%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM396+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 : n007.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 02:24:04 PM UTC 2026
% Result : Theorem 40.21s 7.88s
% Output : CNFRefutation 50.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 43
% Syntax : Number of formulae : 7457 ( 290 unt; 2 def)
% Number of atoms : 81741 (9414 equ)
% Maximal formula atoms : 18 ( 10 avg)
% Number of connectives : 49874 (13237 ~;36493 |; 121 &)
% ( 10 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 12 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 3 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-3 aty)
% Number of variables : 13025 ( 2 sgn13004 !; 21 ?;12761 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f6,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f7,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f8,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f9,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f10,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f11,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f12,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f13,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f14,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(f15,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f17,axiom,
! [X0] : ~ empty(succ(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(f19,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f21,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f22,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f23,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f24,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f26,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f27,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f28,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f29,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f30,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(f31,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f32,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f37,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f38,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(f39,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f41,conjecture,
! [X0] :
( ordinal(X0)
=> ordinal(succ(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_ordinal1) ).
fof(f42,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ordinal(succ(X0)) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f43,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f44,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f45,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f46,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f47,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f48,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f49,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f50,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f51,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f24]) ).
fof(f52,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f37]) ).
fof(f56,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f19]) ).
fof(f60,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f30]) ).
fof(f61,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f56]) ).
fof(f62,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f68,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f69,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0] :
( ~ empty(X0)
| ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f71,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f72,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f75,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f76,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X1,X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f77,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f40]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
? [X0] :
( ordinal(X0)
& ~ ordinal(succ(X0)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f81,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f82,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f45]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f86,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f47]) ).
fof(f87,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f88,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f89,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f90,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f90]) ).
fof(f92,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f71]) ).
fof(f93,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ( in(sK1(X0),X0)
& ~ subset(sK1(X0),X0) )
| epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0) )
& ( ~ in(sK2(X0,X1,X2),X2)
| ( ~ in(sK2(X0,X1,X2),X1)
& ~ in(sK2(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f97]) ).
fof(f99,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) )
& ( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
| epsilon_connected(X0) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f100,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ) )
& ( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
| epsilon_connected(X0) ) ),
inference(rectify,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ) )
& ( ( ~ in(sK4(X0),sK3(X0))
& sK3(X0) != sK4(X0)
& ~ in(sK3(X0),sK4(X0))
& in(sK4(X0),X0)
& in(sK3(X0),X0) )
| epsilon_connected(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X1,sK3(X0)),skolemize(X2,sK4(X0))],[f100]) ).
fof(f102,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f103,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
! [X0] : element(sK5(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f15]) ).
fof(f106,plain,
( ordinal(sK7)
& epsilon_connected(sK7)
& epsilon_transitive(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f26]) ).
fof(f107,plain,
( relation(sK8)
& empty(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f27]) ).
fof(f108,plain,
empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f28]) ).
fof(f109,plain,
( function(sK10)
& empty(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f29]) ).
fof(f110,plain,
( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11)
& empty(sK11)
& function(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f60]) ).
fof(f111,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f31]) ).
fof(f112,plain,
~ empty(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f32]) ).
fof(f117,plain,
( ordinal(sK18)
& ~ ordinal(succ(sK18)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X0,sK18)],[f80]) ).
fof(f118,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f119,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f126,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f128,plain,
! [X0] :
( ~ empty(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f129,plain,
! [X0] :
( ~ empty(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f130,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f131,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f132,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f91]) ).
fof(f133,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f134,plain,
! [X0,X1] :
( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f91]) ).
fof(f135,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f91]) ).
fof(f136,plain,
! [X2,X0] :
( ~ epsilon_transitive(X0)
| ~ in(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f137,plain,
! [X0] :
( in(sK1(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f138,plain,
! [X0] :
( ~ subset(sK1(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f139,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f140,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f141,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f142,plain,
! [X2,X0,X1] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f98]) ).
fof(f143,plain,
! [X2,X0,X1] :
( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f98]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f98]) ).
fof(f145,plain,
! [X3,X0,X4] :
( ~ epsilon_connected(X0)
| in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f146,plain,
! [X0] :
( ~ in(sK4(X0),sK3(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f147,plain,
! [X0] :
( sK3(X0) != sK4(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f148,plain,
! [X0] :
( ~ in(sK3(X0),sK4(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f149,plain,
! [X0] :
( in(sK4(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f150,plain,
! [X0] :
( in(sK3(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f151,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f152,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f154,plain,
! [X0] : element(sK5(X0),X0),
inference(cnf_transformation,[],[f104]) ).
fof(f157,plain,
! [X0] : ~ empty(succ(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f159,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f61]) ).
fof(f160,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f61]) ).
fof(f161,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f61]) ).
fof(f166,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f167,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X1,X0)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f169,plain,
empty(empty_set),
inference(cnf_transformation,[],[f23]) ).
fof(f170,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f51]) ).
fof(f173,plain,
ordinal(sK7),
inference(cnf_transformation,[],[f106]) ).
fof(f174,plain,
epsilon_connected(sK7),
inference(cnf_transformation,[],[f106]) ).
fof(f175,plain,
epsilon_transitive(sK7),
inference(cnf_transformation,[],[f106]) ).
fof(f177,plain,
empty(sK8),
inference(cnf_transformation,[],[f107]) ).
fof(f178,plain,
empty(sK9),
inference(cnf_transformation,[],[f108]) ).
fof(f180,plain,
empty(sK10),
inference(cnf_transformation,[],[f109]) ).
fof(f182,plain,
ordinal(sK11),
inference(cnf_transformation,[],[f110]) ).
fof(f183,plain,
epsilon_connected(sK11),
inference(cnf_transformation,[],[f110]) ).
fof(f184,plain,
epsilon_transitive(sK11),
inference(cnf_transformation,[],[f110]) ).
fof(f185,plain,
empty(sK11),
inference(cnf_transformation,[],[f110]) ).
fof(f189,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f111]) ).
fof(f190,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f112]) ).
fof(f198,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f52]) ).
fof(f199,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f38]) ).
fof(f200,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f201,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f202,plain,
ordinal(sK18),
inference(cnf_transformation,[],[f117]) ).
fof(f203,plain,
~ ordinal(succ(sK18)),
inference(cnf_transformation,[],[f117]) ).
fof(f204,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f205,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f206,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f118]) ).
fof(f207,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f208,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f209,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f86]) ).
fof(f210,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f211,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f212,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f213,plain,
! [X0] : ~ empty(set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f157,f131]) ).
fof(f214,plain,
~ ordinal(set_union2(sK18,singleton(sK18))),
inference(definition_unfolding,[],[f203,f131]) ).
fof(f215,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f133]) ).
fof(f216,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f215]) ).
fof(f217,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f132]) ).
fof(f218,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f141]) ).
fof(f219,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f140]) ).
fof(f220,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f139]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_54,plain,
! [X0: $i] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_55,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_56,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f130]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = X1 )
| ~ in(sK0(X0,X1),X1)
| ( sK0(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X1)
| ( singleton(X0) = X1 )
| ( sK0(X0,X1) = X0 ) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_61,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f216]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_63,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ subset(sK1(X0),X0) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_64,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK1(X0),X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_72,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK3(X0),X0) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_73,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK4(X0),X0) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_74,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK3(X0),sK4(X0)) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_75,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK3(X0) != sK4(X0) ) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_76,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK4(X0),sK3(X0)) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X0,X2)
| ( X0 = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_79,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_80,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_81,plain,
! [X0: $i] : element(sK5(X0),X0),
inference(cnf_transformation,[],[f154]) ).
tcf(c_84,plain,
! [X0: $i] : ~ empty(set_union2(X0,singleton(X0))),
inference(cnf_transformation,[],[f213]) ).
tcf(c_89,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f161]) ).
tcf(c_90,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f160]) ).
tcf(c_91,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f159]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_95,plain,
empty(empty_set),
inference(cnf_transformation,[],[f169]) ).
tcf(c_97,plain,
! [X0: $i] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f170]) ).
tcf(c_100,plain,
epsilon_transitive(sK7),
inference(cnf_transformation,[],[f175]) ).
tcf(c_101,plain,
epsilon_connected(sK7),
inference(cnf_transformation,[],[f174]) ).
tcf(c_102,plain,
ordinal(sK7),
inference(cnf_transformation,[],[f173]) ).
tcf(c_103,plain,
empty(sK8),
inference(cnf_transformation,[],[f177]) ).
tcf(c_105,plain,
empty(sK9),
inference(cnf_transformation,[],[f178]) ).
tcf(c_107,plain,
empty(sK10),
inference(cnf_transformation,[],[f180]) ).
tcf(c_111,plain,
empty(sK11),
inference(cnf_transformation,[],[f185]) ).
tcf(c_112,plain,
epsilon_transitive(sK11),
inference(cnf_transformation,[],[f184]) ).
tcf(c_113,plain,
epsilon_connected(sK11),
inference(cnf_transformation,[],[f183]) ).
tcf(c_114,plain,
ordinal(sK11),
inference(cnf_transformation,[],[f182]) ).
tcf(c_115,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f189]) ).
tcf(c_117,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f190]) ).
tcf(c_125,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f198]) ).
tcf(c_126,plain,
! [X0: $i] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f199]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_129,negated_conjecture,
~ ordinal(set_union2(sK18,singleton(sK18))),
inference(cnf_transformation,[],[f214]) ).
tcf(c_130,negated_conjecture,
ordinal(sK18),
inference(cnf_transformation,[],[f202]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_136,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f211]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_132]) ).
tcf(c_191,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(prop_impl_just,[status(thm)],[c_79]) ).
tcf(c_193,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(prop_impl_just,[status(thm)],[c_80]) ).
tcf(c_201,plain,
! [X0: $i] :
( ~ subset(sK1(X0),X0)
| epsilon_transitive(X0) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
tcf(c_202,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ subset(sK1(X0),X0) ),
inference(renaming,[status(thm)],[c_201]) ).
tcf(c_203,plain,
! [X0: $i] :
( in(sK1(X0),X0)
| epsilon_transitive(X0) ),
inference(prop_impl_just,[status(thm)],[c_64]) ).
tcf(c_204,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK1(X0),X0) ),
inference(renaming,[status(thm)],[c_203]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_134,c_159]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_135,c_159]) ).
tcf(c_964,plain,
! [X0: $i] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ( set_union2(sK18,singleton(sK18)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_129]) ).
tcf(c_965,plain,
( ~ epsilon_connected(set_union2(sK18,singleton(sK18)))
| ~ epsilon_transitive(set_union2(sK18,singleton(sK18))) ),
inference(unflattening,[status(thm)],[c_964]) ).
tcf(c_972,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( X0 != sK18 ) ),
inference(resolution_lifted,[status(thm)],[c_193,c_130]) ).
tcf(c_973,plain,
epsilon_connected(sK18),
inference(unflattening,[status(thm)],[c_972]) ).
tcf(c_977,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( X0 != sK18 ) ),
inference(resolution_lifted,[status(thm)],[c_191,c_130]) ).
tcf(c_978,plain,
epsilon_transitive(sK18),
inference(unflattening,[status(thm)],[c_977]) ).
tcf(c_982,plain,
set_union2(sK18,singleton(sK18)) != empty_set,
inference(resolution_lifted,[status(thm)],[c_91,c_129]) ).
tcf(c_986,plain,
set_union2(sK18,singleton(sK18)) != sK7,
inference(resolution_lifted,[status(thm)],[c_102,c_129]) ).
tcf(c_990,plain,
set_union2(sK18,singleton(sK18)) != sK11,
inference(resolution_lifted,[status(thm)],[c_114,c_129]) ).
tcf(c_994,plain,
set_union2(sK18,singleton(sK18)) != sK18,
inference(resolution_lifted,[status(thm)],[c_129,c_130]) ).
tcf(c_1056,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ in(X1,X0)
| ( X0 != sK18 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_978]) ).
tcf(c_1057,plain,
! [X0: $i] :
( subset(X0,sK18)
| ~ in(X0,sK18) ),
inference(unflattening,[status(thm)],[c_1056]) ).
tcf(c_1065,plain,
! [X0: $i] :
( in(sK1(X0),X0)
| ~ epsilon_connected(set_union2(sK18,singleton(sK18)))
| ( set_union2(sK18,singleton(sK18)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_204,c_965]) ).
tcf(c_1066,plain,
( in(sK1(set_union2(sK18,singleton(sK18))),set_union2(sK18,singleton(sK18)))
| ~ epsilon_connected(set_union2(sK18,singleton(sK18))) ),
inference(unflattening,[status(thm)],[c_1065]) ).
tcf(c_1073,plain,
! [X0: $i] :
( ~ subset(sK1(X0),X0)
| ~ epsilon_connected(set_union2(sK18,singleton(sK18)))
| ( set_union2(sK18,singleton(sK18)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_202,c_965]) ).
tcf(c_1074,plain,
( ~ epsilon_connected(set_union2(sK18,singleton(sK18)))
| ~ subset(sK1(set_union2(sK18,singleton(sK18))),set_union2(sK18,singleton(sK18))) ),
inference(unflattening,[status(thm)],[c_1073]) ).
tcf(c_1466,plain,
( ~ epsilon_connected(set_union2(sK18,singleton(sK18)))
| ~ epsilon_transitive(set_union2(sK18,singleton(sK18))) ),
inference(prop_impl_just,[status(thm)],[c_965]) ).
tcf(c_2420,definition,
iPr_def_10 = singleton(sK18),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2421,definition,
iPr_def_11 = set_union2(sK18,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2422,plain,
iPr_def_11 != sK18,
inference(demodulation,[status(thm)],[c_994,c_2420,c_2421]) ).
tcf(c_2423,plain,
iPr_def_11 != sK11,
inference(demodulation,[status(thm)],[c_990]) ).
tcf(c_2424,plain,
iPr_def_11 != sK7,
inference(demodulation,[status(thm)],[c_986]) ).
tcf(c_2425,plain,
iPr_def_11 != empty_set,
inference(demodulation,[status(thm)],[c_982]) ).
tcf(c_2426,plain,
epsilon_transitive(sK18),
inference(demodulation,[status(thm)],[c_978]) ).
tcf(c_2427,plain,
epsilon_connected(sK18),
inference(demodulation,[status(thm)],[c_973]) ).
tcf(c_2428,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_2430,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2436,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X2)
| ~ subset(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3384,plain,
epsilon_transitive(sK8),
inference(superposition,[status(thm)],[c_103,c_55]) ).
tcf(c_3385,plain,
epsilon_transitive(sK9),
inference(superposition,[status(thm)],[c_105,c_55]) ).
tcf(c_3386,plain,
epsilon_transitive(sK10),
inference(superposition,[status(thm)],[c_107,c_55]) ).
tcf(c_3393,plain,
epsilon_connected(sK8),
inference(superposition,[status(thm)],[c_103,c_56]) ).
tcf(c_3394,plain,
epsilon_connected(sK9),
inference(superposition,[status(thm)],[c_105,c_56]) ).
tcf(c_3395,plain,
epsilon_connected(sK10),
inference(superposition,[status(thm)],[c_107,c_56]) ).
tcf(c_3397,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_58,c_138]) ).
tcf(c_3400,plain,
in(sK18,iPr_def_10),
inference(superposition,[status(thm)],[c_2420,c_61]) ).
tcf(c_3416,plain,
~ empty(set_union2(sK18,iPr_def_10)),
inference(superposition,[status(thm)],[c_2420,c_84]) ).
tcf(c_3417,plain,
~ empty(iPr_def_11),
inference(light_normalisation,[status(thm)],[c_3416,c_2421]) ).
tcf(c_3420,plain,
! [X0: $i] : subset(empty_set,X0),
inference(superposition,[status(thm)],[c_126,c_3397]) ).
tcf(c_3423,plain,
! [X0: $i] : set_union2(empty_set,X0) = X0,
inference(superposition,[status(thm)],[c_126,c_58]) ).
tcf(c_3424,plain,
set_union2(iPr_def_10,sK18) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2421,c_58]) ).
tcf(c_3425,plain,
subset(sK18,iPr_def_11),
inference(superposition,[status(thm)],[c_3424,c_3397]) ).
tcf(c_3426,plain,
subset(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_3424,c_138]) ).
tcf(c_3453,plain,
! [X0: $i] : element(X0,singleton(X0)),
inference(superposition,[status(thm)],[c_61,c_127]) ).
tcf(c_3454,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| element(sK1(X0),X0) ),
inference(superposition,[status(thm)],[c_64,c_127]) ).
tcf(c_3455,plain,
! [X0: $i] :
( epsilon_connected(X0)
| element(sK3(X0),X0) ),
inference(superposition,[status(thm)],[c_72,c_127]) ).
tcf(c_3456,plain,
! [X0: $i] :
( epsilon_connected(X0)
| element(sK4(X0),X0) ),
inference(superposition,[status(thm)],[c_73,c_127]) ).
tcf(c_3457,plain,
element(sK18,iPr_def_10),
inference(superposition,[status(thm)],[c_3400,c_127]) ).
tcf(c_3474,plain,
~ empty(singleton(empty_set)),
inference(superposition,[status(thm)],[c_3423,c_84]) ).
tcf(c_3492,plain,
empty_set = sK8,
inference(superposition,[status(thm)],[c_103,c_136]) ).
tcf(c_3493,plain,
empty_set = sK9,
inference(superposition,[status(thm)],[c_105,c_136]) ).
tcf(c_3494,plain,
empty_set = sK10,
inference(superposition,[status(thm)],[c_107,c_136]) ).
tcf(c_3495,plain,
empty_set = sK11,
inference(superposition,[status(thm)],[c_111,c_136]) ).
tcf(c_3508,plain,
empty_set != iPr_def_11,
inference(demodulation,[status(thm)],[c_2423,c_3495]) ).
tcf(c_3513,plain,
! [X0: $i] : ~ empty(singleton(X0)),
inference(superposition,[status(thm)],[c_61,c_137]) ).
tcf(c_3517,plain,
~ empty(iPr_def_10),
inference(superposition,[status(thm)],[c_3400,c_137]) ).
tcf(c_3522,plain,
! [X0: $i] : ~ in(singleton(X0),X0),
inference(superposition,[status(thm)],[c_61,c_49]) ).
tcf(c_3523,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ in(X0,sK1(X0)) ),
inference(superposition,[status(thm)],[c_64,c_49]) ).
tcf(c_3524,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(X0,sK3(X0)) ),
inference(superposition,[status(thm)],[c_72,c_49]) ).
tcf(c_3525,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(X0,sK4(X0)) ),
inference(superposition,[status(thm)],[c_73,c_49]) ).
tcf(c_3526,plain,
~ in(iPr_def_10,sK18),
inference(superposition,[status(thm)],[c_3400,c_49]) ).
tcf(c_3564,plain,
! [X0: $i] : subset(sK5(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_81,c_133]) ).
tcf(c_3566,plain,
! [X0: $i] :
( epsilon_transitive(powerset(X0))
| subset(sK1(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_3454,c_133]) ).
tcf(c_3567,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| subset(sK3(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_3455,c_133]) ).
tcf(c_3568,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| subset(sK4(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_3456,c_133]) ).
tcf(c_3589,plain,
! [X0: $i] :
( epsilon_transitive(singleton(X0))
| ( sK1(singleton(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_64,c_62]) ).
tcf(c_3590,plain,
! [X0: $i] :
( epsilon_connected(singleton(X0))
| ( sK3(singleton(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_72,c_62]) ).
tcf(c_3591,plain,
! [X0: $i] :
( epsilon_connected(singleton(X0))
| ( sK4(singleton(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_73,c_62]) ).
tcf(c_3592,plain,
! [X0: $i] :
( ( X0 = sK18 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2420,c_62]) ).
tcf(c_3613,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_3423,c_69]) ).
tcf(c_3614,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3424,c_69]) ).
tcf(c_3615,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_69,c_49]) ).
tcf(c_3616,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_69,c_137]) ).
tcf(c_3617,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_69,c_127]) ).
tcf(c_3618,plain,
! [X0: $i,X1: $i] : ~ in(singleton(set_union2(X0,X1)),X0),
inference(superposition,[status(thm)],[c_69,c_3522]) ).
tcf(c_3640,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3424,c_70]) ).
tcf(c_3641,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_70,c_49]) ).
tcf(c_3642,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_70,c_137]) ).
tcf(c_3643,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_70,c_127]) ).
tcf(c_3644,plain,
! [X0: $i,X1: $i] : ~ in(singleton(set_union2(X0,X1)),X1),
inference(superposition,[status(thm)],[c_70,c_3522]) ).
tcf(c_3669,plain,
( epsilon_transitive(iPr_def_10)
| in(sK1(iPr_def_10),iPr_def_11) ),
inference(superposition,[status(thm)],[c_64,c_3614]) ).
tcf(c_3670,plain,
( epsilon_connected(iPr_def_10)
| in(sK3(iPr_def_10),iPr_def_11) ),
inference(superposition,[status(thm)],[c_72,c_3614]) ).
tcf(c_3671,plain,
( epsilon_connected(iPr_def_10)
| in(sK4(iPr_def_10),iPr_def_11) ),
inference(superposition,[status(thm)],[c_73,c_3614]) ).
tcf(c_3672,plain,
in(sK18,iPr_def_11),
inference(superposition,[status(thm)],[c_3400,c_3614]) ).
tcf(c_3679,plain,
~ in(iPr_def_11,sK18),
inference(superposition,[status(thm)],[c_3672,c_49]) ).
tcf(c_3681,plain,
element(sK18,iPr_def_11),
inference(superposition,[status(thm)],[c_3672,c_127]) ).
tcf(c_3686,plain,
( epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK1(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3669,c_49]) ).
tcf(c_3688,plain,
( epsilon_transitive(iPr_def_10)
| element(sK1(iPr_def_10),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3669,c_127]) ).
tcf(c_3697,plain,
( epsilon_connected(iPr_def_10)
| ~ in(iPr_def_11,sK3(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3670,c_49]) ).
tcf(c_3699,plain,
( epsilon_connected(iPr_def_10)
| element(sK3(iPr_def_10),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3670,c_127]) ).
tcf(c_3708,plain,
( epsilon_connected(iPr_def_10)
| ~ in(iPr_def_11,sK4(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3671,c_49]) ).
tcf(c_3710,plain,
( epsilon_connected(iPr_def_10)
| element(sK4(iPr_def_10),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3671,c_127]) ).
tcf(c_3733,plain,
! [X0: $i,X1: $i] :
( ( singleton(X1) = X0 )
| ( sK0(X1,X0) = X1 )
| ~ in(X0,sK0(X1,X0)) ),
inference(superposition,[status(thm)],[c_60,c_49]) ).
tcf(c_3734,plain,
! [X0: $i,X1: $i] :
( ( singleton(X1) = X0 )
| ( sK0(X1,X0) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_60,c_137]) ).
tcf(c_3735,plain,
! [X0: $i,X1: $i] :
( element(sK0(X0,X1),X1)
| ( singleton(X0) = X1 )
| ( sK0(X0,X1) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_127]) ).
tcf(c_3736,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK0(X0,singleton(X1)) = X1 )
| ( sK0(X0,singleton(X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_62]) ).
tcf(c_3737,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,empty_set),X1)
| ( singleton(X0) = empty_set )
| ( sK0(X0,empty_set) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_3613]) ).
tcf(c_3738,plain,
! [X0: $i] :
( in(sK0(X0,iPr_def_10),iPr_def_11)
| ( singleton(X0) = iPr_def_10 )
| ( sK0(X0,iPr_def_10) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_3614]) ).
tcf(c_3768,plain,
! [X0: $i] :
( empty(X0)
| in(sK5(X0),X0) ),
inference(superposition,[status(thm)],[c_81,c_131]) ).
tcf(c_3769,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_132,c_131]) ).
tcf(c_3771,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| empty(X0)
| in(sK1(X0),X0) ),
inference(superposition,[status(thm)],[c_3454,c_131]) ).
tcf(c_3772,plain,
! [X0: $i] :
( epsilon_connected(X0)
| empty(X0)
| in(sK3(X0),X0) ),
inference(superposition,[status(thm)],[c_3455,c_131]) ).
tcf(c_3773,plain,
! [X0: $i] :
( epsilon_connected(X0)
| empty(X0)
| in(sK4(X0),X0) ),
inference(superposition,[status(thm)],[c_3456,c_131]) ).
tcf(c_3776,plain,
( epsilon_transitive(iPr_def_10)
| empty(iPr_def_11)
| in(sK1(iPr_def_10),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3688,c_131]) ).
