) ),
inference(superposition,[status(thm)],[c_15807,c_3029]) ).
tcf(c_34899,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(iPr_def_13,set_intersection2(X1,X0)) = relation_dom(relation_composition(empty_set,iPr_def_14)) ) ),
inference(superposition,[status(thm)],[c_15807,c_3027]) ).
tcf(c_34901,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X1,X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_1965]) ).
tcf(c_34902,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X1,X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_1918]) ).
tcf(c_34903,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_1893]) ).
tcf(c_34906,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = relation_dom(empty_set) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15807,c_144]) ).
tcf(c_34910,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34903,c_73]) ).
tcf(c_34913,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X1,X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34902,c_73]) ).
tcf(c_34916,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X1,X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34901,c_73]) ).
tcf(c_34919,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( set_intersection2(iPr_def_13,set_intersection2(X0,X1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34899,c_2054,c_5997]) ).
tcf(c_34922,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( set_intersection2(sK11,set_intersection2(X0,X1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34898,c_2054,c_6184]) ).
tcf(c_34925,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( set_intersection2(sK12,set_intersection2(X0,X1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34897,c_2054,c_6071]) ).
tcf(c_34929,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( set_intersection2(set_intersection2(X0,X1),sK12) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34893,c_2054,c_4938]) ).
tcf(c_34932,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( set_intersection2(set_intersection2(X0,X1),sK11) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34892,c_2054,c_5102]) ).
tcf(c_34935,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( set_intersection2(set_intersection2(X0,X1),iPr_def_13) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34891,c_2054,c_5508]) ).
tcf(c_34938,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(iPr_def_13,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34890,c_5997]) ).
tcf(c_34942,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(iPr_def_13,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34889,c_5997]) ).
tcf(c_34946,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(iPr_def_13,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34888,c_5997]) ).
tcf(c_34950,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(sK11,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34887,c_6184]) ).
tcf(c_34954,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(sK11,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34886,c_6184]) ).
tcf(c_34958,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK11,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34885,c_6184]) ).
tcf(c_34962,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(sK12,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34884,c_6071]) ).
tcf(c_34966,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(sK12,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34883,c_6071]) ).
tcf(c_34970,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK12,set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34882,c_6071]) ).
tcf(c_34974,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(set_intersection2(X1,X0),sK12))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34877,c_4938]) ).
tcf(c_34978,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(set_intersection2(X1,X0),sK12))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34876,c_4938]) ).
tcf(c_34982,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X1,X0),sK12))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34875,c_4938]) ).
tcf(c_34986,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(set_intersection2(X1,X0),sK11))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34874,c_5102]) ).
tcf(c_34990,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(set_intersection2(X1,X0),sK11))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34873,c_5102]) ).
tcf(c_34994,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X1,X0),sK11))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34872,c_5102]) ).
tcf(c_34998,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(set_intersection2(X1,X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34870,c_5508]) ).
tcf(c_35002,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X1,X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34869,c_5508]) ).
tcf(c_35006,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(set_intersection2(X1,X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34868,c_5508]) ).
tcf(c_35016,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( set_intersection2(relation_dom(sK2),set_intersection2(X0,X1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34896,c_2054,c_7117]) ).
tcf(c_35021,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(relation_dom(sK2),set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34864,c_7117]) ).
tcf(c_35025,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(relation_dom(sK2),set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34860,c_7117]) ).
tcf(c_35029,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(set_intersection2(X1,set_intersection2(X2,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34856,c_22644]) ).
tcf(c_35030,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(set_intersection2(X1,set_intersection2(X2,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35029,c_73]) ).
tcf(c_35033,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X1,set_intersection2(X2,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34855,c_22644]) ).
tcf(c_35034,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X1,set_intersection2(X2,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35033,c_73]) ).
tcf(c_35037,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(relation_dom(sK2),set_intersection2(X1,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34848,c_7117]) ).
tcf(c_35041,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(set_intersection2(X1,set_intersection2(X2,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34847,c_22644]) ).
tcf(c_35042,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(set_intersection2(X1,set_intersection2(X2,X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35041,c_73]) ).
tcf(c_35045,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(iPr_def_13,set_intersection2(X0,X1))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34844,c_73]) ).
tcf(c_35048,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(iPr_def_13,set_intersection2(X0,X1))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34843,c_73]) ).
tcf(c_35051,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),iPr_def_13)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34842,c_73]) ).
tcf(c_35054,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),iPr_def_13)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34841,c_73]) ).
tcf(c_35057,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(sK11,set_intersection2(X0,X1))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34839,c_73]) ).
tcf(c_35060,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(sK11,set_intersection2(X0,X1))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34838,c_73]) ).
tcf(c_35063,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),sK11)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34837,c_73]) ).
tcf(c_35068,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(set_intersection2(set_intersection2(X1,X0),X2))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34834,c_17003]) ).
tcf(c_35069,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(set_intersection2(set_intersection2(X1,X0),X2))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35068,c_73]) ).
tcf(c_35072,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X1,X0),X2))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34833,c_17003]) ).
tcf(c_35073,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X1,X0),X2))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35072,c_73]) ).
tcf(c_35076,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(set_intersection2(set_intersection2(X1,X0),X2))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_34832,c_17003]) ).
tcf(c_35077,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(set_intersection2(set_intersection2(X1,X0),X2))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35076,c_73]) ).
tcf(c_35172,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_11511]) ).
tcf(c_35173,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(relation_dom(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_11511]) ).
tcf(c_35174,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(relation_dom(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_11511]) ).
tcf(c_35175,plain,
sK1(powerset(identity_relation(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_11511]) ).
tcf(c_35176,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_11511]) ).
tcf(c_35177,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_11511]) ).
tcf(c_35178,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_11511]) ).
tcf(c_35179,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_11511]) ).
tcf(c_35180,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(relation_dom(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_11511]) ).
tcf(c_35181,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_11511]) ).
tcf(c_35182,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_11511]) ).
tcf(c_35183,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(relation_dom(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_11511]) ).
tcf(c_35184,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(relation_dom(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_11511]) ).
tcf(c_35185,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(relation_dom(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_11511]) ).
tcf(c_35186,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_11511]) ).
tcf(c_35187,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_11511]) ).
tcf(c_35188,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_11511]) ).
tcf(c_35189,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_11511]) ).
tcf(c_35190,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_11511]) ).
tcf(c_35191,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_11511]) ).
tcf(c_35192,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_11511]) ).
tcf(c_35193,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_11511]) ).
tcf(c_35194,plain,
( ( sK1(powerset(identity_relation(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_11511]) ).
tcf(c_35195,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(relation_dom(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_11511]) ).
tcf(c_35196,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_11511]) ).
tcf(c_35197,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_11511]) ).
tcf(c_35198,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(relation_dom(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_11511]) ).
tcf(c_35572,plain,
( empty(set_intersection2(relation_dom(sK2),sK12))
| ~ in(relation_dom(sK2),sK1(relation_dom(relation_composition(iPr_def_10,sK2)))) ),
inference(superposition,[status(thm)],[c_6018,c_12244]) ).
tcf(c_35573,plain,
( empty(set_intersection2(relation_dom(sK2),sK11))
| ~ in(relation_dom(sK2),sK1(relation_dom(relation_composition(iPr_def_11,sK2)))) ),
inference(superposition,[status(thm)],[c_6133,c_12244]) ).
tcf(c_35574,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| ~ in(relation_dom(sK2),sK1(relation_dom(relation_composition(iPr_def_14,sK2)))) ),
inference(superposition,[status(thm)],[c_6817,c_12244]) ).
tcf(c_35585,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,sK11)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_10262]) ).
tcf(c_35586,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,sK11)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_10262]) ).
tcf(c_35589,plain,
( ( relation_dom(set_intersection2(empty_set,sK11)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_10262]) ).
tcf(c_35591,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),sK11)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_10262]) ).
tcf(c_35592,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),sK11)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_10262]) ).
tcf(c_35593,plain,
relation_dom(set_intersection2(empty_set,sK11)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_35589,c_73]) ).
tcf(c_35598,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),sK11)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35592,c_73]) ).
tcf(c_35601,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),sK11)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35591,c_73]) ).
tcf(c_35609,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(sK12,X0)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_11030]) ).
tcf(c_35610,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(sK12,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_11030]) ).
tcf(c_35613,plain,
( ( identity_relation(set_intersection2(sK12,empty_set)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_11030]) ).
tcf(c_35615,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(sK12,set_intersection2(X0,X1))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_11030]) ).
tcf(c_35616,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(sK12,set_intersection2(X0,X1))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_11030]) ).
tcf(c_35617,plain,
identity_relation(set_intersection2(sK12,empty_set)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_35613,c_73]) ).
tcf(c_35622,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(sK12,set_intersection2(X0,X1))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35616,c_73]) ).
tcf(c_35625,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(sK12,set_intersection2(X0,X1))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35615,c_73]) ).
tcf(c_35633,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(sK12,X0)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_11031]) ).
tcf(c_35634,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(sK12,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_11031]) ).
tcf(c_35637,plain,
( ( relation_dom(set_intersection2(sK12,empty_set)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_11031]) ).
tcf(c_35639,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(sK12,set_intersection2(X0,X1))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_11031]) ).
tcf(c_35640,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(sK12,set_intersection2(X0,X1))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_11031]) ).
tcf(c_35641,plain,
relation_dom(set_intersection2(sK12,empty_set)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_35637,c_73]) ).
tcf(c_35646,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(sK12,set_intersection2(X0,X1))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35640,c_73]) ).
tcf(c_35649,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(sK12,set_intersection2(X0,X1))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35639,c_73]) ).
tcf(c_35683,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,sK12)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_11192]) ).
tcf(c_35684,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,sK12)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_11192]) ).
tcf(c_35687,plain,
( ( identity_relation(set_intersection2(empty_set,sK12)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_11192]) ).
tcf(c_35689,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),sK12)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_11192]) ).
tcf(c_35690,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),sK12)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_11192]) ).
tcf(c_35691,plain,
identity_relation(set_intersection2(empty_set,sK12)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_35687,c_73]) ).
tcf(c_35696,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),sK12)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35690,c_73]) ).
tcf(c_35699,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),sK12)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35689,c_73]) ).
tcf(c_35709,plain,
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( identity_relation(identity_relation(identity_relation(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15808]) ).
tcf(c_35711,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( identity_relation(identity_relation(identity_relation(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15808]) ).
tcf(c_35712,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( identity_relation(identity_relation(identity_relation(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15808]) ).
tcf(c_35713,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( identity_relation(identity_relation(identity_relation(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15808]) ).
tcf(c_35730,plain,
( empty(set_intersection2(iPr_def_13,empty_set))
| ~ in(sK11,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_97,c_12628]) ).
tcf(c_35731,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(sK11,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15801,c_12628]) ).
tcf(c_35732,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(sK11,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15800,c_12628]) ).
tcf(c_35733,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| ~ in(sK11,sK1(relation_dom(relation_composition(iPr_def_14,sK2)))) ),
inference(superposition,[status(thm)],[c_6817,c_12628]) ).
tcf(c_35736,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ in(sK11,sK1(relation_dom(relation_composition(iPr_def_14,sK2)))) ),
inference(light_normalisation,[status(thm)],[c_35733,c_6817]) ).
tcf(c_35756,plain,
( empty(set_intersection2(iPr_def_13,empty_set))
| ~ in(sK12,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_97,c_12662]) ).
tcf(c_35757,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(sK12,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15801,c_12662]) ).
tcf(c_35758,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(sK12,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15800,c_12662]) ).
tcf(c_35759,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| ~ in(sK12,sK1(relation_dom(relation_composition(iPr_def_14,sK2)))) ),
inference(superposition,[status(thm)],[c_6817,c_12662]) ).
tcf(c_35762,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| ~ in(sK12,sK1(relation_dom(relation_composition(iPr_def_14,sK2)))) ),
inference(light_normalisation,[status(thm)],[c_35759,c_6817]) ).
tcf(c_35812,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,sK12)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_11193]) ).
tcf(c_35813,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,sK12)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_11193]) ).
tcf(c_35816,plain,
( ( relation_dom(set_intersection2(empty_set,sK12)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_11193]) ).
tcf(c_35818,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),sK12)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_11193]) ).
tcf(c_35819,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),sK12)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_11193]) ).
tcf(c_35820,plain,
relation_dom(set_intersection2(empty_set,sK12)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_35816,c_73]) ).
tcf(c_35825,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),sK12)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35819,c_73]) ).
tcf(c_35828,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),sK12)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35818,c_73]) ).
tcf(c_35836,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_11512]) ).
tcf(c_35837,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(identity_relation(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_11512]) ).
tcf(c_35838,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(identity_relation(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_11512]) ).
tcf(c_35839,plain,
sK1(powerset(identity_relation(identity_relation(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_11512]) ).
tcf(c_35840,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(identity_relation(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_11512]) ).
tcf(c_35841,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(identity_relation(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_11512]) ).
tcf(c_35842,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(identity_relation(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_11512]) ).
tcf(c_35843,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(identity_relation(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_11512]) ).
tcf(c_35844,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(identity_relation(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_11512]) ).
tcf(c_35845,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(identity_relation(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_11512]) ).
tcf(c_35846,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(identity_relation(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_11512]) ).
tcf(c_35847,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(identity_relation(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_11512]) ).
tcf(c_35848,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(identity_relation(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_11512]) ).
tcf(c_35849,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(identity_relation(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_11512]) ).
tcf(c_35850,plain,
( ( sK1(powerset(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_11512]) ).
tcf(c_35851,plain,
( ( sK1(powerset(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_11512]) ).
tcf(c_35852,plain,
( ( sK1(powerset(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_11512]) ).
tcf(c_35853,plain,
( ( sK1(powerset(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_11512]) ).
tcf(c_35854,plain,
( ( sK1(powerset(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_11512]) ).
tcf(c_35855,plain,
( ( sK1(powerset(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_11512]) ).
tcf(c_35856,plain,
( ( sK1(powerset(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_11512]) ).
tcf(c_35857,plain,
( ( sK1(powerset(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_11512]) ).
tcf(c_35858,plain,
( ( sK1(powerset(identity_relation(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_11512]) ).
tcf(c_35859,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(identity_relation(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_11512]) ).
tcf(c_35860,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_11512]) ).
tcf(c_35861,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_11512]) ).
tcf(c_35862,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(identity_relation(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_11512]) ).
tcf(c_36012,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| in(sK1(sK4(set_intersection2(X0,X1))),X0) ),
inference(superposition,[status(thm)],[c_52,c_12712]) ).
tcf(c_36014,plain,
! [X0: $i] :
( empty(set_intersection2(X0,X0))
| in(sK1(sK4(X0)),X0) ),
inference(superposition,[status(thm)],[c_80,c_12712]) ).
tcf(c_36015,plain,
! [X0: $i] :
( empty(set_intersection2(X0,empty_set))
| in(sK1(sK4(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_97,c_12712]) ).
tcf(c_36016,plain,
! [X0: $i,X1: $i] :
( in(sK1(sK4(empty_set)),X1)
| empty(set_intersection2(relation_dom(X0),X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_12712]) ).
tcf(c_36017,plain,
! [X0: $i] :
( empty(set_intersection2(empty_set,X0))
| in(sK1(sK4(empty_set)),X0) ),
inference(superposition,[status(thm)],[c_1996,c_12712]) ).
tcf(c_36019,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,relation_dom(X0)))
| in(sK1(sK4(empty_set)),relation_dom(X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15801,c_12712]) ).
tcf(c_36020,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,identity_relation(X0)))
| in(sK1(sK4(empty_set)),identity_relation(X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15800,c_12712]) ).
tcf(c_36021,plain,
! [X0: $i,X1: $i] :
( in(sK1(sK4(empty_set)),X1)
| empty(set_intersection2(identity_relation(X0),X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_12712]) ).
tcf(c_36022,plain,
( empty(set_intersection2(sK12,relation_dom(sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_10,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6018,c_12712]) ).
tcf(c_36023,plain,
( empty(set_intersection2(sK11,relation_dom(sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_11,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6133,c_12712]) ).
tcf(c_36024,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6817,c_12712]) ).
tcf(c_36025,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ( apply(identity_relation(X0),sK1(sK4(set_intersection2(X1,X0)))) = sK1(sK4(set_intersection2(X1,X0))) ) ),
inference(superposition,[status(thm)],[c_12712,c_172]) ).
tcf(c_36026,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ~ in(X0,sK1(sK4(set_intersection2(X1,X0)))) ),
inference(superposition,[status(thm)],[c_12712,c_49]) ).
tcf(c_36028,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| element(sK1(sK4(set_intersection2(X0,X1))),X1) ),
inference(superposition,[status(thm)],[c_12712,c_95]) ).
tcf(c_36029,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,set_intersection2(X1,X2)))
| in(sK1(sK4(set_intersection2(X0,set_intersection2(X1,X2)))),X2) ),
inference(superposition,[status(thm)],[c_12712,c_58]) ).
tcf(c_36030,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,set_intersection2(X1,X2)))
| in(sK1(sK4(set_intersection2(X0,set_intersection2(X1,X2)))),X1) ),
inference(superposition,[status(thm)],[c_12712,c_57]) ).
tcf(c_36031,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,relation_dom(relation_composition(X0,X1))))
| ( apply(relation_composition(X0,X1),sK1(sK4(set_intersection2(X2,relation_dom(relation_composition(X0,X1)))))) = apply(X1,apply(X0,sK1(sK4(set_intersection2(X2,relation_dom(relation_composition(X0,X1))))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_12712,c_96]) ).
tcf(c_36033,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(sK4(set_intersection2(X0,iPr_def_13))),sK11) ),
inference(superposition,[status(thm)],[c_12712,c_2102]) ).
tcf(c_36034,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(sK4(set_intersection2(X0,iPr_def_13))),sK12) ),
inference(superposition,[status(thm)],[c_12712,c_2071]) ).
tcf(c_36035,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK12))
| in(sK1(sK4(set_intersection2(X0,sK12))),iPr_def_13)
| ~ in(sK1(sK4(set_intersection2(X0,sK12))),sK11) ),
inference(superposition,[status(thm)],[c_12712,c_2962]) ).
tcf(c_36037,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,sK1(powerset(X1))))
| element(sK1(sK4(set_intersection2(X0,sK1(powerset(X1))))),X1) ),
inference(superposition,[status(thm)],[c_12712,c_2582]) ).
tcf(c_36038,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| empty(set_intersection2(X0,sK4(X1)))
| element(sK1(sK4(set_intersection2(X0,sK4(X1)))),X1) ),
inference(superposition,[status(thm)],[c_12712,c_2583]) ).
tcf(c_36039,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))
| in(sK1(sK4(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12712,c_6028]) ).
tcf(c_36040,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))
| in(sK1(sK4(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))),sK12) ),
inference(superposition,[status(thm)],[c_12712,c_6029]) ).
tcf(c_36041,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))
| in(sK1(sK4(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12712,c_6143]) ).
tcf(c_36042,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))
| in(sK1(sK4(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))),sK11) ),
inference(superposition,[status(thm)],[c_12712,c_6144]) ).
tcf(c_36043,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))
| in(sK1(sK4(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12712,c_6827]) ).
tcf(c_36044,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))
| in(sK1(sK4(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_12712,c_6828]) ).
tcf(c_36046,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,sK1(sK4(powerset(X1)))))
| element(sK1(sK4(set_intersection2(X0,sK1(sK4(powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_12712,c_12696]) ).
tcf(c_36047,plain,
! [X0: $i] :
( empty(empty_set)
| in(sK1(sK4(empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_36017,c_1996]) ).
tcf(c_36048,plain,
( empty(empty_set)
| in(sK1(sK4(empty_set)),empty_set) ),
inference(light_normalisation,[status(thm)],[c_36015,c_97]) ).
tcf(c_36179,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| in(sK1(sK4(set_intersection2(X0,X1))),X1) ),
inference(superposition,[status(thm)],[c_52,c_12713]) ).
tcf(c_36182,plain,
! [X0: $i] :
( empty(set_intersection2(X0,empty_set))
| in(sK1(sK4(empty_set)),X0) ),
inference(superposition,[status(thm)],[c_97,c_12713]) ).
tcf(c_36183,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(relation_dom(X0),X1))
| in(sK1(sK4(empty_set)),relation_dom(X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_12713]) ).
tcf(c_36184,plain,
! [X0: $i] :
( empty(set_intersection2(empty_set,X0))
| in(sK1(sK4(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_1996,c_12713]) ).
tcf(c_36186,plain,
! [X0: $i,X1: $i] :
( in(sK1(sK4(empty_set)),X1)
| empty(set_intersection2(X1,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15801,c_12713]) ).
tcf(c_36187,plain,
! [X0: $i,X1: $i] :
( in(sK1(sK4(empty_set)),X1)
| empty(set_intersection2(X1,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15800,c_12713]) ).
tcf(c_36188,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(identity_relation(X0),X1))
| in(sK1(sK4(empty_set)),identity_relation(X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_12713]) ).
tcf(c_36189,plain,
( empty(set_intersection2(sK12,relation_dom(sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_10,sK2)))),sK12) ),
inference(superposition,[status(thm)],[c_6018,c_12713]) ).
tcf(c_36190,plain,
( empty(set_intersection2(sK11,relation_dom(sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_11,sK2)))),sK11) ),
inference(superposition,[status(thm)],[c_6133,c_12713]) ).
tcf(c_36191,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_6817,c_12713]) ).
tcf(c_36192,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ( apply(identity_relation(X0),sK1(sK4(set_intersection2(X0,X1)))) = sK1(sK4(set_intersection2(X0,X1))) ) ),
inference(superposition,[status(thm)],[c_12713,c_172]) ).
tcf(c_36193,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ~ in(X0,sK1(sK4(set_intersection2(X0,X1)))) ),
inference(superposition,[status(thm)],[c_12713,c_49]) ).
tcf(c_36195,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| element(sK1(sK4(set_intersection2(X0,X1))),X0) ),
inference(superposition,[status(thm)],[c_12713,c_95]) ).