tcf(c_3777,plain,
( epsilon_connected(iPr_def_10)
| empty(iPr_def_11)
| in(sK3(iPr_def_10),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3699,c_131]) ).
tcf(c_3778,plain,
( epsilon_connected(iPr_def_10)
| empty(iPr_def_11)
| in(sK4(iPr_def_10),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3710,c_131]) ).
tcf(c_3802,plain,
! [X0: $i,X1: $i] :
( subset(sK0(X1,X0),X0)
| ( singleton(X1) = X0 )
| ( sK0(X1,X0) = X1 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_60,c_65]) ).
tcf(c_3803,plain,
! [X0: $i] :
( subset(X0,singleton(X0))
| ~ epsilon_transitive(singleton(X0)) ),
inference(superposition,[status(thm)],[c_61,c_65]) ).
tcf(c_3805,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,set_union2(X0,X1))
| ~ in(X2,X0)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_69,c_65]) ).
tcf(c_3806,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,set_union2(X0,X1))
| ~ in(X2,X1)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_70,c_65]) ).
tcf(c_3807,plain,
! [X0: $i] :
( epsilon_connected(X0)
| subset(sK3(X0),X0)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_72,c_65]) ).
tcf(c_3808,plain,
! [X0: $i] :
( epsilon_connected(X0)
| subset(sK4(X0),X0)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_73,c_65]) ).
tcf(c_3809,plain,
( subset(sK18,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3400,c_65]) ).
tcf(c_3810,plain,
( epsilon_transitive(iPr_def_10)
| subset(sK1(iPr_def_10),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3669,c_65]) ).
tcf(c_3811,plain,
( epsilon_connected(iPr_def_10)
| subset(sK3(iPr_def_10),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3670,c_65]) ).
tcf(c_3812,plain,
( epsilon_connected(iPr_def_10)
| subset(sK4(iPr_def_10),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3671,c_65]) ).
tcf(c_3863,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_union2(X1,X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_138,c_128]) ).
tcf(c_3864,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ subset(X0,sK5(powerset(X1))) ),
inference(superposition,[status(thm)],[c_3564,c_128]) ).
tcf(c_3865,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_union2(X2,X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3397,c_128]) ).
tcf(c_3866,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_3420,c_128]) ).
tcf(c_3867,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ subset(X0,sK18) ),
inference(superposition,[status(thm)],[c_3425,c_128]) ).
tcf(c_3868,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ subset(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3426,c_128]) ).
tcf(c_3899,plain,
! [X0: $i] :
( empty(X0)
| subset(sK5(X0),X0)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_3768,c_65]) ).
tcf(c_3900,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK5(X0)) ),
inference(superposition,[status(thm)],[c_3768,c_49]) ).
tcf(c_3903,plain,
! [X0: $i] :
( empty(singleton(X0))
| ( sK5(singleton(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_3768,c_62]) ).
tcf(c_3905,plain,
( empty(iPr_def_10)
| in(sK5(iPr_def_10),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3768,c_3614]) ).
tcf(c_3906,plain,
in(sK5(iPr_def_10),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_3905,c_3517]) ).
tcf(c_3909,plain,
! [X0: $i] : sK5(singleton(X0)) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_3903,c_3513]) ).
tcf(c_3915,plain,
( subset(sK5(iPr_def_10),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3906,c_65]) ).
tcf(c_3916,plain,
~ in(iPr_def_11,sK5(iPr_def_10)),
inference(superposition,[status(thm)],[c_3906,c_49]) ).
tcf(c_3918,plain,
element(sK5(iPr_def_10),iPr_def_11),
inference(superposition,[status(thm)],[c_3906,c_127]) ).
tcf(c_3931,plain,
! [X0: $i] :
( subset(X0,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK18) ),
inference(superposition,[status(thm)],[c_3809,c_128]) ).
tcf(c_3936,plain,
sK5(iPr_def_10) = sK18,
inference(superposition,[status(thm)],[c_2420,c_3909]) ).
tcf(c_3944,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(singleton(set_union2(set_union2(X0,X1),X2)),X0),
inference(superposition,[status(thm)],[c_69,c_3618]) ).
tcf(c_3945,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(singleton(set_union2(set_union2(X0,X1),X2)),X1),
inference(superposition,[status(thm)],[c_70,c_3618]) ).
tcf(c_3950,plain,
! [X0: $i] : ~ in(singleton(X0),empty_set),
inference(superposition,[status(thm)],[c_3423,c_3618]) ).
tcf(c_3951,plain,
~ in(singleton(iPr_def_11),iPr_def_10),
inference(superposition,[status(thm)],[c_3424,c_3618]) ).
tcf(c_3953,plain,
~ in(iPr_def_10,empty_set),
inference(superposition,[status(thm)],[c_2420,c_3950]) ).
tcf(c_3959,plain,
! [X0: $i] :
( in(sK0(X0,sK18),iPr_def_11)
| ( singleton(X0) = sK18 )
| ( sK0(X0,sK18) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_3640]) ).
tcf(c_3963,plain,
( empty(sK18)
| in(sK5(sK18),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3768,c_3640]) ).
tcf(c_3977,plain,
! [X0: $i] :
( ( singleton(X0) = singleton(sK18) )
| ( sK0(X0,iPr_def_10) = sK18 )
| ( sK0(X0,singleton(sK18)) = X0 ) ),
inference(superposition,[status(thm)],[c_2420,c_3736]) ).
tcf(c_3979,plain,
! [X0: $i] :
( ( singleton(X0) = singleton(sK18) )
| ( sK0(X0,iPr_def_10) = X0 )
| ( sK0(X0,singleton(sK18)) = sK18 ) ),
inference(superposition,[status(thm)],[c_2420,c_3736]) ).
tcf(c_3980,plain,
! [X0: $i,X1: $i] :
( in(X1,singleton(X1))
| ( singleton(X0) = singleton(X1) )
| ( sK0(X0,singleton(X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_3736,c_60]) ).
tcf(c_3981,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK0(X1,singleton(X0)) = X1 )
| ~ in(sK0(X1,singleton(X0)),singleton(X0))
| ( X0 != X1 ) ),
inference(superposition,[status(thm)],[c_3736,c_59]) ).
tcf(c_3984,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK0(X0,singleton(X1)) = X1 )
| ~ in(sK0(X0,singleton(X1)),singleton(X1)) ),
inference(superposition,[status(thm)],[c_3736,c_59]) ).
tcf(c_3986,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK0(X1,singleton(X0)) = X0 )
| ( X0 != X1 ) ),
inference(equality_factoring,[status(thm)],[c_3736]) ).
tcf(c_3987,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( sK0(X0,singleton(X1)) = X0 )
| ( X0 != X1 ) ),
inference(equality_factoring,[status(thm)],[c_3736]) ).
tcf(c_3994,plain,
! [X0: $i] :
( ( singleton(X0) = iPr_def_10 )
| ( sK0(X0,iPr_def_10) = sK18 )
| ( sK0(X0,iPr_def_10) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_3979,c_2420]) ).
tcf(c_4023,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,set_union2(X1,X2)),X2)
| in(sK0(X0,set_union2(X1,X2)),X1)
| ( set_union2(X1,X2) = singleton(X0) )
| ( sK0(X0,set_union2(X1,X2)) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_71]) ).
tcf(c_4024,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X0,X1))
| in(sK1(set_union2(X0,X1)),X1)
| in(sK1(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_64,c_71]) ).
tcf(c_4027,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| in(sK3(set_union2(X0,X1)),X1)
| in(sK3(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_72,c_71]) ).
tcf(c_4028,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| in(sK4(set_union2(X0,X1)),X1)
| in(sK4(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_73,c_71]) ).
tcf(c_4029,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,X1))
| in(sK5(set_union2(X0,X1)),X1)
| in(sK5(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_3768,c_71]) ).
tcf(c_4035,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| in(X0,sK18)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3424,c_71]) ).
tcf(c_4062,plain,
! [X0: $i,X1: $i] :
( in(X0,set_union2(singleton(X0),X1))
| ~ in(X0,singleton(X0)) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_4064,plain,
( ~ epsilon_connected(set_union2(sK18,iPr_def_10))
| ~ epsilon_transitive(set_union2(sK18,iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_1466,c_2420]) ).
tcf(c_4065,plain,
( ~ epsilon_connected(iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(demodulation,[status(thm)],[c_4064,c_58,c_3424]) ).
tcf(c_4078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_union2(set_union2(X0,X1),X2) = X3 )
| ~ in(sK2(set_union2(X0,X1),X2,X3),X3)
| ~ in(sK2(set_union2(X0,X1),X2,X3),X0) ),
inference(superposition,[status(thm)],[c_69,c_66]) ).
tcf(c_4079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_union2(set_union2(X0,X1),X2) = X3 )
| ~ in(sK2(set_union2(X0,X1),X2,X3),X3)
| ~ in(sK2(set_union2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_70,c_66]) ).
tcf(c_4095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_union2(X0,X1) = set_union2(X2,X3) )
| ~ in(sK2(X0,X1,set_union2(X2,X3)),X2)
| ~ in(sK2(X0,X1,set_union2(X2,X3)),X1) ),
inference(superposition,[status(thm)],[c_69,c_67]) ).
tcf(c_4096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_union2(X0,X1) = set_union2(X2,X3) )
| ~ in(sK2(X0,X1,set_union2(X2,X3)),X3)
| ~ in(sK2(X0,X1,set_union2(X2,X3)),X1) ),
inference(superposition,[status(thm)],[c_70,c_67]) ).
tcf(c_4113,plain,
( empty(sK18)
| subset(sK5(sK18),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3963,c_65]) ).
tcf(c_4114,plain,
( empty(sK18)
| ~ in(iPr_def_11,sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3963,c_49]) ).
tcf(c_4116,plain,
( empty(sK18)
| element(sK5(sK18),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3963,c_127]) ).
tcf(c_4131,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(singleton(set_union2(X0,set_union2(X1,X2))),X1),
inference(superposition,[status(thm)],[c_69,c_3644]) ).
tcf(c_4132,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(singleton(set_union2(X0,set_union2(X1,X2))),X2),
inference(superposition,[status(thm)],[c_70,c_3644]) ).
tcf(c_4138,plain,
~ in(singleton(iPr_def_11),sK18),
inference(superposition,[status(thm)],[c_3424,c_3644]) ).
tcf(c_4142,plain,
! [X0: $i] :
( ( iPr_def_11 = sK18 )
| ( iPr_def_11 != X0 )
| ( sK18 != X0 ) ),
inference(instantiation,[status(thm)],[c_2430]) ).
tcf(c_4163,plain,
! [X0: $i] : subset(sK5(powerset(empty_set)),X0),
inference(superposition,[status(thm)],[c_3564,c_3866]) ).
tcf(c_4165,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ subset(X0,sK5(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_4163,c_128]) ).
tcf(c_4174,plain,
subset(sK5(powerset(sK18)),iPr_def_11),
inference(superposition,[status(thm)],[c_3564,c_3867]) ).
tcf(c_4175,plain,
subset(empty_set,iPr_def_11),
inference(superposition,[status(thm)],[c_3420,c_3867]) ).
tcf(c_4176,plain,
subset(sK5(powerset(empty_set)),iPr_def_11),
inference(superposition,[status(thm)],[c_4163,c_3867]) ).
tcf(c_4177,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ subset(X0,sK5(powerset(sK18))) ),
inference(superposition,[status(thm)],[c_4174,c_128]) ).
tcf(c_4186,plain,
subset(sK5(powerset(iPr_def_10)),iPr_def_11),
inference(superposition,[status(thm)],[c_3564,c_3868]) ).
tcf(c_4190,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( X0 != X1 ) ),
inference(global_subsumption_just,[status(thm)],[c_3986,c_2436]) ).
tcf(c_4209,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK0(X2,X1))
| in(sK0(X2,X1),X0)
| ( singleton(X2) = X1 )
| ( sK0(X2,X1) = X2 )
| ( sK0(X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_60,c_77]) ).
tcf(c_4210,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ epsilon_connected(singleton(X1))
| ~ in(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_61,c_77]) ).
tcf(c_4211,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X1)
| in(X0,sK1(X1))
| in(sK1(X1),X0)
| ( sK1(X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_77]) ).
tcf(c_4212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X0)
| in(X0,X3)
| ( X0 = X3 )
| ~ in(X3,X1)
| ~ epsilon_connected(set_union2(X1,X2))
| ~ in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_69,c_77]) ).
tcf(c_4213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X0)
| in(X0,X3)
| ( X0 = X3 )
| ~ in(X3,X2)
| ~ epsilon_connected(set_union2(X1,X2))
| ~ in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_70,c_77]) ).
tcf(c_4216,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,sK5(X1))
| in(sK5(X1),X0)
| ( sK5(X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_3768,c_77]) ).
tcf(c_4217,plain,
! [X0: $i] :
( in(sK18,X0)
| in(X0,sK18)
| ( X0 = sK18 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3400,c_77]) ).
tcf(c_4218,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_10)
| in(X0,sK1(iPr_def_10))
| in(sK1(iPr_def_10),X0)
| ( sK1(iPr_def_10) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3669,c_77]) ).
tcf(c_4219,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_10)
| in(X0,sK3(iPr_def_10))
| in(sK3(iPr_def_10),X0)
| ( sK3(iPr_def_10) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3670,c_77]) ).
tcf(c_4220,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_10)
| in(X0,sK4(iPr_def_10))
| in(sK4(iPr_def_10),X0)
| ( sK4(iPr_def_10) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3671,c_77]) ).
tcf(c_4221,plain,
! [X0: $i] :
( in(sK18,X0)
| in(X0,sK18)
| ( X0 = sK18 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3672,c_77]) ).
tcf(c_4222,plain,
! [X0: $i] :
( empty(sK18)
| in(X0,sK5(sK18))
| in(sK5(sK18),X0)
| ( sK5(sK18) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3963,c_77]) ).
tcf(c_4329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),X3)
| in(sK2(X2,X3,X1),X2)
| in(sK2(X2,X3,X1),X0)
| ( set_union2(X2,X3) = X1 )
| ( sK2(X2,X3,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_77]) ).
tcf(c_4330,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X2,X0),X0)
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_68,c_65]) ).
tcf(c_4331,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_68,c_49]) ).
tcf(c_4332,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_68,c_137]) ).
tcf(c_4333,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_68,c_127]) ).
tcf(c_4334,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,singleton(X2)),X1)
| in(sK2(X0,X1,singleton(X2)),X0)
| ( set_union2(X0,X1) = singleton(X2) )
| ( sK2(X0,X1,singleton(X2)) = X2 ) ),
inference(superposition,[status(thm)],[c_68,c_62]) ).
tcf(c_4337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_union2(X2,X3)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X1)
| in(sK2(X0,X1,set_union2(X2,X3)),X0)
| ( set_union2(X0,X1) = set_union2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_68,c_71]) ).
tcf(c_4338,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X2)
| in(sK2(X0,X1,empty_set),X1)
| in(sK2(X0,X1,empty_set),X0)
| ( set_union2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_68,c_3613]) ).
tcf(c_4339,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK18),iPr_def_11)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 ) ),
inference(superposition,[status(thm)],[c_68,c_3640]) ).
tcf(c_4340,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_10),iPr_def_11)
| in(sK2(X0,X1,iPr_def_10),X1)
| in(sK2(X0,X1,iPr_def_10),X0)
| ( set_union2(X0,X1) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_68,c_3614]) ).
tcf(c_4341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),X3)
| in(sK2(X2,X1,X3),X2)
| in(sK2(X2,X1,X3),X0)
| ( set_union2(X2,X1) = X3 )
| ( sK2(X2,X1,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_77]) ).
tcf(c_4342,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X0,X2),X0)
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_68,c_65]) ).
tcf(c_4343,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ~ in(X0,sK2(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_68,c_49]) ).
tcf(c_4344,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_68,c_137]) ).
tcf(c_4345,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_68,c_127]) ).
tcf(c_4346,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,singleton(X1),X2),X2)
| in(sK2(X0,singleton(X1),X2),X0)
| ( set_union2(X0,singleton(X1)) = X2 )
| ( sK2(X0,singleton(X1),X2) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_62]) ).
tcf(c_4349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_union2(X1,X2),X3),X3)
| in(sK2(X0,set_union2(X1,X2),X3),X2)
| in(sK2(X0,set_union2(X1,X2),X3),X1)
| in(sK2(X0,set_union2(X1,X2),X3),X0)
| ( set_union2(X0,set_union2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_68,c_71]) ).
tcf(c_4350,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X1),X2)
| in(sK2(X0,empty_set,X1),X1)
| in(sK2(X0,empty_set,X1),X0)
| ( set_union2(X0,empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_3613]) ).
tcf(c_4351,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK18,X1),iPr_def_11)
| in(sK2(X0,sK18,X1),X1)
| in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_3640]) ).
tcf(c_4352,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_10,X1),iPr_def_11)
| in(sK2(X0,iPr_def_10,X1),X1)
| in(sK2(X0,iPr_def_10,X1),X0)
| ( set_union2(X0,iPr_def_10) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_3614]) ).
tcf(c_4353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X1,X2,X3))
| in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X0)
| ( set_union2(X1,X2) = X3 )
| ( sK2(X1,X2,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_77]) ).
tcf(c_4354,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_68,c_65]) ).
tcf(c_4355,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 )
| ~ in(X0,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_68,c_49]) ).
tcf(c_4356,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_68,c_137]) ).
tcf(c_4357,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_68,c_127]) ).
tcf(c_4358,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(singleton(X0),X1,X2),X2)
| in(sK2(singleton(X0),X1,X2),X1)
| ( set_union2(singleton(X0),X1) = X2 )
| ( sK2(singleton(X0),X1,X2) = X0 ) ),
inference(superposition,[status(thm)],[c_68,c_62]) ).
tcf(c_4361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_union2(X0,X1),X2,X3),X3)
| in(sK2(set_union2(X0,X1),X2,X3),X2)
| in(sK2(set_union2(X0,X1),X2,X3),X1)
| in(sK2(set_union2(X0,X1),X2,X3),X0)
| ( set_union2(set_union2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_68,c_71]) ).
tcf(c_4362,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X0,X1),X2)
| in(sK2(empty_set,X0,X1),X1)
| in(sK2(empty_set,X0,X1),X0)
| ( set_union2(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_3613]) ).
tcf(c_4363,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK18,X0,X1),iPr_def_11)
| in(sK2(sK18,X0,X1),X1)
| in(sK2(sK18,X0,X1),X0)
| ( set_union2(sK18,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_3640]) ).
tcf(c_4364,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_10,X0,X1),iPr_def_11)
| in(sK2(iPr_def_10,X0,X1),X1)
| in(sK2(iPr_def_10,X0,X1),X0)
| ( set_union2(iPr_def_10,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_3614]) ).
tcf(c_4367,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,X1),X1)
| in(sK2(X0,X1,X1),X0)
| ( set_union2(X0,X1) = X1 ) ),
inference(equality_factoring,[status(thm)],[c_68]) ).
tcf(c_4369,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,X0),X1)
| in(sK2(X0,X1,X0),X0)
| ( set_union2(X0,X1) = X0 ) ),
inference(equality_factoring,[status(thm)],[c_68]) ).
tcf(c_4370,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X0,X1),X1)
| in(sK2(X0,X0,X1),X0)
| ( set_union2(X0,X0) = X1 ) ),
inference(equality_factoring,[status(thm)],[c_68]) ).
tcf(c_4371,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X0,X1),X1)
| in(sK2(X0,X0,X1),X0)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_4370,c_97]) ).
tcf(c_4401,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X0,X1),X2)
| in(sK2(empty_set,X0,X1),X1)
| in(sK2(empty_set,X0,X1),X0)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_4362,c_3423]) ).
tcf(c_4418,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X1),X2)
| in(sK2(X0,empty_set,X1),X1)
| in(sK2(X0,empty_set,X1),X0)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_4350,c_126]) ).
tcf(c_4534,plain,
! [X0: $i] :
( subset(sK1(set_union2(sK18,singleton(sK18))),set_union2(sK18,singleton(sK18)))
| ~ subset(X0,set_union2(sK18,singleton(sK18)))
| ~ subset(sK1(set_union2(sK18,singleton(sK18))),X0) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_4536,plain,
! [X0: $i,X1: $i] :
( subset(sK1(set_union2(sK18,singleton(sK18))),set_union2(sK18,singleton(sK18)))
| ~ subset(X0,X1)
| ( set_union2(sK18,singleton(sK18)) != X1 )
| ( sK1(set_union2(sK18,singleton(sK18))) != X0 ) ),
inference(instantiation,[status(thm)],[c_2437]) ).
tcf(c_4548,plain,
( in(sK1(set_union2(sK18,singleton(sK18))),sK18)
| in(sK1(set_union2(sK18,singleton(sK18))),singleton(sK18))
| ~ in(sK1(set_union2(sK18,singleton(sK18))),set_union2(sK18,singleton(sK18))) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_4573,plain,
( subset(sK18,iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_3915,c_3936]) ).
tcf(c_4574,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ subset(X0,sK5(powerset(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_4186,c_128]) ).
tcf(c_4586,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(powerset(X1))
| subset(X0,X1)
| ~ subset(X0,sK1(powerset(X1))) ),
inference(superposition,[status(thm)],[c_3566,c_128]) ).
tcf(c_4587,plain,
! [X0: $i] :
( epsilon_transitive(powerset(empty_set))
| subset(sK1(powerset(empty_set)),X0) ),
inference(superposition,[status(thm)],[c_3566,c_3866]) ).
tcf(c_4588,plain,
( epsilon_transitive(powerset(sK18))
| subset(sK1(powerset(sK18)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3566,c_3867]) ).
tcf(c_4589,plain,
( epsilon_transitive(powerset(iPr_def_10))
| subset(sK1(powerset(iPr_def_10)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3566,c_3868]) ).
tcf(c_4619,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(X1))
| subset(X0,X1)
| ~ subset(X0,sK3(powerset(X1))) ),
inference(superposition,[status(thm)],[c_3567,c_128]) ).
tcf(c_4620,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| subset(sK3(powerset(empty_set)),X0) ),
inference(superposition,[status(thm)],[c_3567,c_3866]) ).
tcf(c_4621,plain,
( epsilon_connected(powerset(sK18))
| subset(sK3(powerset(sK18)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3567,c_3867]) ).
tcf(c_4622,plain,
( epsilon_connected(powerset(iPr_def_10))
| subset(sK3(powerset(iPr_def_10)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3567,c_3868]) ).
tcf(c_4636,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(X1))
| subset(X0,X1)
| ~ subset(X0,sK4(powerset(X1))) ),
inference(superposition,[status(thm)],[c_3568,c_128]) ).
tcf(c_4637,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| subset(sK4(powerset(empty_set)),X0) ),
inference(superposition,[status(thm)],[c_3568,c_3866]) ).
tcf(c_4638,plain,
( epsilon_connected(powerset(sK18))
| subset(sK4(powerset(sK18)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3568,c_3867]) ).
tcf(c_4639,plain,
( epsilon_connected(powerset(iPr_def_10))
| subset(sK4(powerset(iPr_def_10)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3568,c_3868]) ).
tcf(c_4662,plain,
( epsilon_transitive(iPr_def_10)
| ( sK1(iPr_def_10) = sK18 ) ),
inference(superposition,[status(thm)],[c_64,c_3592]) ).
tcf(c_4663,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_10,X0,X1),X1)
| in(sK2(iPr_def_10,X0,X1),X0)
| ( set_union2(iPr_def_10,X0) = X1 )
| ( sK2(iPr_def_10,X0,X1) = sK18 ) ),
inference(superposition,[status(thm)],[c_68,c_3592]) ).
tcf(c_4664,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_10),X1)
| in(sK2(X0,X1,iPr_def_10),X0)
| ( set_union2(X0,X1) = iPr_def_10 )
| ( sK2(X0,X1,iPr_def_10) = sK18 ) ),
inference(superposition,[status(thm)],[c_68,c_3592]) ).
tcf(c_4665,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_10,X1),X1)
| in(sK2(X0,iPr_def_10,X1),X0)
| ( set_union2(X0,iPr_def_10) = X1 )
| ( sK2(X0,iPr_def_10,X1) = sK18 ) ),
inference(superposition,[status(thm)],[c_68,c_3592]) ).
tcf(c_4666,plain,
( epsilon_connected(iPr_def_10)
| ( sK3(iPr_def_10) = sK18 ) ),
inference(superposition,[status(thm)],[c_72,c_3592]) ).