tcf(c_36196,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),X2))
| in(sK1(sK4(set_intersection2(set_intersection2(X0,X1),X2))),X1) ),
inference(superposition,[status(thm)],[c_12713,c_58]) ).
tcf(c_36197,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),X2))
| in(sK1(sK4(set_intersection2(set_intersection2(X0,X1),X2))),X0) ),
inference(superposition,[status(thm)],[c_12713,c_57]) ).
tcf(c_36198,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_dom(relation_composition(X0,X1)),X2))
| ( apply(relation_composition(X0,X1),sK1(sK4(set_intersection2(relation_dom(relation_composition(X0,X1)),X2)))) = apply(X1,apply(X0,sK1(sK4(set_intersection2(relation_dom(relation_composition(X0,X1)),X2))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_12713,c_96]) ).
tcf(c_36200,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(sK4(set_intersection2(iPr_def_13,X0))),sK11) ),
inference(superposition,[status(thm)],[c_12713,c_2102]) ).
tcf(c_36201,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(sK4(set_intersection2(iPr_def_13,X0))),sK12) ),
inference(superposition,[status(thm)],[c_12713,c_2071]) ).
tcf(c_36202,plain,
! [X0: $i] :
( empty(set_intersection2(sK12,X0))
| in(sK1(sK4(set_intersection2(sK12,X0))),iPr_def_13)
| ~ in(sK1(sK4(set_intersection2(sK12,X0))),sK11) ),
inference(superposition,[status(thm)],[c_12713,c_2962]) ).
tcf(c_36204,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(powerset(X0)),X1))
| element(sK1(sK4(set_intersection2(sK1(powerset(X0)),X1))),X0) ),
inference(superposition,[status(thm)],[c_12713,c_2582]) ).
tcf(c_36205,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| empty(set_intersection2(sK4(X0),X1))
| element(sK1(sK4(set_intersection2(sK4(X0),X1))),X0) ),
inference(superposition,[status(thm)],[c_12713,c_2583]) ).
tcf(c_36206,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))
| in(sK1(sK4(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12713,c_6028]) ).
tcf(c_36207,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))
| in(sK1(sK4(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))),sK12) ),
inference(superposition,[status(thm)],[c_12713,c_6029]) ).
tcf(c_36208,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))
| in(sK1(sK4(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12713,c_6143]) ).
tcf(c_36209,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))
| in(sK1(sK4(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))),sK11) ),
inference(superposition,[status(thm)],[c_12713,c_6144]) ).
tcf(c_36210,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))
| in(sK1(sK4(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12713,c_6827]) ).
tcf(c_36211,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))
| in(sK1(sK4(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_12713,c_6828]) ).
tcf(c_36213,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(sK4(powerset(X0))),X1))
| element(sK1(sK4(set_intersection2(sK1(sK4(powerset(X0))),X1))),X0) ),
inference(superposition,[status(thm)],[c_12713,c_12696]) ).
tcf(c_36398,plain,
( empty(sK1(powerset(empty_set)))
| element(sK1(sK4(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_5628,c_12719]) ).
tcf(c_36399,plain,
! [X0: $i] :
( empty(X0)
| empty(sK1(powerset(X0)))
| in(sK1(sK4(sK1(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_12719,c_98]) ).
tcf(c_36400,plain,
! [X0: $i,X1: $i] :
( empty(sK1(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK1(sK4(sK1(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_12719,c_107]) ).
tcf(c_36401,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK1(powerset(powerset(X1))))
| ~ in(X0,sK1(sK4(sK1(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_12719,c_106]) ).
tcf(c_36402,plain,
( empty(empty_set)
| element(sK1(sK4(empty_set)),empty_set) ),
inference(light_normalisation,[status(thm)],[c_36398,c_5628]) ).
tcf(c_36414,plain,
! [X0: $i] :
( empty(X0)
| element(sK1(sK4(sK4(X0))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_12720,c_86,c_12720]) ).
tcf(c_36420,plain,
! [X0: $i] :
( empty(X0)
| in(sK1(sK4(sK4(X0))),X0) ),
inference(superposition,[status(thm)],[c_36414,c_98]) ).
tcf(c_36421,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(X0,sK1(sK4(sK4(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_36414,c_107]) ).
tcf(c_36422,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ~ in(X0,sK1(sK4(sK4(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_36414,c_106]) ).
tcf(c_36425,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK1(sK4(sK4(powerset(X1))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36422,c_69]) ).
tcf(c_36428,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK1(sK4(sK4(powerset(X1))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36421,c_69]) ).
tcf(c_36437,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(X0),sK1(sK4(sK4(X0)))) = sK1(sK4(sK4(X0))) ) ),
inference(superposition,[status(thm)],[c_36420,c_172]) ).
tcf(c_36438,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK1(sK4(sK4(X0)))) ),
inference(superposition,[status(thm)],[c_36420,c_49]) ).
tcf(c_36441,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| in(sK1(sK4(sK4(set_intersection2(X0,X1)))),X1) ),
inference(superposition,[status(thm)],[c_36420,c_58]) ).
tcf(c_36442,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| in(sK1(sK4(sK4(set_intersection2(X0,X1)))),X0) ),
inference(superposition,[status(thm)],[c_36420,c_57]) ).
tcf(c_36443,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom(relation_composition(X0,X1)))
| ( apply(relation_composition(X0,X1),sK1(sK4(sK4(relation_dom(relation_composition(X0,X1)))))) = apply(X1,apply(X0,sK1(sK4(sK4(relation_dom(relation_composition(X0,X1))))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_36420,c_96]) ).
tcf(c_36445,plain,
( empty(iPr_def_13)
| in(sK1(sK4(sK4(iPr_def_13))),sK11) ),
inference(superposition,[status(thm)],[c_36420,c_2102]) ).
tcf(c_36446,plain,
( empty(iPr_def_13)
| in(sK1(sK4(sK4(iPr_def_13))),sK12) ),
inference(superposition,[status(thm)],[c_36420,c_2071]) ).
tcf(c_36447,plain,
( empty(sK12)
| in(sK1(sK4(sK4(sK12))),iPr_def_13)
| ~ in(sK1(sK4(sK4(sK12))),sK11) ),
inference(superposition,[status(thm)],[c_36420,c_2962]) ).
tcf(c_36449,plain,
! [X0: $i] :
( empty(sK1(powerset(X0)))
| element(sK1(sK4(sK4(sK1(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_36420,c_2582]) ).
tcf(c_36450,plain,
! [X0: $i] :
( empty(X0)
| empty(sK4(X0))
| element(sK1(sK4(sK4(sK4(X0)))),X0) ),
inference(superposition,[status(thm)],[c_36420,c_2583]) ).
tcf(c_36451,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| in(sK1(sK4(sK4(relation_dom(relation_composition(iPr_def_10,sK2))))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_36420,c_6028]) ).
tcf(c_36452,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| in(sK1(sK4(sK4(relation_dom(relation_composition(iPr_def_10,sK2))))),sK12) ),
inference(superposition,[status(thm)],[c_36420,c_6029]) ).
tcf(c_36453,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| in(sK1(sK4(sK4(relation_dom(relation_composition(iPr_def_11,sK2))))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_36420,c_6143]) ).
tcf(c_36454,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| in(sK1(sK4(sK4(relation_dom(relation_composition(iPr_def_11,sK2))))),sK11) ),
inference(superposition,[status(thm)],[c_36420,c_6144]) ).
tcf(c_36455,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| in(sK1(sK4(sK4(relation_dom(relation_composition(iPr_def_14,sK2))))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_36420,c_6827]) ).
tcf(c_36456,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| in(sK1(sK4(sK4(relation_dom(relation_composition(iPr_def_14,sK2))))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_36420,c_6828]) ).
tcf(c_36458,plain,
! [X0: $i] :
( empty(sK1(sK4(powerset(X0))))
| element(sK1(sK4(sK4(sK1(sK4(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_36420,c_12696]) ).
tcf(c_36459,plain,
in(sK1(sK4(sK4(iPr_def_13))),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_36446,c_4400]) ).
tcf(c_36460,plain,
in(sK1(sK4(sK4(iPr_def_13))),sK11),
inference(forward_subsumption_resolution,[status(thm)],[c_36445,c_4400]) ).
tcf(c_36486,plain,
( in(sK1(sK4(sK4(sK12))),iPr_def_13)
| ~ in(sK1(sK4(sK4(sK12))),sK11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36447,c_3280]) ).
tcf(c_36545,plain,
apply(identity_relation(sK12),sK1(sK4(sK4(iPr_def_13)))) = sK1(sK4(sK4(iPr_def_13))),
inference(superposition,[status(thm)],[c_36459,c_172]) ).
tcf(c_36546,plain,
~ in(sK12,sK1(sK4(sK4(iPr_def_13)))),
inference(superposition,[status(thm)],[c_36459,c_49]) ).
tcf(c_36548,plain,
element(sK1(sK4(sK4(iPr_def_13))),sK12),
inference(superposition,[status(thm)],[c_36459,c_95]) ).
tcf(c_36549,plain,
( in(sK1(sK4(sK4(iPr_def_13))),iPr_def_13)
| ~ in(sK1(sK4(sK4(iPr_def_13))),sK11) ),
inference(superposition,[status(thm)],[c_36459,c_2962]) ).
tcf(c_36552,plain,
apply(iPr_def_10,sK1(sK4(sK4(iPr_def_13)))) = sK1(sK4(sK4(iPr_def_13))),
inference(light_normalisation,[status(thm)],[c_36545,c_1147]) ).
tcf(c_36605,plain,
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( identity_relation(identity_relation(relation_dom(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15809]) ).
tcf(c_36607,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( identity_relation(identity_relation(relation_dom(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15809]) ).
tcf(c_36608,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( identity_relation(identity_relation(relation_dom(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15809]) ).
tcf(c_36609,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( identity_relation(identity_relation(relation_dom(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15809]) ).
tcf(c_36634,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| ~ in(sK11,sK1(relation_dom(relation_composition(iPr_def_14,sK2)))) ),
inference(superposition,[status(thm)],[c_6817,c_12879]) ).
tcf(c_36637,plain,
apply(identity_relation(sK11),sK1(sK4(sK4(iPr_def_13)))) = sK1(sK4(sK4(iPr_def_13))),
inference(superposition,[status(thm)],[c_36460,c_172]) ).
tcf(c_36638,plain,
~ in(sK11,sK1(sK4(sK4(iPr_def_13)))),
inference(superposition,[status(thm)],[c_36460,c_49]) ).
tcf(c_36640,plain,
element(sK1(sK4(sK4(iPr_def_13))),sK11),
inference(superposition,[status(thm)],[c_36460,c_95]) ).
tcf(c_36641,plain,
apply(iPr_def_11,sK1(sK4(sK4(iPr_def_13)))) = sK1(sK4(sK4(iPr_def_13))),
inference(light_normalisation,[status(thm)],[c_36637,c_1148]) ).
tcf(c_36669,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| ~ in(sK12,sK1(relation_dom(relation_composition(iPr_def_14,sK2)))) ),
inference(superposition,[status(thm)],[c_6817,c_12899]) ).
tcf(c_36712,plain,
! [X0: $i] :
( ( identity_relation(sK1(sK4(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_14339]) ).
tcf(c_36713,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(sK4(powerset(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_14339]) ).
tcf(c_36714,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(sK4(powerset(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_14339]) ).
tcf(c_36715,plain,
identity_relation(sK1(sK4(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_14339]) ).
tcf(c_36716,plain,
! [X0: $i] :
( ( identity_relation(sK1(sK4(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_14339]) ).
tcf(c_36717,plain,
! [X0: $i] :
( ( identity_relation(sK1(sK4(powerset(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_14339]) ).
tcf(c_36718,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(sK4(powerset(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_14339]) ).
tcf(c_36719,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(sK4(powerset(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_14339]) ).
tcf(c_36720,plain,
! [X0: $i] :
( ( identity_relation(sK1(sK4(powerset(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_14339]) ).
tcf(c_36721,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(sK4(powerset(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_14339]) ).
tcf(c_36722,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(sK4(powerset(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_14339]) ).
tcf(c_36723,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(sK4(powerset(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_14339]) ).
tcf(c_36724,plain,
! [X0: $i] :
( ( identity_relation(sK1(sK4(powerset(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_14339]) ).
tcf(c_36725,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(sK4(powerset(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_14339]) ).
tcf(c_36726,plain,
( ( identity_relation(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_14339]) ).
tcf(c_36727,plain,
( ( identity_relation(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_14339]) ).
tcf(c_36728,plain,
( ( identity_relation(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_14339]) ).
tcf(c_36729,plain,
( ( identity_relation(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_14339]) ).
tcf(c_36730,plain,
( ( identity_relation(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_14339]) ).
tcf(c_36731,plain,
( ( identity_relation(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_14339]) ).
tcf(c_36732,plain,
( ( identity_relation(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_14339]) ).
tcf(c_36733,plain,
( ( identity_relation(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_14339]) ).
tcf(c_36734,plain,
( ( identity_relation(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_14339]) ).
tcf(c_36735,plain,
! [X0: $i] :
( ( identity_relation(sK1(sK4(powerset(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_14339]) ).
tcf(c_36736,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(sK4(powerset(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_14339]) ).
tcf(c_36737,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(sK4(powerset(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_14339]) ).
tcf(c_36738,plain,
! [X0: $i] :
( ( identity_relation(sK1(sK4(powerset(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_14339]) ).
tcf(c_36856,plain,
! [X0: $i] :
( ( relation_dom(sK1(sK4(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_14340]) ).
tcf(c_36857,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(sK4(powerset(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_14340]) ).
tcf(c_36858,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(sK4(powerset(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_14340]) ).
tcf(c_36859,plain,
relation_dom(sK1(sK4(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_14340]) ).
tcf(c_36860,plain,
! [X0: $i] :
( ( relation_dom(sK1(sK4(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_14340]) ).
tcf(c_36861,plain,
! [X0: $i] :
( ( relation_dom(sK1(sK4(powerset(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_14340]) ).
tcf(c_36862,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(sK4(powerset(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_14340]) ).
tcf(c_36863,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(sK4(powerset(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_14340]) ).
tcf(c_36864,plain,
! [X0: $i] :
( ( relation_dom(sK1(sK4(powerset(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_14340]) ).
tcf(c_36865,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(sK4(powerset(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_14340]) ).
tcf(c_36866,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(sK4(powerset(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_14340]) ).
tcf(c_36867,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(sK4(powerset(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_14340]) ).
tcf(c_36868,plain,
! [X0: $i] :
( ( relation_dom(sK1(sK4(powerset(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_14340]) ).
tcf(c_36869,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(sK4(powerset(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_14340]) ).
tcf(c_36870,plain,
( ( relation_dom(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_14340]) ).
tcf(c_36871,plain,
( ( relation_dom(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_14340]) ).
tcf(c_36872,plain,
( ( relation_dom(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_14340]) ).
tcf(c_36873,plain,
( ( relation_dom(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_14340]) ).
tcf(c_36874,plain,
( ( relation_dom(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_14340]) ).
tcf(c_36875,plain,
( ( relation_dom(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_14340]) ).
tcf(c_36876,plain,
( ( relation_dom(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_14340]) ).
tcf(c_36877,plain,
( ( relation_dom(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_14340]) ).
tcf(c_36878,plain,
( ( relation_dom(sK1(sK4(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_14340]) ).
tcf(c_36879,plain,
! [X0: $i] :
( ( relation_dom(sK1(sK4(powerset(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_14340]) ).
tcf(c_36880,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(sK4(powerset(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_14340]) ).
tcf(c_36881,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(sK4(powerset(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_14340]) ).
tcf(c_36882,plain,
! [X0: $i] :
( ( relation_dom(sK1(sK4(powerset(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_14340]) ).
tcf(c_37094,plain,
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( identity_relation(relation_dom(relation_dom(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15810]) ).
tcf(c_37096,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( identity_relation(relation_dom(relation_dom(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15810]) ).
tcf(c_37097,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( identity_relation(relation_dom(relation_dom(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15810]) ).
tcf(c_37098,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( identity_relation(relation_dom(relation_dom(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15810]) ).
tcf(c_37112,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(relation_dom(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_14939]) ).
tcf(c_37113,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(relation_dom(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_14939]) ).
tcf(c_37114,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(relation_dom(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_14939]) ).
tcf(c_37115,plain,
sK1(sK4(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_14939]) ).
tcf(c_37116,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_14939]) ).
tcf(c_37117,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(relation_dom(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_14939]) ).
tcf(c_37118,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_14939]) ).
tcf(c_37119,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(relation_dom(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_14939]) ).
tcf(c_37120,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(relation_dom(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_14939]) ).
tcf(c_37121,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_14939]) ).
tcf(c_37122,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(relation_dom(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_14939]) ).
tcf(c_37123,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(relation_dom(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_14939]) ).
tcf(c_37124,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(relation_dom(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_14939]) ).
tcf(c_37125,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(relation_dom(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_14939]) ).
tcf(c_37126,plain,
( ( sK1(sK4(powerset(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_14939]) ).
tcf(c_37127,plain,
( ( sK1(sK4(powerset(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_14939]) ).
tcf(c_37128,plain,
( ( sK1(sK4(powerset(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_14939]) ).
tcf(c_37129,plain,
( ( sK1(sK4(powerset(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_14939]) ).
tcf(c_37130,plain,
( ( sK1(sK4(powerset(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_14939]) ).
tcf(c_37131,plain,
( ( sK1(sK4(powerset(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_14939]) ).
tcf(c_37132,plain,
( ( sK1(sK4(powerset(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_14939]) ).
tcf(c_37133,plain,
( ( sK1(sK4(powerset(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_14939]) ).
tcf(c_37134,plain,
( ( sK1(sK4(powerset(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_14939]) ).
tcf(c_37135,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(relation_dom(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_14939]) ).
tcf(c_37136,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_14939]) ).
tcf(c_37137,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_14939]) ).
tcf(c_37138,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(relation_dom(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_14939]) ).
tcf(c_37321,plain,
( relation(iPr_def_13)
| ( apply(identity_relation(sK11),sK1(sK11)) = sK1(sK11) )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_15821,c_2347]) ).
tcf(c_37327,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(relation_composition(identity_relation(X1),X0)) = set_intersection2(relation_dom(X0),X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_15822,c_103]) ).
tcf(c_37336,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(identity_relation(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_14940]) ).
tcf(c_37337,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(identity_relation(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_14940]) ).
tcf(c_37338,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(identity_relation(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_14940]) ).
tcf(c_37339,plain,
sK1(sK4(powerset(identity_relation(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_14940]) ).
tcf(c_37340,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(identity_relation(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_14940]) ).
tcf(c_37341,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(identity_relation(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_14940]) ).
tcf(c_37342,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(identity_relation(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_14940]) ).
tcf(c_37343,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(identity_relation(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_14940]) ).
tcf(c_37344,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(identity_relation(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_14940]) ).
tcf(c_37345,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(identity_relation(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_14940]) ).
tcf(c_37346,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(identity_relation(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_14940]) ).
tcf(c_37347,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(identity_relation(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_14940]) ).
tcf(c_37348,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(identity_relation(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_14940]) ).
tcf(c_37349,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(identity_relation(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_14940]) ).
tcf(c_37350,plain,
( ( sK1(sK4(powerset(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_14940]) ).
tcf(c_37351,plain,
( ( sK1(sK4(powerset(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_14940]) ).
tcf(c_37352,plain,
( ( sK1(sK4(powerset(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_14940]) ).
tcf(c_37353,plain,
( ( sK1(sK4(powerset(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_14940]) ).
tcf(c_37354,plain,
( ( sK1(sK4(powerset(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_14940]) ).
tcf(c_37355,plain,
( ( sK1(sK4(powerset(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_14940]) ).
tcf(c_37356,plain,
( ( sK1(sK4(powerset(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_14940]) ).
tcf(c_37357,plain,
( ( sK1(sK4(powerset(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_14940]) ).
tcf(c_37358,plain,
( ( sK1(sK4(powerset(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_14940]) ).
tcf(c_37359,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(identity_relation(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_14940]) ).
tcf(c_37360,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_14940]) ).
tcf(c_37361,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_14940]) ).
tcf(c_37362,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(identity_relation(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_14940]) ).
tcf(c_37510,plain,
( ( apply(identity_relation(sK2),sK1(sK2)) = sK1(sK2) )
| ( identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_18299]) ).
tcf(c_37517,plain,
( ( apply(identity_relation(sK2),sK1(sK2)) = sK1(sK2) )
| ( relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_18300]) ).
tcf(c_37524,plain,
( ( apply(identity_relation(sK2),sK1(sK2)) = sK1(sK2) )
| ( identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_18563]) ).
tcf(c_37531,plain,
( ( apply(identity_relation(sK2),sK1(sK2)) = sK1(sK2) )
| ( relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_18564]) ).
tcf(c_37540,plain,
( ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) )
| ( relation_dom(relation_dom(relation_dom(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2472,c_15811]) ).
tcf(c_37542,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( relation_dom(relation_dom(relation_dom(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15807,c_15811]) ).
tcf(c_37543,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) )
| ( relation_dom(relation_dom(relation_dom(set_intersection2(X0,X1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15805,c_15811]) ).
tcf(c_37544,plain,
( ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set )
| ( relation_dom(relation_dom(relation_dom(powerset(empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15811]) ).
tcf(c_37568,plain,
( empty(set_intersection2(relation_dom(sK2),sK12))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_10,sK2)))),sK12) ),
inference(superposition,[status(thm)],[c_6018,c_36012]) ).
tcf(c_37569,plain,
( empty(set_intersection2(relation_dom(sK2),sK11))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_11,sK2)))),sK11) ),
inference(superposition,[status(thm)],[c_6133,c_36012]) ).
tcf(c_37570,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_6817,c_36012]) ).
tcf(c_37571,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ( apply(identity_relation(X0),sK1(sK4(set_intersection2(X0,X1)))) = sK1(sK4(set_intersection2(X0,X1))) ) ),
inference(superposition,[status(thm)],[c_36012,c_172]) ).