tcf(c_4667,plain,
( epsilon_connected(iPr_def_10)
| ( sK4(iPr_def_10) = sK18 ) ),
inference(superposition,[status(thm)],[c_73,c_3592]) ).
tcf(c_4723,plain,
( subset(sK18,iPr_def_10)
| ~ epsilon_transitive(singleton(sK18)) ),
inference(superposition,[status(thm)],[c_2420,c_3803]) ).
tcf(c_4724,plain,
! [X0: $i,X1: $i] :
( subset(X0,singleton(X1))
| ~ epsilon_transitive(singleton(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3803,c_128]) ).
tcf(c_4733,plain,
( epsilon_transitive(iPr_def_10)
| ( sK1(singleton(sK18)) = sK18 ) ),
inference(superposition,[status(thm)],[c_2420,c_3589]) ).
tcf(c_4739,plain,
( epsilon_connected(iPr_def_10)
| ( sK3(singleton(sK18)) = sK18 ) ),
inference(superposition,[status(thm)],[c_2420,c_3590]) ).
tcf(c_4745,plain,
( epsilon_connected(iPr_def_10)
| ( sK4(singleton(sK18)) = sK18 ) ),
inference(superposition,[status(thm)],[c_2420,c_3591]) ).
tcf(c_4751,plain,
epsilon_transitive(powerset(empty_set)),
inference(superposition,[status(thm)],[c_4587,c_63]) ).
tcf(c_4760,plain,
! [X0: $i] :
( epsilon_transitive(powerset(sK18))
| subset(X0,iPr_def_11)
| ~ subset(X0,sK1(powerset(sK18))) ),
inference(superposition,[status(thm)],[c_4588,c_128]) ).
tcf(c_4769,plain,
! [X0: $i] :
( epsilon_transitive(powerset(iPr_def_10))
| subset(X0,iPr_def_11)
| ~ subset(X0,sK1(powerset(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_4589,c_128]) ).
tcf(c_4786,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(empty_set))
| subset(X0,X1)
| ~ subset(X0,sK3(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_4620,c_128]) ).
tcf(c_4788,plain,
( epsilon_connected(powerset(empty_set))
| subset(sK3(powerset(empty_set)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4620,c_3867]) ).
tcf(c_4799,plain,
! [X0: $i] :
( epsilon_connected(powerset(sK18))
| subset(X0,iPr_def_11)
| ~ subset(X0,sK3(powerset(sK18))) ),
inference(superposition,[status(thm)],[c_4621,c_128]) ).
tcf(c_4808,plain,
! [X0: $i] :
( epsilon_connected(powerset(iPr_def_10))
| subset(X0,iPr_def_11)
| ~ subset(X0,sK3(powerset(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_4622,c_128]) ).
tcf(c_4817,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(empty_set))
| subset(X0,X1)
| ~ subset(X0,sK4(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_4637,c_128]) ).
tcf(c_4819,plain,
( epsilon_connected(powerset(empty_set))
| subset(sK4(powerset(empty_set)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4637,c_3867]) ).
tcf(c_4838,plain,
! [X0: $i] :
( epsilon_connected(powerset(sK18))
| subset(X0,iPr_def_11)
| ~ subset(X0,sK4(powerset(sK18))) ),
inference(superposition,[status(thm)],[c_4638,c_128]) ).
tcf(c_4847,plain,
! [X0: $i] :
( epsilon_connected(powerset(iPr_def_10))
| subset(X0,iPr_def_11)
| ~ subset(X0,sK4(powerset(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_4639,c_128]) ).
tcf(c_4861,plain,
! [X0: $i] :
( ( singleton(X0) = iPr_def_10 )
| ( sK0(X0,iPr_def_10) = X0 )
| ~ in(sK0(X0,iPr_def_10),iPr_def_10)
| ( X0 != sK18 ) ),
inference(superposition,[status(thm)],[c_3994,c_59]) ).
tcf(c_4864,plain,
! [X0: $i] :
( ( singleton(X0) = iPr_def_10 )
| ( sK0(X0,iPr_def_10) = sK18 )
| ~ in(sK0(X0,iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3994,c_59]) ).
tcf(c_4866,plain,
! [X0: $i] :
( ( singleton(X0) = iPr_def_10 )
| ( sK0(X0,iPr_def_10) = sK18 )
| ( X0 != sK18 ) ),
inference(equality_factoring,[status(thm)],[c_3994]) ).
tcf(c_4867,plain,
! [X0: $i] :
( ( singleton(X0) = iPr_def_10 )
| ( sK0(X0,iPr_def_10) = X0 )
| ( X0 != sK18 ) ),
inference(equality_factoring,[status(thm)],[c_3994]) ).
tcf(c_4899,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_3423,c_3616]) ).
tcf(c_4911,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_3423,c_3617]) ).
tcf(c_4912,plain,
! [X0: $i] :
( element(X0,iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3424,c_3617]) ).
tcf(c_4923,plain,
! [X0: $i] :
( element(sK0(X0,iPr_def_10),iPr_def_11)
| ( singleton(X0) = iPr_def_10 )
| ( sK0(X0,iPr_def_10) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_4912]) ).
tcf(c_4925,plain,
! [X0: $i,X1: $i] :
( element(sK2(iPr_def_10,X0,X1),iPr_def_11)
| in(sK2(iPr_def_10,X0,X1),X1)
| in(sK2(iPr_def_10,X0,X1),X0)
| ( set_union2(iPr_def_10,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_4912]) ).
tcf(c_4926,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,iPr_def_10),iPr_def_11)
| in(sK2(X0,X1,iPr_def_10),X1)
| in(sK2(X0,X1,iPr_def_10),X0)
| ( set_union2(X0,X1) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_68,c_4912]) ).
tcf(c_4927,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,iPr_def_10,X1),iPr_def_11)
| in(sK2(X0,iPr_def_10,X1),X1)
| in(sK2(X0,iPr_def_10,X1),X0)
| ( set_union2(X0,iPr_def_10) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_4912]) ).
tcf(c_4930,plain,
( empty(iPr_def_10)
| element(sK5(iPr_def_10),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3768,c_4912]) ).
tcf(c_4932,plain,
( empty(iPr_def_10)
| element(sK18,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_4930,c_3936]) ).
tcf(c_4973,plain,
! [X0: $i,X1: $i] :
( ( singleton(X1) = empty_set )
| ( sK0(X1,empty_set) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_60,c_4899]) ).
tcf(c_4975,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| in(sK2(empty_set,X1,X2),X1)
| ( set_union2(empty_set,X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_68,c_4899]) ).
tcf(c_4976,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,empty_set),X2)
| in(sK2(X1,X2,empty_set),X1)
| ( set_union2(X1,X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_68,c_4899]) ).
tcf(c_4977,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,empty_set,X2),X2)
| in(sK2(X1,empty_set,X2),X1)
| ( set_union2(X1,empty_set) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_68,c_4899]) ).
tcf(c_5002,plain,
! [X0: $i,X1: $i] :
( element(sK0(X0,empty_set),X1)
| ( singleton(X0) = empty_set )
| ( sK0(X0,empty_set) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_4911]) ).
tcf(c_5004,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(empty_set,X0,X1),X2)
| in(sK2(empty_set,X0,X1),X1)
| in(sK2(empty_set,X0,X1),X0)
| ( set_union2(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_4911]) ).
tcf(c_5005,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,empty_set),X2)
| in(sK2(X0,X1,empty_set),X1)
| in(sK2(X0,X1,empty_set),X0)
| ( set_union2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_68,c_4911]) ).
tcf(c_5006,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,empty_set,X1),X2)
| in(sK2(X0,empty_set,X1),X1)
| in(sK2(X0,empty_set,X1),X0)
| ( set_union2(X0,empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_4911]) ).
tcf(c_5013,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,empty_set,X1),X2)
| in(sK2(X0,empty_set,X1),X1)
| in(sK2(X0,empty_set,X1),X0)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_5006,c_126]) ).
tcf(c_5022,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(empty_set,X0,X1),X2)
| in(sK2(empty_set,X0,X1),X1)
| in(sK2(empty_set,X0,X1),X0)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_5004,c_3423]) ).
tcf(c_5047,plain,
! [X0: $i] :
( element(X0,iPr_def_11)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3424,c_3643]) ).
tcf(c_5056,plain,
! [X0: $i] :
( element(sK0(X0,sK18),iPr_def_11)
| ( singleton(X0) = sK18 )
| ( sK0(X0,sK18) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_5047]) ).
tcf(c_5058,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK18,X0,X1),iPr_def_11)
| in(sK2(sK18,X0,X1),X1)
| in(sK2(sK18,X0,X1),X0)
| ( set_union2(sK18,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_5047]) ).
tcf(c_5059,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,sK18),iPr_def_11)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 ) ),
inference(superposition,[status(thm)],[c_68,c_5047]) ).
tcf(c_5060,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK18,X1),iPr_def_11)
| in(sK2(X0,sK18,X1),X1)
| in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_5047]) ).
tcf(c_5097,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X1)
| subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ subset(X0,sK3(X1)) ),
inference(superposition,[status(thm)],[c_3807,c_128]) ).
tcf(c_5100,plain,
( epsilon_connected(iPr_def_10)
| subset(sK3(iPr_def_10),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3807,c_3868]) ).
tcf(c_5117,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X1)
| subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ subset(X0,sK4(X1)) ),
inference(superposition,[status(thm)],[c_3808,c_128]) ).
tcf(c_5120,plain,
( epsilon_connected(iPr_def_10)
| subset(sK4(iPr_def_10),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3808,c_3868]) ).
tcf(c_5142,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_10)
| subset(X0,iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ subset(X0,sK1(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3810,c_128]) ).
tcf(c_5154,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_10)
| subset(X0,iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ subset(X0,sK3(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3811,c_128]) ).
tcf(c_5166,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_10)
| subset(X0,iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ subset(X0,sK4(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3812,c_128]) ).
tcf(c_5183,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X0,X1))
| ~ subset(sK1(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_3863,c_63]) ).
tcf(c_5184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X2,set_union2(X1,X3))
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3863,c_128]) ).
tcf(c_5196,plain,
! [X0: $i] : subset(sK5(powerset(sK5(powerset(X0)))),X0),
inference(superposition,[status(thm)],[c_3564,c_3864]) ).
tcf(c_5198,plain,
! [X0: $i] :
( epsilon_transitive(powerset(sK5(powerset(X0))))
| subset(sK1(powerset(sK5(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3566,c_3864]) ).
tcf(c_5199,plain,
! [X0: $i] :
( epsilon_connected(powerset(sK5(powerset(X0))))
| subset(sK3(powerset(sK5(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3567,c_3864]) ).
tcf(c_5200,plain,
! [X0: $i] :
( epsilon_connected(powerset(sK5(powerset(X0))))
| subset(sK4(powerset(sK5(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3568,c_3864]) ).
tcf(c_5201,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(X0)))
| subset(sK3(sK5(powerset(X0))),X0)
| ~ epsilon_transitive(sK5(powerset(X0))) ),
inference(superposition,[status(thm)],[c_3807,c_3864]) ).
tcf(c_5202,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(X0)))
| subset(sK4(sK5(powerset(X0))),X0)
| ~ epsilon_transitive(sK5(powerset(X0))) ),
inference(superposition,[status(thm)],[c_3808,c_3864]) ).
tcf(c_5249,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ subset(X0,sK5(powerset(sK5(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_5196,c_128]) ).
tcf(c_5250,plain,
! [X0: $i] : subset(sK5(powerset(sK5(powerset(empty_set)))),X0),
inference(superposition,[status(thm)],[c_5196,c_3866]) ).
tcf(c_5251,plain,
subset(sK5(powerset(sK5(powerset(sK18)))),iPr_def_11),
inference(superposition,[status(thm)],[c_5196,c_3867]) ).
tcf(c_5252,plain,
! [X0: $i] : subset(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),X0),
inference(superposition,[status(thm)],[c_5196,c_3864]) ).
tcf(c_5253,plain,
subset(sK5(powerset(sK5(powerset(iPr_def_10)))),iPr_def_11),
inference(superposition,[status(thm)],[c_5196,c_3868]) ).
tcf(c_5262,plain,
iPr_def_11 = iPr_def_11,
inference(instantiation,[status(thm)],[c_2428]) ).
tcf(c_5277,plain,
( ( singleton(sK18) = iPr_def_10 )
| ( sK0(sK18,iPr_def_10) = sK18 ) ),
inference(equality_resolution,[status(thm)],[c_4866]) ).
tcf(c_5290,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X0,X1))
| ~ subset(sK1(set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_3865,c_63]) ).
tcf(c_5291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X2,set_union2(X3,X1))
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3865,c_128]) ).
tcf(c_5305,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ subset(X0,sK5(X1)) ),
inference(superposition,[status(thm)],[c_3899,c_128]) ).
tcf(c_5307,plain,
( empty(sK18)
| subset(sK5(sK18),iPr_def_11)
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_3899,c_3867]) ).
tcf(c_5308,plain,
! [X0: $i] :
( empty(sK5(powerset(X0)))
| subset(sK5(sK5(powerset(X0))),X0)
| ~ epsilon_transitive(sK5(powerset(X0))) ),
inference(superposition,[status(thm)],[c_3899,c_3864]) ).
tcf(c_5309,plain,
( empty(iPr_def_10)
| subset(sK5(iPr_def_10),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3899,c_3868]) ).
tcf(c_5310,plain,
( empty(iPr_def_10)
| subset(sK18,iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_5309,c_3936]) ).
tcf(c_5311,plain,
( empty(sK18)
| subset(sK5(sK18),iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5307,c_2426]) ).
tcf(c_5325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(singleton(set_union2(set_union2(set_union2(X0,X1),X2),X3)),X0),
inference(superposition,[status(thm)],[c_69,c_3944]) ).
tcf(c_5326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(singleton(set_union2(set_union2(set_union2(X0,X1),X2),X3)),X1),
inference(superposition,[status(thm)],[c_70,c_3944]) ).
tcf(c_5335,plain,
! [X0: $i,X1: $i] : ~ in(singleton(set_union2(X0,X1)),empty_set),
inference(superposition,[status(thm)],[c_3423,c_3944]) ).
tcf(c_5336,plain,
! [X0: $i] : ~ in(singleton(set_union2(iPr_def_11,X0)),iPr_def_10),
inference(superposition,[status(thm)],[c_3424,c_3944]) ).
tcf(c_5345,plain,
! [X0: $i] : ~ in(singleton(set_union2(X0,iPr_def_11)),iPr_def_10),
inference(superposition,[status(thm)],[c_58,c_5336]) ).
tcf(c_5354,plain,
! [X0: $i] :
( empty(sK18)
| subset(X0,iPr_def_11)
| ~ subset(X0,sK5(sK18)) ),
inference(superposition,[status(thm)],[c_5311,c_128]) ).
tcf(c_5363,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ subset(X0,sK5(powerset(sK5(powerset(empty_set))))) ),
inference(superposition,[status(thm)],[c_5250,c_128]) ).
tcf(c_5379,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ subset(X0,sK5(powerset(sK5(powerset(sK18))))) ),
inference(superposition,[status(thm)],[c_5251,c_128]) ).
tcf(c_5407,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ subset(X0,sK5(powerset(sK5(powerset(iPr_def_10))))) ),
inference(superposition,[status(thm)],[c_5253,c_128]) ).
tcf(c_5418,plain,
( empty(sK18)
| subset(sK5(powerset(sK5(sK18))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3564,c_5354]) ).
tcf(c_5419,plain,
( empty(sK18)
| subset(empty_set,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3420,c_5354]) ).
tcf(c_5420,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| subset(sK1(powerset(sK5(sK18))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3566,c_5354]) ).
tcf(c_5421,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK3(powerset(sK5(sK18))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3567,c_5354]) ).
tcf(c_5422,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK4(powerset(sK5(sK18))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3568,c_5354]) ).
tcf(c_5423,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK3(sK5(sK18)),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3807,c_5354]) ).
tcf(c_5424,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK4(sK5(sK18)),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3808,c_5354]) ).
tcf(c_5425,plain,
( empty(sK18)
| empty(sK5(sK18))
| subset(sK5(sK5(sK18)),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3899,c_5354]) ).
tcf(c_5426,plain,
( empty(sK18)
| subset(sK5(powerset(empty_set)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4163,c_5354]) ).
tcf(c_5427,plain,
( empty(sK18)
| epsilon_connected(powerset(empty_set))
| subset(sK3(powerset(empty_set)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4620,c_5354]) ).
tcf(c_5428,plain,
( empty(sK18)
| epsilon_connected(powerset(empty_set))
| subset(sK4(powerset(empty_set)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4637,c_5354]) ).
tcf(c_5429,plain,
( empty(sK18)
| subset(sK5(powerset(sK5(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5196,c_5354]) ).
tcf(c_5430,plain,
( empty(sK18)
| subset(sK5(powerset(sK5(powerset(empty_set)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5250,c_5354]) ).
tcf(c_5463,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ in(sK18,iPr_def_11)
| ~ subset(iPr_def_11,X0) ),
inference(instantiation,[status(thm)],[c_359]) ).
tcf(c_5465,plain,
! [X0: $i] :
( in(sK18,set_union2(iPr_def_11,X0))
| ~ in(sK18,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_5471,plain,
( ~ empty(empty_set)
| ~ subset(iPr_def_11,empty_set)
| ~ in(sK18,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_5463]) ).
tcf(c_5478,plain,
! [X0: $i] :
( empty(sK18)
| subset(X0,iPr_def_11)
| ~ subset(X0,sK5(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_5418,c_128]) ).
tcf(c_5491,plain,
! [X0: $i] :
( empty(sK18)
| subset(X0,iPr_def_11)
| ~ subset(X0,sK5(powerset(sK5(powerset(sK5(sK18)))))) ),
inference(superposition,[status(thm)],[c_5429,c_128]) ).
tcf(c_5502,plain,
! [X0: $i] :
( empty(sK18)
| subset(X0,iPr_def_11)
| epsilon_transitive(powerset(sK5(sK18)))
| ~ subset(X0,sK1(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_5420,c_128]) ).
tcf(c_5516,plain,
! [X0: $i] :
( empty(sK18)
| subset(X0,iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| ~ subset(X0,sK3(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_5421,c_128]) ).
tcf(c_5528,plain,
! [X0: $i] :
( empty(sK18)
| subset(X0,iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| ~ subset(X0,sK4(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_5422,c_128]) ).
tcf(c_5547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,X2)),X3)),X1),
inference(superposition,[status(thm)],[c_69,c_3945]) ).
tcf(c_5548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,X2)),X3)),X2),
inference(superposition,[status(thm)],[c_70,c_3945]) ).
tcf(c_5558,plain,
! [X0: $i] : ~ in(singleton(set_union2(iPr_def_11,X0)),sK18),
inference(superposition,[status(thm)],[c_3424,c_3945]) ).
tcf(c_5571,plain,
! [X0: $i] : ~ in(singleton(set_union2(X0,iPr_def_11)),sK18),
inference(superposition,[status(thm)],[c_58,c_5558]) ).
tcf(c_5584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,X2),X3))),X1),
inference(superposition,[status(thm)],[c_69,c_4131]) ).
tcf(c_5585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,X2),X3))),X2),
inference(superposition,[status(thm)],[c_70,c_4131]) ).
tcf(c_5597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,X3)))),X2),
inference(superposition,[status(thm)],[c_69,c_4132]) ).
tcf(c_5598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,X3)))),X3),
inference(superposition,[status(thm)],[c_70,c_4132]) ).
tcf(c_5718,plain,
! [X0: $i] :
( epsilon_transitive(powerset(sK5(powerset(empty_set))))
| subset(sK1(powerset(sK5(powerset(empty_set)))),X0) ),
inference(superposition,[status(thm)],[c_3566,c_4165]) ).
tcf(c_5719,plain,
! [X0: $i] :
( epsilon_connected(powerset(sK5(powerset(empty_set))))
| subset(sK3(powerset(sK5(powerset(empty_set)))),X0) ),
inference(superposition,[status(thm)],[c_3567,c_4165]) ).
tcf(c_5720,plain,
! [X0: $i] :
( epsilon_connected(powerset(sK5(powerset(empty_set))))
| subset(sK4(powerset(sK5(powerset(empty_set)))),X0) ),
inference(superposition,[status(thm)],[c_3568,c_4165]) ).
tcf(c_5721,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(empty_set)))
| subset(sK3(sK5(powerset(empty_set))),X0)
| ~ epsilon_transitive(sK5(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_3807,c_4165]) ).
tcf(c_5722,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(empty_set)))
| subset(sK4(sK5(powerset(empty_set))),X0)
| ~ epsilon_transitive(sK5(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_3808,c_4165]) ).
tcf(c_5723,plain,
! [X0: $i] :
( empty(sK5(powerset(empty_set)))
| subset(sK5(sK5(powerset(empty_set))),X0)
| ~ epsilon_transitive(sK5(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_3899,c_4165]) ).
tcf(c_5727,plain,
! [X0: $i] : subset(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),X0),
inference(superposition,[status(thm)],[c_5196,c_4165]) ).
tcf(c_5794,plain,
! [X0: $i] :
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(X0,iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ subset(X0,sK3(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_5423,c_128]) ).
tcf(c_5809,plain,
! [X0: $i] :
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(X0,iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ subset(X0,sK4(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_5424,c_128]) ).
tcf(c_5824,plain,
! [X0: $i] :
( empty(sK18)
| empty(sK5(sK18))
| subset(X0,iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ subset(X0,sK5(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_5425,c_128]) ).
tcf(c_5840,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(powerset(sK5(sK18)))))
| subset(sK1(powerset(sK5(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3566,c_5478]) ).
tcf(c_5841,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(powerset(sK5(sK18)))))
| subset(sK3(powerset(sK5(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3567,c_5478]) ).
tcf(c_5842,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(powerset(sK5(sK18)))))
| subset(sK4(powerset(sK5(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3568,c_5478]) ).
tcf(c_5843,plain,
( empty(sK18)
| epsilon_connected(sK5(powerset(sK5(sK18))))
| subset(sK3(sK5(powerset(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_3807,c_5478]) ).
tcf(c_5844,plain,
( empty(sK18)
| epsilon_connected(sK5(powerset(sK5(sK18))))
| subset(sK4(sK5(powerset(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_3808,c_5478]) ).
tcf(c_5845,plain,
( empty(sK18)
| empty(sK5(powerset(sK5(sK18))))
| subset(sK5(sK5(powerset(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_3899,c_5478]) ).
tcf(c_5849,plain,
( empty(sK18)
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5196,c_5478]) ).
tcf(c_5900,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(powerset(sK5(powerset(sK5(sK18)))))))
| subset(sK1(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3566,c_5491]) ).
tcf(c_5901,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(powerset(sK5(powerset(sK5(sK18)))))))
| subset(sK3(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3567,c_5491]) ).
tcf(c_5902,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(powerset(sK5(powerset(sK5(sK18)))))))
| subset(sK4(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3568,c_5491]) ).
tcf(c_5903,plain,
( empty(sK18)
| epsilon_connected(sK5(powerset(sK5(powerset(sK5(sK18))))))
| subset(sK3(sK5(powerset(sK5(powerset(sK5(sK18)))))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK5(sK18)))))) ),
inference(superposition,[status(thm)],[c_3807,c_5491]) ).
tcf(c_5904,plain,
( empty(sK18)
| epsilon_connected(sK5(powerset(sK5(powerset(sK5(sK18))))))
| subset(sK4(sK5(powerset(sK5(powerset(sK5(sK18)))))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK5(sK18)))))) ),
inference(superposition,[status(thm)],[c_3808,c_5491]) ).
tcf(c_5905,plain,
( empty(sK18)
| empty(sK5(powerset(sK5(powerset(sK5(sK18))))))
| subset(sK5(sK5(powerset(sK5(powerset(sK5(sK18)))))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK5(sK18)))))) ),
inference(superposition,[status(thm)],[c_3899,c_5491]) ).
tcf(c_5909,plain,
( empty(sK18)
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5196,c_5491]) ).
tcf(c_5967,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| subset(sK5(powerset(sK1(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3564,c_5502]) ).
tcf(c_5968,plain,
( empty(sK18)
| subset(empty_set,iPr_def_11)
| epsilon_transitive(powerset(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_3420,c_5502]) ).
tcf(c_5969,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| epsilon_transitive(powerset(sK1(powerset(sK5(sK18)))))
| subset(sK1(powerset(sK1(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3566,c_5502]) ).
tcf(c_5970,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| epsilon_connected(powerset(sK1(powerset(sK5(sK18)))))
| subset(sK3(powerset(sK1(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3567,c_5502]) ).