tcf(c_37572,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ~ in(X0,sK1(sK4(set_intersection2(X0,X1)))) ),
inference(superposition,[status(thm)],[c_36012,c_49]) ).
tcf(c_37574,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| element(sK1(sK4(set_intersection2(X0,X1))),X0) ),
inference(superposition,[status(thm)],[c_36012,c_95]) ).
tcf(c_37575,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,set_intersection2(X0,X1)))
| in(sK1(sK4(set_intersection2(set_intersection2(X0,X1),X2))),X1) ),
inference(superposition,[status(thm)],[c_36012,c_58]) ).
tcf(c_37576,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,set_intersection2(X0,X1)))
| in(sK1(sK4(set_intersection2(set_intersection2(X0,X1),X2))),X0) ),
inference(superposition,[status(thm)],[c_36012,c_57]) ).
tcf(c_37577,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,relation_dom(relation_composition(X0,X1))))
| ( apply(relation_composition(X0,X1),sK1(sK4(set_intersection2(relation_dom(relation_composition(X0,X1)),X2)))) = apply(X1,apply(X0,sK1(sK4(set_intersection2(relation_dom(relation_composition(X0,X1)),X2))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_36012,c_96]) ).
tcf(c_37579,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(sK4(set_intersection2(iPr_def_13,X0))),sK11) ),
inference(superposition,[status(thm)],[c_36012,c_2102]) ).
tcf(c_37580,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(sK4(set_intersection2(iPr_def_13,X0))),sK12) ),
inference(superposition,[status(thm)],[c_36012,c_2071]) ).
tcf(c_37581,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK12))
| in(sK1(sK4(set_intersection2(sK12,X0))),iPr_def_13)
| ~ in(sK1(sK4(set_intersection2(sK12,X0))),sK11) ),
inference(superposition,[status(thm)],[c_36012,c_2962]) ).
tcf(c_37583,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,sK1(powerset(X0))))
| element(sK1(sK4(set_intersection2(sK1(powerset(X0)),X1))),X0) ),
inference(superposition,[status(thm)],[c_36012,c_2582]) ).
tcf(c_37584,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| empty(set_intersection2(X1,sK4(X0)))
| element(sK1(sK4(set_intersection2(sK4(X0),X1))),X0) ),
inference(superposition,[status(thm)],[c_36012,c_2583]) ).
tcf(c_37585,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))
| in(sK1(sK4(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_36012,c_6028]) ).
tcf(c_37586,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))
| in(sK1(sK4(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))),sK12) ),
inference(superposition,[status(thm)],[c_36012,c_6029]) ).
tcf(c_37587,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))
| in(sK1(sK4(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_36012,c_6143]) ).
tcf(c_37588,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))
| in(sK1(sK4(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))),sK11) ),
inference(superposition,[status(thm)],[c_36012,c_6144]) ).
tcf(c_37589,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))
| in(sK1(sK4(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_36012,c_6827]) ).
tcf(c_37590,plain,
! [X0: $i] :
( empty(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))
| in(sK1(sK4(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_36012,c_6828]) ).
tcf(c_37592,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,sK1(sK4(powerset(X0)))))
| element(sK1(sK4(set_intersection2(sK1(sK4(powerset(X0))),X1))),X0) ),
inference(superposition,[status(thm)],[c_36012,c_12696]) ).
tcf(c_37745,plain,
! [X0: $i] :
( empty(set_intersection2(X0,X0))
| element(sK1(sK4(X0)),X0) ),
inference(superposition,[status(thm)],[c_80,c_36028]) ).
tcf(c_37746,plain,
! [X0: $i] :
( empty(set_intersection2(X0,empty_set))
| element(sK1(sK4(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_97,c_36028]) ).
tcf(c_37747,plain,
! [X0: $i,X1: $i] :
( element(sK1(sK4(empty_set)),X1)
| empty(set_intersection2(relation_dom(X0),X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_36028]) ).
tcf(c_37748,plain,
! [X0: $i] :
( empty(set_intersection2(empty_set,X0))
| element(sK1(sK4(empty_set)),X0) ),
inference(superposition,[status(thm)],[c_1996,c_36028]) ).
tcf(c_37750,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,relation_dom(X0)))
| element(sK1(sK4(empty_set)),relation_dom(X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15801,c_36028]) ).
tcf(c_37751,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,identity_relation(X0)))
| element(sK1(sK4(empty_set)),identity_relation(X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15800,c_36028]) ).
tcf(c_37752,plain,
! [X0: $i,X1: $i] :
( element(sK1(sK4(empty_set)),X1)
| empty(set_intersection2(identity_relation(X0),X1))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_36028]) ).
tcf(c_37753,plain,
( empty(set_intersection2(sK12,relation_dom(sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_10,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6018,c_36028]) ).
tcf(c_37754,plain,
( empty(set_intersection2(sK11,relation_dom(sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_11,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6133,c_36028]) ).
tcf(c_37755,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6817,c_36028]) ).
tcf(c_37757,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X1,powerset(X2)))
| ~ empty(X2)
| ~ in(X0,sK1(sK4(set_intersection2(X1,powerset(X2))))) ),
inference(superposition,[status(thm)],[c_36028,c_107]) ).
tcf(c_37758,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| empty(set_intersection2(X1,powerset(X2)))
| ~ in(X0,sK1(sK4(set_intersection2(X1,powerset(X2))))) ),
inference(superposition,[status(thm)],[c_36028,c_106]) ).
tcf(c_37759,plain,
! [X0: $i] :
( empty(empty_set)
| element(sK1(sK4(empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_37748,c_1996]) ).
tcf(c_37762,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_37755,c_6817]) ).
tcf(c_37765,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_11,sK2)))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_37754,c_6133]) ).
tcf(c_37768,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_10,sK2)))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_37753,c_6018]) ).
tcf(c_37817,plain,
( empty(set_intersection2(relation_dom(sK2),sK12))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_10,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6018,c_36179]) ).
tcf(c_37818,plain,
( empty(set_intersection2(relation_dom(sK2),sK11))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_11,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6133,c_36179]) ).
tcf(c_37819,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6817,c_36179]) ).
tcf(c_37820,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ( apply(identity_relation(X0),sK1(sK4(set_intersection2(X1,X0)))) = sK1(sK4(set_intersection2(X1,X0))) ) ),
inference(superposition,[status(thm)],[c_36179,c_172]) ).
tcf(c_37821,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ~ in(X0,sK1(sK4(set_intersection2(X1,X0)))) ),
inference(superposition,[status(thm)],[c_36179,c_49]) ).
tcf(c_37823,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| element(sK1(sK4(set_intersection2(X0,X1))),X1) ),
inference(superposition,[status(thm)],[c_36179,c_95]) ).
tcf(c_37824,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X1,X2),X0))
| in(sK1(sK4(set_intersection2(X0,set_intersection2(X1,X2)))),X2) ),
inference(superposition,[status(thm)],[c_36179,c_58]) ).
tcf(c_37825,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X1,X2),X0))
| in(sK1(sK4(set_intersection2(X0,set_intersection2(X1,X2)))),X1) ),
inference(superposition,[status(thm)],[c_36179,c_57]) ).
tcf(c_37826,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_dom(relation_composition(X0,X1)),X2))
| ( apply(relation_composition(X0,X1),sK1(sK4(set_intersection2(X2,relation_dom(relation_composition(X0,X1)))))) = apply(X1,apply(X0,sK1(sK4(set_intersection2(X2,relation_dom(relation_composition(X0,X1))))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_36179,c_96]) ).
tcf(c_37828,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(sK4(set_intersection2(X0,iPr_def_13))),sK11) ),
inference(superposition,[status(thm)],[c_36179,c_2102]) ).
tcf(c_37829,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(sK4(set_intersection2(X0,iPr_def_13))),sK12) ),
inference(superposition,[status(thm)],[c_36179,c_2071]) ).
tcf(c_37830,plain,
! [X0: $i] :
( empty(set_intersection2(sK12,X0))
| in(sK1(sK4(set_intersection2(X0,sK12))),iPr_def_13)
| ~ in(sK1(sK4(set_intersection2(X0,sK12))),sK11) ),
inference(superposition,[status(thm)],[c_36179,c_2962]) ).
tcf(c_37832,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(powerset(X1)),X0))
| element(sK1(sK4(set_intersection2(X0,sK1(powerset(X1))))),X1) ),
inference(superposition,[status(thm)],[c_36179,c_2582]) ).
tcf(c_37833,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| empty(set_intersection2(sK4(X1),X0))
| element(sK1(sK4(set_intersection2(X0,sK4(X1)))),X1) ),
inference(superposition,[status(thm)],[c_36179,c_2583]) ).
tcf(c_37834,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))
| in(sK1(sK4(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_36179,c_6028]) ).
tcf(c_37835,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0))
| in(sK1(sK4(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))))),sK12) ),
inference(superposition,[status(thm)],[c_36179,c_6029]) ).
tcf(c_37836,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))
| in(sK1(sK4(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_36179,c_6143]) ).
tcf(c_37837,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0))
| in(sK1(sK4(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))))),sK11) ),
inference(superposition,[status(thm)],[c_36179,c_6144]) ).
tcf(c_37838,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))
| in(sK1(sK4(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_36179,c_6827]) ).
tcf(c_37839,plain,
! [X0: $i] :
( empty(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0))
| in(sK1(sK4(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_36179,c_6828]) ).
tcf(c_37841,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(sK4(powerset(X1))),X0))
| element(sK1(sK4(set_intersection2(X0,sK1(sK4(powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_36179,c_12696]) ).
tcf(c_37973,plain,
( ( apply(identity_relation(sK2),sK1(sK2)) = sK1(sK2) )
| ( identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_18785]) ).
tcf(c_37985,plain,
( ( apply(identity_relation(sK2),sK1(sK2)) = sK1(sK2) )
| ( relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_18786]) ).
tcf(c_37995,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X0,X1)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_20870]) ).
tcf(c_37999,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(empty_set,X0)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_20870]) ).
tcf(c_38001,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_20870]) ).
tcf(c_38002,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_20870]) ).
tcf(c_38006,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38002,c_73]) ).
tcf(c_38009,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38001,c_73]) ).
tcf(c_38018,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X0,X1)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_20871]) ).
tcf(c_38022,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(empty_set,X0)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_20871]) ).
tcf(c_38024,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_20871]) ).
tcf(c_38025,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_20871]) ).
tcf(c_38029,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38025,c_73]) ).
tcf(c_38032,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38024,c_73]) ).
tcf(c_38041,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,X0)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_21141]) ).
tcf(c_38045,plain,
! [X0: $i] :
( ( identity_relation(set_intersection2(X0,empty_set)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_21141]) ).
tcf(c_38047,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ( identity_relation(set_intersection2(X0,set_intersection2(X1,X2))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_21141]) ).
tcf(c_38048,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(X0,set_intersection2(X1,X2))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_21141]) ).
tcf(c_38052,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( identity_relation(set_intersection2(X0,set_intersection2(X1,X2))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38048,c_73]) ).
tcf(c_38055,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ( identity_relation(set_intersection2(X0,set_intersection2(X1,X2))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38047,c_73]) ).
tcf(c_38063,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,X0)) = empty_set )
| ( apply(identity_relation(identity_relation(X0)),sK1(identity_relation(X0))) = sK1(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_2544,c_21142]) ).
tcf(c_38067,plain,
! [X0: $i] :
( ( relation_dom(set_intersection2(X0,empty_set)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_2472,c_21142]) ).
tcf(c_38069,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ( relation_dom(set_intersection2(X0,set_intersection2(X1,X2))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15807,c_21142]) ).
tcf(c_38070,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(X0,set_intersection2(X1,X2))) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_15805,c_21142]) ).
tcf(c_38074,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_dom(set_intersection2(X0,set_intersection2(X1,X2))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38070,c_73]) ).
tcf(c_38077,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ( relation_dom(set_intersection2(X0,set_intersection2(X1,X2))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38069,c_73]) ).
tcf(c_38099,plain,
( ( sK1(powerset(powerset(empty_set))) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15812]) ).
tcf(c_38108,plain,
! [X0: $i] :
( empty(set_intersection2(X0,empty_set))
| element(sK1(sK4(empty_set)),X0) ),
inference(superposition,[status(thm)],[c_97,c_36195]) ).
tcf(c_38109,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(relation_dom(X0),X1))
| element(sK1(sK4(empty_set)),relation_dom(X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_36195]) ).
tcf(c_38110,plain,
! [X0: $i] :
( empty(set_intersection2(empty_set,X0))
| element(sK1(sK4(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_1996,c_36195]) ).
tcf(c_38112,plain,
! [X0: $i,X1: $i] :
( element(sK1(sK4(empty_set)),X1)
| empty(set_intersection2(X1,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15801,c_36195]) ).
tcf(c_38113,plain,
! [X0: $i,X1: $i] :
( element(sK1(sK4(empty_set)),X1)
| empty(set_intersection2(X1,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15800,c_36195]) ).
tcf(c_38114,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(identity_relation(X0),X1))
| element(sK1(sK4(empty_set)),identity_relation(X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_36195]) ).
tcf(c_38115,plain,
( empty(set_intersection2(sK12,relation_dom(sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_10,sK2)))),sK12) ),
inference(superposition,[status(thm)],[c_6018,c_36195]) ).
tcf(c_38116,plain,
( empty(set_intersection2(sK11,relation_dom(sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_11,sK2)))),sK11) ),
inference(superposition,[status(thm)],[c_6133,c_36195]) ).
tcf(c_38117,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_6817,c_36195]) ).
tcf(c_38119,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(powerset(X1),X2))
| ~ empty(X1)
| ~ in(X0,sK1(sK4(set_intersection2(powerset(X1),X2)))) ),
inference(superposition,[status(thm)],[c_36195,c_107]) ).
tcf(c_38120,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X1)
| empty(set_intersection2(powerset(X1),X2))
| ~ in(X0,sK1(sK4(set_intersection2(powerset(X1),X2)))) ),
inference(superposition,[status(thm)],[c_36195,c_106]) ).
tcf(c_38123,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_38117,c_6817]) ).
tcf(c_38126,plain,
( empty(relation_dom(relation_composition(iPr_def_11,sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_11,sK2)))),sK11) ),
inference(light_normalisation,[status(thm)],[c_38116,c_6133]) ).
tcf(c_38129,plain,
( empty(relation_dom(relation_composition(iPr_def_10,sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_10,sK2)))),sK12) ),
inference(light_normalisation,[status(thm)],[c_38115,c_6018]) ).
tcf(c_38167,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,sK1(sK4(sK4(powerset(X1)))),X2),X1)
| in(sK0(X0,sK1(sK4(sK4(powerset(X1)))),X2),X2)
| ( set_intersection2(X0,sK1(sK4(sK4(powerset(X1))))) = X2 ) ),
inference(superposition,[status(thm)],[c_55,c_36425]) ).
tcf(c_38168,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(sK1(sK4(sK4(powerset(X0)))),X1,X2),X2)
| element(sK0(sK1(sK4(sK4(powerset(X0)))),X1,X2),X0)
| ( set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_2239,c_36425]) ).
tcf(c_38169,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(sK1(sK4(sK4(powerset(X0)))),X1,X2),X0)
| in(sK0(sK1(sK4(sK4(powerset(X0)))),X1,X2),X2)
| ( set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_54,c_36425]) ).
tcf(c_38170,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X1,X2,sK1(sK4(sK4(powerset(X0))))),X0)
| in(sK0(X1,X2,sK1(sK4(sK4(powerset(X0))))),X2)
| ( sK1(sK4(sK4(powerset(X0)))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_55,c_36425]) ).
tcf(c_38171,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X1,X2,sK1(sK4(sK4(powerset(X0))))),X0)
| in(sK0(X1,X2,sK1(sK4(sK4(powerset(X0))))),X1)
| ( sK1(sK4(sK4(powerset(X0)))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_54,c_36425]) ).
tcf(c_38172,plain,
! [X0: $i] :
( empty(sK1(sK4(sK4(powerset(X0)))))
| element(sK1(sK1(sK4(sK4(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_2137,c_36425]) ).
tcf(c_38173,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(sK4(sK4(powerset(X1)))),X0))
| element(sK1(set_intersection2(X0,sK1(sK4(sK4(powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_7250,c_36425]) ).
tcf(c_38174,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,sK1(sK4(sK4(powerset(X1))))))
| element(sK1(set_intersection2(X0,sK1(sK4(sK4(powerset(X1)))))),X1) ),
inference(superposition,[status(thm)],[c_2201,c_36425]) ).
tcf(c_38175,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))
| element(sK1(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)),X0) ),
inference(superposition,[status(thm)],[c_2732,c_36425]) ).
tcf(c_38176,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))
| element(sK1(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)),X0) ),
inference(superposition,[status(thm)],[c_2202,c_36425]) ).
tcf(c_38177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK0(sK1(sK4(sK4(powerset(X0)))),X1,set_intersection2(X2,X3)),X0)
| in(sK0(sK1(sK4(sK4(powerset(X0)))),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_2241,c_36425]) ).
tcf(c_38178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK0(X2,X3,set_intersection2(X0,sK1(sK4(sK4(powerset(X1)))))),X1)
| in(sK0(X2,X3,set_intersection2(X0,sK1(sK4(sK4(powerset(X1)))))),X2)
| ( set_intersection2(X0,sK1(sK4(sK4(powerset(X1))))) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_2241,c_36425]) ).
tcf(c_38179,plain,
! [X0: $i,X1: $i] :
( element(sK0(empty_set,X1,sK1(sK4(sK4(powerset(X0))))),X0)
| ( sK1(sK4(sK4(powerset(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5683,c_36425]) ).
tcf(c_38180,plain,
! [X0: $i,X1: $i] :
( element(sK0(X1,empty_set,sK1(sK4(sK4(powerset(X0))))),X0)
| ( sK1(sK4(sK4(powerset(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5686,c_36425]) ).
tcf(c_38181,plain,
! [X0: $i] :
( empty(sK1(sK4(sK4(powerset(X0)))))
| element(sK1(sK4(sK1(sK4(sK4(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_12691,c_36425]) ).
tcf(c_38182,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(sK4(sK4(powerset(X1)))),X0))
| element(sK1(sK4(set_intersection2(X0,sK1(sK4(sK4(powerset(X1))))))),X1) ),
inference(superposition,[status(thm)],[c_36179,c_36425]) ).
tcf(c_38183,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,sK1(sK4(sK4(powerset(X1))))))
| element(sK1(sK4(set_intersection2(X0,sK1(sK4(sK4(powerset(X1))))))),X1) ),
inference(superposition,[status(thm)],[c_12712,c_36425]) ).
tcf(c_38184,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))
| element(sK1(sK4(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))),X0) ),
inference(superposition,[status(thm)],[c_36012,c_36425]) ).
tcf(c_38185,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))
| element(sK1(sK4(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))),X0) ),
inference(superposition,[status(thm)],[c_12713,c_36425]) ).
tcf(c_38186,plain,
! [X0: $i] :
( empty(sK1(sK4(sK4(powerset(X0)))))
| element(sK1(sK4(sK4(sK1(sK4(sK4(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_36420,c_36425]) ).
tcf(c_38285,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,sK1(sK4(sK4(powerset(X0)))),X2),X2)
| ( set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_36428]) ).
tcf(c_38286,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(sK1(sK4(sK4(powerset(X0)))),X1,X2),X2)
| ( set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2239,c_36428]) ).
tcf(c_38287,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(sK1(sK4(sK4(powerset(X0)))),X1,X2),X2)
| ( set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_36428]) ).
tcf(c_38288,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,sK1(sK4(sK4(powerset(X0))))),X2)
| ( sK1(sK4(sK4(powerset(X0)))) = set_intersection2(X1,X2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_36428]) ).
tcf(c_38289,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,X2,sK1(sK4(sK4(powerset(X0))))),X1)
| ( sK1(sK4(sK4(powerset(X0)))) = set_intersection2(X1,X2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_54,c_36428]) ).
tcf(c_38295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(sK1(sK4(sK4(powerset(X0)))),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2241,c_36428]) ).
tcf(c_38296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))),X2)
| ( set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2241,c_36428]) ).
tcf(c_38297,plain,
! [X0: $i] :
( ( sK1(sK4(sK4(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5683,c_36428]) ).
tcf(c_38301,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12712,c_36428]) ).
tcf(c_38303,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12713,c_36428]) ).
tcf(c_38304,plain,
! [X0: $i] :
( empty(sK1(sK4(sK4(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36420,c_36428]) ).
tcf(c_38441,plain,
( empty(set_intersection2(relation_dom(sK2),sK12))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_10,sK2)))),sK12) ),
inference(superposition,[status(thm)],[c_6018,c_37574]) ).
tcf(c_38442,plain,
( empty(set_intersection2(relation_dom(sK2),sK11))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_11,sK2)))),sK11) ),
inference(superposition,[status(thm)],[c_6133,c_37574]) ).
tcf(c_38443,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),iPr_def_13) ),
inference(superposition,[status(thm)],[c_6817,c_37574]) ).
tcf(c_38445,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,powerset(X1)))
| ~ empty(X1)
| ~ in(X0,sK1(sK4(set_intersection2(powerset(X1),X2)))) ),
inference(superposition,[status(thm)],[c_37574,c_107]) ).
tcf(c_38446,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X1)
| empty(set_intersection2(X2,powerset(X1)))
| ~ in(X0,sK1(sK4(set_intersection2(powerset(X1),X2)))) ),
inference(superposition,[status(thm)],[c_37574,c_106]) ).
tcf(c_38465,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(X0)))) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_2518]) ).
tcf(c_38466,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(X0)))) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_2517]) ).
tcf(c_38467,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_110]) ).
tcf(c_38468,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(identity_relation(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_14940]) ).
tcf(c_38469,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(relation_dom(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_14939]) ).
tcf(c_38470,plain,
! [X0: $i] :
( ( relation_dom(sK1(sK4(powerset(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_14340]) ).
tcf(c_38471,plain,
! [X0: $i] :
( ( identity_relation(sK1(sK4(powerset(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_14339]) ).
tcf(c_38472,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(identity_relation(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_11512]) ).
tcf(c_38473,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(relation_dom(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_11511]) ).
tcf(c_38474,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(identity_relation(sK1(sK4(sK4(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_9639]) ).
tcf(c_38475,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_9440]) ).
tcf(c_38476,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(identity_relation(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_9238]) ).
tcf(c_38477,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(identity_relation(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_9052]) ).
tcf(c_38478,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(relation_dom(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_11348]) ).
tcf(c_38479,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(relation_dom(sK1(sK4(sK4(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_9638]) ).
tcf(c_38480,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(relation_dom(sK1(sK4(sK4(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_9517]) ).
tcf(c_38481,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_9439]) ).
tcf(c_38482,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(identity_relation(sK1(sK4(sK4(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_8531]) ).
tcf(c_38483,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_9319]) ).
tcf(c_38484,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(relation_dom(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_9237]) ).
tcf(c_38485,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(relation_dom(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_9051]) ).
tcf(c_38486,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(relation_dom(sK1(sK4(sK4(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_8530]) ).
tcf(c_38487,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(identity_relation(sK1(sK4(sK4(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_8457]) ).
tcf(c_38488,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(relation_dom(sK1(sK4(sK4(powerset(X0))))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_8456]) ).
tcf(c_38489,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_8377]) ).
tcf(c_38490,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_8376]) ).
tcf(c_38491,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_8270]) ).
tcf(c_38492,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_8269]) ).
tcf(c_38493,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_7757]) ).
tcf(c_38494,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_7756]) ).
tcf(c_38495,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_7679]) ).
tcf(c_38496,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_7593]) ).
tcf(c_38497,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_7544]) ).
tcf(c_38498,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_5633]) ).
tcf(c_38499,plain,
! [X0: $i] :
( ( sK1(powerset(sK1(powerset(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_5632]) ).
tcf(c_38500,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_5631]) ).
tcf(c_38501,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_4063]) ).
tcf(c_38502,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK1(powerset(sK1(sK4(sK4(powerset(X0)))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_4062]) ).
tcf(c_38503,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_4061]) ).
tcf(c_38504,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_4014]) ).
tcf(c_38505,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,sK1(powerset(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_4013]) ).
tcf(c_38506,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_4012]) ).
tcf(c_38507,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1(powerset(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3936]) ).
tcf(c_38508,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK1(powerset(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3935]) ).
tcf(c_38509,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK1(powerset(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3934]) ).
tcf(c_38510,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3177]) ).
tcf(c_38511,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3176]) ).
tcf(c_38512,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3175]) ).
tcf(c_38513,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3081]) ).
tcf(c_38514,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3080]) ).
tcf(c_38515,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3079]) ).
tcf(c_38516,plain,
! [X0: $i] :
( ( sK1(sK4(powerset(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_14104]) ).
tcf(c_38517,plain,
! [X0: $i] :
( ( sK1(powerset(identity_relation(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_5630]) ).
tcf(c_38518,plain,
! [X0: $i] :
( ( sK1(powerset(relation_dom(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_5629]) ).
tcf(c_38519,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(sK1(sK4(sK4(powerset(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_4060]) ).
tcf(c_38520,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(sK1(sK4(sK4(powerset(X0))))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_4059]) ).
tcf(c_38521,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,identity_relation(sK1(sK4(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_4011]) ).
tcf(c_38522,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(sK1(sK4(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_4010]) ).
tcf(c_38523,plain,
! [X0: $i] :
( ( relation_dom(sK1(powerset(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3938]) ).
tcf(c_38524,plain,
! [X0: $i] :
( ( identity_relation(sK1(powerset(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3937]) ).
tcf(c_38525,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3179]) ).
tcf(c_38526,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3178]) ).
tcf(c_38527,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3083]) ).
tcf(c_38528,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3082]) ).
tcf(c_38529,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(identity_relation(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_2687]) ).
tcf(c_38530,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(relation_dom(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_2686]) ).
tcf(c_38531,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(relation_dom(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_2658]) ).
tcf(c_38532,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_2637]) ).
tcf(c_38533,plain,
! [X0: $i] :
( ( sK1(powerset(sK1(sK4(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3939]) ).
tcf(c_38534,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3180]) ).
tcf(c_38535,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_3084]) ).
tcf(c_38536,plain,
! [X0: $i] :
( ( identity_relation(identity_relation(sK1(sK4(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_2474]) ).
tcf(c_38537,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(sK1(sK4(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_2473]) ).
tcf(c_38538,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1(sK4(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_2055]) ).
tcf(c_38539,plain,
! [X0: $i] :
( ( identity_relation(sK1(sK4(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_2184]) ).
tcf(c_38540,plain,
! [X0: $i] :
( ( relation_dom(sK1(sK4(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_2013]) ).
tcf(c_38542,plain,
! [X0: $i] :
( relation(sK1(sK4(sK4(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_51]) ).
tcf(c_38543,plain,
! [X0: $i] :
( function(sK1(sK4(sK4(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_50]) ).
tcf(c_38937,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(identity_relation(X1),sK1(sK4(sK4(powerset(X0)))))) = set_intersection2(relation_dom(sK1(sK4(sK4(powerset(X0))))),X1) )
| ~ empty(X0)
| ~ relation(sK1(sK4(sK4(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_38543,c_103]) ).
tcf(c_38951,plain,
! [X0: $i] :
( in(sK1(sK4(empty_set)),sK11)
| empty(set_intersection2(relation_dom(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_36033]) ).
tcf(c_38952,plain,
( empty(set_intersection2(empty_set,iPr_def_13))
| in(sK1(sK4(empty_set)),sK11) ),
inference(superposition,[status(thm)],[c_1996,c_36033]) ).
tcf(c_38953,plain,
! [X0: $i] :
( in(sK1(sK4(empty_set)),sK11)
| empty(set_intersection2(identity_relation(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_36033]) ).
tcf(c_38954,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(sK11),sK1(sK4(set_intersection2(X0,iPr_def_13)))) = sK1(sK4(set_intersection2(X0,iPr_def_13))) ) ),
inference(superposition,[status(thm)],[c_36033,c_172]) ).
tcf(c_38955,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ~ in(sK11,sK1(sK4(set_intersection2(X0,iPr_def_13)))) ),
inference(superposition,[status(thm)],[c_36033,c_49]) ).
tcf(c_38957,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| element(sK1(sK4(set_intersection2(X0,iPr_def_13))),sK11) ),
inference(superposition,[status(thm)],[c_36033,c_95]) ).
tcf(c_38964,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(iPr_def_11,sK1(sK4(set_intersection2(X0,iPr_def_13)))) = sK1(sK4(set_intersection2(X0,iPr_def_13))) ) ),
inference(light_normalisation,[status(thm)],[c_38954,c_1148]) ).
tcf(c_38984,plain,
! [X0: $i] :
( in(sK1(sK4(empty_set)),sK12)
| empty(set_intersection2(relation_dom(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_36034]) ).
tcf(c_38985,plain,
( empty(set_intersection2(empty_set,iPr_def_13))
| in(sK1(sK4(empty_set)),sK12) ),
inference(superposition,[status(thm)],[c_1996,c_36034]) ).
tcf(c_38986,plain,
! [X0: $i] :
( in(sK1(sK4(empty_set)),sK12)
| empty(set_intersection2(identity_relation(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_36034]) ).
tcf(c_38987,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(sK12),sK1(sK4(set_intersection2(X0,iPr_def_13)))) = sK1(sK4(set_intersection2(X0,iPr_def_13))) ) ),
inference(superposition,[status(thm)],[c_36034,c_172]) ).
tcf(c_38988,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ~ in(sK12,sK1(sK4(set_intersection2(X0,iPr_def_13)))) ),
inference(superposition,[status(thm)],[c_36034,c_49]) ).
tcf(c_38990,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| element(sK1(sK4(set_intersection2(X0,iPr_def_13))),sK12) ),
inference(superposition,[status(thm)],[c_36034,c_95]) ).
tcf(c_38991,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(sK4(set_intersection2(X0,iPr_def_13))),iPr_def_13)
| ~ in(sK1(sK4(set_intersection2(X0,iPr_def_13))),sK11) ),
inference(superposition,[status(thm)],[c_36034,c_2962]) ).
tcf(c_39001,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(iPr_def_10,sK1(sK4(set_intersection2(X0,iPr_def_13)))) = sK1(sK4(set_intersection2(X0,iPr_def_13))) ) ),
inference(light_normalisation,[status(thm)],[c_38987,c_1147]) ).
tcf(c_39028,plain,
( empty(set_intersection2(iPr_def_13,empty_set))
| in(sK1(sK4(empty_set)),sK11) ),
inference(superposition,[status(thm)],[c_97,c_36200]) ).
tcf(c_39029,plain,
! [X0: $i] :
( in(sK1(sK4(empty_set)),sK11)
| empty(set_intersection2(iPr_def_13,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15801,c_36200]) ).
tcf(c_39030,plain,
! [X0: $i] :
( in(sK1(sK4(empty_set)),sK11)
| empty(set_intersection2(iPr_def_13,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15800,c_36200]) ).
tcf(c_39031,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),sK11) ),
inference(superposition,[status(thm)],[c_6817,c_36200]) ).
tcf(c_39032,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(sK11),sK1(sK4(set_intersection2(iPr_def_13,X0)))) = sK1(sK4(set_intersection2(iPr_def_13,X0))) ) ),
inference(superposition,[status(thm)],[c_36200,c_172]) ).
tcf(c_39033,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ~ in(sK11,sK1(sK4(set_intersection2(iPr_def_13,X0)))) ),
inference(superposition,[status(thm)],[c_36200,c_49]) ).
tcf(c_39035,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| element(sK1(sK4(set_intersection2(iPr_def_13,X0))),sK11) ),
inference(superposition,[status(thm)],[c_36200,c_95]) ).
tcf(c_39042,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),sK11) ),
inference(light_normalisation,[status(thm)],[c_39031,c_6817]) ).
tcf(c_39045,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(iPr_def_11,sK1(sK4(set_intersection2(iPr_def_13,X0)))) = sK1(sK4(set_intersection2(iPr_def_13,X0))) ) ),
inference(light_normalisation,[status(thm)],[c_39032,c_1148]) ).
tcf(c_39103,plain,
! [X0: $i] :
( ( set_intersection2(powerset(empty_set),X0) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15813]) ).
tcf(c_39105,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ in(X0,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15813,c_12244]) ).
tcf(c_39111,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ in(X0,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15813,c_2739]) ).
tcf(c_39117,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| element(sK1(sK4(empty_set)),X0)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_37574]) ).
tcf(c_39118,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| element(sK1(sK4(empty_set)),X0)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_36195]) ).
tcf(c_39119,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| in(sK1(sK4(empty_set)),X1)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_36179]) ).
tcf(c_39120,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| element(sK1(sK4(empty_set)),X1)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_36028]) ).
tcf(c_39121,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| in(sK1(sK4(empty_set)),X0)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_36012]) ).
tcf(c_39122,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| in(sK1(sK4(empty_set)),X0)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_12713]) ).
tcf(c_39123,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| in(sK1(sK4(empty_set)),X1)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_12712]) ).
tcf(c_39143,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,empty_set)
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_15813,c_56]) ).
tcf(c_39147,plain,
( ( empty_set = iPr_def_13 )
| ( apply(identity_relation(sK12),sK1(sK12)) = sK1(sK12) ) ),
inference(superposition,[status(thm)],[c_15813,c_1150]) ).
tcf(c_39148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,empty_set),X2)
| in(sK0(X2,X3,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_2241]) ).
tcf(c_39149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,empty_set),X1)
| in(sK0(X2,X3,set_intersection2(X0,X1)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_2241]) ).
tcf(c_39150,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(sK4(empty_set)),sK11)
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_36200]) ).
tcf(c_39151,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) )
| ~ in(sK12,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15813,c_12899]) ).
tcf(c_39152,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) )
| ~ in(sK11,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15813,c_12879]) ).
tcf(c_39153,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) )
| ~ in(sK12,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15813,c_12662]) ).
tcf(c_39154,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) )
| ~ in(sK11,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15813,c_12628]) ).
tcf(c_39155,plain,
! [X0: $i] :
( element(sK1(empty_set),sK12)
| empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_12901]) ).
tcf(c_39156,plain,
! [X0: $i] :
( element(sK1(empty_set),sK11)
| empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_12853]) ).
tcf(c_39157,plain,
! [X0: $i] :
( element(sK1(empty_set),sK12)
| empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_12664]) ).
tcf(c_39158,plain,
! [X0: $i] :
( element(sK1(empty_set),sK11)
| empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_12630]) ).
tcf(c_39159,plain,
! [X0: $i] :
( in(sK1(empty_set),sK12)
| empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_7924]) ).
tcf(c_39160,plain,
! [X0: $i] :
( in(sK1(empty_set),sK11)
| empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_7923]) ).
tcf(c_39161,plain,
! [X0: $i] :
( in(sK1(empty_set),sK12)
| empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_7268]) ).
tcf(c_39162,plain,
! [X0: $i] :
( in(sK1(empty_set),sK11)
| empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_7267]) ).
tcf(c_39166,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(sK4(empty_set)),sK12)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_36034]) ).
tcf(c_39167,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(sK4(empty_set)),sK11)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_36033]) ).
tcf(c_39168,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(sK12,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15813,c_13894]) ).
tcf(c_39169,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(sK11,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15813,c_13778]) ).
tcf(c_39170,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(sK12,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15813,c_8246]) ).
tcf(c_39171,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ~ in(sK11,sK1(empty_set)) ),
inference(superposition,[status(thm)],[c_15813,c_8221]) ).
tcf(c_39172,plain,
! [X0: $i] :
( element(sK1(empty_set),sK12)
| empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_13896]) ).
tcf(c_39173,plain,
! [X0: $i] :
( element(sK1(empty_set),sK11)
| empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_13659]) ).
tcf(c_39174,plain,
! [X0: $i] :
( in(sK1(empty_set),sK12)
| empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_12252]) ).
tcf(c_39175,plain,
! [X0: $i] :
( in(sK1(empty_set),sK11)
| empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_12251]) ).
tcf(c_39176,plain,
! [X0: $i] :
( element(sK1(empty_set),sK12)
| empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_8248]) ).
tcf(c_39177,plain,
! [X0: $i] :
( element(sK1(empty_set),sK11)
| empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_8223]) ).
tcf(c_39178,plain,
! [X0: $i] :
( in(sK1(empty_set),sK12)
| empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_2747]) ).
tcf(c_39179,plain,
! [X0: $i] :
( in(sK1(empty_set),sK11)
| empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_2746]) ).
tcf(c_39189,plain,
( ( relation_dom(relation_composition(iPr_def_10,sK2)) = empty_set )
| ( apply(identity_relation(sK12),sK1(sK12)) = sK1(sK12) ) ),
inference(superposition,[status(thm)],[c_15813,c_6018]) ).
tcf(c_39190,plain,
( ( relation_dom(relation_composition(iPr_def_11,sK2)) = empty_set )
| ( apply(identity_relation(sK11),sK1(sK11)) = sK1(sK11) ) ),
inference(superposition,[status(thm)],[c_15813,c_6133]) ).
tcf(c_39191,plain,
( ( relation_dom(relation_composition(iPr_def_14,sK2)) = empty_set )
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_6817]) ).
tcf(c_39284,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39143,c_5671]) ).
tcf(c_39366,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| element(sK1(sK4(empty_set)),X1)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_37823]) ).
tcf(c_39376,plain,
( empty(set_intersection2(relation_dom(sK2),sK12))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_10,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6018,c_37823]) ).
tcf(c_39377,plain,
( empty(set_intersection2(relation_dom(sK2),sK11))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_11,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6133,c_37823]) ).
tcf(c_39378,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6817,c_37823]) ).
tcf(c_39380,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(powerset(X2),X1))
| ~ empty(X2)
| ~ in(X0,sK1(sK4(set_intersection2(X1,powerset(X2))))) ),
inference(superposition,[status(thm)],[c_37823,c_107]) ).
tcf(c_39381,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| empty(set_intersection2(powerset(X2),X1))
| ~ in(X0,sK1(sK4(set_intersection2(X1,powerset(X2))))) ),
inference(superposition,[status(thm)],[c_37823,c_106]) ).
tcf(c_39435,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| element(sK1(sK4(empty_set)),sK11)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_38957]) ).
tcf(c_39436,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| element(sK1(sK4(set_intersection2(iPr_def_13,X0))),sK11) ),
inference(superposition,[status(thm)],[c_52,c_38957]) ).
tcf(c_39438,plain,
! [X0: $i] :
( element(sK1(sK4(empty_set)),sK11)
| empty(set_intersection2(relation_dom(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_38957]) ).
tcf(c_39439,plain,
( empty(set_intersection2(empty_set,iPr_def_13))
| element(sK1(sK4(empty_set)),sK11) ),
inference(superposition,[status(thm)],[c_1996,c_38957]) ).
tcf(c_39440,plain,
! [X0: $i] :
( element(sK1(sK4(empty_set)),sK11)
| empty(set_intersection2(identity_relation(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_38957]) ).
tcf(c_39471,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| element(sK1(sK4(empty_set)),sK12)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_38990]) ).
tcf(c_39472,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| element(sK1(sK4(set_intersection2(iPr_def_13,X0))),sK12) ),
inference(superposition,[status(thm)],[c_52,c_38990]) ).
tcf(c_39474,plain,
! [X0: $i] :
( element(sK1(sK4(empty_set)),sK12)
| empty(set_intersection2(relation_dom(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15799,c_38990]) ).
tcf(c_39475,plain,
( empty(set_intersection2(empty_set,iPr_def_13))
| element(sK1(sK4(empty_set)),sK12) ),
inference(superposition,[status(thm)],[c_1996,c_38990]) ).
tcf(c_39476,plain,
! [X0: $i] :
( element(sK1(sK4(empty_set)),sK12)
| empty(set_intersection2(identity_relation(X0),iPr_def_13))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15798,c_38990]) ).
tcf(c_39502,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(sK4(empty_set)),sK12)
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_36201]) ).
tcf(c_39505,plain,
( empty(set_intersection2(iPr_def_13,empty_set))
| in(sK1(sK4(empty_set)),sK12) ),
inference(superposition,[status(thm)],[c_97,c_36201]) ).
tcf(c_39506,plain,
! [X0: $i] :
( in(sK1(sK4(empty_set)),sK12)
| empty(set_intersection2(iPr_def_13,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15801,c_36201]) ).
tcf(c_39507,plain,
! [X0: $i] :
( in(sK1(sK4(empty_set)),sK12)
| empty(set_intersection2(iPr_def_13,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15800,c_36201]) ).
tcf(c_39508,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),sK12) ),
inference(superposition,[status(thm)],[c_6817,c_36201]) ).
tcf(c_39509,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(sK12),sK1(sK4(set_intersection2(iPr_def_13,X0)))) = sK1(sK4(set_intersection2(iPr_def_13,X0))) ) ),
inference(superposition,[status(thm)],[c_36201,c_172]) ).
tcf(c_39510,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ~ in(sK12,sK1(sK4(set_intersection2(iPr_def_13,X0)))) ),
inference(superposition,[status(thm)],[c_36201,c_49]) ).
tcf(c_39512,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| element(sK1(sK4(set_intersection2(iPr_def_13,X0))),sK12) ),
inference(superposition,[status(thm)],[c_36201,c_95]) ).
tcf(c_39513,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(sK4(set_intersection2(iPr_def_13,X0))),iPr_def_13)
| ~ in(sK1(sK4(set_intersection2(iPr_def_13,X0))),sK11) ),
inference(superposition,[status(thm)],[c_36201,c_2962]) ).
tcf(c_39520,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),sK12) ),
inference(light_normalisation,[status(thm)],[c_39508,c_6817]) ).
tcf(c_39527,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(iPr_def_10,sK1(sK4(set_intersection2(iPr_def_13,X0)))) = sK1(sK4(set_intersection2(iPr_def_13,X0))) ) ),
inference(light_normalisation,[status(thm)],[c_39509,c_1147]) ).
tcf(c_39665,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(sK4(empty_set)),sK11)
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_37579]) ).
tcf(c_39671,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),sK11) ),
inference(superposition,[status(thm)],[c_6817,c_37579]) ).
tcf(c_39672,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(sK11),sK1(sK4(set_intersection2(iPr_def_13,X0)))) = sK1(sK4(set_intersection2(iPr_def_13,X0))) ) ),
inference(superposition,[status(thm)],[c_37579,c_172]) ).
tcf(c_39673,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ~ in(sK11,sK1(sK4(set_intersection2(iPr_def_13,X0)))) ),
inference(superposition,[status(thm)],[c_37579,c_49]) ).
tcf(c_39681,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(iPr_def_11,sK1(sK4(set_intersection2(iPr_def_13,X0)))) = sK1(sK4(set_intersection2(iPr_def_13,X0))) ) ),
inference(light_normalisation,[status(thm)],[c_39672,c_1148]) ).
tcf(c_39689,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(sK4(empty_set)),sK12)
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_37580]) ).
tcf(c_39695,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| in(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),sK12) ),
inference(superposition,[status(thm)],[c_6817,c_37580]) ).
tcf(c_39696,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(identity_relation(sK12),sK1(sK4(set_intersection2(iPr_def_13,X0)))) = sK1(sK4(set_intersection2(iPr_def_13,X0))) ) ),
inference(superposition,[status(thm)],[c_37580,c_172]) ).
tcf(c_39697,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ~ in(sK12,sK1(sK4(set_intersection2(iPr_def_13,X0)))) ),
inference(superposition,[status(thm)],[c_37580,c_49]) ).
tcf(c_39700,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| in(sK1(sK4(set_intersection2(iPr_def_13,X0))),iPr_def_13)
| ~ in(sK1(sK4(set_intersection2(iPr_def_13,X0))),sK11) ),
inference(superposition,[status(thm)],[c_37580,c_2962]) ).