tcf(c_5971,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| epsilon_connected(powerset(sK1(powerset(sK5(sK18)))))
| subset(sK4(powerset(sK1(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3568,c_5502]) ).
tcf(c_5972,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| epsilon_connected(sK1(powerset(sK5(sK18))))
| subset(sK3(sK1(powerset(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK1(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_3807,c_5502]) ).
tcf(c_5973,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| epsilon_connected(sK1(powerset(sK5(sK18))))
| subset(sK4(sK1(powerset(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK1(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_3808,c_5502]) ).
tcf(c_5974,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| empty(sK1(powerset(sK5(sK18))))
| subset(sK5(sK1(powerset(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK1(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_3899,c_5502]) ).
tcf(c_5975,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| subset(sK5(powerset(empty_set)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4163,c_5502]) ).
tcf(c_5976,plain,
( empty(sK18)
| epsilon_connected(powerset(empty_set))
| epsilon_transitive(powerset(sK5(sK18)))
| subset(sK3(powerset(empty_set)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4620,c_5502]) ).
tcf(c_5977,plain,
( empty(sK18)
| epsilon_connected(powerset(empty_set))
| epsilon_transitive(powerset(sK5(sK18)))
| subset(sK4(powerset(empty_set)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4637,c_5502]) ).
tcf(c_5978,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| subset(sK5(powerset(sK5(powerset(sK1(powerset(sK5(sK18))))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5196,c_5502]) ).
tcf(c_5979,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| subset(sK5(powerset(sK5(powerset(empty_set)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5250,c_5502]) ).
tcf(c_6057,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK5(powerset(sK3(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3564,c_5516]) ).
tcf(c_6058,plain,
( empty(sK18)
| subset(empty_set,iPr_def_11)
| epsilon_connected(powerset(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_3420,c_5516]) ).
tcf(c_6059,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| epsilon_transitive(powerset(sK3(powerset(sK5(sK18)))))
| subset(sK1(powerset(sK3(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3566,c_5516]) ).
tcf(c_6060,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| epsilon_connected(powerset(sK3(powerset(sK5(sK18)))))
| subset(sK3(powerset(sK3(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3567,c_5516]) ).
tcf(c_6061,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| epsilon_connected(powerset(sK3(powerset(sK5(sK18)))))
| subset(sK4(powerset(sK3(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3568,c_5516]) ).
tcf(c_6062,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| epsilon_connected(sK3(powerset(sK5(sK18))))
| subset(sK3(sK3(powerset(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK3(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_3807,c_5516]) ).
tcf(c_6063,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| epsilon_connected(sK3(powerset(sK5(sK18))))
| subset(sK4(sK3(powerset(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK3(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_3808,c_5516]) ).
tcf(c_6064,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| empty(sK3(powerset(sK5(sK18))))
| subset(sK5(sK3(powerset(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK3(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_3899,c_5516]) ).
tcf(c_6065,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK5(powerset(empty_set)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4163,c_5516]) ).
tcf(c_6066,plain,
( empty(sK18)
| epsilon_connected(powerset(empty_set))
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK3(powerset(empty_set)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4620,c_5516]) ).
tcf(c_6067,plain,
( empty(sK18)
| epsilon_connected(powerset(empty_set))
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK4(powerset(empty_set)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4637,c_5516]) ).
tcf(c_6068,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK5(powerset(sK5(powerset(sK3(powerset(sK5(sK18))))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5196,c_5516]) ).
tcf(c_6069,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK5(powerset(sK5(powerset(empty_set)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5250,c_5516]) ).
tcf(c_6120,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK5(powerset(sK4(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3564,c_5528]) ).
tcf(c_6122,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| epsilon_transitive(powerset(sK4(powerset(sK5(sK18)))))
| subset(sK1(powerset(sK4(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3566,c_5528]) ).
tcf(c_6123,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| epsilon_connected(powerset(sK4(powerset(sK5(sK18)))))
| subset(sK3(powerset(sK4(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3567,c_5528]) ).
tcf(c_6124,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| epsilon_connected(powerset(sK4(powerset(sK5(sK18)))))
| subset(sK4(powerset(sK4(powerset(sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3568,c_5528]) ).
tcf(c_6125,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| epsilon_connected(sK4(powerset(sK5(sK18))))
| subset(sK3(sK4(powerset(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK4(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_3807,c_5528]) ).
tcf(c_6126,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| epsilon_connected(sK4(powerset(sK5(sK18))))
| subset(sK4(sK4(powerset(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK4(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_3808,c_5528]) ).
tcf(c_6127,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| empty(sK4(powerset(sK5(sK18))))
| subset(sK5(sK4(powerset(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK4(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_3899,c_5528]) ).
tcf(c_6131,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK5(powerset(sK5(powerset(sK4(powerset(sK5(sK18))))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5196,c_5528]) ).
tcf(c_6195,plain,
( epsilon_transitive(powerset(sK5(powerset(sK18))))
| subset(sK1(powerset(sK5(powerset(sK18)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3566,c_4177]) ).
tcf(c_6196,plain,
( epsilon_connected(powerset(sK5(powerset(sK18))))
| subset(sK3(powerset(sK5(powerset(sK18)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3567,c_4177]) ).
tcf(c_6197,plain,
( epsilon_connected(powerset(sK5(powerset(sK18))))
| subset(sK4(powerset(sK5(powerset(sK18)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3568,c_4177]) ).
tcf(c_6198,plain,
( epsilon_connected(sK5(powerset(sK18)))
| subset(sK3(sK5(powerset(sK18))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK18))) ),
inference(superposition,[status(thm)],[c_3807,c_4177]) ).
tcf(c_6199,plain,
( epsilon_connected(sK5(powerset(sK18)))
| subset(sK4(sK5(powerset(sK18))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK18))) ),
inference(superposition,[status(thm)],[c_3808,c_4177]) ).
tcf(c_6200,plain,
( empty(sK5(powerset(sK18)))
| subset(sK5(sK5(powerset(sK18))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK18))) ),
inference(superposition,[status(thm)],[c_3899,c_4177]) ).
tcf(c_6204,plain,
subset(sK5(powerset(sK5(powerset(sK5(powerset(sK18)))))),iPr_def_11),
inference(superposition,[status(thm)],[c_5196,c_4177]) ).
tcf(c_6205,plain,
subset(sK5(powerset(sK5(powerset(empty_set)))),iPr_def_11),
inference(superposition,[status(thm)],[c_5250,c_4177]) ).
tcf(c_6236,plain,
( epsilon_transitive(powerset(sK5(powerset(iPr_def_10))))
| subset(sK1(powerset(sK5(powerset(iPr_def_10)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3566,c_4574]) ).
tcf(c_6237,plain,
( epsilon_connected(powerset(sK5(powerset(iPr_def_10))))
| subset(sK3(powerset(sK5(powerset(iPr_def_10)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3567,c_4574]) ).
tcf(c_6238,plain,
( epsilon_connected(powerset(sK5(powerset(iPr_def_10))))
| subset(sK4(powerset(sK5(powerset(iPr_def_10)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3568,c_4574]) ).
tcf(c_6239,plain,
( epsilon_connected(sK5(powerset(iPr_def_10)))
| subset(sK3(sK5(powerset(iPr_def_10))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_3807,c_4574]) ).
tcf(c_6240,plain,
( epsilon_connected(sK5(powerset(iPr_def_10)))
| subset(sK4(sK5(powerset(iPr_def_10))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_3808,c_4574]) ).
tcf(c_6241,plain,
( empty(sK5(powerset(iPr_def_10)))
| subset(sK5(sK5(powerset(iPr_def_10))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_3899,c_4574]) ).
tcf(c_6245,plain,
subset(sK5(powerset(sK5(powerset(sK5(powerset(iPr_def_10)))))),iPr_def_11),
inference(superposition,[status(thm)],[c_5196,c_4574]) ).
tcf(c_6282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(set_union2(X2,X3),X0)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_69,c_3615]) ).
tcf(c_6283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(set_union2(X3,X2),X0)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_70,c_3615]) ).
tcf(c_6288,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,empty_set)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_3423,c_3615]) ).
tcf(c_6289,plain,
! [X0: $i] :
( ~ in(iPr_def_11,X0)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3424,c_3615]) ).
tcf(c_6325,plain,
! [X0: $i] :
( ( singleton(X0) = iPr_def_10 )
| ( sK0(X0,iPr_def_10) = X0 )
| ~ in(iPr_def_11,sK0(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_60,c_6289]) ).
tcf(c_6327,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_10,X0,X1),X1)
| in(sK2(iPr_def_10,X0,X1),X0)
| ( set_union2(iPr_def_10,X0) = X1 )
| ~ in(iPr_def_11,sK2(iPr_def_10,X0,X1)) ),
inference(superposition,[status(thm)],[c_68,c_6289]) ).
tcf(c_6328,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_10),X1)
| in(sK2(X0,X1,iPr_def_10),X0)
| ( set_union2(X0,X1) = iPr_def_10 )
| ~ in(iPr_def_11,sK2(X0,X1,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_68,c_6289]) ).
tcf(c_6329,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_10,X1),X1)
| in(sK2(X0,iPr_def_10,X1),X0)
| ( set_union2(X0,iPr_def_10) = X1 )
| ~ in(iPr_def_11,sK2(X0,iPr_def_10,X1)) ),
inference(superposition,[status(thm)],[c_68,c_6289]) ).
tcf(c_6332,plain,
( empty(iPr_def_10)
| ~ in(iPr_def_11,sK5(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3768,c_6289]) ).
tcf(c_6334,plain,
( empty(iPr_def_10)
| ~ in(iPr_def_11,sK18) ),
inference(light_normalisation,[status(thm)],[c_6332,c_3936]) ).
tcf(c_6365,plain,
! [X0: $i,X1: $i] :
( ( singleton(X1) = X0 )
| ( sK0(X1,X0) = X1 )
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_60,c_6288]) ).
tcf(c_6367,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_64,c_6288]) ).
tcf(c_6368,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 )
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_68,c_6288]) ).
tcf(c_6369,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_68,c_6288]) ).
tcf(c_6370,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_68,c_6288]) ).
tcf(c_6371,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ in(set_union2(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_69,c_6288]) ).
tcf(c_6372,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(set_union2(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_70,c_6288]) ).
tcf(c_6373,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_72,c_6288]) ).
tcf(c_6375,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_3768,c_6288]) ).
tcf(c_6380,plain,
~ in(iPr_def_11,empty_set),
inference(superposition,[status(thm)],[c_3672,c_6288]) ).
tcf(c_6435,plain,
! [X0: $i] :
( epsilon_transitive(sK0(X0,empty_set))
| ( singleton(X0) = empty_set )
| ( sK0(X0,empty_set) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_6367]) ).
tcf(c_6437,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK2(empty_set,X0,X1))
| in(sK2(empty_set,X0,X1),X1)
| in(sK2(empty_set,X0,X1),X0)
| ( set_union2(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_6367]) ).
tcf(c_6438,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK2(X0,X1,empty_set))
| in(sK2(X0,X1,empty_set),X1)
| in(sK2(X0,X1,empty_set),X0)
| ( set_union2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_68,c_6367]) ).
tcf(c_6439,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK2(X0,empty_set,X1))
| in(sK2(X0,empty_set,X1),X1)
| in(sK2(X0,empty_set,X1),X0)
| ( set_union2(X0,empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_6367]) ).
tcf(c_6446,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK2(X0,empty_set,X1))
| in(sK2(X0,empty_set,X1),X1)
| in(sK2(X0,empty_set,X1),X0)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_6439,c_126]) ).
tcf(c_6455,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK2(empty_set,X0,X1))
| in(sK2(empty_set,X0,X1),X1)
| in(sK2(empty_set,X0,X1),X0)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_6437,c_3423]) ).
tcf(c_6492,plain,
! [X0: $i] :
( epsilon_connected(sK0(X0,empty_set))
| ( singleton(X0) = empty_set )
| ( sK0(X0,empty_set) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_6373]) ).
tcf(c_6494,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK2(empty_set,X0,X1))
| in(sK2(empty_set,X0,X1),X1)
| in(sK2(empty_set,X0,X1),X0)
| ( set_union2(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_6373]) ).
tcf(c_6495,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK2(X0,X1,empty_set))
| in(sK2(X0,X1,empty_set),X1)
| in(sK2(X0,X1,empty_set),X0)
| ( set_union2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_68,c_6373]) ).
tcf(c_6496,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK2(X0,empty_set,X1))
| in(sK2(X0,empty_set,X1),X1)
| in(sK2(X0,empty_set,X1),X0)
| ( set_union2(X0,empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_6373]) ).
tcf(c_6503,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK2(X0,empty_set,X1))
| in(sK2(X0,empty_set,X1),X1)
| in(sK2(X0,empty_set,X1),X0)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_6496,c_126]) ).
tcf(c_6512,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK2(empty_set,X0,X1))
| in(sK2(empty_set,X0,X1),X1)
| in(sK2(empty_set,X0,X1),X0)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_6494,c_3423]) ).
tcf(c_6529,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK5(powerset(sK3(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3564,c_5794]) ).
tcf(c_6530,plain,
( empty(sK18)
| subset(empty_set,iPr_def_11)
| epsilon_connected(sK5(sK18))
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3420,c_5794]) ).
tcf(c_6531,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| epsilon_transitive(powerset(sK3(sK5(sK18))))
| subset(sK1(powerset(sK3(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3566,c_5794]) ).
tcf(c_6532,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| epsilon_connected(powerset(sK3(sK5(sK18))))
| subset(sK3(powerset(sK3(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3567,c_5794]) ).
tcf(c_6533,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| epsilon_connected(powerset(sK3(sK5(sK18))))
| subset(sK4(powerset(sK3(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3568,c_5794]) ).
tcf(c_6534,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| epsilon_connected(sK3(sK5(sK18)))
| subset(sK3(sK3(sK5(sK18))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK3(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_3807,c_5794]) ).
tcf(c_6535,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| epsilon_connected(sK3(sK5(sK18)))
| subset(sK4(sK3(sK5(sK18))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK3(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_3808,c_5794]) ).
tcf(c_6536,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| empty(sK3(sK5(sK18)))
| subset(sK5(sK3(sK5(sK18))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK3(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_3899,c_5794]) ).
tcf(c_6537,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK5(powerset(empty_set)),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_4163,c_5794]) ).
tcf(c_6538,plain,
( empty(sK18)
| epsilon_connected(powerset(empty_set))
| epsilon_connected(sK5(sK18))
| subset(sK3(powerset(empty_set)),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_4620,c_5794]) ).
tcf(c_6539,plain,
( empty(sK18)
| epsilon_connected(powerset(empty_set))
| epsilon_connected(sK5(sK18))
| subset(sK4(powerset(empty_set)),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_4637,c_5794]) ).
tcf(c_6540,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK5(powerset(sK5(powerset(sK3(sK5(sK18)))))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_5196,c_5794]) ).
tcf(c_6541,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK5(powerset(sK5(powerset(empty_set)))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_5250,c_5794]) ).
tcf(c_6615,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK5(powerset(sK4(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3564,c_5809]) ).
tcf(c_6617,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| epsilon_transitive(powerset(sK4(sK5(sK18))))
| subset(sK1(powerset(sK4(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3566,c_5809]) ).
tcf(c_6618,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| epsilon_connected(powerset(sK4(sK5(sK18))))
| subset(sK3(powerset(sK4(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3567,c_5809]) ).
tcf(c_6619,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| epsilon_connected(powerset(sK4(sK5(sK18))))
| subset(sK4(powerset(sK4(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3568,c_5809]) ).
tcf(c_6620,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| epsilon_connected(sK4(sK5(sK18)))
| subset(sK3(sK4(sK5(sK18))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK4(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_3807,c_5809]) ).
tcf(c_6621,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| epsilon_connected(sK4(sK5(sK18)))
| subset(sK4(sK4(sK5(sK18))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK4(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_3808,c_5809]) ).
tcf(c_6622,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| empty(sK4(sK5(sK18)))
| subset(sK5(sK4(sK5(sK18))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK4(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_3899,c_5809]) ).
tcf(c_6626,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK5(powerset(sK5(powerset(sK4(sK5(sK18)))))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_5196,c_5809]) ).
tcf(c_6702,plain,
( empty(sK18)
| empty(sK5(sK18))
| subset(sK5(powerset(sK5(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3564,c_5824]) ).
tcf(c_6703,plain,
( empty(sK18)
| subset(empty_set,iPr_def_11)
| empty(sK5(sK18))
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3420,c_5824]) ).
tcf(c_6704,plain,
( empty(sK18)
| empty(sK5(sK18))
| epsilon_transitive(powerset(sK5(sK5(sK18))))
| subset(sK1(powerset(sK5(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3566,c_5824]) ).
tcf(c_6705,plain,
( empty(sK18)
| empty(sK5(sK18))
| epsilon_connected(powerset(sK5(sK5(sK18))))
| subset(sK3(powerset(sK5(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3567,c_5824]) ).
tcf(c_6706,plain,
( empty(sK18)
| empty(sK5(sK18))
| epsilon_connected(powerset(sK5(sK5(sK18))))
| subset(sK4(powerset(sK5(sK5(sK18)))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3568,c_5824]) ).
tcf(c_6707,plain,
( empty(sK18)
| empty(sK5(sK18))
| epsilon_connected(sK5(sK5(sK18)))
| subset(sK3(sK5(sK5(sK18))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK5(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_3807,c_5824]) ).
tcf(c_6708,plain,
( empty(sK18)
| empty(sK5(sK18))
| epsilon_connected(sK5(sK5(sK18)))
| subset(sK4(sK5(sK5(sK18))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK5(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_3808,c_5824]) ).
tcf(c_6709,plain,
( empty(sK18)
| empty(sK5(sK18))
| empty(sK5(sK5(sK18)))
| subset(sK5(sK5(sK5(sK18))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK5(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_3899,c_5824]) ).
tcf(c_6710,plain,
( empty(sK18)
| empty(sK5(sK18))
| subset(sK5(powerset(empty_set)),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_4163,c_5824]) ).
tcf(c_6711,plain,
( empty(sK18)
| epsilon_connected(powerset(empty_set))
| empty(sK5(sK18))
| subset(sK3(powerset(empty_set)),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_4620,c_5824]) ).
tcf(c_6712,plain,
( empty(sK18)
| epsilon_connected(powerset(empty_set))
| empty(sK5(sK18))
| subset(sK4(powerset(empty_set)),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_4637,c_5824]) ).
tcf(c_6713,plain,
( empty(sK18)
| empty(sK5(sK18))
| subset(sK5(powerset(sK5(powerset(sK5(sK5(sK18)))))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_5196,c_5824]) ).
tcf(c_6714,plain,
( empty(sK18)
| empty(sK5(sK18))
| subset(sK5(powerset(sK5(powerset(empty_set)))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_5250,c_5824]) ).
tcf(c_6795,plain,
! [X0: $i] :
( empty(sK18)
| subset(X0,iPr_def_11)
| ~ subset(X0,sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18)))))))) ),
inference(superposition,[status(thm)],[c_5849,c_128]) ).
tcf(c_6804,plain,
! [X0: $i] :
( empty(sK18)
| subset(X0,iPr_def_11)
| ~ subset(X0,sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18)))))))))) ),
inference(superposition,[status(thm)],[c_5909,c_128]) ).
tcf(c_6815,plain,
! [X0: $i] :
( empty(sK18)
| subset(X0,iPr_def_11)
| epsilon_transitive(powerset(sK5(sK18)))
| ~ subset(X0,sK5(powerset(sK1(powerset(sK5(sK18)))))) ),
inference(superposition,[status(thm)],[c_5967,c_128]) ).
tcf(c_6834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(set_union2(X2,X3),X1)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_69,c_3641]) ).
tcf(c_6835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(set_union2(X3,X2),X1)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_70,c_3641]) ).
tcf(c_6841,plain,
! [X0: $i] :
( ~ in(iPr_def_11,X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3424,c_3641]) ).
tcf(c_6890,plain,
! [X0: $i] :
( ( singleton(X0) = sK18 )
| ( sK0(X0,sK18) = X0 )
| ~ in(iPr_def_11,sK0(X0,sK18)) ),
inference(superposition,[status(thm)],[c_60,c_6841]) ).
tcf(c_6892,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK18,X0,X1),X1)
| in(sK2(sK18,X0,X1),X0)
| ( set_union2(sK18,X0) = X1 )
| ~ in(iPr_def_11,sK2(sK18,X0,X1)) ),
inference(superposition,[status(thm)],[c_68,c_6841]) ).
tcf(c_6893,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ~ in(iPr_def_11,sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_68,c_6841]) ).
tcf(c_6894,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK18,X1),X1)
| in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 )
| ~ in(iPr_def_11,sK2(X0,sK18,X1)) ),
inference(superposition,[status(thm)],[c_68,c_6841]) ).
tcf(c_6924,plain,
( subset(sK5(powerset(sK18)),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3564,c_3931]) ).
tcf(c_6925,plain,
( subset(empty_set,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3420,c_3931]) ).
tcf(c_6926,plain,
( epsilon_transitive(powerset(sK18))
| subset(sK1(powerset(sK18)),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3566,c_3931]) ).
tcf(c_6927,plain,
( epsilon_connected(powerset(sK18))
| subset(sK3(powerset(sK18)),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3567,c_3931]) ).
tcf(c_6928,plain,
( epsilon_connected(powerset(sK18))
| subset(sK4(powerset(sK18)),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3568,c_3931]) ).
tcf(c_6931,plain,
( empty(sK18)
| subset(sK5(sK18),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_3899,c_3931]) ).
tcf(c_6932,plain,
( subset(sK5(powerset(empty_set)),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4163,c_3931]) ).
tcf(c_6933,plain,
( epsilon_connected(powerset(empty_set))
| subset(sK3(powerset(empty_set)),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4620,c_3931]) ).
tcf(c_6934,plain,
( epsilon_connected(powerset(empty_set))
| subset(sK4(powerset(empty_set)),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4637,c_3931]) ).
tcf(c_6935,plain,
( subset(sK5(powerset(sK5(powerset(sK18)))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5196,c_3931]) ).
tcf(c_6936,plain,
( subset(sK5(powerset(sK5(powerset(empty_set)))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5250,c_3931]) ).
tcf(c_6956,plain,
( empty(sK18)
| subset(sK5(sK18),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6931,c_2426]) ).
tcf(c_6989,plain,
! [X0: $i] :
( in(sK0(X0,iPr_def_11),iPr_def_10)
| in(sK0(X0,iPr_def_11),sK18)
| ( singleton(X0) = iPr_def_11 )
| ( sK0(X0,iPr_def_11) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_4035]) ).
tcf(c_6990,plain,
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_64,c_4035]) ).
tcf(c_6991,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_11,X0,X1),iPr_def_10)
| in(sK2(iPr_def_11,X0,X1),sK18)
| in(sK2(iPr_def_11,X0,X1),X1)
| in(sK2(iPr_def_11,X0,X1),X0)
| ( set_union2(iPr_def_11,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_4035]) ).
tcf(c_6992,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,iPr_def_11),sK18)
| in(sK2(X0,X1,iPr_def_11),X1)
| in(sK2(X0,X1,iPr_def_11),X0)
| ( set_union2(X0,X1) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_68,c_4035]) ).
tcf(c_6993,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_11,X1),iPr_def_10)
| in(sK2(X0,iPr_def_11,X1),sK18)
| in(sK2(X0,iPr_def_11,X1),X1)
| in(sK2(X0,iPr_def_11,X1),X0)
| ( set_union2(X0,iPr_def_11) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_4035]) ).
tcf(c_6994,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_72,c_4035]) ).
tcf(c_6995,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_73,c_4035]) ).
tcf(c_6996,plain,
( empty(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_3768,c_4035]) ).
tcf(c_6997,plain,
( epsilon_transitive(iPr_def_10)
| in(sK1(iPr_def_10),iPr_def_10)
| in(sK1(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_3669,c_4035]) ).
tcf(c_6998,plain,
( epsilon_connected(iPr_def_10)
| in(sK3(iPr_def_10),iPr_def_10)
| in(sK3(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_3670,c_4035]) ).
tcf(c_6999,plain,
( epsilon_connected(iPr_def_10)
| in(sK4(iPr_def_10),iPr_def_10)
| in(sK4(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_3671,c_4035]) ).
tcf(c_7001,plain,
( empty(sK18)
| in(sK5(sK18),iPr_def_10)
| in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_3963,c_4035]) ).
tcf(c_7014,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6996,c_3417]) ).