tcf(c_39709,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| ( apply(iPr_def_10,sK1(sK4(set_intersection2(iPr_def_13,X0)))) = sK1(sK4(set_intersection2(iPr_def_13,X0))) ) ),
inference(light_normalisation,[status(thm)],[c_39696,c_1147]) ).
tcf(c_39717,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(sK4(empty_set)),sK11)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_37828]) ).
tcf(c_39723,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(sK11),sK1(sK4(set_intersection2(X0,iPr_def_13)))) = sK1(sK4(set_intersection2(X0,iPr_def_13))) ) ),
inference(superposition,[status(thm)],[c_37828,c_172]) ).
tcf(c_39724,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ~ in(sK11,sK1(sK4(set_intersection2(X0,iPr_def_13)))) ),
inference(superposition,[status(thm)],[c_37828,c_49]) ).
tcf(c_39726,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| element(sK1(sK4(set_intersection2(X0,iPr_def_13))),sK11) ),
inference(superposition,[status(thm)],[c_37828,c_95]) ).
tcf(c_39734,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(iPr_def_11,sK1(sK4(set_intersection2(X0,iPr_def_13)))) = sK1(sK4(set_intersection2(X0,iPr_def_13))) ) ),
inference(light_normalisation,[status(thm)],[c_39723,c_1148]) ).
tcf(c_39742,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(sK4(empty_set)),sK12)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15813,c_37829]) ).
tcf(c_39748,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(identity_relation(sK12),sK1(sK4(set_intersection2(X0,iPr_def_13)))) = sK1(sK4(set_intersection2(X0,iPr_def_13))) ) ),
inference(superposition,[status(thm)],[c_37829,c_172]) ).
tcf(c_39749,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ~ in(sK12,sK1(sK4(set_intersection2(X0,iPr_def_13)))) ),
inference(superposition,[status(thm)],[c_37829,c_49]) ).
tcf(c_39751,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| element(sK1(sK4(set_intersection2(X0,iPr_def_13))),sK12) ),
inference(superposition,[status(thm)],[c_37829,c_95]) ).
tcf(c_39752,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| in(sK1(sK4(set_intersection2(X0,iPr_def_13))),iPr_def_13)
| ~ in(sK1(sK4(set_intersection2(X0,iPr_def_13))),sK11) ),
inference(superposition,[status(thm)],[c_37829,c_2962]) ).
tcf(c_39763,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| ( apply(iPr_def_10,sK1(sK4(set_intersection2(X0,iPr_def_13)))) = sK1(sK4(set_intersection2(X0,iPr_def_13))) ) ),
inference(light_normalisation,[status(thm)],[c_39748,c_1147]) ).
tcf(c_39770,plain,
! [X0: $i] :
( ( sK1(sK4(sK4(powerset(X0)))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_38297]) ).
tcf(c_39771,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(relation_composition(X0,X1))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_38297]) ).
tcf(c_39772,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(relation_composition(X1,X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_38297]) ).
tcf(c_39773,plain,
sK1(sK4(sK4(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_38297]) ).
tcf(c_39774,plain,
! [X0: $i] :
( ( sK1(sK4(sK4(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_38297]) ).
tcf(c_39775,plain,
! [X0: $i] :
( ( sK1(sK4(sK4(powerset(identity_relation(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_38297]) ).
tcf(c_39776,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_38297]) ).
tcf(c_39777,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(set_intersection2(X0,X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_38297]) ).
tcf(c_39778,plain,
! [X0: $i] :
( ( sK1(sK4(sK4(powerset(sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_38297]) ).
tcf(c_39779,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_38297]) ).
tcf(c_39780,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(set_intersection2(X1,X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_38297]) ).
tcf(c_39781,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(set_intersection2(X1,sK1(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_38297]) ).
tcf(c_39782,plain,
! [X0: $i] :
( ( sK1(sK4(sK4(powerset(set_intersection2(relation_dom(sK2),X0))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_38297]) ).
tcf(c_39783,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(set_intersection2(sK1(powerset(X0)),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_38297]) ).
tcf(c_39784,plain,
( ( sK1(sK4(sK4(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_38297]) ).
tcf(c_39785,plain,
( ( sK1(sK4(sK4(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_38297]) ).
tcf(c_39786,plain,
( ( sK1(sK4(sK4(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_38297]) ).
tcf(c_39787,plain,
( ( sK1(sK4(sK4(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_38297]) ).
tcf(c_39788,plain,
( ( sK1(sK4(sK4(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_38297]) ).
tcf(c_39789,plain,
( ( sK1(sK4(sK4(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_38297]) ).
tcf(c_39790,plain,
( ( sK1(sK4(sK4(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_38297]) ).
tcf(c_39791,plain,
( ( sK1(sK4(sK4(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_38297]) ).
tcf(c_39792,plain,
( ( sK1(sK4(sK4(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_38297]) ).
tcf(c_39793,plain,
! [X0: $i] :
( ( sK1(sK4(sK4(powerset(sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_38297]) ).
tcf(c_39794,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(set_intersection2(sK1(sK4(powerset(X0))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_38297]) ).
tcf(c_39795,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(set_intersection2(X1,sK1(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_38297]) ).
tcf(c_39796,plain,
! [X0: $i] :
( ( sK1(sK4(sK4(powerset(set_intersection2(X0,relation_dom(sK2)))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_38297]) ).
tcf(c_39797,plain,
! [X0: $i] :
( ( sK1(sK4(sK4(powerset(sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_38297]) ).
tcf(c_39916,plain,
! [X0: $i] :
( ( set_intersection2(sK4(sK4(powerset(empty_set))),X0) = empty_set )
| ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15813]) ).
tcf(c_39917,plain,
( ( sK1(powerset(sK4(sK4(powerset(empty_set))))) = empty_set )
| ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15812]) ).
tcf(c_39918,plain,
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( relation_dom(relation_dom(relation_dom(sK4(sK4(powerset(empty_set)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15811]) ).
tcf(c_39919,plain,
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( identity_relation(relation_dom(relation_dom(sK4(sK4(powerset(empty_set)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15810]) ).
tcf(c_39920,plain,
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( identity_relation(identity_relation(relation_dom(sK4(sK4(powerset(empty_set)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15809]) ).
tcf(c_39921,plain,
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( identity_relation(identity_relation(identity_relation(sK4(sK4(powerset(empty_set)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15808]) ).
tcf(c_39922,plain,
! [X0: $i] :
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( identity_relation(set_intersection2(X0,sK4(sK4(powerset(empty_set))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15807]) ).
tcf(c_39923,plain,
! [X0: $i] :
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( relation_dom(set_intersection2(X0,sK4(sK4(powerset(empty_set))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15806]) ).
tcf(c_39924,plain,
! [X0: $i] :
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( identity_relation(set_intersection2(sK4(sK4(powerset(empty_set))),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15805]) ).
tcf(c_39925,plain,
! [X0: $i] :
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( relation_dom(set_intersection2(sK4(sK4(powerset(empty_set))),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15804]) ).
tcf(c_39926,plain,
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( identity_relation(sK1(powerset(sK4(sK4(powerset(empty_set)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15803]) ).
tcf(c_39927,plain,
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( relation_dom(sK1(powerset(sK4(sK4(powerset(empty_set)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15802]) ).
tcf(c_39928,plain,
! [X0: $i] :
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( set_intersection2(X0,relation_dom(sK4(sK4(powerset(empty_set))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15801]) ).
tcf(c_39929,plain,
! [X0: $i] :
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( set_intersection2(X0,identity_relation(sK4(sK4(powerset(empty_set))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15800]) ).
tcf(c_39930,plain,
! [X0: $i] :
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( set_intersection2(relation_dom(sK4(sK4(powerset(empty_set)))),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15799]) ).
tcf(c_39931,plain,
! [X0: $i] :
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( set_intersection2(identity_relation(sK4(sK4(powerset(empty_set)))),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15798]) ).
tcf(c_39932,plain,
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( sK1(powerset(relation_dom(sK4(sK4(powerset(empty_set)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15797]) ).
tcf(c_39933,plain,
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( sK1(powerset(identity_relation(sK4(sK4(powerset(empty_set)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15796]) ).
tcf(c_39934,plain,
( ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set )
| ( sK1(sK4(powerset(sK4(sK4(powerset(empty_set)))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15795]) ).
tcf(c_39935,plain,
( empty(sK4(sK4(powerset(empty_set))))
| ~ in(sK4(sK4(powerset(empty_set))),empty_set) ),
inference(superposition,[status(thm)],[c_39773,c_2198]) ).
tcf(c_39936,plain,
( empty(sK4(sK4(powerset(empty_set))))
| in(empty_set,sK4(sK4(powerset(empty_set)))) ),
inference(superposition,[status(thm)],[c_39773,c_2137]) ).
tcf(c_39937,plain,
element(empty_set,sK4(sK4(powerset(empty_set)))),
inference(superposition,[status(thm)],[c_39773,c_61]) ).
tcf(c_40070,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,sK1(sK4(sK4(powerset(X0))))) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_2518]) ).
tcf(c_40071,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,sK1(sK4(sK4(powerset(X0))))) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_2517]) ).
tcf(c_40072,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,sK1(sK4(sK4(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_110]) ).
tcf(c_40073,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_38297]) ).
tcf(c_40074,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_14940]) ).
tcf(c_40075,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_14939]) ).
tcf(c_40076,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(sK4(powerset(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_14340]) ).
tcf(c_40077,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(sK4(powerset(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_14339]) ).
tcf(c_40078,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_11512]) ).
tcf(c_40079,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_11511]) ).
tcf(c_40080,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_9639]) ).
tcf(c_40081,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_9440]) ).
tcf(c_40082,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_9238]) ).
tcf(c_40083,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_9052]) ).
tcf(c_40084,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_11348]) ).
tcf(c_40085,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_9638]) ).
tcf(c_40086,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_9517]) ).
tcf(c_40087,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_9439]) ).
tcf(c_40088,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_8531]) ).
tcf(c_40089,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_9319]) ).
tcf(c_40090,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_9237]) ).
tcf(c_40091,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_9051]) ).
tcf(c_40092,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_8530]) ).
tcf(c_40093,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_8457]) ).
tcf(c_40094,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_8456]) ).
tcf(c_40095,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_8377]) ).
tcf(c_40096,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_8376]) ).
tcf(c_40097,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_8270]) ).
tcf(c_40098,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_8269]) ).
tcf(c_40099,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_7757]) ).
tcf(c_40100,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_7756]) ).
tcf(c_40101,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_7679]) ).
tcf(c_40102,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_7593]) ).
tcf(c_40103,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_7544]) ).
tcf(c_40104,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(X1,set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_5633]) ).
tcf(c_40105,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(sK1(powerset(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_5632]) ).
tcf(c_40106,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_5631]) ).
tcf(c_40107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X1,set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_4063]) ).
tcf(c_40108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_4062]) ).
tcf(c_40109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))),X2),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_4061]) ).
tcf(c_40110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X3,sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_4014]) ).
tcf(c_40111,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,sK1(powerset(set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_4013]) ).
tcf(c_40112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(set_intersection2(X2,sK1(sK4(sK4(powerset(X0))))),X3)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_4012]) ).
tcf(c_40113,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1(powerset(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3936]) ).
tcf(c_40114,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK1(powerset(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3935]) ).
tcf(c_40115,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK1(powerset(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3934]) ).
tcf(c_40116,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3177]) ).
tcf(c_40117,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3176]) ).
tcf(c_40118,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3175]) ).
tcf(c_40119,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3081]) ).
tcf(c_40120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3080]) ).
tcf(c_40121,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3079]) ).
tcf(c_40122,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_14104]) ).
tcf(c_40123,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_5630]) ).
tcf(c_40124,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_5629]) ).
tcf(c_40125,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_4060]) ).
tcf(c_40126,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_4059]) ).
tcf(c_40127,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(X2,sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_4011]) ).
tcf(c_40128,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(X2,sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_4010]) ).
tcf(c_40129,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3938]) ).
tcf(c_40130,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3937]) ).
tcf(c_40131,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3179]) ).
tcf(c_40132,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3178]) ).
tcf(c_40133,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(X2,sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3083]) ).
tcf(c_40134,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(X2,sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_3082]) ).
tcf(c_40135,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_2687]) ).
tcf(c_40136,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_2686]) ).
tcf(c_40137,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_2658]) ).
tcf(c_40138,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_2637]) ).
tcf(c_40148,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_51]) ).
tcf(c_40149,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_50]) ).
tcf(c_40804,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( set_intersection2(X2,set_intersection2(X0,X1)) = empty_set )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_15807,c_15814]) ).
tcf(c_40805,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( set_intersection2(X2,set_intersection2(X0,X1)) = empty_set )
| ( apply(empty_set,sK1(set_intersection2(X0,X1))) = sK1(set_intersection2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_15805,c_15814]) ).
tcf(c_40806,plain,
! [X0: $i] :
( ( set_intersection2(X0,powerset(empty_set)) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15814]) ).
tcf(c_40808,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK4(sK4(powerset(empty_set)))) = empty_set )
| ( apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_39773,c_15814]) ).
tcf(c_40848,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,empty_set)
| ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_15814,c_56]) ).
tcf(c_40852,plain,
( ( empty_set = iPr_def_13 )
| ( apply(identity_relation(sK11),sK1(sK11)) = sK1(sK11) ) ),
inference(superposition,[status(thm)],[c_15814,c_1150]) ).
tcf(c_40853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,empty_set),X2)
| in(sK0(X2,X3,set_intersection2(X1,X0)),X0)
| ( set_intersection2(X1,X0) = set_intersection2(X2,X3) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15814,c_2241]) ).
tcf(c_40854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,X3,empty_set),X0)
| in(sK0(X2,X3,set_intersection2(X1,X0)),X2)
| ( set_intersection2(X1,X0) = set_intersection2(X2,X3) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15814,c_2241]) ).
tcf(c_40876,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| element(sK1(sK4(empty_set)),sK12)
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15814,c_38990]) ).
tcf(c_40877,plain,
! [X0: $i] :
( empty(set_intersection2(X0,iPr_def_13))
| element(sK1(sK4(empty_set)),sK11)
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15814,c_38957]) ).
tcf(c_40916,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK1(X2)) = sK1(X2) )
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40848,c_5671]) ).
tcf(c_40939,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| element(sK1(sK4(empty_set)),sK11)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15814,c_39035]) ).
tcf(c_40941,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| element(sK1(sK4(empty_set)),sK11)
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_39035]) ).
tcf(c_40944,plain,
( empty(set_intersection2(iPr_def_13,empty_set))
| element(sK1(sK4(empty_set)),sK11) ),
inference(superposition,[status(thm)],[c_97,c_39035]) ).
tcf(c_40945,plain,
! [X0: $i] :
( element(sK1(sK4(empty_set)),sK11)
| empty(set_intersection2(iPr_def_13,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15801,c_39035]) ).
tcf(c_40946,plain,
! [X0: $i] :
( element(sK1(sK4(empty_set)),sK11)
| empty(set_intersection2(iPr_def_13,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15800,c_39035]) ).
tcf(c_40947,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),sK11) ),
inference(superposition,[status(thm)],[c_6817,c_39035]) ).
tcf(c_40951,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),sK11) ),
inference(light_normalisation,[status(thm)],[c_40947,c_6817]) ).
tcf(c_40980,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),sK11) ),
inference(superposition,[status(thm)],[c_6817,c_39436]) ).
tcf(c_40996,plain,
( empty(set_intersection2(relation_dom(sK2),iPr_def_13))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),sK12) ),
inference(superposition,[status(thm)],[c_6817,c_39472]) ).
tcf(c_41013,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2) = identity_relation(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_2518]) ).
tcf(c_41014,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2) = relation_dom(X1) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_2517]) ).
tcf(c_41015,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_110]) ).
tcf(c_41016,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(sK4(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_38297]) ).
tcf(c_41017,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_14940]) ).
tcf(c_41018,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_14939]) ).
tcf(c_41019,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(sK4(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_14340]) ).
tcf(c_41020,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(sK4(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_14339]) ).
tcf(c_41021,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_11512]) ).
tcf(c_41022,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_11511]) ).
tcf(c_41023,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_9639]) ).
tcf(c_41024,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_9440]) ).
tcf(c_41025,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_9238]) ).
tcf(c_41026,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_9052]) ).
tcf(c_41027,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_11348]) ).
tcf(c_41028,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_9638]) ).
tcf(c_41029,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_9517]) ).
tcf(c_41030,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_9439]) ).
tcf(c_41031,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_8531]) ).
tcf(c_41032,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_9319]) ).
tcf(c_41033,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_9237]) ).
tcf(c_41034,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_9051]) ).
tcf(c_41035,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_8530]) ).
tcf(c_41036,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_8457]) ).
tcf(c_41037,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_8456]) ).
tcf(c_41038,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_8377]) ).
tcf(c_41039,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_8376]) ).
tcf(c_41040,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_8270]) ).
tcf(c_41041,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_8269]) ).
tcf(c_41042,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_7757]) ).
tcf(c_41043,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_7756]) ).
tcf(c_41044,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_7679]) ).
tcf(c_41045,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_7593]) ).
tcf(c_41046,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_7544]) ).
tcf(c_41047,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(X1,set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_5633]) ).
tcf(c_41048,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(sK1(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_5632]) ).
tcf(c_41049,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK1(powerset(set_intersection2(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_5631]) ).
tcf(c_41050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X1,set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_4063]) ).
tcf(c_41051,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK1(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_4062]) ).
tcf(c_41052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1),X2),X3) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_4061]) ).
tcf(c_41053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(X2,set_intersection2(sK1(sK4(sK4(powerset(X0)))),X3))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_4014]) ).
tcf(c_41054,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,sK1(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_4013]) ).
tcf(c_41055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2),X3)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_4012]) ).
tcf(c_41056,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3936]) ).
tcf(c_41057,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(sK1(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3935]) ).
tcf(c_41058,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(sK1(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3934]) ).
tcf(c_41059,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3177]) ).
tcf(c_41060,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3176]) ).
tcf(c_41061,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3175]) ).
tcf(c_41062,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3081]) ).
tcf(c_41063,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(relation_dom(set_intersection2(X1,set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3080]) ).
tcf(c_41064,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(identity_relation(set_intersection2(X1,set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3079]) ).
tcf(c_41065,plain,
! [X0: $i,X1: $i] :
( ( sK1(sK4(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_14104]) ).
tcf(c_41066,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_5630]) ).
tcf(c_41067,plain,
! [X0: $i,X1: $i] :
( ( sK1(powerset(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_5629]) ).
tcf(c_41068,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_4060]) ).
tcf(c_41069,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_4059]) ).
tcf(c_41070,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_4011]) ).
tcf(c_41071,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_4010]) ).
tcf(c_41072,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3938]) ).
tcf(c_41073,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(sK1(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3937]) ).
tcf(c_41074,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3179]) ).
tcf(c_41075,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3178]) ).
tcf(c_41076,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3083]) ).
tcf(c_41077,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_relation(set_intersection2(X1,set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_3082]) ).
tcf(c_41078,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_2687]) ).
tcf(c_41079,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(identity_relation(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_2686]) ).
tcf(c_41080,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(relation_dom(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_2658]) ).
tcf(c_41081,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_2637]) ).
tcf(c_41091,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_51]) ).
tcf(c_41092,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_50]) ).
tcf(c_41354,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| element(sK1(sK4(empty_set)),sK12)
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15814,c_39512]) ).
tcf(c_41356,plain,
! [X0: $i] :
( empty(set_intersection2(iPr_def_13,X0))
| element(sK1(sK4(empty_set)),sK12)
| ( apply(identity_relation(iPr_def_13),sK1(iPr_def_13)) = sK1(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_15813,c_39512]) ).
tcf(c_41359,plain,
( empty(set_intersection2(iPr_def_13,empty_set))
| element(sK1(sK4(empty_set)),sK12) ),
inference(superposition,[status(thm)],[c_97,c_39512]) ).
tcf(c_41360,plain,
! [X0: $i] :
( element(sK1(sK4(empty_set)),sK12)
| empty(set_intersection2(iPr_def_13,relation_dom(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15801,c_39512]) ).
tcf(c_41361,plain,
! [X0: $i] :
( element(sK1(sK4(empty_set)),sK12)
| empty(set_intersection2(iPr_def_13,identity_relation(X0)))
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15800,c_39512]) ).
tcf(c_41362,plain,
( empty(set_intersection2(iPr_def_13,relation_dom(sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),sK12) ),
inference(superposition,[status(thm)],[c_6817,c_39512]) ).
tcf(c_41366,plain,
( empty(relation_dom(relation_composition(iPr_def_14,sK2)))
| element(sK1(sK4(relation_dom(relation_composition(iPr_def_14,sK2)))),sK12) ),
inference(light_normalisation,[status(thm)],[c_41362,c_6817]) ).
tcf(c_41409,plain,
in(empty_set,sK4(sK4(powerset(empty_set)))),
inference(global_subsumption_just,[status(thm)],[c_39936,c_117,c_2352,c_2914,c_5401,c_39937]) ).
tcf(c_41411,plain,
apply(identity_relation(sK4(sK4(powerset(empty_set)))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_41409,c_172]) ).
tcf(c_41412,plain,
~ in(sK4(sK4(powerset(empty_set))),empty_set),
inference(superposition,[status(thm)],[c_41409,c_49]) ).
tcf(c_41413,plain,
~ empty(sK4(sK4(powerset(empty_set)))),
inference(superposition,[status(thm)],[c_41409,c_109]) ).
tcf(c_41416,plain,
apply(identity_relation(sK4(sK4(powerset(empty_set)))),sK1(sK4(sK4(powerset(empty_set))))) = sK1(sK4(sK4(powerset(empty_set)))),
inference(superposition,[status(thm)],[c_2544,c_41413]) ).
tcf(c_41444,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(identity_relation(X2),set_intersection2(X0,sK1(sK4(sK4(powerset(X1))))))) = set_intersection2(relation_dom(set_intersection2(X0,sK1(sK4(sK4(powerset(X1)))))),X2) )
| ~ empty(X1)
| ~ relation(set_intersection2(X0,sK1(sK4(sK4(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_40149,c_103]) ).
tcf(c_41475,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_composition(identity_relation(X2),set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))) = set_intersection2(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)),X2) )
| ~ empty(X0)
| ~ relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)) ),
inference(superposition,[status(thm)],[c_41092,c_103]) ).
tcf(c_41486,plain,
( ( identity_relation(identity_relation(empty_set)) = empty_set )
| ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) ) ),
inference(superposition,[status(thm)],[c_2472,c_15815]) ).
tcf(c_41490,plain,
( ( identity_relation(identity_relation(powerset(empty_set))) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15815]) ).
tcf(c_41498,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ( apply(identity_relation(X0),sK0(X0,X1,X0)) = sK0(X0,X1,X0) ) ),
inference(superposition,[status(thm)],[c_2253,c_172]) ).
tcf(c_41499,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ in(X0,sK0(X0,X1,X0)) ),
inference(superposition,[status(thm)],[c_2253,c_49]) ).
tcf(c_41500,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2253,c_109]) ).
tcf(c_41501,plain,
! [X0: $i,X1: $i] :
( element(sK0(X0,X1,X0),X0)
| ( set_intersection2(X0,X1) = X0 ) ),
inference(superposition,[status(thm)],[c_2253,c_95]) ).
tcf(c_41503,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_2253,c_58]) ).
tcf(c_41504,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_2253,c_57]) ).
tcf(c_41505,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_composition(X0,X1)),X2) = relation_dom(relation_composition(X0,X1)) )
| ( apply(relation_composition(X0,X1),sK0(relation_dom(relation_composition(X0,X1)),X2,relation_dom(relation_composition(X0,X1)))) = apply(X1,apply(X0,sK0(relation_dom(relation_composition(X0,X1)),X2,relation_dom(relation_composition(X0,X1))))) )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_2253,c_96]) ).
tcf(c_41507,plain,
! [X0: $i] :
( in(sK0(iPr_def_13,X0,iPr_def_13),sK11)
| ( set_intersection2(iPr_def_13,X0) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2253,c_2102]) ).
tcf(c_41508,plain,
! [X0: $i] :
( in(sK0(iPr_def_13,X0,iPr_def_13),sK12)
| ( set_intersection2(iPr_def_13,X0) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2253,c_2071]) ).
tcf(c_41509,plain,
! [X0: $i] :
( in(sK0(sK12,X0,sK12),iPr_def_13)
| ( set_intersection2(sK12,X0) = sK12 )
| ~ in(sK0(sK12,X0,sK12),sK11) ),
inference(superposition,[status(thm)],[c_2253,c_2962]) ).
tcf(c_41510,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK1(powerset(X0)),X1) = sK1(powerset(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2253,c_2933]) ).
tcf(c_41511,plain,
! [X0: $i,X1: $i] :
( element(sK0(sK1(powerset(X0)),X1,sK1(powerset(X0))),X0)
| ( set_intersection2(sK1(powerset(X0)),X1) = sK1(powerset(X0)) ) ),
inference(superposition,[status(thm)],[c_2253,c_2582]) ).
tcf(c_41512,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(sK0(sK4(X0),X1,sK4(X0)),X0)
| ( set_intersection2(sK4(X0),X1) = sK4(X0) ) ),
inference(superposition,[status(thm)],[c_2253,c_2583]) ).
tcf(c_41513,plain,
! [X0: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_10,sK2)),X0,relation_dom(relation_composition(iPr_def_10,sK2))),relation_dom(sK2))
| ( set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = relation_dom(relation_composition(iPr_def_10,sK2)) ) ),
inference(superposition,[status(thm)],[c_2253,c_6028]) ).
tcf(c_41514,plain,
! [X0: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_10,sK2)),X0,relation_dom(relation_composition(iPr_def_10,sK2))),sK12)
| ( set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = relation_dom(relation_composition(iPr_def_10,sK2)) ) ),
inference(superposition,[status(thm)],[c_2253,c_6029]) ).
tcf(c_41515,plain,
! [X0: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_11,sK2)),X0,relation_dom(relation_composition(iPr_def_11,sK2))),relation_dom(sK2))
| ( set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = relation_dom(relation_composition(iPr_def_11,sK2)) ) ),
inference(superposition,[status(thm)],[c_2253,c_6143]) ).
tcf(c_41516,plain,
! [X0: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_11,sK2)),X0,relation_dom(relation_composition(iPr_def_11,sK2))),sK11)
| ( set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = relation_dom(relation_composition(iPr_def_11,sK2)) ) ),
inference(superposition,[status(thm)],[c_2253,c_6144]) ).
tcf(c_41517,plain,
! [X0: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_14,sK2)),X0,relation_dom(relation_composition(iPr_def_14,sK2))),relation_dom(sK2))
| ( set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = relation_dom(relation_composition(iPr_def_14,sK2)) ) ),
inference(superposition,[status(thm)],[c_2253,c_6827]) ).
tcf(c_41518,plain,
! [X0: $i] :
( in(sK0(relation_dom(relation_composition(iPr_def_14,sK2)),X0,relation_dom(relation_composition(iPr_def_14,sK2))),iPr_def_13)
| ( set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = relation_dom(relation_composition(iPr_def_14,sK2)) ) ),
inference(superposition,[status(thm)],[c_2253,c_6828]) ).
tcf(c_41519,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK1(sK4(powerset(X0))),X1) = sK1(sK4(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2253,c_12699]) ).
tcf(c_41520,plain,
! [X0: $i,X1: $i] :
( element(sK0(sK1(sK4(powerset(X0))),X1,sK1(sK4(powerset(X0)))),X0)
| ( set_intersection2(sK1(sK4(powerset(X0))),X1) = sK1(sK4(powerset(X0))) ) ),
inference(superposition,[status(thm)],[c_2253,c_12696]) ).
tcf(c_41521,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1) = sK1(sK4(sK4(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2253,c_36428]) ).
tcf(c_41522,plain,
! [X0: $i,X1: $i] :
( element(sK0(sK1(sK4(sK4(powerset(X0)))),X1,sK1(sK4(sK4(powerset(X0))))),X0)
| ( set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1) = sK1(sK4(sK4(powerset(X0)))) ) ),
inference(superposition,[status(thm)],[c_2253,c_36425]) ).
tcf(c_41634,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_41500]) ).
tcf(c_41635,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_composition(X0,X1),X2) = relation_composition(X0,X1) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_41500]) ).
tcf(c_41636,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_composition(X1,X0),X2) = relation_composition(X1,X0) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_41500]) ).
tcf(c_41638,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(X0),X1) = relation_dom(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_41500]) ).
tcf(c_41639,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(X0),X1) = identity_relation(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_41500]) ).
tcf(c_41640,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_41500]) ).
tcf(c_41641,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_41500]) ).
tcf(c_41643,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,X0),X2) = set_intersection2(X1,X0) )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_41500]) ).
tcf(c_41644,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,X0),X2) = set_intersection2(X1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_41500]) ).
tcf(c_41645,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,sK1(powerset(X0))),X2) = set_intersection2(X1,sK1(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_41500]) ).
tcf(c_41646,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(relation_dom(sK2),X0),X1) = set_intersection2(relation_dom(sK2),X0) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_41500]) ).
tcf(c_41647,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(sK1(powerset(X0)),X1),X2) = set_intersection2(sK1(powerset(X0)),X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_41500]) ).
tcf(c_41648,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = relation_dom(relation_composition(iPr_def_10,sK2)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_41500]) ).
tcf(c_41649,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = relation_dom(relation_composition(iPr_def_10,sK2)) )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_41500]) ).
tcf(c_41650,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = relation_dom(relation_composition(iPr_def_10,sK2)) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_41500]) ).
tcf(c_41651,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = relation_dom(relation_composition(iPr_def_11,sK2)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_41500]) ).
tcf(c_41652,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = relation_dom(relation_composition(iPr_def_11,sK2)) )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_41500]) ).
tcf(c_41653,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = relation_dom(relation_composition(iPr_def_11,sK2)) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_41500]) ).
tcf(c_41654,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = relation_dom(relation_composition(iPr_def_14,sK2)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_41500]) ).
tcf(c_41655,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = relation_dom(relation_composition(iPr_def_14,sK2)) )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_41500]) ).
tcf(c_41656,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = relation_dom(relation_composition(iPr_def_14,sK2)) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_41500]) ).
tcf(c_41658,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(sK1(sK4(powerset(X0))),X1),X2) = set_intersection2(sK1(sK4(powerset(X0))),X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_41500]) ).
tcf(c_41659,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,sK1(sK4(powerset(X0)))),X2) = set_intersection2(X1,sK1(sK4(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_41500]) ).
tcf(c_41660,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,relation_dom(sK2)),X1) = set_intersection2(X0,relation_dom(sK2)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_41500]) ).
tcf(c_41662,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1),X2) = set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_41500]) ).
tcf(c_41663,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))),X2) = set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_41500]) ).
tcf(c_41845,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(X0),X1) = relation_dom(X0) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_41638]) ).
tcf(c_41846,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_composition(X0,X1)),X2) = relation_dom(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_41638]) ).
tcf(c_41847,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(relation_composition(X1,X0)),X2) = relation_dom(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_41638]) ).
tcf(c_41848,plain,
! [X0: $i] : set_intersection2(relation_dom(empty_set),X0) = relation_dom(empty_set),
inference(superposition,[status(thm)],[c_73,c_41638]) ).
tcf(c_41849,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(relation_dom(X0)),X1) = relation_dom(relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_41638]) ).
tcf(c_41850,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(identity_relation(X0)),X1) = relation_dom(identity_relation(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_41638]) ).
tcf(c_41851,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X0,X1)),X2) = relation_dom(set_intersection2(X0,X1)) )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_41638]) ).
tcf(c_41852,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X0,X1)),X2) = relation_dom(set_intersection2(X0,X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_41638]) ).
tcf(c_41853,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(sK1(powerset(X0))),X1) = relation_dom(sK1(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_41638]) ).
tcf(c_41854,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X1,X0)),X2) = relation_dom(set_intersection2(X1,X0)) )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_41638]) ).
tcf(c_41855,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X1,X0)),X2) = relation_dom(set_intersection2(X1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_41638]) ).
tcf(c_41856,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X1,sK1(powerset(X0)))),X2) = relation_dom(set_intersection2(X1,sK1(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_41638]) ).
tcf(c_41857,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(set_intersection2(relation_dom(sK2),X0)),X1) = relation_dom(set_intersection2(relation_dom(sK2),X0)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_41638]) ).
tcf(c_41858,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(sK1(powerset(X0)),X1)),X2) = relation_dom(set_intersection2(sK1(powerset(X0)),X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_41638]) ).
tcf(c_41859,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0) = relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_41638]) ).
tcf(c_41860,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0) = relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))) )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_41638]) ).
tcf(c_41861,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),X0) = relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_41638]) ).
tcf(c_41862,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0) = relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_41638]) ).
tcf(c_41863,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0) = relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))) )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_41638]) ).
tcf(c_41864,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),X0) = relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_41638]) ).
tcf(c_41865,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0) = relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_41638]) ).
tcf(c_41866,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0) = relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))) )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_41638]) ).
tcf(c_41867,plain,
! [X0: $i] :
( ( set_intersection2(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),X0) = relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_41638]) ).
tcf(c_41868,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(sK1(sK4(powerset(X0)))),X1) = relation_dom(sK1(sK4(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_41638]) ).
tcf(c_41869,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1)),X2) = relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_41638]) ).
tcf(c_41870,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0))))),X2) = relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_41638]) ).
tcf(c_41871,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X0,relation_dom(sK2))),X1) = relation_dom(set_intersection2(X0,relation_dom(sK2))) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_41638]) ).
tcf(c_41872,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(sK1(sK4(sK4(powerset(X0))))),X1) = relation_dom(sK1(sK4(sK4(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_41638]) ).
tcf(c_41873,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)),X2) = relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_41638]) ).
tcf(c_41874,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))),X2) = relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_41638]) ).
tcf(c_42148,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,X1) = empty_set )
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_2544,c_2311]) ).
tcf(c_42149,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X2,relation_composition(X0,X1)) = empty_set )
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_2311]) ).
tcf(c_42150,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X2,relation_composition(X1,X0)) = empty_set )
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_2311]) ).
tcf(c_42151,plain,
! [X0: $i] :
( ( relation_composition(X0,empty_set) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_73,c_2311]) ).
tcf(c_42152,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,relation_dom(X0)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_2311]) ).
tcf(c_42153,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,identity_relation(X0)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_2311]) ).
tcf(c_42154,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,set_intersection2(X0,X2)) = empty_set )
| ~ relation(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_2311]) ).
tcf(c_42155,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,set_intersection2(X0,X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_2311]) ).
tcf(c_42156,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,sK1(powerset(X0))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_2311]) ).
tcf(c_42157,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,set_intersection2(X2,X0)) = empty_set )
| ~ relation(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_2311]) ).
tcf(c_42158,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,set_intersection2(X2,X0)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_2311]) ).
tcf(c_42159,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,set_intersection2(X2,sK1(powerset(X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_2311]) ).
tcf(c_42160,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,set_intersection2(relation_dom(sK2),X1)) = empty_set )
| ~ empty(sK2)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17673,c_2311]) ).
tcf(c_42161,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,set_intersection2(sK1(powerset(X0)),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_2311]) ).
tcf(c_42162,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ empty(sK2)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17955,c_2311]) ).
tcf(c_42163,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ relation(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_2311]) ).
tcf(c_42164,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ relation(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_2311]) ).
tcf(c_42165,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ empty(sK2)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17956,c_2311]) ).
tcf(c_42166,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ relation(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_2311]) ).
tcf(c_42167,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ relation(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_2311]) ).
tcf(c_42168,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ empty(sK2)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17957,c_2311]) ).
tcf(c_42169,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ relation(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_2311]) ).
tcf(c_42170,plain,
! [X0: $i] :
( ( relation_composition(X0,relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ relation(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_2311]) ).
tcf(c_42171,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,sK1(sK4(powerset(X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_2311]) ).
tcf(c_42172,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,set_intersection2(sK1(sK4(powerset(X0))),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_2311]) ).
tcf(c_42173,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,set_intersection2(X2,sK1(sK4(powerset(X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_2311]) ).
tcf(c_42174,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,set_intersection2(X1,relation_dom(sK2))) = empty_set )
| ~ empty(sK2)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17695,c_2311]) ).
tcf(c_42175,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,sK1(sK4(sK4(powerset(X0))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_2311]) ).
tcf(c_42176,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_2311]) ).
tcf(c_42177,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_2311]) ).
tcf(c_42452,plain,
! [X0: $i] :
( ( relation_composition(X0,empty_set) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15821,c_42151]) ).
tcf(c_42453,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_composition(X1,X0),empty_set) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_63,c_42151]) ).
tcf(c_42454,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_composition(X1,X0),empty_set) = empty_set )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_42151]) ).
tcf(c_42456,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_composition(X0,X1),empty_set) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_79,c_42151]) ).
tcf(c_42458,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(X1,X0),empty_set) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20751,c_42151]) ).
tcf(c_42459,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(X1,X0),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3085,c_42151]) ).
tcf(c_42460,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(X1,X0),empty_set) = empty_set )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_42151]) ).
tcf(c_42461,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(X0),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_77,c_42151]) ).
tcf(c_42462,plain,
relation_composition(sK2,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_81,c_42151]) ).
tcf(c_42463,plain,
relation_composition(sK6,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_89,c_42151]) ).
tcf(c_42464,plain,
relation_composition(sK9,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_93,c_42151]) ).
tcf(c_42468,plain,
relation_composition(iPr_def_12,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_2156,c_42151]) ).
tcf(c_42469,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(X0,X1),empty_set) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20748,c_42151]) ).
tcf(c_42470,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(X0,X1),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3181,c_42151]) ).
tcf(c_42471,plain,
! [X0: $i] :
( ( relation_composition(sK1(powerset(X0)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3940,c_42151]) ).
tcf(c_42472,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(relation_dom(sK2),X0),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17396,c_42151]) ).
tcf(c_42473,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(X1,sK1(powerset(X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5587,c_42151]) ).
tcf(c_42474,plain,
( ( relation_composition(relation_dom(relation_composition(iPr_def_10,sK2)),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17426,c_42151]) ).
tcf(c_42475,plain,
( ( relation_composition(relation_dom(relation_composition(iPr_def_10,sK2)),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10963,c_42151]) ).
tcf(c_42476,plain,
( ( relation_composition(relation_dom(relation_composition(iPr_def_10,sK2)),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6020,c_42151]) ).
tcf(c_42477,plain,
( ( relation_composition(relation_dom(relation_composition(iPr_def_11,sK2)),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17427,c_42151]) ).
tcf(c_42478,plain,
( ( relation_composition(relation_dom(relation_composition(iPr_def_11,sK2)),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_9976,c_42151]) ).
tcf(c_42479,plain,
( ( relation_composition(relation_dom(relation_composition(iPr_def_11,sK2)),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6135,c_42151]) ).
tcf(c_42480,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(sK1(powerset(X0)),X1),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6506,c_42151]) ).
tcf(c_42481,plain,
( ( relation_composition(relation_dom(relation_composition(iPr_def_14,sK2)),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17428,c_42151]) ).
tcf(c_42482,plain,
( ( relation_composition(relation_dom(relation_composition(iPr_def_14,sK2)),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8196,c_42151]) ).
tcf(c_42483,plain,
( ( relation_composition(relation_dom(relation_composition(iPr_def_14,sK2)),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6819,c_42151]) ).
tcf(c_42484,plain,
! [X0: $i] :
( ( relation_composition(sK1(sK4(powerset(X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14342,c_42151]) ).
tcf(c_42485,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(X1,sK1(sK4(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14598,c_42151]) ).
tcf(c_42486,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(sK1(sK4(powerset(X0))),X1),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14748,c_42151]) ).
tcf(c_42487,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(X0,relation_dom(sK2)),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17408,c_42151]) ).
tcf(c_42488,plain,
! [X0: $i] :
( ( relation_composition(sK1(sK4(sK4(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38542,c_42151]) ).
tcf(c_42489,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_40148,c_42151]) ).
tcf(c_42490,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_41091,c_42151]) ).
tcf(c_42595,plain,
! [X0: $i] :
( ( apply(relation_composition(sK2,empty_set),X0) = apply(empty_set,apply(sK2,X0)) )
| ~ relation(sK2)
| ~ relation(empty_set)
| ~ function(sK2)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_42462,c_96]) ).
tcf(c_42596,plain,
! [X0: $i] :
( ( apply(empty_set,apply(sK2,X0)) = apply(empty_set,X0) )
| ~ relation(sK2)
| ~ relation(empty_set)
| ~ function(sK2)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_42595,c_2054,c_42462]) ).
tcf(c_42605,plain,
! [X0: $i] :
( ( apply(relation_composition(sK6,empty_set),X0) = apply(empty_set,apply(sK6,X0)) )
| ~ relation(sK6)
| ~ relation(empty_set)
| ~ function(sK6)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_42463,c_96]) ).
tcf(c_42606,plain,
! [X0: $i] :
( ( apply(empty_set,apply(sK6,X0)) = apply(empty_set,X0) )
| ~ relation(sK6)
| ~ relation(empty_set)
| ~ function(sK6)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_42605,c_2054,c_42463]) ).
tcf(c_42615,plain,
! [X0: $i] :
( ( apply(relation_composition(sK9,empty_set),X0) = apply(empty_set,apply(sK9,X0)) )
| ~ relation(sK9)
| ~ relation(empty_set)
| ~ function(sK9)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_42464,c_96]) ).
tcf(c_42616,plain,
! [X0: $i] :
( ( apply(empty_set,apply(sK9,X0)) = apply(empty_set,X0) )
| ~ relation(sK9)
| ~ relation(empty_set)
| ~ function(sK9)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_42615,c_2054,c_42464]) ).
tcf(c_42625,plain,
! [X0: $i] :
( ( apply(relation_composition(iPr_def_12,empty_set),X0) = apply(empty_set,apply(iPr_def_12,X0)) )
| ~ relation(iPr_def_12)
| ~ relation(empty_set)
| ~ function(iPr_def_12)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_42468,c_96]) ).
tcf(c_42626,plain,
! [X0: $i] :
( ( apply(empty_set,apply(iPr_def_12,X0)) = apply(empty_set,X0) )
| ~ relation(iPr_def_12)
| ~ relation(empty_set)
| ~ function(iPr_def_12)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_42625,c_2054,c_42468]) ).
tcf(c_42631,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(X0),empty_set) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_42461]) ).
tcf(c_42632,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_composition(X0,X1)),empty_set) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_42461]) ).
tcf(c_42633,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_composition(X1,X0)),empty_set) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_42461]) ).
tcf(c_42634,plain,
relation_composition(relation_dom(empty_set),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_73,c_42461]) ).
tcf(c_42635,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(X0)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_42461]) ).
tcf(c_42636,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(identity_relation(X0)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_42461]) ).
tcf(c_42637,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(set_intersection2(X0,X1)),empty_set) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_42461]) ).
tcf(c_42638,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(set_intersection2(X0,X1)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_42461]) ).
tcf(c_42639,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK1(powerset(X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_42461]) ).
tcf(c_42640,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(set_intersection2(X1,X0)),empty_set) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_42461]) ).
tcf(c_42641,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(set_intersection2(X1,X0)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_42461]) ).
tcf(c_42642,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(set_intersection2(X1,sK1(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_42461]) ).
tcf(c_42643,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(set_intersection2(relation_dom(sK2),X0)),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_42461]) ).
tcf(c_42644,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(set_intersection2(sK1(powerset(X0)),X1)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_42461]) ).
tcf(c_42645,plain,
( ( relation_composition(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_42461]) ).
tcf(c_42646,plain,
( ( relation_composition(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_42461]) ).
tcf(c_42647,plain,
( ( relation_composition(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_42461]) ).