tcf(c_7091,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,empty_set)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_3423,c_6371]) ).
tcf(c_7097,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_6375,c_4899]) ).
tcf(c_7098,plain,
! [X0: $i] :
( ( singleton(X0) = empty_set )
| ( sK0(X0,empty_set) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_7097]) ).
tcf(c_7100,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X0,X1),X1)
| in(sK2(empty_set,X0,X1),X0)
| ( set_union2(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_7097]) ).
tcf(c_7101,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,empty_set),X1)
| in(sK2(X0,X1,empty_set),X0)
| ( set_union2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_68,c_7097]) ).
tcf(c_7102,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,empty_set,X1),X1)
| in(sK2(X0,empty_set,X1),X0)
| ( set_union2(X0,empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_7097]) ).
tcf(c_7108,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,empty_set,X1),X1)
| in(sK2(X0,empty_set,X1),X0)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_7102,c_126]) ).
tcf(c_7115,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X0,X1),X1)
| in(sK2(empty_set,X0,X1),X0)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_7100,c_3423]) ).
tcf(c_7124,plain,
! [X0: $i] :
( subset(X0,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK5(powerset(sK18))) ),
inference(superposition,[status(thm)],[c_6924,c_128]) ).
tcf(c_7134,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7014,c_77]) ).
tcf(c_7135,plain,
( subset(sK5(iPr_def_11),sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_7014,c_65]) ).
tcf(c_7136,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| ~ in(sK18,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7014,c_49]) ).
tcf(c_7137,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_7014,c_137]) ).
tcf(c_7138,plain,
( element(sK5(iPr_def_11),sK18)
| in(sK5(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7014,c_127]) ).
tcf(c_7139,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| ~ in(iPr_def_11,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7014,c_6841]) ).
tcf(c_7140,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7014,c_5047]) ).
tcf(c_7141,plain,
( in(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7014,c_3640]) ).
tcf(c_7152,plain,
( subset(sK5(iPr_def_11),sK18)
| in(sK5(iPr_def_11),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7135,c_2426]) ).
tcf(c_7155,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7134,c_2427]) ).
tcf(c_7166,plain,
! [X0: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_7137,c_77]) ).
tcf(c_7167,plain,
( subset(sK5(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_7137,c_65]) ).
tcf(c_7168,plain,
( ~ empty(sK18)
| ~ in(iPr_def_10,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7137,c_49]) ).
tcf(c_7170,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_7137,c_127]) ).
tcf(c_7171,plain,
( ~ empty(sK18)
| ~ in(iPr_def_11,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7137,c_6289]) ).
tcf(c_7172,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_7137,c_4912]) ).
tcf(c_7173,plain,
( ( sK5(iPr_def_11) = sK18 )
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_7137,c_3592]) ).
tcf(c_7174,plain,
( in(sK5(iPr_def_11),iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_7137,c_3614]) ).
tcf(c_7199,plain,
! [X0: $i] :
( subset(X0,sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| ~ subset(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7152,c_128]) ).
tcf(c_7200,plain,
( subset(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_7152,c_3931]) ).
tcf(c_7201,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7152,c_3867]) ).
tcf(c_7217,plain,
! [X0: $i] :
( empty(sK18)
| subset(X0,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK5(sK18)) ),
inference(superposition,[status(thm)],[c_6956,c_128]) ).
tcf(c_7234,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_77]) ).
tcf(c_7235,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_65]) ).
tcf(c_7236,plain,
! [X0: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ in(iPr_def_10,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7155,c_49]) ).
tcf(c_7238,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_127]) ).
tcf(c_7239,plain,
! [X0: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7155,c_6289]) ).
tcf(c_7240,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_11)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_4912]) ).
tcf(c_7241,plain,
! [X0: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_3592]) ).
tcf(c_7242,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_11)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_3614]) ).
tcf(c_7243,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK5(iPr_def_11) = X1 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7155,c_77]) ).
tcf(c_7244,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_65]) ).
tcf(c_7246,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_137]) ).
tcf(c_7247,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_127]) ).
tcf(c_7248,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK2(sK5(iPr_def_11),X0,X1))
| ( set_union2(sK5(iPr_def_11),X0) = X1 )
| ( sK2(sK5(iPr_def_11),X0,X1) = sK5(iPr_def_11) )
| ~ in(sK2(sK5(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK5(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_7155,c_66]) ).
tcf(c_7249,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK2(X0,X1,sK5(iPr_def_11)))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_7155,c_67]) ).
tcf(c_7250,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(sK5(iPr_def_11)))
| ( singleton(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(singleton(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_3522]) ).
tcf(c_7251,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(sK5(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_3641]) ).
tcf(c_7252,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(sK5(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_3615]) ).
tcf(c_7253,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_3618]) ).
tcf(c_7254,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_3644]) ).
tcf(c_7256,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_3944]) ).
tcf(c_7257,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_3945]) ).
tcf(c_7258,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_4131]) ).
tcf(c_7259,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_4132]) ).
tcf(c_7260,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_7155,c_77]) ).
tcf(c_7261,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),X0)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_65]) ).
tcf(c_7263,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_137]) ).
tcf(c_7264,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_127]) ).
tcf(c_7265,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(singleton(X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_62]) ).
tcf(c_7266,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_71]) ).
tcf(c_7267,plain,
( in(empty_set,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_7097]) ).
tcf(c_7268,plain,
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ in(iPr_def_11,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7155,c_6841]) ).
tcf(c_7269,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_5047]) ).
tcf(c_7271,plain,
( epsilon_transitive(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK1(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK1(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK1(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_3523]) ).
tcf(c_7272,plain,
( epsilon_connected(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK3(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK3(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_3524]) ).
tcf(c_7273,plain,
( epsilon_connected(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK4(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK4(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_3525]) ).
tcf(c_7279,plain,
( empty(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK5(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_3900]) ).
tcf(c_7555,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| ~ subset(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7201,c_128]) ).
tcf(c_7563,plain,
( subset(sK5(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7200,c_65]) ).
tcf(c_7570,plain,
! [X0: $i] :
( subset(X0,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7563,c_128]) ).
tcf(c_7571,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_7563,c_3868]) ).
tcf(c_7587,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3564,c_7199]) ).
tcf(c_7588,plain,
( subset(empty_set,sK18)
| in(sK5(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3420,c_7199]) ).
tcf(c_7589,plain,
( epsilon_transitive(powerset(sK5(iPr_def_11)))
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK1(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3566,c_7199]) ).
tcf(c_7590,plain,
( epsilon_connected(powerset(sK5(iPr_def_11)))
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK3(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3567,c_7199]) ).
tcf(c_7591,plain,
( epsilon_connected(powerset(sK5(iPr_def_11)))
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK4(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3568,c_7199]) ).
tcf(c_7592,plain,
( epsilon_connected(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK3(sK5(iPr_def_11)),sK18)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3807,c_7199]) ).
tcf(c_7593,plain,
( epsilon_connected(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK4(sK5(iPr_def_11)),sK18)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3808,c_7199]) ).
tcf(c_7594,plain,
( empty(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(sK5(iPr_def_11)),sK18)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3899,c_7199]) ).
tcf(c_7595,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4163,c_7199]) ).
tcf(c_7596,plain,
( epsilon_connected(powerset(empty_set))
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK3(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4620,c_7199]) ).
tcf(c_7597,plain,
( epsilon_connected(powerset(empty_set))
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK4(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4637,c_7199]) ).
tcf(c_7598,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(powerset(sK5(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_5196,c_7199]) ).
tcf(c_7599,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(powerset(empty_set)))),sK18) ),
inference(superposition,[status(thm)],[c_5250,c_7199]) ).
tcf(c_7688,plain,
( empty(sK18)
| subset(sK5(powerset(sK5(sK18))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3564,c_7217]) ).
tcf(c_7689,plain,
( empty(sK18)
| subset(empty_set,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3420,c_7217]) ).
tcf(c_7690,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| subset(sK1(powerset(sK5(sK18))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3566,c_7217]) ).
tcf(c_7691,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK3(powerset(sK5(sK18))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3567,c_7217]) ).
tcf(c_7692,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK4(powerset(sK5(sK18))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3568,c_7217]) ).
tcf(c_7693,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK3(sK5(sK18)),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3807,c_7217]) ).
tcf(c_7694,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK4(sK5(sK18)),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3808,c_7217]) ).
tcf(c_7695,plain,
( empty(sK18)
| empty(sK5(sK18))
| subset(sK5(sK5(sK18)),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_3899,c_7217]) ).
tcf(c_7696,plain,
( empty(sK18)
| subset(sK5(powerset(empty_set)),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4163,c_7217]) ).
tcf(c_7699,plain,
( empty(sK18)
| subset(sK5(powerset(sK5(powerset(sK5(sK18))))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5196,c_7217]) ).
tcf(c_7700,plain,
( empty(sK18)
| subset(sK5(powerset(sK5(powerset(empty_set)))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5250,c_7217]) ).
tcf(c_7757,plain,
! [X0: $i] :
( in(empty_set,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = empty_set )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(empty_set,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_7267,c_77]) ).
tcf(c_7758,plain,
( subset(sK5(iPr_def_11),iPr_def_10)
| in(empty_set,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = empty_set )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_7267,c_65]) ).
tcf(c_7759,plain,
( in(empty_set,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18)
| ~ in(iPr_def_10,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7267,c_49]) ).
tcf(c_7761,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| in(empty_set,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_7267,c_127]) ).
tcf(c_7762,plain,
( in(empty_set,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18)
| ~ in(iPr_def_11,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7267,c_6289]) ).
tcf(c_7763,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(empty_set,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_7267,c_4912]) ).
tcf(c_7764,plain,
( in(empty_set,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_7267,c_3592]) ).
tcf(c_7765,plain,
( in(empty_set,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_11)
| ( sK5(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_7267,c_3614]) ).
tcf(c_7836,plain,
! [X0: $i] :
( ( singleton(X0) = empty_set )
| ~ in(sK0(X0,empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_7098,c_59]) ).
tcf(c_7861,plain,
! [X0: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ empty(sK18)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_7174,c_77]) ).
tcf(c_7862,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_7174,c_65]) ).
tcf(c_7902,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7571,c_128]) ).
tcf(c_7909,plain,
in(sK5(iPr_def_11),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_7141,c_3614]) ).
tcf(c_7910,plain,
! [X0: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_7909,c_77]) ).
tcf(c_7911,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_7909,c_65]) ).
tcf(c_7912,plain,
~ in(iPr_def_11,sK5(iPr_def_11)),
inference(superposition,[status(thm)],[c_7909,c_49]) ).
tcf(c_7914,plain,
element(sK5(iPr_def_11),iPr_def_11),
inference(superposition,[status(thm)],[c_7909,c_127]) ).
tcf(c_7934,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X0)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7263,c_77]) ).
tcf(c_7935,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7263,c_65]) ).
tcf(c_7936,plain,
! [X0: $i] :
( in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18)
| ~ in(iPr_def_10,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7263,c_49]) ).
tcf(c_7938,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7263,c_127]) ).
tcf(c_7940,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_11)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7263,c_4912]) ).
tcf(c_7941,plain,
! [X0: $i] :
( in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7263,c_3592]) ).
tcf(c_7943,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| in(sK5(iPr_def_11),iPr_def_10)
| ( X0 = X1 )
| ( sK5(iPr_def_11) = X1 )
| ~ empty(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7263,c_77]) ).
tcf(c_7944,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7263,c_65]) ).
tcf(c_7945,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_7263,c_49]) ).
tcf(c_7946,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7263,c_137]) ).
tcf(c_7947,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7263,c_127]) ).
tcf(c_7948,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(sK5(iPr_def_11),X0) = X1 )
| ( sK2(sK5(iPr_def_11),X0,X1) = sK5(iPr_def_11) )
| ~ empty(sK2(sK5(iPr_def_11),X0,X1))
| ~ in(sK2(sK5(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK5(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_7263,c_66]) ).
tcf(c_7949,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ empty(sK2(X0,X1,sK5(iPr_def_11)))
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_7263,c_67]) ).
tcf(c_7950,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ empty(singleton(sK5(iPr_def_11)))
| ~ in(singleton(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_3522]) ).
tcf(c_7951,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(sK5(iPr_def_11),X1)
| ~ empty(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_3641]) ).
tcf(c_7952,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(sK5(iPr_def_11),X0)
| ~ empty(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_3615]) ).
tcf(c_7953,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ empty(singleton(set_union2(sK5(iPr_def_11),X0)))
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_3618]) ).
tcf(c_7954,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,sK5(iPr_def_11))))
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_3644]) ).
tcf(c_7956,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)))
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_3944]) ).
tcf(c_7957,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)))
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_3945]) ).
tcf(c_7958,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))))
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_4131]) ).
tcf(c_7959,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))))
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_4132]) ).
tcf(c_8068,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK5(iPr_def_11) = X1 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7238,c_77]) ).
tcf(c_8069,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| subset(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7238,c_65]) ).
tcf(c_8071,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7238,c_137]) ).
tcf(c_8072,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| element(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7238,c_127]) ).
tcf(c_8073,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK2(sK5(iPr_def_11),X0,X1))
| ( set_union2(sK5(iPr_def_11),X0) = X1 )
| ( sK2(sK5(iPr_def_11),X0,X1) = sK5(iPr_def_11) )
| ~ in(sK2(sK5(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK5(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_7238,c_66]) ).
tcf(c_8074,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK2(X0,X1,sK5(iPr_def_11)))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_7238,c_67]) ).
tcf(c_8075,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(sK5(iPr_def_11)))
| ( singleton(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(singleton(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_3522]) ).
tcf(c_8076,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(sK5(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_3641]) ).
tcf(c_8077,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(sK5(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_3615]) ).
tcf(c_8078,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_3618]) ).
tcf(c_8079,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_3644]) ).
tcf(c_8081,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_3944]) ).
tcf(c_8082,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_3945]) ).
tcf(c_8083,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_4131]) ).
tcf(c_8084,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_4132]) ).
tcf(c_8087,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_7238,c_77]) ).
tcf(c_8088,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),X0)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7238,c_65]) ).
tcf(c_8091,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7238,c_127]) ).
tcf(c_8092,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(singleton(X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_62]) ).
tcf(c_8093,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_71]) ).
tcf(c_8096,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| element(sK5(iPr_def_11),iPr_def_10)
| in(sK18,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_7238,c_5047]) ).
tcf(c_8098,plain,
( epsilon_transitive(sK5(iPr_def_11))
| element(sK5(iPr_def_11),iPr_def_10)
| in(sK1(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK1(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK1(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_3523]) ).
tcf(c_8099,plain,
( epsilon_connected(sK5(iPr_def_11))
| element(sK5(iPr_def_11),iPr_def_10)
| in(sK3(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK3(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK3(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_3524]) ).
tcf(c_8100,plain,
( epsilon_connected(sK5(iPr_def_11))
| element(sK5(iPr_def_11),iPr_def_10)
| in(sK4(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK4(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK4(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_3525]) ).
tcf(c_8106,plain,
( empty(sK5(iPr_def_11))
| element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK5(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_3900]) ).
tcf(c_8309,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK5(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7246,c_77]) ).
tcf(c_8310,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7246,c_65]) ).
tcf(c_8311,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(iPr_def_10,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7246,c_49]) ).
tcf(c_8315,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7246,c_4912]) ).
tcf(c_8316,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7246,c_3592]) ).
tcf(c_8318,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_7246,c_77]) ).
tcf(c_8319,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7246,c_65]) ).
tcf(c_8320,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = X0 )
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7246,c_49]) ).
tcf(c_8322,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7246,c_127]) ).
tcf(c_8323,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ empty(sK5(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7246,c_62]) ).
tcf(c_8324,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ empty(sK5(iPr_def_11))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7246,c_71]) ).
tcf(c_8325,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = empty_set )
| ~ empty(sK5(iPr_def_11))
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_7246,c_7097]) ).
tcf(c_8327,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = sK18 )
| ~ empty(sK5(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_7246,c_5047]) ).
tcf(c_8329,plain,
( epsilon_transitive(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK1(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ empty(sK5(iPr_def_11))
| ~ in(sK1(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7246,c_3523]) ).
tcf(c_8330,plain,
( epsilon_connected(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK3(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ empty(sK5(iPr_def_11))
| ~ in(sK3(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7246,c_3524]) ).
tcf(c_8331,plain,
( epsilon_connected(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK4(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ empty(sK5(iPr_def_11))
| ~ in(sK4(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7246,c_3525]) ).
tcf(c_8508,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),X0)
| in(powerset(X0),sK5(iPr_def_11))
| ( powerset(X0) = sK5(iPr_def_11) )
| ~ in(powerset(X0),sK18) ),
inference(superposition,[status(thm)],[c_7264,c_133]) ).
tcf(c_8544,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ subset(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7911,c_128]) ).
tcf(c_8555,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_6990,c_77]) ).
tcf(c_8556,plain,
( epsilon_transitive(iPr_def_11)
| subset(sK1(iPr_def_11),sK18)
| in(sK1(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_6990,c_65]) ).
tcf(c_8557,plain,
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| ~ in(sK18,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_6990,c_49]) ).
tcf(c_8558,plain,
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_6990,c_137]) ).
tcf(c_8559,plain,
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),sK18)
| in(sK1(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_6990,c_127]) ).
tcf(c_8560,plain,
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| ~ in(iPr_def_11,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_6990,c_6841]) ).
tcf(c_8561,plain,
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_6990,c_5047]) ).
tcf(c_8562,plain,
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_6990,c_3640]) ).
tcf(c_8581,plain,
( epsilon_transitive(iPr_def_11)
| subset(sK1(iPr_def_11),sK18)
| in(sK1(iPr_def_11),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8556,c_2426]) ).
tcf(c_8585,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8555,c_2427]) ).
tcf(c_8611,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_10)
| subset(X0,iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK3(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5100,c_128]) ).
tcf(c_8624,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_10)
| subset(X0,iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK4(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5120,c_128]) ).
tcf(c_8636,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| subset(X0,sK18)
| in(sK1(iPr_def_11),iPr_def_10)
| ~ subset(X0,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_8581,c_128]) ).
tcf(c_8637,plain,
( epsilon_transitive(iPr_def_11)
| subset(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8581,c_3931]) ).
tcf(c_8638,plain,
( epsilon_transitive(iPr_def_11)
| subset(sK1(iPr_def_11),iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8581,c_3867]) ).
tcf(c_8680,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_77]) ).
tcf(c_8681,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| subset(sK1(iPr_def_11),iPr_def_10)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_65]) ).
tcf(c_8682,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ in(iPr_def_10,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_8585,c_49]) ).
tcf(c_8684,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),iPr_def_10)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_127]) ).
tcf(c_8685,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_8585,c_6289]) ).
tcf(c_8686,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_4912]) ).
tcf(c_8687,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_3592]) ).
tcf(c_8688,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_3614]) ).
tcf(c_8689,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK1(iPr_def_11) = X1 )
| ~ epsilon_connected(sK1(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_8585,c_77]) ).
tcf(c_8690,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| subset(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK1(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_65]) ).
tcf(c_8692,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X0 )
| ~ empty(sK1(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_137]) ).
tcf(c_8693,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| element(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_127]) ).
tcf(c_8694,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),sK2(sK1(iPr_def_11),X0,X1))
| ( set_union2(sK1(iPr_def_11),X0) = X1 )
| ( sK2(sK1(iPr_def_11),X0,X1) = sK1(iPr_def_11) )
| ~ in(sK2(sK1(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK1(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_8585,c_66]) ).
tcf(c_8695,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),sK2(X0,X1,sK1(iPr_def_11)))
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ( sK2(X0,X1,sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ in(sK2(X0,X1,sK1(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK1(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_8585,c_67]) ).
tcf(c_8696,plain,
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),singleton(sK1(iPr_def_11)))
| ( singleton(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ in(singleton(sK1(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_3522]) ).
tcf(c_8698,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ~ in(sK1(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_3641]) ).
tcf(c_8699,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ~ in(sK1(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_3615]) ).
tcf(c_8700,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),singleton(set_union2(sK1(iPr_def_11),X0)))
| ( singleton(set_union2(sK1(iPr_def_11),X0)) = sK1(iPr_def_11) )
| ~ in(singleton(set_union2(sK1(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_3618]) ).
tcf(c_8701,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),singleton(set_union2(X0,sK1(iPr_def_11))))
| ( singleton(set_union2(X0,sK1(iPr_def_11))) = sK1(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK1(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_3644]) ).
tcf(c_8702,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),singleton(set_union2(set_union2(sK1(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK1(iPr_def_11),X0),X1)) = sK1(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK1(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_3944]) ).
tcf(c_8703,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),singleton(set_union2(set_union2(X0,sK1(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK1(iPr_def_11)),X1)) = sK1(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK1(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_3945]) ).
tcf(c_8704,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),singleton(set_union2(X0,set_union2(sK1(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK1(iPr_def_11),X1))) = sK1(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK1(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_4131]) ).
tcf(c_8705,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK1(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK1(iPr_def_11)))) = sK1(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK1(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_4132]) ).
tcf(c_8706,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_8585,c_77]) ).
tcf(c_8707,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| subset(sK1(iPr_def_11),X0)
| in(X0,sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_65]) ).
tcf(c_8709,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(X0,sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_137]) ).
tcf(c_8710,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| element(sK1(iPr_def_11),X0)
| in(X0,sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_127]) ).
tcf(c_8711,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(singleton(X0),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ( singleton(X0) = sK1(iPr_def_11) )
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_62]) ).
tcf(c_8712,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| in(set_union2(X0,X1),sK1(iPr_def_11))
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_71]) ).
tcf(c_8713,plain,
( epsilon_transitive(iPr_def_11)
| in(empty_set,sK1(iPr_def_11))
| in(sK1(iPr_def_11),iPr_def_10)
| ( sK1(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_7097]) ).
tcf(c_8714,plain,
( epsilon_transitive(iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(sK1(iPr_def_11),iPr_def_10)
| ( sK1(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ in(iPr_def_11,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_8585,c_6841]) ).
tcf(c_8715,plain,
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(sK1(iPr_def_11),iPr_def_10)
| ( sK1(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_5047]) ).
tcf(c_8716,plain,
( epsilon_transitive(iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(sK1(iPr_def_11),iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10)
| ( sK1(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_8585,c_3640]) ).
tcf(c_8717,plain,
( epsilon_transitive(iPr_def_11)
| epsilon_transitive(sK1(iPr_def_11))
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(sK1(iPr_def_11)),sK1(iPr_def_11))
| ( sK1(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ in(sK1(sK1(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_3523]) ).
tcf(c_8718,plain,
( epsilon_transitive(iPr_def_11)
| epsilon_connected(sK1(iPr_def_11))
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK3(sK1(iPr_def_11)),sK1(iPr_def_11))
| ( sK3(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ in(sK3(sK1(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_3524]) ).
tcf(c_8719,plain,
( epsilon_transitive(iPr_def_11)
| epsilon_connected(sK1(iPr_def_11))
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK4(sK1(iPr_def_11)),sK1(iPr_def_11))
| ( sK4(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ in(sK4(sK1(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_3525]) ).
tcf(c_8725,plain,
( epsilon_transitive(iPr_def_11)
| empty(sK1(iPr_def_11))
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK5(sK1(iPr_def_11)),sK1(iPr_def_11))
| ( sK5(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ in(sK5(sK1(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_8585,c_3900]) ).
tcf(c_9163,plain,
( subset(sK1(set_union2(sK18,singleton(sK18))),set_union2(sK18,singleton(sK18)))
| ~ subset(sK18,set_union2(sK18,singleton(sK18)))
| ~ subset(sK1(set_union2(sK18,singleton(sK18))),sK18) ),
inference(instantiation,[status(thm)],[c_4534]) ).
tcf(c_9164,plain,
subset(sK18,set_union2(sK18,singleton(sK18))),
inference(instantiation,[status(thm)],[c_138]) ).
tcf(c_9169,plain,
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8638,c_63]) ).
tcf(c_9176,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_9169,c_77]) ).
tcf(c_9177,plain,
( epsilon_transitive(iPr_def_11)
| subset(sK1(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_9169,c_65]) ).
tcf(c_9178,plain,
( epsilon_transitive(iPr_def_11)
| ~ in(iPr_def_10,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9169,c_49]) ).
tcf(c_9180,plain,
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_9169,c_127]) ).
tcf(c_9181,plain,
( epsilon_transitive(iPr_def_11)
| ~ in(iPr_def_11,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9169,c_6289]) ).