tcf(c_42648,plain,
( ( relation_composition(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_42461]) ).
tcf(c_42649,plain,
( ( relation_composition(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_42461]) ).
tcf(c_42650,plain,
( ( relation_composition(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_42461]) ).
tcf(c_42651,plain,
( ( relation_composition(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_42461]) ).
tcf(c_42652,plain,
( ( relation_composition(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_42461]) ).
tcf(c_42653,plain,
( ( relation_composition(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_42461]) ).
tcf(c_42654,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK1(sK4(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_42461]) ).
tcf(c_42655,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_42461]) ).
tcf(c_42656,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_42461]) ).
tcf(c_42657,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(set_intersection2(X0,relation_dom(sK2))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_42461]) ).
tcf(c_42658,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(sK1(sK4(sK4(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_42461]) ).
tcf(c_42659,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_42461]) ).
tcf(c_42660,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_42461]) ).
tcf(c_42662,plain,
! [X0: $i] :
( ( relation_composition(X0,empty_set) = empty_set )
| ~ empty(X0) ),
inference(light_normalisation,[status(thm)],[c_42636,c_144]) ).
tcf(c_42808,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(X0),X1) = identity_relation(X0) )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_41639]) ).
tcf(c_42809,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_composition(X0,X1)),X2) = identity_relation(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_41639]) ).
tcf(c_42810,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(relation_composition(X1,X0)),X2) = identity_relation(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_41639]) ).
tcf(c_42811,plain,
! [X0: $i] : set_intersection2(identity_relation(empty_set),X0) = identity_relation(empty_set),
inference(superposition,[status(thm)],[c_73,c_41639]) ).
tcf(c_42812,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(relation_dom(X0)),X1) = identity_relation(relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_41639]) ).
tcf(c_42813,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(identity_relation(X0)),X1) = identity_relation(identity_relation(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_41639]) ).
tcf(c_42814,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X0,X1)),X2) = identity_relation(set_intersection2(X0,X1)) )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_41639]) ).
tcf(c_42815,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X0,X1)),X2) = identity_relation(set_intersection2(X0,X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_41639]) ).
tcf(c_42816,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(sK1(powerset(X0))),X1) = identity_relation(sK1(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_41639]) ).
tcf(c_42817,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X1,X0)),X2) = identity_relation(set_intersection2(X1,X0)) )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_41639]) ).
tcf(c_42818,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X1,X0)),X2) = identity_relation(set_intersection2(X1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_41639]) ).
tcf(c_42819,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X1,sK1(powerset(X0)))),X2) = identity_relation(set_intersection2(X1,sK1(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_41639]) ).
tcf(c_42820,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(set_intersection2(relation_dom(sK2),X0)),X1) = identity_relation(set_intersection2(relation_dom(sK2),X0)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_41639]) ).
tcf(c_42821,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(sK1(powerset(X0)),X1)),X2) = identity_relation(set_intersection2(sK1(powerset(X0)),X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_41639]) ).
tcf(c_42822,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))),X0) = identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_41639]) ).
tcf(c_42823,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))),X0) = identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))) )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_41639]) ).
tcf(c_42824,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))),X0) = identity_relation(relation_dom(relation_composition(iPr_def_10,sK2))) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_41639]) ).
tcf(c_42825,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))),X0) = identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_41639]) ).
tcf(c_42826,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))),X0) = identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))) )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_41639]) ).
tcf(c_42827,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))),X0) = identity_relation(relation_dom(relation_composition(iPr_def_11,sK2))) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_41639]) ).
tcf(c_42828,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))),X0) = identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_41639]) ).
tcf(c_42829,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))),X0) = identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))) )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_41639]) ).
tcf(c_42830,plain,
! [X0: $i] :
( ( set_intersection2(identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))),X0) = identity_relation(relation_dom(relation_composition(iPr_def_14,sK2))) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_41639]) ).
tcf(c_42831,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(sK1(sK4(powerset(X0)))),X1) = identity_relation(sK1(sK4(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_41639]) ).
tcf(c_42832,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1)),X2) = identity_relation(set_intersection2(sK1(sK4(powerset(X0))),X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_41639]) ).
tcf(c_42833,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0))))),X2) = identity_relation(set_intersection2(X1,sK1(sK4(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_41639]) ).
tcf(c_42834,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X0,relation_dom(sK2))),X1) = identity_relation(set_intersection2(X0,relation_dom(sK2))) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_41639]) ).
tcf(c_42835,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(identity_relation(sK1(sK4(sK4(powerset(X0))))),X1) = identity_relation(sK1(sK4(sK4(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_41639]) ).
tcf(c_42836,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)),X2) = identity_relation(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_41639]) ).
tcf(c_42837,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))),X2) = identity_relation(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_41639]) ).
tcf(c_42983,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_composition(set_intersection2(X0,X1),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_42459]) ).
tcf(c_42984,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X2,relation_composition(X0,X1)),empty_set) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_42459]) ).
tcf(c_42985,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X2,relation_composition(X1,X0)),empty_set) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_42459]) ).
tcf(c_42986,plain,
! [X0: $i] : relation_composition(set_intersection2(X0,empty_set),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_73,c_42459]) ).
tcf(c_42987,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(X1,relation_dom(X0)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_42459]) ).
tcf(c_42988,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(X1,identity_relation(X0)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_42459]) ).
tcf(c_42989,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X1,set_intersection2(X0,X2)),empty_set) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_42459]) ).
tcf(c_42990,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X1,set_intersection2(X0,X2)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_42459]) ).
tcf(c_42992,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X1,set_intersection2(X2,X0)),empty_set) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_42459]) ).
tcf(c_42993,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X1,set_intersection2(X2,X0)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_42459]) ).
tcf(c_42994,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X1,set_intersection2(X2,sK1(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_42459]) ).
tcf(c_42995,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(X0,set_intersection2(relation_dom(sK2),X1)),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_42459]) ).
tcf(c_42996,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X1,set_intersection2(sK1(powerset(X0)),X2)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_42459]) ).
tcf(c_42997,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_42459]) ).
tcf(c_42998,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_42459]) ).
tcf(c_42999,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2))),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_42459]) ).
tcf(c_43000,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_42459]) ).
tcf(c_43001,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_42459]) ).
tcf(c_43002,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2))),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_42459]) ).
tcf(c_43003,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_42459]) ).
tcf(c_43004,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_42459]) ).
tcf(c_43005,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2))),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_42459]) ).
tcf(c_43007,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X1,set_intersection2(sK1(sK4(powerset(X0))),X2)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_42459]) ).
tcf(c_43008,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X1,set_intersection2(X2,sK1(sK4(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_42459]) ).
tcf(c_43009,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(X0,set_intersection2(X1,relation_dom(sK2))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_42459]) ).
tcf(c_43011,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X1,set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2)),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_42459]) ).
tcf(c_43012,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X1,set_intersection2(X2,sK1(sK4(sK4(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_42459]) ).
tcf(c_43191,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_composition(set_intersection2(X0,X1),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_42470]) ).
tcf(c_43192,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(relation_composition(X0,X1),X2),empty_set) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_42470]) ).
tcf(c_43193,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(relation_composition(X1,X0),X2),empty_set) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_42470]) ).
tcf(c_43194,plain,
! [X0: $i] : relation_composition(set_intersection2(empty_set,X0),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_73,c_42470]) ).
tcf(c_43195,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(relation_dom(X0),X1),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_42470]) ).
tcf(c_43196,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(identity_relation(X0),X1),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_42470]) ).
tcf(c_43197,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(set_intersection2(X0,X1),X2),empty_set) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_42470]) ).
tcf(c_43198,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(set_intersection2(X0,X1),X2),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_42470]) ).
tcf(c_43200,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(set_intersection2(X1,X0),X2),empty_set) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_42470]) ).
tcf(c_43201,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(set_intersection2(X1,X0),X2),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_42470]) ).
tcf(c_43202,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(set_intersection2(X1,sK1(powerset(X0))),X2),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_42470]) ).
tcf(c_43203,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(set_intersection2(relation_dom(sK2),X0),X1),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_42470]) ).
tcf(c_43204,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(set_intersection2(sK1(powerset(X0)),X1),X2),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_42470]) ).
tcf(c_43205,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_42470]) ).
tcf(c_43206,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_42470]) ).
tcf(c_43207,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_42470]) ).
tcf(c_43208,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_42470]) ).
tcf(c_43209,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_42470]) ).
tcf(c_43210,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_42470]) ).
tcf(c_43211,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_42470]) ).
tcf(c_43212,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_42470]) ).
tcf(c_43213,plain,
! [X0: $i] :
( ( relation_composition(set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_42470]) ).
tcf(c_43215,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(set_intersection2(sK1(sK4(powerset(X0))),X1),X2),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_42470]) ).
tcf(c_43216,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(set_intersection2(X1,sK1(sK4(powerset(X0)))),X2),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_42470]) ).
tcf(c_43217,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(set_intersection2(X0,relation_dom(sK2)),X1),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_42470]) ).
tcf(c_43219,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1),X2),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_42470]) ).
tcf(c_43220,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))),X2),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_42470]) ).
tcf(c_43426,plain,
! [X0: $i] :
( ( relation_composition(sK1(powerset(X0)),empty_set) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_42471]) ).
tcf(c_43427,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(powerset(relation_composition(X0,X1))),empty_set) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_42471]) ).
tcf(c_43428,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(powerset(relation_composition(X1,X0))),empty_set) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_42471]) ).
tcf(c_43429,plain,
relation_composition(sK1(powerset(empty_set)),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_73,c_42471]) ).
tcf(c_43430,plain,
! [X0: $i] :
( ( relation_composition(sK1(powerset(relation_dom(X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_42471]) ).
tcf(c_43431,plain,
! [X0: $i] :
( ( relation_composition(sK1(powerset(identity_relation(X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_42471]) ).
tcf(c_43432,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(powerset(set_intersection2(X0,X1))),empty_set) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_42471]) ).
tcf(c_43433,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(powerset(set_intersection2(X0,X1))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_42471]) ).
tcf(c_43434,plain,
! [X0: $i] :
( ( relation_composition(sK1(powerset(sK1(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_42471]) ).
tcf(c_43435,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(powerset(set_intersection2(X1,X0))),empty_set) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_42471]) ).
tcf(c_43436,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(powerset(set_intersection2(X1,X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_42471]) ).
tcf(c_43437,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(powerset(set_intersection2(X1,sK1(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_42471]) ).
tcf(c_43438,plain,
! [X0: $i] :
( ( relation_composition(sK1(powerset(set_intersection2(relation_dom(sK2),X0))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_42471]) ).
tcf(c_43439,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(powerset(set_intersection2(sK1(powerset(X0)),X1))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_42471]) ).
tcf(c_43440,plain,
( ( relation_composition(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_42471]) ).
tcf(c_43441,plain,
( ( relation_composition(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_42471]) ).
tcf(c_43442,plain,
( ( relation_composition(sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2)))),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_42471]) ).
tcf(c_43443,plain,
( ( relation_composition(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_42471]) ).
tcf(c_43444,plain,
( ( relation_composition(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_42471]) ).
tcf(c_43445,plain,
( ( relation_composition(sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2)))),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_42471]) ).
tcf(c_43446,plain,
( ( relation_composition(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_42471]) ).
tcf(c_43447,plain,
( ( relation_composition(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_42471]) ).
tcf(c_43448,plain,
( ( relation_composition(sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2)))),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_42471]) ).
tcf(c_43449,plain,
! [X0: $i] :
( ( relation_composition(sK1(powerset(sK1(sK4(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_42471]) ).
tcf(c_43450,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(powerset(set_intersection2(sK1(sK4(powerset(X0))),X1))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_42471]) ).
tcf(c_43451,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(powerset(set_intersection2(X1,sK1(sK4(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_42471]) ).
tcf(c_43452,plain,
! [X0: $i] :
( ( relation_composition(sK1(powerset(set_intersection2(X0,relation_dom(sK2)))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_42471]) ).
tcf(c_43453,plain,
! [X0: $i] :
( ( relation_composition(sK1(powerset(sK1(sK4(sK4(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_42471]) ).
tcf(c_43454,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_42471]) ).
tcf(c_43455,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(powerset(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_42471]) ).
tcf(c_43538,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(X0)),empty_set) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_42635]) ).
tcf(c_43539,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_dom(relation_composition(X0,X1))),empty_set) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_42635]) ).
tcf(c_43540,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_dom(relation_composition(X1,X0))),empty_set) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_42635]) ).
tcf(c_43541,plain,
relation_composition(relation_dom(relation_dom(empty_set)),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_73,c_42635]) ).
tcf(c_43542,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(relation_dom(X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_42635]) ).
tcf(c_43543,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(identity_relation(X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_42635]) ).
tcf(c_43544,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_dom(set_intersection2(X0,X1))),empty_set) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_42635]) ).
tcf(c_43545,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_dom(set_intersection2(X0,X1))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_42635]) ).
tcf(c_43546,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(sK1(powerset(X0)))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_42635]) ).
tcf(c_43547,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_dom(set_intersection2(X1,X0))),empty_set) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_42635]) ).
tcf(c_43548,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_dom(set_intersection2(X1,X0))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_42635]) ).
tcf(c_43549,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_dom(set_intersection2(X1,sK1(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_42635]) ).
tcf(c_43550,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(set_intersection2(relation_dom(sK2),X0))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_42635]) ).
tcf(c_43551,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_dom(set_intersection2(sK1(powerset(X0)),X1))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_42635]) ).
tcf(c_43552,plain,
( ( relation_composition(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_42635]) ).
tcf(c_43553,plain,
( ( relation_composition(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_42635]) ).
tcf(c_43554,plain,
( ( relation_composition(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_42635]) ).
tcf(c_43555,plain,
( ( relation_composition(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_42635]) ).
tcf(c_43556,plain,
( ( relation_composition(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_42635]) ).
tcf(c_43557,plain,
( ( relation_composition(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_42635]) ).
tcf(c_43558,plain,
( ( relation_composition(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_42635]) ).
tcf(c_43559,plain,
( ( relation_composition(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))),empty_set) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_42635]) ).
tcf(c_43560,plain,
( ( relation_composition(relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))),empty_set) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_42635]) ).
tcf(c_43561,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(sK1(sK4(powerset(X0))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_42635]) ).
tcf(c_43562,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_42635]) ).
tcf(c_43563,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_42635]) ).
tcf(c_43564,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(set_intersection2(X0,relation_dom(sK2)))),empty_set) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_42635]) ).
tcf(c_43565,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_dom(sK1(sK4(sK4(powerset(X0)))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_42635]) ).
tcf(c_43566,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_42635]) ).
tcf(c_43567,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))),empty_set) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_42635]) ).
tcf(c_43694,plain,
( ( identity_relation(relation_dom(empty_set)) = empty_set )
| ( apply(empty_set,sK1(empty_set)) = sK1(empty_set) ) ),
inference(superposition,[status(thm)],[c_2472,c_15816]) ).
tcf(c_43698,plain,
( ( identity_relation(relation_dom(powerset(empty_set))) = empty_set )
| ( apply(identity_relation(powerset(empty_set)),empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_5628,c_15816]) ).
tcf(c_43713,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,X0) = empty_set )
| ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_2544,c_2363]) ).
tcf(c_43714,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(relation_composition(X0,X1),X2) = empty_set )
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_2363]) ).
tcf(c_43715,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(relation_composition(X1,X0),X2) = empty_set )
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_2363]) ).
tcf(c_43716,plain,
! [X0: $i] :
( ( relation_composition(empty_set,X0) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_73,c_2363]) ).
tcf(c_43717,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(relation_dom(X0),X1) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_2363]) ).
tcf(c_43718,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X0),X1) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_2363]) ).
tcf(c_43719,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X0,X2),X1) = empty_set )
| ~ relation(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_2363]) ).
tcf(c_43720,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X0,X2),X1) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_2363]) ).
tcf(c_43721,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(powerset(X0)),X1) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_2363]) ).
tcf(c_43722,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X2,X0),X1) = empty_set )
| ~ relation(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_2363]) ).
tcf(c_43723,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X2,X0),X1) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_2363]) ).
tcf(c_43724,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X2,sK1(powerset(X0))),X1) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_2363]) ).
tcf(c_43725,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(relation_dom(sK2),X1),X0) = empty_set )
| ~ empty(sK2)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17673,c_2363]) ).
tcf(c_43726,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(sK1(powerset(X0)),X2),X1) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_2363]) ).
tcf(c_43727,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = empty_set )
| ~ empty(sK2)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17955,c_2363]) ).
tcf(c_43728,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = empty_set )
| ~ relation(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_2363]) ).
tcf(c_43729,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_composition(iPr_def_10,sK2)),X0) = empty_set )
| ~ relation(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_2363]) ).
tcf(c_43730,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = empty_set )
| ~ empty(sK2)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17956,c_2363]) ).
tcf(c_43731,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = empty_set )
| ~ relation(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_2363]) ).
tcf(c_43732,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_composition(iPr_def_11,sK2)),X0) = empty_set )
| ~ relation(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_2363]) ).
tcf(c_43733,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = empty_set )
| ~ empty(sK2)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17957,c_2363]) ).
tcf(c_43734,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = empty_set )
| ~ relation(X0)
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_2363]) ).
tcf(c_43735,plain,
! [X0: $i] :
( ( relation_composition(relation_dom(relation_composition(iPr_def_14,sK2)),X0) = empty_set )
| ~ relation(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_2363]) ).
tcf(c_43736,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(sK4(powerset(X0))),X1) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_2363]) ).
tcf(c_43737,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(sK1(sK4(powerset(X0))),X2),X1) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_2363]) ).
tcf(c_43738,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X2,sK1(sK4(powerset(X0)))),X1) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_2363]) ).
tcf(c_43739,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(set_intersection2(X1,relation_dom(sK2)),X0) = empty_set )
| ~ empty(sK2)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_17695,c_2363]) ).
tcf(c_43740,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(sK1(sK4(sK4(powerset(X0)))),X1) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_2363]) ).
tcf(c_43741,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2),X1) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_2363]) ).
tcf(c_43742,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(set_intersection2(X2,sK1(sK4(sK4(powerset(X0))))),X1) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_2363]) ).
tcf(c_43920,plain,
! [X0: $i] :
( ( relation_composition(empty_set,X0) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_15821,c_43716]) ).
tcf(c_43921,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_composition(X1,X0)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_63,c_43716]) ).
tcf(c_43922,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_composition(X1,X0)) = empty_set )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_59,c_43716]) ).
tcf(c_43924,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_composition(X0,X1)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_79,c_43716]) ).
tcf(c_43926,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20751,c_43716]) ).
tcf(c_43927,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3085,c_43716]) ).
tcf(c_43928,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,X0)) = empty_set )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_43716]) ).
tcf(c_43929,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_77,c_43716]) ).
tcf(c_43931,plain,
relation_composition(empty_set,sK6) = empty_set,
inference(superposition,[status(thm)],[c_89,c_43716]) ).
tcf(c_43932,plain,
relation_composition(empty_set,sK9) = empty_set,
inference(superposition,[status(thm)],[c_93,c_43716]) ).
tcf(c_43937,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(X0,X1)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20748,c_43716]) ).
tcf(c_43938,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(X0,X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3181,c_43716]) ).
tcf(c_43939,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK1(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3940,c_43716]) ).
tcf(c_43940,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(relation_dom(sK2),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17396,c_43716]) ).
tcf(c_43941,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,sK1(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5587,c_43716]) ).
tcf(c_43942,plain,
( ( relation_composition(empty_set,relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17426,c_43716]) ).
tcf(c_43943,plain,
( ( relation_composition(empty_set,relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10963,c_43716]) ).
tcf(c_43944,plain,
( ( relation_composition(empty_set,relation_dom(relation_composition(iPr_def_10,sK2))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6020,c_43716]) ).
tcf(c_43945,plain,
( ( relation_composition(empty_set,relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17427,c_43716]) ).
tcf(c_43946,plain,
( ( relation_composition(empty_set,relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_9976,c_43716]) ).
tcf(c_43947,plain,
( ( relation_composition(empty_set,relation_dom(relation_composition(iPr_def_11,sK2))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6135,c_43716]) ).
tcf(c_43948,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(sK1(powerset(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6506,c_43716]) ).
tcf(c_43949,plain,
( ( relation_composition(empty_set,relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17428,c_43716]) ).
tcf(c_43950,plain,
( ( relation_composition(empty_set,relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8196,c_43716]) ).
tcf(c_43951,plain,
( ( relation_composition(empty_set,relation_dom(relation_composition(iPr_def_14,sK2))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6819,c_43716]) ).
tcf(c_43952,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK1(sK4(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14342,c_43716]) ).
tcf(c_43953,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,sK1(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14598,c_43716]) ).
tcf(c_43954,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(sK1(sK4(powerset(X0))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14748,c_43716]) ).
tcf(c_43955,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(X0,relation_dom(sK2))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17408,c_43716]) ).
tcf(c_43956,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK1(sK4(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38542,c_43716]) ).
tcf(c_43957,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_40148,c_43716]) ).
tcf(c_43958,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_41091,c_43716]) ).
tcf(c_44155,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,sK6),X0) = apply(sK6,apply(empty_set,X0)) )
| ~ relation(sK6)
| ~ relation(empty_set)
| ~ function(sK6)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_43931,c_96]) ).
tcf(c_44156,plain,
! [X0: $i] :
( ( apply(sK6,apply(empty_set,X0)) = apply(empty_set,X0) )
| ~ relation(sK6)
| ~ relation(empty_set)
| ~ function(sK6)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_44155,c_2054,c_43931]) ).
tcf(c_44165,plain,
! [X0: $i] :
( ( apply(relation_composition(empty_set,sK9),X0) = apply(sK9,apply(empty_set,X0)) )
| ~ relation(sK9)
| ~ relation(empty_set)
| ~ function(sK9)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_43932,c_96]) ).