tcf(c_9182,plain,
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),iPr_def_11) ),
inference(superposition,[status(thm)],[c_9169,c_4912]) ).
tcf(c_9183,plain,
( epsilon_transitive(iPr_def_11)
| ( sK1(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_9169,c_3592]) ).
tcf(c_9184,plain,
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_11) ),
inference(superposition,[status(thm)],[c_9169,c_3614]) ).
tcf(c_9219,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| in(sK5(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X1 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7241,c_77]) ).
tcf(c_9220,plain,
! [X0: $i] :
( subset(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7241,c_65]) ).
tcf(c_9223,plain,
! [X0: $i] :
( element(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7241,c_127]) ).
tcf(c_9224,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),sK2(sK5(iPr_def_11),X0,X1))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(sK5(iPr_def_11),X0) = X1 )
| ( sK2(sK5(iPr_def_11),X0,X1) = sK5(iPr_def_11) )
| ~ in(sK2(sK5(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK5(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_7241,c_66]) ).
tcf(c_9225,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),sK2(X0,X1,sK5(iPr_def_11)))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_7241,c_67]) ).
tcf(c_9226,plain,
( in(sK5(iPr_def_11),singleton(sK5(iPr_def_11)))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(singleton(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_3522]) ).
tcf(c_9227,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),set_union2(X0,X1))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(sK5(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_3641]) ).
tcf(c_9228,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),set_union2(X0,X1))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(sK5(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_3615]) ).
tcf(c_9229,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_3618]) ).
tcf(c_9230,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_3644]) ).
tcf(c_9232,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_3944]) ).
tcf(c_9233,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_3945]) ).
tcf(c_9234,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_4131]) ).
tcf(c_9235,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_4132]) ).
tcf(c_9240,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_7241,c_77]) ).
tcf(c_9241,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),X0)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7241,c_65]) ).
tcf(c_9244,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),X0)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7241,c_127]) ).
tcf(c_9245,plain,
! [X0: $i] :
( in(singleton(X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_62]) ).
tcf(c_9246,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_71]) ).
tcf(c_9249,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_7241,c_5047]) ).
tcf(c_9251,plain,
( epsilon_transitive(sK5(iPr_def_11))
| in(sK1(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK1(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK1(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_3523]) ).
tcf(c_9252,plain,
( epsilon_connected(sK5(iPr_def_11))
| in(sK3(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK3(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_3524]) ).
tcf(c_9253,plain,
( epsilon_connected(sK5(iPr_def_11))
| in(sK4(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK4(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_3525]) ).
tcf(c_9259,plain,
( empty(sK5(iPr_def_11))
| in(sK5(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK5(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_3900]) ).
tcf(c_9459,plain,
! [X0: $i,X1: $i] :
( in(X0,sK0(X1,iPr_def_10))
| in(sK0(X1,iPr_def_10),X0)
| ( singleton(X1) = iPr_def_10 )
| ( sK0(X1,iPr_def_10) = X1 )
| ( sK0(X1,iPr_def_10) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3738,c_77]) ).
tcf(c_9460,plain,
! [X0: $i] :
( subset(sK0(X0,iPr_def_10),iPr_def_11)
| ( singleton(X0) = iPr_def_10 )
| ( sK0(X0,iPr_def_10) = X0 )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3738,c_65]) ).
tcf(c_9464,plain,
! [X0: $i] :
( in(sK0(X0,iPr_def_10),iPr_def_10)
| in(sK0(X0,iPr_def_10),sK18)
| ( singleton(X0) = iPr_def_10 )
| ( sK0(X0,iPr_def_10) = X0 ) ),
inference(superposition,[status(thm)],[c_3738,c_4035]) ).
tcf(c_9489,plain,
( epsilon_transitive(iPr_def_11)
| empty(iPr_def_10)
| in(sK1(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_9180,c_131]) ).
tcf(c_9501,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| subset(X0,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9177,c_128]) ).
tcf(c_9502,plain,
( epsilon_transitive(iPr_def_11)
| subset(sK1(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_9177,c_3868]) ).
tcf(c_9515,plain,
( ( sK1(iPr_def_11) = sK18 )
| ~ epsilon_connected(iPr_def_11) ),
inference(superposition,[status(thm)],[c_9183,c_4065]) ).
tcf(c_9532,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,set_union2(X1,X0))
| ~ in(X2,X0)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_58,c_3805]) ).
tcf(c_9534,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ in(X1,X0)
| ~ epsilon_transitive(set_union2(X0,X0)) ),
inference(superposition,[status(thm)],[c_97,c_3805]) ).
tcf(c_9535,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ in(X1,X0)
| ~ epsilon_transitive(set_union2(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_126,c_3805]) ).
tcf(c_9536,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ in(X1,empty_set)
| ~ epsilon_transitive(set_union2(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_3423,c_3805]) ).
tcf(c_9537,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ in(X0,iPr_def_10)
| ~ epsilon_transitive(set_union2(iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_3424,c_3805]) ).
tcf(c_9539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,set_union2(X0,X1))
| ~ subset(X3,X2)
| ~ in(X2,X0)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_128]) ).
tcf(c_9540,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_9537,c_3424]) ).
tcf(c_9544,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_9536,c_3423]) ).
tcf(c_9565,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_6994,c_77]) ).
tcf(c_9566,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),sK18)
| in(sK3(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_6994,c_65]) ).
tcf(c_9567,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ~ in(sK18,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_6994,c_49]) ).
tcf(c_9568,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_6994,c_137]) ).
tcf(c_9569,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),sK18)
| in(sK3(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_6994,c_127]) ).
tcf(c_9570,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_6994,c_6841]) ).
tcf(c_9571,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_6994,c_5047]) ).
tcf(c_9572,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_6994,c_3640]) ).
tcf(c_9591,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),sK18)
| in(sK3(iPr_def_11),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9566,c_2426]) ).
tcf(c_9595,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9565,c_2427]) ).
tcf(c_9635,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_9568,c_77]) ).
tcf(c_9636,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_9568,c_65]) ).
tcf(c_9637,plain,
( epsilon_connected(iPr_def_11)
| ~ empty(sK18)
| ~ in(iPr_def_10,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9568,c_49]) ).
tcf(c_9639,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_9568,c_127]) ).
tcf(c_9640,plain,
( epsilon_connected(iPr_def_11)
| ~ empty(sK18)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9568,c_6289]) ).
tcf(c_9641,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_9568,c_4912]) ).
tcf(c_9642,plain,
( epsilon_connected(iPr_def_11)
| ( sK3(iPr_def_11) = sK18 )
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_9568,c_3592]) ).
tcf(c_9643,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_9568,c_3614]) ).
tcf(c_9694,plain,
( epsilon_connected(iPr_def_11)
| empty(iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_9639,c_131]) ).
tcf(c_9704,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ subset(X0,sK5(powerset(sK5(powerset(sK5(powerset(X1))))))) ),
inference(superposition,[status(thm)],[c_5252,c_128]) ).
tcf(c_9706,plain,
( subset(sK5(powerset(sK5(powerset(sK5(powerset(sK18)))))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5252,c_3931]) ).
tcf(c_9708,plain,
! [X0: $i] : subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))))),X0),
inference(superposition,[status(thm)],[c_5252,c_3864]) ).
tcf(c_9710,plain,
! [X0: $i] : subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))))),X0),
inference(superposition,[status(thm)],[c_5252,c_4165]) ).
tcf(c_9711,plain,
subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK18)))))))),iPr_def_11),
inference(superposition,[status(thm)],[c_5252,c_4177]) ).
tcf(c_9712,plain,
subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(iPr_def_10)))))))),iPr_def_11),
inference(superposition,[status(thm)],[c_5252,c_4574]) ).
tcf(c_9713,plain,
( empty(sK18)
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5252,c_7217]) ).
tcf(c_9716,plain,
( empty(sK18)
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5252,c_5491]) ).
tcf(c_9717,plain,
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK1(powerset(sK5(sK18))))))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5252,c_5502]) ).
tcf(c_9718,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK3(powerset(sK5(sK18))))))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5252,c_5516]) ).
tcf(c_9719,plain,
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK4(powerset(sK5(sK18))))))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5252,c_5528]) ).
tcf(c_9720,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK3(sK5(sK18)))))))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_5252,c_5794]) ).
tcf(c_9721,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK4(sK5(sK18)))))))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_5252,c_5809]) ).
tcf(c_9722,plain,
( empty(sK18)
| empty(sK5(sK18))
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK5(sK18)))))))),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_5252,c_5824]) ).
tcf(c_9723,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(iPr_def_11))))))),sK18) ),
inference(superposition,[status(thm)],[c_5252,c_7199]) ).
tcf(c_9805,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ subset(X0,sK5(powerset(sK5(powerset(sK5(powerset(empty_set))))))) ),
inference(superposition,[status(thm)],[c_5727,c_128]) ).
tcf(c_9844,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ subset(X0,sK5(powerset(sK5(powerset(sK5(powerset(sK18))))))) ),
inference(superposition,[status(thm)],[c_6204,c_128]) ).
tcf(c_9848,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ subset(X0,sK5(powerset(sK5(powerset(sK5(powerset(iPr_def_10))))))) ),
inference(superposition,[status(thm)],[c_6245,c_128]) ).
tcf(c_9862,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,sK18)
| in(sK3(iPr_def_11),iPr_def_10)
| ~ subset(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9591,c_128]) ).
tcf(c_9863,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_9591,c_3931]) ).
tcf(c_9864,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_9591,c_3867]) ).
tcf(c_9897,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_77]) ).
tcf(c_9898,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_65]) ).
tcf(c_9899,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ in(iPr_def_10,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9595,c_49]) ).
tcf(c_9901,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_127]) ).
tcf(c_9902,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9595,c_6289]) ).
tcf(c_9903,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_4912]) ).
tcf(c_9904,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_3592]) ).
tcf(c_9905,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_3614]) ).
tcf(c_9906,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK3(iPr_def_11) = X1 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9595,c_77]) ).
tcf(c_9907,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_65]) ).
tcf(c_9909,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_137]) ).
tcf(c_9910,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_127]) ).
tcf(c_9911,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK2(sK3(iPr_def_11),X0,X1))
| ( set_union2(sK3(iPr_def_11),X0) = X1 )
| ( sK2(sK3(iPr_def_11),X0,X1) = sK3(iPr_def_11) )
| ~ in(sK2(sK3(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK3(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_9595,c_66]) ).
tcf(c_9912,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK2(X0,X1,sK3(iPr_def_11)))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( sK2(X0,X1,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_9595,c_67]) ).
tcf(c_9913,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_76]) ).
tcf(c_9914,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(sK3(iPr_def_11)))
| ( singleton(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(singleton(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_3522]) ).
tcf(c_9916,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(sK3(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_3641]) ).
tcf(c_9917,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(sK3(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_3615]) ).
tcf(c_9918,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_3618]) ).
tcf(c_9919,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_3644]) ).
tcf(c_9920,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_3944]) ).
tcf(c_9921,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_3945]) ).
tcf(c_9922,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_4131]) ).
tcf(c_9923,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_4132]) ).
tcf(c_9924,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_9595,c_77]) ).
tcf(c_9925,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),X0)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_65]) ).
tcf(c_9927,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_137]) ).
tcf(c_9928,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_127]) ).
tcf(c_9929,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(singleton(X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_62]) ).
tcf(c_9930,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_71]) ).
tcf(c_9931,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_74]) ).
tcf(c_9932,plain,
( epsilon_connected(iPr_def_11)
| in(empty_set,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_7097]) ).
tcf(c_9933,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9595,c_6841]) ).
tcf(c_9934,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_5047]) ).
tcf(c_9935,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_3640]) ).
tcf(c_9936,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK1(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK1(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK1(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_3523]) ).
tcf(c_9937,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK3(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_3524]) ).
tcf(c_9938,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK4(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK4(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_3525]) ).
tcf(c_9944,plain,
( epsilon_connected(iPr_def_11)
| empty(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK5(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK5(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_3900]) ).
tcf(c_10373,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ~ subset(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9864,c_128]) ).
tcf(c_10383,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9863,c_65]) ).
tcf(c_10393,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_10383,c_128]) ).
tcf(c_10394,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_10383,c_3868]) ).
tcf(c_10412,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3564,c_9862]) ).
tcf(c_10413,plain,
( epsilon_connected(iPr_def_11)
| subset(empty_set,sK18)
| in(sK3(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3420,c_9862]) ).
tcf(c_10414,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(powerset(sK3(iPr_def_11)))
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK1(powerset(sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3566,c_9862]) ).
tcf(c_10415,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(sK3(iPr_def_11)))
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(powerset(sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3567,c_9862]) ).
tcf(c_10416,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(sK3(iPr_def_11)))
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK4(powerset(sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3568,c_9862]) ).
tcf(c_10417,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(sK3(iPr_def_11)),sK18)
| ~ epsilon_transitive(sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3807,c_9862]) ).
tcf(c_10418,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK4(sK3(iPr_def_11)),sK18)
| ~ epsilon_transitive(sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3808,c_9862]) ).
tcf(c_10419,plain,
( epsilon_connected(iPr_def_11)
| empty(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK5(sK3(iPr_def_11)),sK18)
| ~ epsilon_transitive(sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3899,c_9862]) ).
tcf(c_10420,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4163,c_9862]) ).
tcf(c_10421,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(empty_set))
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4620,c_9862]) ).
tcf(c_10422,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(empty_set))
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK4(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4637,c_9862]) ).
tcf(c_10423,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(powerset(sK3(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_5196,c_9862]) ).
tcf(c_10424,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(powerset(empty_set)))),sK18) ),
inference(superposition,[status(thm)],[c_5250,c_9862]) ).
tcf(c_10425,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK3(iPr_def_11))))))),sK18) ),
inference(superposition,[status(thm)],[c_5252,c_9862]) ).
tcf(c_10426,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),sK18) ),
inference(superposition,[status(thm)],[c_5727,c_9862]) ).
tcf(c_10497,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(empty_set,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = empty_set )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(empty_set,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_9932,c_77]) ).
tcf(c_10498,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_10)
| in(empty_set,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = empty_set )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_9932,c_65]) ).
tcf(c_10499,plain,
( epsilon_connected(iPr_def_11)
| in(empty_set,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18)
| ~ in(iPr_def_10,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9932,c_49]) ).
tcf(c_10501,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(empty_set,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_9932,c_127]) ).
tcf(c_10502,plain,
( epsilon_connected(iPr_def_11)
| in(empty_set,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9932,c_6289]) ).
tcf(c_10503,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(empty_set,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_9932,c_4912]) ).
tcf(c_10504,plain,
( epsilon_connected(iPr_def_11)
| in(empty_set,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_9932,c_3592]) ).
tcf(c_10505,plain,
( epsilon_connected(iPr_def_11)
| in(empty_set,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_11)
| ( sK3(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_9932,c_3614]) ).
tcf(c_10578,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9913,c_74,c_75]) ).
tcf(c_10600,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X0)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9927,c_77]) ).
tcf(c_10601,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9927,c_65]) ).
tcf(c_10602,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18)
| ~ in(iPr_def_10,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9927,c_49]) ).
tcf(c_10604,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9927,c_127]) ).
tcf(c_10605,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9927,c_6289]) ).
tcf(c_10606,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9927,c_4912]) ).
tcf(c_10607,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9927,c_3592]) ).
tcf(c_10608,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_11)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9927,c_3614]) ).
tcf(c_10609,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK3(iPr_def_11),iPr_def_10)
| ( X0 = X1 )
| ( sK3(iPr_def_11) = X1 )
| ~ empty(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9927,c_77]) ).
tcf(c_10610,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9927,c_65]) ).
tcf(c_10611,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_9927,c_49]) ).
tcf(c_10612,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9927,c_137]) ).
tcf(c_10613,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9927,c_127]) ).
tcf(c_10614,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(sK3(iPr_def_11),X0) = X1 )
| ( sK2(sK3(iPr_def_11),X0,X1) = sK3(iPr_def_11) )
| ~ empty(sK2(sK3(iPr_def_11),X0,X1))
| ~ in(sK2(sK3(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK3(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_9927,c_66]) ).
tcf(c_10615,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( sK2(X0,X1,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ empty(sK2(X0,X1,sK3(iPr_def_11)))
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_9927,c_67]) ).
tcf(c_10616,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ empty(sK4(iPr_def_11))
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_76]) ).
tcf(c_10617,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ empty(singleton(sK3(iPr_def_11)))
| ~ in(singleton(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_3522]) ).
tcf(c_10619,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(sK3(iPr_def_11),X1)
| ~ empty(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_3641]) ).
tcf(c_10620,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(sK3(iPr_def_11),X0)
| ~ empty(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_3615]) ).
tcf(c_10621,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ empty(singleton(set_union2(sK3(iPr_def_11),X0)))
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_3618]) ).
tcf(c_10622,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,sK3(iPr_def_11))))
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_3644]) ).
tcf(c_10623,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)))
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_3944]) ).
tcf(c_10624,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)))
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_3945]) ).
tcf(c_10625,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))))
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_4131]) ).
tcf(c_10626,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))))
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_4132]) ).
tcf(c_10973,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,set_union2(X1,X0))
| ~ in(X2,X1)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_58,c_3806]) ).
tcf(c_10976,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ in(X1,empty_set)
| ~ epsilon_transitive(set_union2(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_126,c_3806]) ).
tcf(c_10977,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ in(X1,X0)
| ~ epsilon_transitive(set_union2(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_3423,c_3806]) ).
tcf(c_10978,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ in(X0,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_3424,c_3806]) ).
tcf(c_10980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,set_union2(X0,X1))
| ~ subset(X3,X2)
| ~ in(X2,X1)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_128]) ).
tcf(c_10981,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ in(X0,sK18) ),
inference(light_normalisation,[status(thm)],[c_10978,c_3424]) ).
tcf(c_11001,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_6995,c_77]) ).
tcf(c_11002,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),sK18)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_6995,c_65]) ).
tcf(c_11003,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ in(sK18,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_6995,c_49]) ).
tcf(c_11004,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_6995,c_137]) ).
tcf(c_11005,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),sK18)
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_6995,c_127]) ).
tcf(c_11006,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ in(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_6995,c_6841]) ).
tcf(c_11007,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_6995,c_5047]) ).
tcf(c_11008,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_6995,c_3640]) ).
tcf(c_11009,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_6995,c_10578]) ).
tcf(c_11031,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),sK18)
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11002,c_2426]) ).
tcf(c_11035,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11001,c_2427]) ).
tcf(c_11063,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_11004,c_77]) ).
tcf(c_11064,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_11004,c_65]) ).
tcf(c_11065,plain,
( epsilon_connected(iPr_def_11)
| ~ empty(sK18)
| ~ in(iPr_def_10,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11004,c_49]) ).
tcf(c_11067,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_11004,c_127]) ).
tcf(c_11068,plain,
( epsilon_connected(iPr_def_11)
| ~ empty(sK18)
| ~ in(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11004,c_6289]) ).
tcf(c_11069,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_11004,c_4912]) ).
tcf(c_11070,plain,
( epsilon_connected(iPr_def_11)
| ( sK4(iPr_def_11) = sK18 )
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_11004,c_3592]) ).
tcf(c_11071,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_11004,c_3614]) ).
tcf(c_11108,plain,
( epsilon_connected(iPr_def_11)
| empty(iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_11067,c_131]) ).
tcf(c_11127,plain,
( epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9502,c_63]) ).
tcf(c_11134,plain,
( epsilon_transitive(iPr_def_11)
| ( sK1(iPr_def_10) = sK18 ) ),
inference(superposition,[status(thm)],[c_4662,c_11127]) ).
tcf(c_11141,plain,
( ( sK1(iPr_def_10) = sK18 )
| ~ epsilon_connected(iPr_def_11) ),
inference(superposition,[status(thm)],[c_11134,c_4065]) ).
tcf(c_11154,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,sK18)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ subset(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11031,c_128]) ).
tcf(c_11155,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_11031,c_3931]) ).
tcf(c_11156,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_11031,c_3867]) ).
tcf(c_11181,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,sK4(iPr_def_11))
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_77]) ).
tcf(c_11182,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_65]) ).
tcf(c_11183,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ in(iPr_def_10,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11035,c_49]) ).
tcf(c_11185,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_127]) ).
tcf(c_11186,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11035,c_6289]) ).
tcf(c_11187,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_11)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_4912]) ).
tcf(c_11188,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_3592]) ).
tcf(c_11189,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_11)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_3614]) ).
tcf(c_11190,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK4(iPr_def_11) = X1 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11035,c_77]) ).
tcf(c_11191,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_65]) ).
tcf(c_11193,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_137]) ).
tcf(c_11194,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_127]) ).
tcf(c_11195,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(sK4(iPr_def_11),X0,X1))
| ( set_union2(sK4(iPr_def_11),X0) = X1 )
| ( sK2(sK4(iPr_def_11),X0,X1) = sK4(iPr_def_11) )
| ~ in(sK2(sK4(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK4(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_11035,c_66]) ).
tcf(c_11196,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(X0,X1,sK4(iPr_def_11)))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ( sK2(X0,X1,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_11035,c_67]) ).
tcf(c_11197,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_74]) ).
tcf(c_11198,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(sK4(iPr_def_11)))
| ( singleton(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(singleton(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_3522]) ).
tcf(c_11200,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_3641]) ).
tcf(c_11201,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_3615]) ).
tcf(c_11202,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_3618]) ).
tcf(c_11203,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_3644]) ).
tcf(c_11204,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_3944]) ).
tcf(c_11205,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_3945]) ).
tcf(c_11206,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_4131]) ).
tcf(c_11207,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_4132]) ).
tcf(c_11208,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X1,sK4(iPr_def_11))
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_11035,c_77]) ).
tcf(c_11209,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),X0)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_65]) ).
tcf(c_11211,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_137]) ).
tcf(c_11212,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_127]) ).
tcf(c_11213,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(singleton(X0),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_62]) ).
tcf(c_11214,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_71]) ).
tcf(c_11215,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_76]) ).
tcf(c_11216,plain,
( epsilon_connected(iPr_def_11)
| in(empty_set,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_7097]) ).
tcf(c_11217,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ in(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11035,c_6841]) ).
tcf(c_11218,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_5047]) ).
tcf(c_11219,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_3640]) ).
tcf(c_11220,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK1(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK1(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK1(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_3523]) ).
tcf(c_11221,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK3(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK3(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_3524]) ).
tcf(c_11222,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK4(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK4(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_3525]) ).
tcf(c_11228,plain,
( epsilon_connected(iPr_def_11)
| empty(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK5(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK5(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_3900]) ).
tcf(c_11229,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_10578]) ).
tcf(c_11539,plain,
! [X0: $i] :
( subset(sK1(set_union2(sK18,singleton(sK18))),set_union2(sK18,singleton(sK18)))
| ~ subset(X0,set_union2(sK18,singleton(sK18)))
| ( set_union2(sK18,singleton(sK18)) != set_union2(sK18,singleton(sK18)) )
| ( sK1(set_union2(sK18,singleton(sK18))) != X0 ) ),
inference(instantiation,[status(thm)],[c_4536]) ).
tcf(c_11540,plain,
set_union2(sK18,singleton(sK18)) = set_union2(sK18,singleton(sK18)),
inference(instantiation,[status(thm)],[c_2428]) ).
tcf(c_11578,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ subset(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11156,c_128]) ).
tcf(c_11588,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11155,c_65]) ).
tcf(c_11598,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11588,c_128]) ).
tcf(c_11599,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_11588,c_3868]) ).
tcf(c_11617,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3564,c_11154]) ).
tcf(c_11618,plain,
( epsilon_connected(iPr_def_11)
| subset(empty_set,sK18)
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3420,c_11154]) ).
tcf(c_11619,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(powerset(sK4(iPr_def_11)))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK1(powerset(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3566,c_11154]) ).
tcf(c_11620,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(sK4(iPr_def_11)))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK3(powerset(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3567,c_11154]) ).
tcf(c_11621,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(sK4(iPr_def_11)))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(powerset(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3568,c_11154]) ).
tcf(c_11622,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK3(sK4(iPr_def_11)),sK18)
| ~ epsilon_transitive(sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3807,c_11154]) ).
tcf(c_11623,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(sK4(iPr_def_11)),sK18)
| ~ epsilon_transitive(sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3808,c_11154]) ).
tcf(c_11624,plain,
( epsilon_connected(iPr_def_11)
| empty(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK5(sK4(iPr_def_11)),sK18)
| ~ epsilon_transitive(sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3899,c_11154]) ).
tcf(c_11625,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4163,c_11154]) ).
tcf(c_11626,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(empty_set))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK3(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4620,c_11154]) ).
tcf(c_11627,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(empty_set))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4637,c_11154]) ).
tcf(c_11628,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(powerset(sK4(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_5196,c_11154]) ).
tcf(c_11629,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(powerset(empty_set)))),sK18) ),
inference(superposition,[status(thm)],[c_5250,c_11154]) ).
tcf(c_11630,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK4(iPr_def_11))))))),sK18) ),
inference(superposition,[status(thm)],[c_5252,c_11154]) ).
tcf(c_11631,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),sK18) ),
inference(superposition,[status(thm)],[c_5727,c_11154]) ).
tcf(c_11686,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(empty_set,sK4(iPr_def_11))
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = empty_set )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(empty_set,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_11216,c_77]) ).
tcf(c_11687,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_10)
| in(empty_set,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = empty_set )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_11216,c_65]) ).
tcf(c_11688,plain,
( epsilon_connected(iPr_def_11)
| in(empty_set,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18)
| ~ in(iPr_def_10,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11216,c_49]) ).
tcf(c_11690,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(empty_set,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_11216,c_127]) ).
tcf(c_11691,plain,
( epsilon_connected(iPr_def_11)
| in(empty_set,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18)
| ~ in(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11216,c_6289]) ).
tcf(c_11692,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_11)
| in(empty_set,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_11216,c_4912]) ).
tcf(c_11693,plain,
( epsilon_connected(iPr_def_11)
| in(empty_set,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_11216,c_3592]) ).
tcf(c_11694,plain,
( epsilon_connected(iPr_def_11)
| in(empty_set,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_11)
| ( sK4(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_11216,c_3614]) ).
tcf(c_11771,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11197,c_76,c_75]) ).
tcf(c_11782,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_11771]) ).
tcf(c_11795,plain,
! [X0: $i,X1: $i] :
( in(X0,sK0(X1,sK18))
| in(sK0(X1,sK18),X0)
| ( singleton(X1) = sK18 )
| ( sK0(X1,sK18) = X1 )
| ( sK0(X1,sK18) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3959,c_77]) ).
tcf(c_11796,plain,
! [X0: $i] :
( subset(sK0(X0,sK18),iPr_def_11)
| ( singleton(X0) = sK18 )
| ( sK0(X0,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3959,c_65]) ).
tcf(c_11800,plain,
! [X0: $i] :
( in(sK0(X0,sK18),iPr_def_10)
| in(sK0(X0,sK18),sK18)
| ( singleton(X0) = sK18 )
| ( sK0(X0,sK18) = X0 ) ),
inference(superposition,[status(thm)],[c_3959,c_4035]) ).
tcf(c_11829,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X0,X1),iPr_def_11)
| in(sK2(iPr_def_10,X0,X1),X1)
| in(sK2(iPr_def_10,X0,X1),X0)
| ( set_union2(iPr_def_10,X0) = X1 )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_68,c_9540]) ).
tcf(c_11830,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,iPr_def_10),iPr_def_11)
| in(sK2(X0,X1,iPr_def_10),X1)
| in(sK2(X0,X1,iPr_def_10),X0)
| ( set_union2(X0,X1) = iPr_def_10 )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_68,c_9540]) ).
tcf(c_11831,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_10,X1),iPr_def_11)
| in(sK2(X0,iPr_def_10,X1),X1)
| in(sK2(X0,iPr_def_10,X1),X0)
| ( set_union2(X0,iPr_def_10) = X1 )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_68,c_9540]) ).
tcf(c_11834,plain,
( empty(iPr_def_10)
| subset(sK5(iPr_def_10),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3768,c_9540]) ).
tcf(c_11837,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_11)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9927,c_9540]) ).
tcf(c_11838,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_11)
| in(empty_set,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = empty_set )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_9932,c_9540]) ).
tcf(c_11839,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_9540]) ).
tcf(c_11840,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_9568,c_9540]) ).
tcf(c_11841,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_11)
| in(empty_set,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = empty_set )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_11216,c_9540]) ).
tcf(c_11842,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_11)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_9540]) ).
tcf(c_11843,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_11004,c_9540]) ).
tcf(c_11844,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7246,c_9540]) ).
tcf(c_11845,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),iPr_def_11)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7263,c_9540]) ).
tcf(c_11846,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| in(empty_set,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = empty_set )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_7267,c_9540]) ).
tcf(c_11847,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),iPr_def_11)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_9540]) ).
tcf(c_11855,plain,
( empty(iPr_def_10)
| subset(sK18,iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_11834,c_3936]) ).
tcf(c_11972,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9569,c_131]) ).
tcf(c_11983,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_10394,c_128]) ).
tcf(c_12001,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,sK4(iPr_def_11))
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X0)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11211,c_77]) ).
tcf(c_12002,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11211,c_65]) ).
tcf(c_12003,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18)
| ~ in(iPr_def_10,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11211,c_49]) ).
tcf(c_12005,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11211,c_127]) ).
tcf(c_12006,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_11)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11211,c_9540]) ).
tcf(c_12007,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11211,c_6289]) ).
tcf(c_12008,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_11)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11211,c_4912]) ).
tcf(c_12009,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11211,c_3592]) ).
tcf(c_12010,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_11)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11211,c_3614]) ).
tcf(c_12011,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK4(iPr_def_11),iPr_def_10)
| ( X0 = X1 )
| ( sK4(iPr_def_11) = X1 )
| ~ empty(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11211,c_77]) ).
tcf(c_12012,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11211,c_65]) ).
tcf(c_12013,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_11211,c_49]) ).
tcf(c_12014,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11211,c_137]) ).
tcf(c_12015,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11211,c_127]) ).
tcf(c_12016,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(sK4(iPr_def_11),X0) = X1 )
| ( sK2(sK4(iPr_def_11),X0,X1) = sK4(iPr_def_11) )
| ~ empty(sK2(sK4(iPr_def_11),X0,X1))
| ~ in(sK2(sK4(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK4(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_11211,c_66]) ).
tcf(c_12017,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ( sK2(X0,X1,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ empty(sK2(X0,X1,sK4(iPr_def_11)))
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_11211,c_67]) ).
tcf(c_12018,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_74]) ).
tcf(c_12019,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ empty(singleton(sK4(iPr_def_11)))
| ~ in(singleton(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_3522]) ).
tcf(c_12021,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),X1)
| ~ empty(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_3641]) ).
tcf(c_12022,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),X0)
| ~ empty(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_3615]) ).
tcf(c_12023,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ empty(singleton(set_union2(sK4(iPr_def_11),X0)))
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_3618]) ).
tcf(c_12024,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,sK4(iPr_def_11))))
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_3644]) ).
tcf(c_12025,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)))
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_3944]) ).
tcf(c_12026,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)))
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_3945]) ).
tcf(c_12027,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))))
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_4131]) ).
tcf(c_12028,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))))
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_4132]) ).
tcf(c_12200,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9901,c_131]) ).
tcf(c_12201,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK3(iPr_def_11) = X1 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9901,c_77]) ).
tcf(c_12202,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| subset(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9901,c_65]) ).
tcf(c_12204,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9901,c_137]) ).
tcf(c_12205,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| element(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9901,c_127]) ).
tcf(c_12206,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK2(sK3(iPr_def_11),X0,X1))
| ( set_union2(sK3(iPr_def_11),X0) = X1 )
| ( sK2(sK3(iPr_def_11),X0,X1) = sK3(iPr_def_11) )
| ~ in(sK2(sK3(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK3(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_9901,c_66]) ).
tcf(c_12207,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK2(X0,X1,sK3(iPr_def_11)))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( sK2(X0,X1,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_9901,c_67]) ).
tcf(c_12208,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_76]) ).
tcf(c_12209,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(sK3(iPr_def_11)))
| ( singleton(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(singleton(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_3522]) ).
tcf(c_12211,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(sK3(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_3641]) ).
tcf(c_12212,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(sK3(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_3615]) ).
tcf(c_12213,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_3618]) ).
tcf(c_12214,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_3644]) ).
tcf(c_12215,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_3944]) ).
tcf(c_12216,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_3945]) ).
tcf(c_12217,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_4131]) ).
tcf(c_12218,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_4132]) ).
tcf(c_12219,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_9901,c_77]) ).
tcf(c_12220,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),X0)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9901,c_65]) ).
tcf(c_12223,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9901,c_127]) ).
tcf(c_12224,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(singleton(X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_62]) ).
tcf(c_12225,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_71]) ).
tcf(c_12226,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_74]) ).
tcf(c_12228,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK18,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9901,c_6841]) ).
tcf(c_12229,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK18,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9901,c_5047]) ).
tcf(c_12230,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_11)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9901,c_3640]) ).
tcf(c_12231,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK3(iPr_def_11))
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK1(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK1(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK1(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_3523]) ).
tcf(c_12232,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK3(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_3524]) ).
tcf(c_12233,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK4(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK4(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK4(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_3525]) ).
tcf(c_12240,plain,
( epsilon_connected(iPr_def_11)
| empty(sK3(iPr_def_11))
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK5(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK5(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK5(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_3900]) ).
tcf(c_12241,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK18,sK3(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9901,c_11771]) ).
tcf(c_12525,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK3(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9909,c_77]) ).
tcf(c_12526,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9909,c_65]) ).
tcf(c_12527,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(iPr_def_10,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9909,c_49]) ).
tcf(c_12530,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9909,c_9540]) ).
tcf(c_12531,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9909,c_6289]) ).
tcf(c_12532,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9909,c_4912]) ).
tcf(c_12533,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9909,c_3592]) ).
tcf(c_12534,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9909,c_3614]) ).
tcf(c_12535,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_9909,c_77]) ).
tcf(c_12536,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9909,c_65]) ).
tcf(c_12537,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9909,c_49]) ).
tcf(c_12539,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9909,c_127]) ).
tcf(c_12540,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_62]) ).
tcf(c_12541,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_71]) ).
tcf(c_12542,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_74]) ).
tcf(c_12543,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = empty_set )
| ~ empty(sK3(iPr_def_11))
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_9909,c_7097]) ).
tcf(c_12544,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ empty(sK3(iPr_def_11))
| ~ in(sK18,sK18)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9909,c_6841]) ).
tcf(c_12547,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK1(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ in(sK1(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_3523]) ).
tcf(c_12548,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ in(sK3(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_3524]) ).
tcf(c_12549,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK4(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ in(sK4(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_3525]) ).
tcf(c_12763,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9910,c_131]) ).
tcf(c_12813,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ in(X0,sK18) ),
inference(global_subsumption_just,[status(thm)],[c_10981,c_1057,c_3867]) ).
tcf(c_12820,plain,
! [X0: $i] :
( subset(sK0(X0,sK18),iPr_def_11)
| ( singleton(X0) = sK18 )
| ( sK0(X0,sK18) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_12813]) ).
tcf(c_12822,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,X1),iPr_def_11)
| in(sK2(sK18,X0,X1),X1)
| in(sK2(sK18,X0,X1),X0)
| ( set_union2(sK18,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_12813]) ).
tcf(c_12823,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_11)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 ) ),
inference(superposition,[status(thm)],[c_68,c_12813]) ).
tcf(c_12824,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,X1),iPr_def_11)
| in(sK2(X0,sK18,X1),X1)
| in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 ) ),
inference(superposition,[status(thm)],[c_68,c_12813]) ).
tcf(c_12831,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_7241,c_12813]) ).
tcf(c_12834,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_12813]) ).
tcf(c_12836,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9901,c_12813]) ).
tcf(c_12837,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_12813]) ).
tcf(c_12838,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_12813]) ).
tcf(c_12898,plain,
! [X0: $i] :
( ( X0 = sK18 )
| ~ in(X0,singleton(sK18)) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_12903,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = sK18 )
| ~ in(sK2(X0,X1,sK18),sK18)
| ~ in(sK2(X0,X1,sK18),X1) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_12925,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11005,c_131]) ).
tcf(c_12944,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11599,c_128]) ).
tcf(c_12954,plain,
! [X0: $i] :
( subset(X0,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK5(powerset(sK5(powerset(sK18))))) ),
inference(superposition,[status(thm)],[c_6935,c_128]) ).
tcf(c_12974,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(X0)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9928,c_131]) ).
tcf(c_12975,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),X0)
| in(powerset(X0),sK3(iPr_def_11))
| ( powerset(X0) = sK3(iPr_def_11) )
| ~ in(powerset(X0),sK18) ),
inference(superposition,[status(thm)],[c_9928,c_133]) ).
tcf(c_13006,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11185,c_131]) ).
tcf(c_13007,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK4(iPr_def_11) = X1 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11185,c_77]) ).
tcf(c_13008,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| subset(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11185,c_65]) ).
tcf(c_13010,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11185,c_137]) ).
tcf(c_13011,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| element(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11185,c_127]) ).
tcf(c_13012,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(sK4(iPr_def_11),X0,X1))
| ( set_union2(sK4(iPr_def_11),X0) = X1 )
| ( sK2(sK4(iPr_def_11),X0,X1) = sK4(iPr_def_11) )
| ~ in(sK2(sK4(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK4(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_11185,c_66]) ).
tcf(c_13013,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(X0,X1,sK4(iPr_def_11)))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ( sK2(X0,X1,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_11185,c_67]) ).
tcf(c_13014,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_74]) ).
tcf(c_13015,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(sK4(iPr_def_11)))
| ( singleton(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(singleton(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_3522]) ).
tcf(c_13017,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_3641]) ).
tcf(c_13018,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_3615]) ).
tcf(c_13019,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_3618]) ).
tcf(c_13020,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_3644]) ).
tcf(c_13021,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_3944]) ).
tcf(c_13022,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_3945]) ).
tcf(c_13023,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_4131]) ).
tcf(c_13024,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_4132]) ).
tcf(c_13026,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(X1,sK4(iPr_def_11))
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_11185,c_77]) ).
tcf(c_13027,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),X0)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11185,c_65]) ).
tcf(c_13030,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11185,c_127]) ).
tcf(c_13031,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(singleton(X0),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_62]) ).
tcf(c_13032,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_71]) ).
tcf(c_13033,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_76]) ).
tcf(c_13035,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11185,c_12813]) ).
tcf(c_13036,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK18,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ in(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11185,c_6841]) ).
tcf(c_13037,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK18,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11185,c_5047]) ).
tcf(c_13038,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_11)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11185,c_3640]) ).
tcf(c_13039,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK4(iPr_def_11))
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK1(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK1(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK1(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_3523]) ).
tcf(c_13040,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK3(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK3(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK3(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_3524]) ).
tcf(c_13041,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK4(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK4(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_3525]) ).
tcf(c_13048,plain,
( epsilon_connected(iPr_def_11)
| empty(sK4(iPr_def_11))
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK5(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK5(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK5(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_3900]) ).
tcf(c_13049,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK18,sK4(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11185,c_10578]) ).
tcf(c_13371,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK4(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11193,c_77]) ).
tcf(c_13372,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11193,c_65]) ).
tcf(c_13373,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(iPr_def_10,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11193,c_49]) ).
tcf(c_13376,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11193,c_9540]) ).
tcf(c_13377,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11193,c_6289]) ).
tcf(c_13378,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11193,c_4912]) ).
tcf(c_13379,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11193,c_3592]) ).
tcf(c_13380,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11193,c_3614]) ).
tcf(c_13381,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_11193,c_77]) ).
tcf(c_13382,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11193,c_65]) ).
tcf(c_13383,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11193,c_49]) ).
tcf(c_13385,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11193,c_127]) ).
tcf(c_13386,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = X0 )
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ empty(sK4(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_11193,c_62]) ).
tcf(c_13387,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ empty(sK4(iPr_def_11))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11193,c_71]) ).
tcf(c_13388,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ empty(sK4(iPr_def_11))
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11193,c_76]) ).
tcf(c_13389,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = empty_set )
| ~ empty(sK4(iPr_def_11))
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_11193,c_7097]) ).
tcf(c_13391,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ empty(sK4(iPr_def_11))
| ~ in(sK18,sK18)
| ~ in(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11193,c_6841]) ).
tcf(c_13394,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK1(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ empty(sK4(iPr_def_11))
| ~ in(sK1(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11193,c_3523]) ).
tcf(c_13395,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK3(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ empty(sK4(iPr_def_11))
| ~ in(sK3(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11193,c_3524]) ).
tcf(c_13396,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ empty(sK4(iPr_def_11))
| ~ in(sK4(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11193,c_3525]) ).
tcf(c_13616,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X2,X0),X1)
| ( singleton(X2) = X0 )
| ( sK0(X2,X0) = X2 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_60,c_358]) ).
tcf(c_13617,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ subset(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_61,c_358]) ).
tcf(c_13618,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| element(sK1(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_358]) ).
tcf(c_13619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X2,X3),X1)
| in(sK2(X0,X2,X3),X3)
| in(sK2(X0,X2,X3),X2)
| ( set_union2(X0,X2) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_358]) ).
tcf(c_13620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,X0),X1)
| in(sK2(X2,X3,X0),X3)
| in(sK2(X2,X3,X0),X2)
| ( set_union2(X2,X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_358]) ).
tcf(c_13621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X0,X3),X1)
| in(sK2(X2,X0,X3),X3)
| in(sK2(X2,X0,X3),X2)
| ( set_union2(X2,X0) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_358]) ).
tcf(c_13622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X3,X2)
| ~ in(X3,X0)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_69,c_358]) ).
tcf(c_13623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X3,X2)
| ~ in(X3,X1)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_70,c_358]) ).
tcf(c_13624,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| element(sK3(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_72,c_358]) ).
tcf(c_13625,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| element(sK4(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_73,c_358]) ).
tcf(c_13626,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(sK5(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3768,c_358]) ).
tcf(c_13627,plain,
! [X0: $i] :
( element(sK18,X0)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_3400,c_358]) ).
tcf(c_13628,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_10)
| element(sK1(iPr_def_10),X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_3669,c_358]) ).
tcf(c_13629,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_10)
| element(sK3(iPr_def_10),X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_3670,c_358]) ).
tcf(c_13630,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_10)
| element(sK4(iPr_def_10),X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_3671,c_358]) ).
tcf(c_13631,plain,
! [X0: $i] :
( element(sK18,X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_3672,c_358]) ).
tcf(c_13632,plain,
! [X0: $i,X1: $i] :
( element(sK0(X1,iPr_def_10),X0)
| ( singleton(X1) = iPr_def_10 )
| ( sK0(X1,iPr_def_10) = X1 )
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_3738,c_358]) ).
tcf(c_13633,plain,
! [X0: $i,X1: $i] :
( element(sK0(X1,sK18),X0)
| ( singleton(X1) = sK18 )
| ( sK0(X1,sK18) = X1 )
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_3959,c_358]) ).
tcf(c_13634,plain,
! [X0: $i] :
( empty(sK18)
| element(sK5(sK18),X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_3963,c_358]) ).
tcf(c_13635,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),X0)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_9169,c_358]) ).
tcf(c_13636,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| ~ subset(sK18,X0) ),
inference(superposition,[status(thm)],[c_6994,c_358]) ).
tcf(c_13637,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(sK3(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9909,c_358]) ).
tcf(c_13638,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X1)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9927,c_358]) ).
tcf(c_13639,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(empty_set,sK3(iPr_def_11))
| element(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_9932,c_358]) ).
tcf(c_13640,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X1)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_358]) ).
tcf(c_13641,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X0)
| ~ empty(sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_9568,c_358]) ).
tcf(c_13642,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| ~ subset(sK18,X0) ),
inference(superposition,[status(thm)],[c_6995,c_358]) ).
tcf(c_13643,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(sK4(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11193,c_358]) ).
tcf(c_13644,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X1)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11211,c_358]) ).
tcf(c_13645,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(empty_set,sK4(iPr_def_11))
| element(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_11216,c_358]) ).
tcf(c_13646,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X1)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_358]) ).
tcf(c_13647,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X0)
| ~ empty(sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_11004,c_358]) ).
tcf(c_13648,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| ~ subset(sK18,X0) ),
inference(superposition,[status(thm)],[c_7014,c_358]) ).
tcf(c_13649,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ empty(sK5(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7246,c_358]) ).
tcf(c_13650,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7263,c_358]) ).
tcf(c_13651,plain,
! [X0: $i] :
( in(empty_set,sK5(iPr_def_11))
| element(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_7267,c_358]) ).
tcf(c_13652,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_358]) ).
tcf(c_13653,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),X0)
| ~ empty(sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_7137,c_358]) ).
tcf(c_13654,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7241,c_358]) ).
tcf(c_13655,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X0 )
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7246,c_358]) ).
tcf(c_13656,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X1)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7238,c_358]) ).
tcf(c_13657,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X1)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7155,c_358]) ).
tcf(c_13658,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_7241,c_358]) ).
tcf(c_13659,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_7238,c_358]) ).
tcf(c_13660,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = X1 )
| ~ empty(X1)
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_7263,c_358]) ).
tcf(c_13661,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_7155,c_358]) ).
tcf(c_13662,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_7909,c_358]) ).
tcf(c_13663,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_9909,c_358]) ).
tcf(c_13664,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X1)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_9901,c_358]) ).
tcf(c_13665,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X1)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_9595,c_358]) ).
tcf(c_13666,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(X1,X0)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_9901,c_358]) ).
tcf(c_13667,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(X1,X0)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = X1 )
| ~ empty(X1)
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_9927,c_358]) ).
tcf(c_13668,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(X1,X0)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_9595,c_358]) ).
tcf(c_13669,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_11193,c_358]) ).
tcf(c_13670,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X1)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_11185,c_358]) ).
tcf(c_13671,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X1)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_11035,c_358]) ).
tcf(c_13672,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(X1,X0)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_11185,c_358]) ).
tcf(c_13673,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(X1,X0)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = X1 )
| ~ empty(X1)
| ~ in(X1,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_11211,c_358]) ).
tcf(c_13674,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(X1,X0)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_11035,c_358]) ).
tcf(c_14235,plain,
! [X0: $i,X1: $i] : element(X0,set_union2(singleton(X0),X1)),
inference(superposition,[status(thm)],[c_138,c_13617]) ).
tcf(c_14236,plain,
! [X0: $i,X1: $i] : element(X0,set_union2(X1,singleton(X0))),
inference(superposition,[status(thm)],[c_3397,c_13617]) ).
tcf(c_14237,plain,
! [X0: $i] :
( element(X0,singleton(singleton(X0)))
| ~ epsilon_transitive(singleton(singleton(X0))) ),
inference(superposition,[status(thm)],[c_3803,c_13617]) ).
tcf(c_14238,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_union2(X1,X2))
| ~ subset(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_3863,c_13617]) ).
tcf(c_14239,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_union2(X2,X1))
| ~ epsilon_transitive(set_union2(X2,X1))
| ~ in(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_3806,c_13617]) ).
tcf(c_14240,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_union2(X1,X2))
| ~ epsilon_transitive(set_union2(X1,X2))
| ~ in(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_3805,c_13617]) ).
tcf(c_14241,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_union2(X2,X1))
| ~ subset(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_3865,c_13617]) ).
tcf(c_14277,plain,
! [X0: $i] : element(sK18,set_union2(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_2420,c_14235]) ).
tcf(c_14278,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(singleton(X0),X1))
| in(X0,set_union2(singleton(X0),X1)) ),
inference(superposition,[status(thm)],[c_14235,c_131]) ).
tcf(c_14312,plain,
! [X0: $i] : element(sK18,set_union2(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_58,c_14277]) ).
tcf(c_14317,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_10,X0))
| in(sK18,set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_14277,c_131]) ).
tcf(c_14326,plain,
! [X0: $i] :
( empty(set_union2(X0,iPr_def_10))
| in(sK18,set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_14312,c_131]) ).
tcf(c_14335,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X1,singleton(X0)))
| in(X0,set_union2(X1,singleton(X0))) ),
inference(superposition,[status(thm)],[c_14236,c_131]) ).
tcf(c_14355,plain,
( element(sK18,singleton(iPr_def_10))
| ~ epsilon_transitive(singleton(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3803,c_13627]) ).
tcf(c_14356,plain,
! [X0: $i,X1: $i] :
( element(sK18,set_union2(X0,X1))
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_3863,c_13627]) ).
tcf(c_14357,plain,
! [X0: $i,X1: $i] :
( element(sK18,set_union2(X0,X1))
| ~ in(iPr_def_10,X1)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_13627]) ).
tcf(c_14358,plain,
! [X0: $i,X1: $i] :
( element(sK18,set_union2(X0,X1))
| ~ in(iPr_def_10,X0)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_13627]) ).