tcf(c_44166,plain,
! [X0: $i] :
( ( apply(sK9,apply(empty_set,X0)) = apply(empty_set,X0) )
| ~ relation(sK9)
| ~ relation(empty_set)
| ~ function(sK9)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_44165,c_2054,c_43932]) ).
tcf(c_44171,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(X0)) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_43929]) ).
tcf(c_44172,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_composition(X0,X1))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_43929]) ).
tcf(c_44173,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_composition(X1,X0))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_43929]) ).
tcf(c_44174,plain,
relation_composition(empty_set,relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_43929]) ).
tcf(c_44175,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_43929]) ).
tcf(c_44176,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_43929]) ).
tcf(c_44177,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(set_intersection2(X0,X1))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_43929]) ).
tcf(c_44178,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(set_intersection2(X0,X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_43929]) ).
tcf(c_44179,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(sK1(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_43929]) ).
tcf(c_44180,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(set_intersection2(X1,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_43929]) ).
tcf(c_44181,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(set_intersection2(X1,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_43929]) ).
tcf(c_44182,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(set_intersection2(X1,sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_43929]) ).
tcf(c_44183,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(set_intersection2(relation_dom(sK2),X0))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_43929]) ).
tcf(c_44184,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(set_intersection2(sK1(powerset(X0)),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_43929]) ).
tcf(c_44185,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_43929]) ).
tcf(c_44186,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_43929]) ).
tcf(c_44187,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_43929]) ).
tcf(c_44188,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_43929]) ).
tcf(c_44189,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_43929]) ).
tcf(c_44190,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_43929]) ).
tcf(c_44191,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_43929]) ).
tcf(c_44192,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_43929]) ).
tcf(c_44193,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_43929]) ).
tcf(c_44194,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(sK1(sK4(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_43929]) ).
tcf(c_44195,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_43929]) ).
tcf(c_44196,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_43929]) ).
tcf(c_44197,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(set_intersection2(X0,relation_dom(sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_43929]) ).
tcf(c_44198,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(sK1(sK4(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_43929]) ).
tcf(c_44199,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_43929]) ).
tcf(c_44200,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_43929]) ).
tcf(c_44202,plain,
! [X0: $i] :
( ( relation_composition(empty_set,X0) = empty_set )
| ~ empty(X0) ),
inference(light_normalisation,[status(thm)],[c_44176,c_144]) ).
tcf(c_44370,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK1(X1)) = sK1(X1) )
| ( relation_composition(empty_set,set_intersection2(X0,X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_43927]) ).
tcf(c_44371,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(X2,relation_composition(X0,X1))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_43927]) ).
tcf(c_44372,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(X2,relation_composition(X1,X0))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_43927]) ).
tcf(c_44373,plain,
! [X0: $i] : relation_composition(empty_set,set_intersection2(X0,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_43927]) ).
tcf(c_44374,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_43927]) ).
tcf(c_44375,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,identity_relation(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_43927]) ).
tcf(c_44376,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,set_intersection2(X0,X2))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_43927]) ).
tcf(c_44377,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,set_intersection2(X0,X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_43927]) ).
tcf(c_44379,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,set_intersection2(X2,X0))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_43927]) ).
tcf(c_44380,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,set_intersection2(X2,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_43927]) ).
tcf(c_44381,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,set_intersection2(X2,sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_43927]) ).
tcf(c_44382,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(X0,set_intersection2(relation_dom(sK2),X1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_43927]) ).
tcf(c_44383,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,set_intersection2(sK1(powerset(X0)),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_43927]) ).
tcf(c_44384,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_43927]) ).
tcf(c_44385,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_43927]) ).
tcf(c_44386,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(X0,relation_dom(relation_composition(iPr_def_10,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_43927]) ).
tcf(c_44387,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_43927]) ).
tcf(c_44388,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_43927]) ).
tcf(c_44389,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(X0,relation_dom(relation_composition(iPr_def_11,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_43927]) ).
tcf(c_44390,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_43927]) ).
tcf(c_44391,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_43927]) ).
tcf(c_44392,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(X0,relation_dom(relation_composition(iPr_def_14,sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_43927]) ).
tcf(c_44394,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,set_intersection2(sK1(sK4(powerset(X0))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_43927]) ).
tcf(c_44395,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,set_intersection2(X2,sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_43927]) ).
tcf(c_44396,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(X0,set_intersection2(X1,relation_dom(sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_43927]) ).
tcf(c_44398,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,set_intersection2(sK1(sK4(sK4(powerset(X0)))),X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_43927]) ).
tcf(c_44399,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(X1,set_intersection2(X2,sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_43927]) ).
tcf(c_44678,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) )
| ( relation_composition(empty_set,set_intersection2(X0,X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_2544,c_43938]) ).
tcf(c_44679,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(relation_composition(X0,X1),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_43938]) ).
tcf(c_44680,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(relation_composition(X1,X0),X2)) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_43938]) ).
tcf(c_44681,plain,
! [X0: $i] : relation_composition(empty_set,set_intersection2(empty_set,X0)) = empty_set,
inference(superposition,[status(thm)],[c_73,c_43938]) ).
tcf(c_44682,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(relation_dom(X0),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_43938]) ).
tcf(c_44683,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(identity_relation(X0),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_43938]) ).
tcf(c_44684,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(set_intersection2(X0,X1),X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_43938]) ).
tcf(c_44685,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(set_intersection2(X0,X1),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_43938]) ).
tcf(c_44687,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(set_intersection2(X1,X0),X2)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_43938]) ).
tcf(c_44688,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(set_intersection2(X1,X0),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_43938]) ).
tcf(c_44689,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(set_intersection2(X1,sK1(powerset(X0))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_43938]) ).
tcf(c_44690,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(set_intersection2(relation_dom(sK2),X0),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_43938]) ).
tcf(c_44691,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(set_intersection2(sK1(powerset(X0)),X1),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_43938]) ).
tcf(c_44692,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_43938]) ).
tcf(c_44693,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_43938]) ).
tcf(c_44694,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(relation_dom(relation_composition(iPr_def_10,sK2)),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_43938]) ).
tcf(c_44695,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_43938]) ).
tcf(c_44696,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_43938]) ).
tcf(c_44697,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(relation_dom(relation_composition(iPr_def_11,sK2)),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_43938]) ).
tcf(c_44698,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_43938]) ).
tcf(c_44699,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0)) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_43938]) ).
tcf(c_44700,plain,
! [X0: $i] :
( ( relation_composition(empty_set,set_intersection2(relation_dom(relation_composition(iPr_def_14,sK2)),X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_43938]) ).
tcf(c_44702,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(set_intersection2(sK1(sK4(powerset(X0))),X1),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_43938]) ).
tcf(c_44703,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(set_intersection2(X1,sK1(sK4(powerset(X0)))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_43938]) ).
tcf(c_44704,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,set_intersection2(set_intersection2(X0,relation_dom(sK2)),X1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_43938]) ).
tcf(c_44706,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_43938]) ).
tcf(c_44707,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(empty_set,set_intersection2(set_intersection2(X1,sK1(sK4(sK4(powerset(X0))))),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_43938]) ).
tcf(c_45012,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK1(powerset(X0))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_43939]) ).
tcf(c_45013,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,sK1(powerset(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_43939]) ).
tcf(c_45014,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,sK1(powerset(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_43939]) ).
tcf(c_45015,plain,
relation_composition(empty_set,sK1(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_43939]) ).
tcf(c_45016,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK1(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_43939]) ).
tcf(c_45017,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK1(powerset(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_43939]) ).
tcf(c_45018,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,sK1(powerset(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_43939]) ).
tcf(c_45019,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,sK1(powerset(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_43939]) ).
tcf(c_45020,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK1(powerset(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_43939]) ).
tcf(c_45021,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,sK1(powerset(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_43939]) ).
tcf(c_45022,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,sK1(powerset(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_43939]) ).
tcf(c_45023,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,sK1(powerset(set_intersection2(X1,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_43939]) ).
tcf(c_45024,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK1(powerset(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_43939]) ).
tcf(c_45025,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,sK1(powerset(set_intersection2(sK1(powerset(X0)),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_43939]) ).
tcf(c_45026,plain,
( ( relation_composition(empty_set,sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_43939]) ).
tcf(c_45027,plain,
( ( relation_composition(empty_set,sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_43939]) ).
tcf(c_45028,plain,
( ( relation_composition(empty_set,sK1(powerset(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_43939]) ).
tcf(c_45029,plain,
( ( relation_composition(empty_set,sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_43939]) ).
tcf(c_45030,plain,
( ( relation_composition(empty_set,sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_43939]) ).
tcf(c_45031,plain,
( ( relation_composition(empty_set,sK1(powerset(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_43939]) ).
tcf(c_45032,plain,
( ( relation_composition(empty_set,sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_43939]) ).
tcf(c_45033,plain,
( ( relation_composition(empty_set,sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_43939]) ).
tcf(c_45034,plain,
( ( relation_composition(empty_set,sK1(powerset(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_43939]) ).
tcf(c_45035,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK1(powerset(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_43939]) ).
tcf(c_45036,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,sK1(powerset(set_intersection2(sK1(sK4(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_43939]) ).
tcf(c_45037,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,sK1(powerset(set_intersection2(X1,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_43939]) ).
tcf(c_45038,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK1(powerset(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_43939]) ).
tcf(c_45039,plain,
! [X0: $i] :
( ( relation_composition(empty_set,sK1(powerset(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_43939]) ).
tcf(c_45040,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,sK1(powerset(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_43939]) ).
tcf(c_45041,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,sK1(powerset(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_43939]) ).
tcf(c_45184,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(X0))) = empty_set )
| ( apply(identity_relation(X0),sK1(X0)) = sK1(X0) ) ),
inference(superposition,[status(thm)],[c_2544,c_44175]) ).
tcf(c_45185,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_composition(X0,X1)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_78,c_44175]) ).
tcf(c_45186,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_composition(X1,X0)))) = empty_set )
| ~ relation(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_62,c_44175]) ).
tcf(c_45187,plain,
relation_composition(empty_set,relation_dom(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_73,c_44175]) ).
tcf(c_45188,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_44175]) ).
tcf(c_45189,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(identity_relation(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2127,c_44175]) ).
tcf(c_45190,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20816,c_44175]) ).
tcf(c_45191,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3072,c_44175]) ).
tcf(c_45192,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(sK1(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3895,c_44175]) ).
tcf(c_45193,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20819,c_44175]) ).
tcf(c_45194,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2740,c_44175]) ).
tcf(c_45195,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(set_intersection2(X1,sK1(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3896,c_44175]) ).
tcf(c_45196,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(set_intersection2(relation_dom(sK2),X0)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17673,c_44175]) ).
tcf(c_45197,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(set_intersection2(sK1(powerset(X0)),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5574,c_44175]) ).
tcf(c_45198,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17955,c_44175]) ).
tcf(c_45199,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_11008,c_44175]) ).
tcf(c_45200,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_10,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6021,c_44175]) ).
tcf(c_45201,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17956,c_44175]) ).
tcf(c_45202,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_10037,c_44175]) ).
tcf(c_45203,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_11,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6136,c_44175]) ).
tcf(c_45204,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17957,c_44175]) ).
tcf(c_45205,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(identity_relation(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_8755,c_44175]) ).
tcf(c_45206,plain,
( ( relation_composition(empty_set,relation_dom(relation_dom(relation_dom(relation_composition(iPr_def_14,sK2))))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6820,c_44175]) ).
tcf(c_45207,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(sK1(sK4(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14106,c_44175]) ).
tcf(c_45208,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(set_intersection2(sK1(sK4(powerset(X0))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14101,c_44175]) ).
tcf(c_45209,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_14099,c_44175]) ).
tcf(c_45210,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(set_intersection2(X0,relation_dom(sK2))))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_17695,c_44175]) ).
tcf(c_45211,plain,
! [X0: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(sK1(sK4(sK4(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38304,c_44175]) ).
tcf(c_45212,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(set_intersection2(sK1(sK4(sK4(powerset(X0)))),X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38303,c_44175]) ).
tcf(c_45213,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(empty_set,relation_dom(relation_dom(set_intersection2(X1,sK1(sK4(sK4(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38301,c_44175]) ).
tcf(c_45366,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_45213,c_45212,c_45211,c_45210,c_45209,c_45208,c_45207,c_45206,c_45205,c_45204,c_45203,c_45202,c_45201,c_45200,c_45199,c_45198,c_45197,c_45196,c_45195,c_45194,c_45193,c_45192,c_45191,c_45190,c_45189,c_45188,c_45187,c_45186,c_45185,c_45184,c_45041,c_45040,c_45039,c_45038,c_45037,c_45036,c_45035,c_45034,c_45033,c_45032,c_45031,c_45030,c_45029,c_45028,c_45027,c_45026,c_45025,c_45024,c_45023,c_45022,c_45021,c_45020,c_45019,c_45018,c_45017,c_45016,c_45015,c_45014,c_45013,c_45012,c_44707,c_44706,c_44704,c_44703,c_44702,c_44700,c_44699,c_44698,c_44697,c_44696,c_44695,c_44694,c_44693,c_44692,c_44691,c_44690,c_44689,c_44688,c_44687,c_44685,c_44684,c_44683,c_44682,c_44681,c_44680,c_44679,c_44678,c_44399,c_44398,c_44396,c_44395,c_44394,c_44392,c_44391,c_44390,c_44389,c_44388,c_44387,c_44386,c_44385,c_44384,c_44383,c_44382,c_44381,c_44380,c_44379,c_44377,c_44376,c_44375,c_44374,c_44373,c_44372,c_44371,c_44370,c_44202,c_44200,c_44199,c_44198,c_44197,c_44196,c_44195,c_44194,c_44193,c_44192,c_44191,c_44190,c_44189,c_44188,c_44187,c_44186,c_44185,c_44184,c_44183,c_44182,c_44181,c_44180,c_44179,c_44178,c_44177,c_44176,c_44175,c_44174,c_44173,c_44172,c_44171,c_43958,c_43957,c_43956,c_43955,c_43954,c_43953,c_43952,c_43951,c_43950,c_43949,c_43947,c_43946,c_43945,c_43944,c_43943,c_43942,c_43940,c_43937,c_43926,c_43920,c_43742,c_43741,c_43740,c_43739,c_43738,c_43737,c_43736,c_43735,c_43734,c_43733,c_43732,c_43731,c_43730,c_43729,c_43728,c_43727,c_43725,c_43722,c_43719,c_43698,c_43694,c_43567,c_43566,c_43565,c_43564,c_43563,c_43562,c_43561,c_43560,c_43559,c_43558,c_43557,c_43556,c_43555,c_43554,c_43553,c_43552,c_43551,c_43550,c_43549,c_43548,c_43547,c_43546,c_43545,c_43544,c_43543,c_43542,c_43541,c_43540,c_43539,c_43538,c_43455,c_43454,c_43453,c_43452,c_43451,c_43450,c_43449,c_43448,c_43447,c_43446,c_43445,c_43444,c_43443,c_43442,c_43441,c_43440,c_43439,c_43438,c_43437,c_43436,c_43435,c_43434,c_43433,c_43432,c_43431,c_43430,c_43429,c_43428,c_43427,c_43426,c_43220,c_43219,c_43217,c_43216,c_43215,c_43213,c_43212,c_43211,c_43210,c_43209,c_43208,c_43207,c_43206,c_43205,c_43204,c_43203,c_43202,c_43201,c_43200,c_43198,c_43197,c_43196,c_43195,c_43194,c_43193,c_43192,c_43191,c_43012,c_43011,c_43009,c_43008,c_43007,c_43005,c_43004,c_43003,c_43002,c_43001,c_43000,c_42999,c_42998,c_42997,c_42996,c_42995,c_42994,c_42993,c_42992,c_42990,c_42989,c_42988,c_42987,c_42986,c_42985,c_42984,c_42983,c_42837,c_42836,c_42835,c_42834,c_42833,c_42832,c_42831,c_42830,c_42829,c_42828,c_42827,c_42826,c_42825,c_42824,c_42823,c_42822,c_42821,c_42820,c_42819,c_42818,c_42817,c_42816,c_42815,c_42814,c_42813,c_42812,c_42811,c_42810,c_42809,c_42808,c_42660,c_42659,c_42658,c_42657,c_42656,c_42655,c_42654,c_42653,c_42652,c_42651,c_42650,c_42649,c_42648,c_42647,c_42646,c_42645,c_42643,c_42640,c_42637,c_42490,c_42489,c_42488,c_42487,c_42486,c_42485,c_42484,c_42483,c_42482,c_42481,c_42479,c_42478,c_42477,c_42476,c_42475,c_42474,c_42472,c_42469,c_42458,c_42177,c_42176,c_42175,c_42174,c_42173,c_42172,c_42171,c_42170,c_42169,c_42168,c_42167,c_42166,c_42165,c_42164,c_42163,c_42162,c_42160,c_42157,c_42154,c_41874,c_41873,c_41872,c_41871,c_41870,c_41869,c_41868,c_41867,c_41866,c_41865,c_41864,c_41863,c_41862,c_41861,c_41860,c_41859,c_41858,c_41857,c_41856,c_41855,c_41854,c_41853,c_41852,c_41851,c_41850,c_41849,c_41848,c_41847,c_41846,c_41845,c_41663,c_41662,c_41660,c_41659,c_41658,c_41656,c_41655,c_41654,c_41653,c_41652,c_41651,c_41650,c_41649,c_41648,c_41646,c_41643,c_41640,c_41522,c_41521,c_41520,c_41519,c_41518,c_41517,c_41516,c_41515,c_41514,c_41513,c_41490,c_41486,c_41475,c_41444,c_41416,c_41413,c_41412,c_41411,c_41409,c_41366,c_41362,c_41361,c_41360,c_41359,c_41356,c_41354,c_41092,c_41091,c_41081,c_41080,c_41079,c_41078,c_41077,c_41076,c_41075,c_41074,c_41073,c_41072,c_41071,c_41070,c_41069,c_41068,c_41067,c_41066,c_41065,c_41064,c_41063,c_41062,c_41061,c_41060,c_41059,c_41058,c_41057,c_41056,c_41055,c_41054,c_41053,c_41052,c_41051,c_41050,c_41049,c_41048,c_41047,c_41046,c_41045,c_41044,c_41043,c_41042,c_41041,c_41040,c_41039,c_41038,c_41037,c_41036,c_41035,c_41034,c_41033,c_41032,c_41031,c_41030,c_41029,c_41028,c_41027,c_41026,c_41025,c_41024,c_41023,c_41022,c_41021,c_41020,c_41019,c_41018,c_41017,c_41016,c_41015,c_41014,c_41013,c_40996,c_40980,c_40951,c_40947,c_40946,c_40945,c_40944,c_40941,c_40939,c_40916,c_40877,c_40876,c_40854,c_40853,c_40848,c_40808,c_40806,c_40805,c_40804,c_40852,c_40149,c_40148,c_40138,c_40137,c_40136,c_40135,c_40134,c_40133,c_40132,c_40131,c_40130,c_40129,c_40128,c_40127,c_40126,c_40125,c_40124,c_40123,c_40122,c_40121,c_40120,c_40119,c_40118,c_40117,c_40116,c_40115,c_40114,c_40113,c_40112,c_40111,c_40110,c_40109,c_40108,c_40107,c_40106,c_40105,c_40104,c_40103,c_40102,c_40101,c_40100,c_40099,c_40098,c_40097,c_40096,c_40095,c_40094,c_40093,c_40092,c_40091,c_40090,c_40089,c_40088,c_40087,c_40086,c_40085,c_40084,c_40083,c_40082,c_40081,c_40080,c_40079,c_40078,c_40077,c_40076,c_40075,c_40074,c_40073,c_40072,c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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU011+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Thu Sep 24 12:33:20 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.34 Running first-order theorem proving
% 0.09/0.34 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35
% 0.09/0.35 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.35
% 0.09/0.35 % Detected problem language: tptp
% 0.09/0.36 % Proving...
% 13.94/2.61 % SZS status Started for theBenchmark.p
% 13.94/2.61 % SZS status Theorem for theBenchmark.p
% 13.94/2.61
% 13.94/2.61 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 13.94/2.61
% 13.94/2.61 % ------ iProver source info
% 13.94/2.61
% 13.94/2.61 % git: date: 2026-07-19 20:42:38 +0200
% 13.94/2.61 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 13.94/2.61 % git: non_committed_changes: false
% 13.94/2.61
% 13.94/2.61 % ------ Parsing...
% 13.94/2.61 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 13.94/2.61
% 13.94/2.61 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 13.94/2.61
% 13.94/2.61 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 13.94/2.61
% 13.94/2.61 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 13.94/2.61 % ------ Proving...
% 13.94/2.61 % ------ Problem Properties
% 13.94/2.61
% 13.94/2.61 %
% 13.94/2.61 % clauses 63
% 13.94/2.61 % conjectures 0
% 13.94/2.61 % EPR 20
% 13.94/2.61 % Horn 57
% 13.94/2.61 % unary 28
% 13.94/2.61 % binary 13
% 13.94/2.61 % lits 136
% 13.94/2.61 % lits eq 26
% 13.94/2.61 % fd_pure 0
% 13.94/2.61 % fd_pseudo 0
% 13.94/2.61 % fd_cond 1
% 13.94/2.61 % fd_pseudo_cond 6
% 13.94/2.61 % AC symbols 0
% 13.94/2.61
% 13.94/2.61 % ------ Schedule dynamic 5 is on
% 13.94/2.61
% 13.94/2.61 % ------ no conjectures: strip conj schedule
% 13.94/2.61
% 13.94/2.61 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 13.94/2.61
% 13.94/2.61
% 13.94/2.61 % ------
% 13.94/2.61 % Current options:
% 13.94/2.61 % ------
% 13.94/2.61
% 13.94/2.61
% 13.94/2.61 %
% 13.94/2.61
% 13.94/2.61 % ------ Proving...
% 13.94/2.61 %
% 13.94/2.61
% 13.94/2.61 % SZS status Theorem for theBenchmark.p
% 13.94/2.61
% 13.94/2.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 13.94/2.67
% 13.94/2.67
%------------------------------------------------------------------------------