tcf(c_14359,plain,
! [X0: $i,X1: $i] :
( element(sK18,set_union2(X1,X0))
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_3865,c_13627]) ).
tcf(c_14378,plain,
! [X0: $i] : element(sK18,set_union2(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_138,c_13631]) ).
tcf(c_14379,plain,
! [X0: $i] : element(sK18,set_union2(X0,iPr_def_11)),
inference(superposition,[status(thm)],[c_3397,c_13631]) ).
tcf(c_14380,plain,
( element(sK18,singleton(iPr_def_11))
| ~ epsilon_transitive(singleton(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3803,c_13631]) ).
tcf(c_14381,plain,
! [X0: $i,X1: $i] :
( element(sK18,set_union2(X0,X1))
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_3863,c_13631]) ).
tcf(c_14382,plain,
! [X0: $i,X1: $i] :
( element(sK18,set_union2(X0,X1))
| ~ in(iPr_def_11,X1)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_13631]) ).
tcf(c_14383,plain,
! [X0: $i,X1: $i] :
( element(sK18,set_union2(X0,X1))
| ~ in(iPr_def_11,X0)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_13631]) ).
tcf(c_14384,plain,
! [X0: $i,X1: $i] :
( element(sK18,set_union2(X1,X0))
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_3865,c_13631]) ).
tcf(c_14449,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11194,c_131]) ).
tcf(c_14470,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(X0)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11212,c_131]) ).
tcf(c_14471,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),X0)
| in(powerset(X0),sK4(iPr_def_11))
| ( powerset(X0) = sK4(iPr_def_11) )
| ~ in(powerset(X0),sK18) ),
inference(superposition,[status(thm)],[c_11212,c_133]) ).
tcf(c_14514,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,set_union2(X2,X1)),X2)
| in(sK0(X0,set_union2(X1,X2)),X1)
| ( set_union2(X1,X2) = singleton(X0) )
| ( sK0(X0,set_union2(X1,X2)) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_4023]) ).
tcf(c_14518,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X1)
| in(sK0(X0,set_union2(empty_set,X1)),empty_set)
| ( set_union2(empty_set,X1) = singleton(X0) )
| ( sK0(X0,set_union2(empty_set,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_3423,c_4023]) ).
tcf(c_14519,plain,
! [X0: $i] :
( in(sK0(X0,iPr_def_11),sK18)
| in(sK0(X0,set_union2(iPr_def_10,sK18)),iPr_def_10)
| ( set_union2(iPr_def_10,sK18) = singleton(X0) )
| ( sK0(X0,set_union2(iPr_def_10,sK18)) = X0 ) ),
inference(superposition,[status(thm)],[c_3424,c_4023]) ).
tcf(c_14520,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,set_union2(X2,X1)),X1)
| in(sK0(X0,set_union2(X1,X2)),X2)
| ( set_union2(X1,X2) = singleton(X0) )
| ( sK0(X0,set_union2(X1,X2)) = X0 ) ),
inference(superposition,[status(thm)],[c_58,c_4023]) ).
tcf(c_14523,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X1)
| in(sK0(X0,set_union2(X1,empty_set)),empty_set)
| ( set_union2(X1,empty_set) = singleton(X0) )
| ( sK0(X0,set_union2(X1,empty_set)) = X0 ) ),
inference(superposition,[status(thm)],[c_126,c_4023]) ).
tcf(c_14525,plain,
! [X0: $i] :
( in(sK0(X0,iPr_def_11),iPr_def_10)
| in(sK0(X0,set_union2(iPr_def_10,sK18)),sK18)
| ( set_union2(iPr_def_10,sK18) = singleton(X0) )
| ( sK0(X0,set_union2(iPr_def_10,sK18)) = X0 ) ),
inference(superposition,[status(thm)],[c_3424,c_4023]) ).
tcf(c_14526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK0(X2,set_union2(X3,X0)),X1)
| in(sK0(X2,set_union2(X3,X0)),X3)
| ( set_union2(X3,X0) = singleton(X2) )
| ( sK0(X2,set_union2(X3,X0)) = X2 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4023,c_358]) ).
tcf(c_14527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK0(X2,set_union2(X3,X1)))
| in(sK0(X2,set_union2(X3,X1)),X3)
| in(sK0(X2,set_union2(X3,X1)),X0)
| ( set_union2(X3,X1) = singleton(X2) )
| ( sK0(X2,set_union2(X3,X1)) = X2 )
| ( sK0(X2,set_union2(X3,X1)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4023,c_77]) ).
tcf(c_14528,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK0(X1,set_union2(X2,X0)),X0)
| in(sK0(X1,set_union2(X2,X0)),X2)
| ( set_union2(X2,X0) = singleton(X1) )
| ( sK0(X1,set_union2(X2,X0)) = X1 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4023,c_65]) ).
tcf(c_14529,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,set_union2(X2,X0)),X2)
| ( set_union2(X2,X0) = singleton(X1) )
| ( sK0(X1,set_union2(X2,X0)) = X1 )
| ~ in(X0,sK0(X1,set_union2(X2,X0))) ),
inference(superposition,[status(thm)],[c_4023,c_49]) ).
tcf(c_14530,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,set_union2(X2,X0)),X2)
| ( set_union2(X2,X0) = singleton(X1) )
| ( sK0(X1,set_union2(X2,X0)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4023,c_137]) ).
tcf(c_14531,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,set_union2(X1,X2)),X2)
| in(sK0(X0,set_union2(X1,X2)),X1)
| ( set_union2(X1,X2) = singleton(X0) )
| ( sK0(X0,set_union2(X1,X2)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_127]) ).
tcf(c_14532,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,set_union2(X1,singleton(X2))),X1)
| ( set_union2(X1,singleton(X2)) = singleton(X0) )
| ( sK0(X0,set_union2(X1,singleton(X2))) = X2 )
| ( sK0(X0,set_union2(X1,singleton(X2))) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_62]) ).
tcf(c_14533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X0,set_union2(X1,set_union2(X2,X3))),X3)
| in(sK0(X0,set_union2(X1,set_union2(X2,X3))),X2)
| in(sK0(X0,set_union2(X1,set_union2(X2,X3))),X1)
| ( set_union2(X1,set_union2(X2,X3)) = singleton(X0) )
| ( sK0(X0,set_union2(X1,set_union2(X2,X3))) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_71]) ).
tcf(c_14534,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(X1,empty_set)),X1)
| ( set_union2(X1,empty_set) = singleton(X0) )
| ( sK0(X0,set_union2(X1,empty_set)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_7097]) ).
tcf(c_14535,plain,
! [X0: $i,X1: $i] :
( subset(sK0(X0,set_union2(X1,sK18)),iPr_def_11)
| in(sK0(X0,set_union2(X1,sK18)),X1)
| ( set_union2(X1,sK18) = singleton(X0) )
| ( sK0(X0,set_union2(X1,sK18)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_12813]) ).
tcf(c_14536,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(X1,sK18)),X1)
| ( set_union2(X1,sK18) = singleton(X0) )
| ( sK0(X0,set_union2(X1,sK18)) = X0 )
| ~ in(iPr_def_11,sK0(X0,set_union2(X1,sK18))) ),
inference(superposition,[status(thm)],[c_4023,c_6841]) ).
tcf(c_14537,plain,
! [X0: $i,X1: $i] :
( element(sK0(X0,set_union2(X1,sK18)),iPr_def_11)
| in(sK0(X0,set_union2(X1,sK18)),X1)
| ( set_union2(X1,sK18) = singleton(X0) )
| ( sK0(X0,set_union2(X1,sK18)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_5047]) ).
tcf(c_14538,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(X1,sK18)),iPr_def_11)
| in(sK0(X0,set_union2(X1,sK18)),X1)
| ( set_union2(X1,sK18) = singleton(X0) )
| ( sK0(X0,set_union2(X1,sK18)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_3640]) ).
tcf(c_14539,plain,
! [X0: $i,X1: $i] :
( subset(sK0(X0,set_union2(X1,iPr_def_10)),iPr_def_11)
| in(sK0(X0,set_union2(X1,iPr_def_10)),X1)
| ( set_union2(X1,iPr_def_10) = singleton(X0) )
| ( sK0(X0,set_union2(X1,iPr_def_10)) = X0 )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4023,c_9540]) ).
tcf(c_14540,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(X1,iPr_def_10)),X1)
| ( set_union2(X1,iPr_def_10) = singleton(X0) )
| ( sK0(X0,set_union2(X1,iPr_def_10)) = X0 )
| ~ in(iPr_def_11,sK0(X0,set_union2(X1,iPr_def_10))) ),
inference(superposition,[status(thm)],[c_4023,c_6289]) ).
tcf(c_14541,plain,
! [X0: $i,X1: $i] :
( element(sK0(X0,set_union2(X1,iPr_def_10)),iPr_def_11)
| in(sK0(X0,set_union2(X1,iPr_def_10)),X1)
| ( set_union2(X1,iPr_def_10) = singleton(X0) )
| ( sK0(X0,set_union2(X1,iPr_def_10)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_4912]) ).
tcf(c_14542,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(X1,iPr_def_10)),X1)
| ( set_union2(X1,iPr_def_10) = singleton(X0) )
| ( sK0(X0,set_union2(X1,iPr_def_10)) = sK18 )
| ( sK0(X0,set_union2(X1,iPr_def_10)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_3592]) ).
tcf(c_14543,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(X1,iPr_def_10)),iPr_def_11)
| in(sK0(X0,set_union2(X1,iPr_def_10)),X1)
| ( set_union2(X1,iPr_def_10) = singleton(X0) )
| ( sK0(X0,set_union2(X1,iPr_def_10)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_3614]) ).
tcf(c_14544,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(X1,iPr_def_11)),iPr_def_10)
| in(sK0(X0,set_union2(X1,iPr_def_11)),sK18)
| in(sK0(X0,set_union2(X1,iPr_def_11)),X1)
| ( set_union2(X1,iPr_def_11) = singleton(X0) )
| ( sK0(X0,set_union2(X1,iPr_def_11)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_4035]) ).
tcf(c_14545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK0(X2,set_union2(X0,X3)),X1)
| in(sK0(X2,set_union2(X0,X3)),X3)
| ( set_union2(X0,X3) = singleton(X2) )
| ( sK0(X2,set_union2(X0,X3)) = X2 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4023,c_358]) ).
tcf(c_14546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK0(X2,set_union2(X1,X3)))
| in(sK0(X2,set_union2(X1,X3)),X3)
| in(sK0(X2,set_union2(X1,X3)),X0)
| ( set_union2(X1,X3) = singleton(X2) )
| ( sK0(X2,set_union2(X1,X3)) = X2 )
| ( sK0(X2,set_union2(X1,X3)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4023,c_77]) ).
tcf(c_14547,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK0(X1,set_union2(X0,X2)),X0)
| in(sK0(X1,set_union2(X0,X2)),X2)
| ( set_union2(X0,X2) = singleton(X1) )
| ( sK0(X1,set_union2(X0,X2)) = X1 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4023,c_65]) ).
tcf(c_14548,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,set_union2(X0,X2)),X2)
| ( set_union2(X0,X2) = singleton(X1) )
| ( sK0(X1,set_union2(X0,X2)) = X1 )
| ~ in(X0,sK0(X1,set_union2(X0,X2))) ),
inference(superposition,[status(thm)],[c_4023,c_49]) ).
tcf(c_14549,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X1,set_union2(X0,X2)),X2)
| ( set_union2(X0,X2) = singleton(X1) )
| ( sK0(X1,set_union2(X0,X2)) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4023,c_137]) ).
tcf(c_14550,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK0(X0,set_union2(X1,X2)),X1)
| in(sK0(X0,set_union2(X1,X2)),X2)
| ( set_union2(X1,X2) = singleton(X0) )
| ( sK0(X0,set_union2(X1,X2)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_127]) ).
tcf(c_14551,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,set_union2(singleton(X1),X2)),X2)
| ( set_union2(singleton(X1),X2) = singleton(X0) )
| ( sK0(X0,set_union2(singleton(X1),X2)) = X1 )
| ( sK0(X0,set_union2(singleton(X1),X2)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_62]) ).
tcf(c_14552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X0,set_union2(set_union2(X1,X2),X3)),X3)
| in(sK0(X0,set_union2(set_union2(X1,X2),X3)),X2)
| in(sK0(X0,set_union2(set_union2(X1,X2),X3)),X1)
| ( set_union2(set_union2(X1,X2),X3) = singleton(X0) )
| ( sK0(X0,set_union2(set_union2(X1,X2),X3)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_71]) ).
tcf(c_14553,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(empty_set,X1)),X1)
| ( set_union2(empty_set,X1) = singleton(X0) )
| ( sK0(X0,set_union2(empty_set,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_7097]) ).
tcf(c_14554,plain,
! [X0: $i,X1: $i] :
( subset(sK0(X0,set_union2(sK18,X1)),iPr_def_11)
| in(sK0(X0,set_union2(sK18,X1)),X1)
| ( set_union2(sK18,X1) = singleton(X0) )
| ( sK0(X0,set_union2(sK18,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_12813]) ).
tcf(c_14555,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(sK18,X1)),X1)
| ( set_union2(sK18,X1) = singleton(X0) )
| ( sK0(X0,set_union2(sK18,X1)) = X0 )
| ~ in(iPr_def_11,sK0(X0,set_union2(sK18,X1))) ),
inference(superposition,[status(thm)],[c_4023,c_6841]) ).
tcf(c_14556,plain,
! [X0: $i,X1: $i] :
( element(sK0(X0,set_union2(sK18,X1)),iPr_def_11)
| in(sK0(X0,set_union2(sK18,X1)),X1)
| ( set_union2(sK18,X1) = singleton(X0) )
| ( sK0(X0,set_union2(sK18,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_5047]) ).
tcf(c_14557,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(sK18,X1)),iPr_def_11)
| in(sK0(X0,set_union2(sK18,X1)),X1)
| ( set_union2(sK18,X1) = singleton(X0) )
| ( sK0(X0,set_union2(sK18,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_3640]) ).
tcf(c_14558,plain,
! [X0: $i,X1: $i] :
( subset(sK0(X0,set_union2(iPr_def_10,X1)),iPr_def_11)
| in(sK0(X0,set_union2(iPr_def_10,X1)),X1)
| ( set_union2(iPr_def_10,X1) = singleton(X0) )
| ( sK0(X0,set_union2(iPr_def_10,X1)) = X0 )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4023,c_9540]) ).
tcf(c_14559,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(iPr_def_10,X1)),X1)
| ( set_union2(iPr_def_10,X1) = singleton(X0) )
| ( sK0(X0,set_union2(iPr_def_10,X1)) = X0 )
| ~ in(iPr_def_11,sK0(X0,set_union2(iPr_def_10,X1))) ),
inference(superposition,[status(thm)],[c_4023,c_6289]) ).
tcf(c_14560,plain,
! [X0: $i,X1: $i] :
( element(sK0(X0,set_union2(iPr_def_10,X1)),iPr_def_11)
| in(sK0(X0,set_union2(iPr_def_10,X1)),X1)
| ( set_union2(iPr_def_10,X1) = singleton(X0) )
| ( sK0(X0,set_union2(iPr_def_10,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_4912]) ).
tcf(c_14561,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(iPr_def_10,X1)),X1)
| ( set_union2(iPr_def_10,X1) = singleton(X0) )
| ( sK0(X0,set_union2(iPr_def_10,X1)) = sK18 )
| ( sK0(X0,set_union2(iPr_def_10,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_3592]) ).
tcf(c_14562,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(iPr_def_10,X1)),iPr_def_11)
| in(sK0(X0,set_union2(iPr_def_10,X1)),X1)
| ( set_union2(iPr_def_10,X1) = singleton(X0) )
| ( sK0(X0,set_union2(iPr_def_10,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_3614]) ).
tcf(c_14563,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(iPr_def_11,X1)),iPr_def_10)
| in(sK0(X0,set_union2(iPr_def_11,X1)),sK18)
| in(sK0(X0,set_union2(iPr_def_11,X1)),X1)
| ( set_union2(iPr_def_11,X1) = singleton(X0) )
| ( sK0(X0,set_union2(iPr_def_11,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_4035]) ).
tcf(c_14564,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(X1,X1)),X1)
| ( set_union2(X1,X1) = singleton(X0) )
| ( sK0(X0,set_union2(X1,X1)) = X0 ) ),
inference(equality_factoring,[status(thm)],[c_4023]) ).
tcf(c_14584,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X1)
| ( set_union2(X1,empty_set) = singleton(X0) )
| ( sK0(X0,set_union2(X1,empty_set)) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14523,c_7097]) ).
tcf(c_14589,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X1)
| ( set_union2(empty_set,X1) = singleton(X0) )
| ( sK0(X0,set_union2(empty_set,X1)) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14518,c_7097]) ).
tcf(c_14982,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_11,X0))
| in(sK18,set_union2(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_14378,c_131]) ).
tcf(c_14990,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_10,X0))
| in(sK18,set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_58,c_14317]) ).
tcf(c_14995,plain,
! [X0: $i,X1: $i] :
( element(sK18,X1)
| empty(set_union2(iPr_def_10,X0))
| ~ subset(set_union2(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_14317,c_358]) ).
tcf(c_14996,plain,
! [X0: $i,X1: $i] :
( in(sK18,X0)
| in(X0,sK18)
| empty(set_union2(iPr_def_10,X1))
| ( X0 = sK18 )
| ~ epsilon_connected(set_union2(iPr_def_10,X1))
| ~ in(X0,set_union2(iPr_def_10,X1)) ),
inference(superposition,[status(thm)],[c_14317,c_77]) ).
tcf(c_14997,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_10,X0))
| subset(sK18,set_union2(iPr_def_10,X0))
| ~ epsilon_transitive(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_14317,c_65]) ).
tcf(c_14998,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_10,X0))
| ~ in(set_union2(iPr_def_10,X0),sK18) ),
inference(superposition,[status(thm)],[c_14317,c_49]) ).
tcf(c_15027,plain,
! [X0: $i] :
( empty(set_union2(X0,iPr_def_10))
| in(sK18,set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_58,c_14326]) ).
tcf(c_15031,plain,
! [X0: $i,X1: $i] :
( element(sK18,X1)
| empty(set_union2(X0,iPr_def_10))
| ~ subset(set_union2(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_14326,c_358]) ).
tcf(c_15032,plain,
! [X0: $i,X1: $i] :
( in(sK18,X0)
| in(X0,sK18)
| empty(set_union2(X1,iPr_def_10))
| ( X0 = sK18 )
| ~ epsilon_connected(set_union2(X1,iPr_def_10))
| ~ in(X0,set_union2(X1,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_14326,c_77]) ).
tcf(c_15033,plain,
! [X0: $i] :
( empty(set_union2(X0,iPr_def_10))
| subset(sK18,set_union2(X0,iPr_def_10))
| ~ epsilon_transitive(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_14326,c_65]) ).
tcf(c_15034,plain,
! [X0: $i] :
( empty(set_union2(X0,iPr_def_10))
| ~ in(set_union2(X0,iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_14326,c_49]) ).
tcf(c_15059,plain,
! [X0: $i] : in(sK18,set_union2(iPr_def_11,X0)),
inference(global_subsumption_just,[status(thm)],[c_14982,c_3672,c_5465]) ).
tcf(c_15062,plain,
! [X0: $i] : in(sK18,set_union2(X0,iPr_def_11)),
inference(superposition,[status(thm)],[c_58,c_15059]) ).
tcf(c_15066,plain,
! [X0: $i,X1: $i] :
( element(sK18,X1)
| ~ subset(set_union2(iPr_def_11,X0),X1) ),
inference(superposition,[status(thm)],[c_15059,c_358]) ).
tcf(c_15067,plain,
! [X0: $i,X1: $i] :
( in(sK18,X0)
| in(X0,sK18)
| ( X0 = sK18 )
| ~ epsilon_connected(set_union2(iPr_def_11,X1))
| ~ in(X0,set_union2(iPr_def_11,X1)) ),
inference(superposition,[status(thm)],[c_15059,c_77]) ).
tcf(c_15068,plain,
! [X0: $i] :
( subset(sK18,set_union2(iPr_def_11,X0))
| ~ epsilon_transitive(set_union2(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_15059,c_65]) ).
tcf(c_15069,plain,
! [X0: $i] : ~ in(set_union2(iPr_def_11,X0),sK18),
inference(superposition,[status(thm)],[c_15059,c_49]) ).
tcf(c_15070,plain,
! [X0: $i] : ~ empty(set_union2(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_15059,c_137]) ).
tcf(c_15124,plain,
! [X0: $i,X1: $i] :
( element(sK18,X1)
| ~ subset(set_union2(X0,iPr_def_11),X1) ),
inference(superposition,[status(thm)],[c_15062,c_358]) ).
tcf(c_15125,plain,
! [X0: $i,X1: $i] :
( in(sK18,X0)
| in(X0,sK18)
| ( X0 = sK18 )
| ~ epsilon_connected(set_union2(X1,iPr_def_11))
| ~ in(X0,set_union2(X1,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15062,c_77]) ).
tcf(c_15126,plain,
! [X0: $i] :
( subset(sK18,set_union2(X0,iPr_def_11))
| ~ epsilon_transitive(set_union2(X0,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15062,c_65]) ).
tcf(c_15127,plain,
! [X0: $i] : ~ in(set_union2(X0,iPr_def_11),sK18),
inference(superposition,[status(thm)],[c_15062,c_49]) ).
tcf(c_15128,plain,
! [X0: $i] : ~ empty(set_union2(X0,iPr_def_11)),
inference(superposition,[status(thm)],[c_15062,c_137]) ).
tcf(c_15165,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ~ epsilon_transitive(X1)
| ~ in(X1,sK18)
| ~ subset(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7261,c_128]) ).
tcf(c_15166,plain,
! [X0: $i] :
( in(empty_set,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = empty_set )
| ~ epsilon_transitive(empty_set)
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_7261,c_3866]) ).
tcf(c_15167,plain,
( subset(sK5(iPr_def_11),iPr_def_10)
| in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_7261,c_3931]) ).
tcf(c_15168,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = sK18 )
| ~ epsilon_transitive(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_7261,c_3867]) ).
tcf(c_15169,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),X0)
| in(sK5(powerset(X0)),sK5(iPr_def_11))
| ( sK5(powerset(X0)) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(powerset(X0)))
| ~ in(sK5(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_3864]) ).
tcf(c_15171,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),X0)
| in(sK5(powerset(empty_set)),sK5(iPr_def_11))
| ( sK5(powerset(empty_set)) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(powerset(empty_set)))
| ~ in(sK5(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_4165]) ).
tcf(c_15174,plain,
( empty(sK18)
| subset(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK5(iPr_def_11))
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18))
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_7217]) ).
tcf(c_15178,plain,
( empty(sK18)
| subset(sK5(iPr_def_11),iPr_def_11)
| epsilon_transitive(powerset(sK5(sK18)))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK1(powerset(sK5(sK18))),sK5(iPr_def_11))
| ( sK1(powerset(sK5(sK18))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK1(powerset(sK5(sK18))))
| ~ in(sK1(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_5502]) ).
tcf(c_15179,plain,
( empty(sK18)
| subset(sK5(iPr_def_11),iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(powerset(sK5(sK18))),sK5(iPr_def_11))
| ( sK3(powerset(sK5(sK18))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK3(powerset(sK5(sK18))))
| ~ in(sK3(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_5516]) ).
tcf(c_15180,plain,
( empty(sK18)
| subset(sK5(iPr_def_11),iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(powerset(sK5(sK18))),sK5(iPr_def_11))
| ( sK4(powerset(sK5(sK18))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK4(powerset(sK5(sK18))))
| ~ in(sK4(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_5528]) ).
tcf(c_15188,plain,
! [X0: $i] :
( in(empty_set,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15166,c_89]) ).
tcf(c_15194,plain,
( subset(sK5(iPr_def_11),iPr_def_10)
| in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15167,c_2426]) ).
tcf(c_15297,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X0,X1))
| in(sK1(set_union2(X1,X0)),X1)
| in(sK1(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_58,c_4024]) ).
tcf(c_15300,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,empty_set))
| in(sK1(X0),empty_set)
| in(sK1(set_union2(X0,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_126,c_4024]) ).
tcf(c_15301,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(empty_set,X0))
| in(sK1(X0),X0)
| in(sK1(set_union2(empty_set,X0)),empty_set) ),
inference(superposition,[status(thm)],[c_3423,c_4024]) ).
tcf(c_15302,plain,
( epsilon_transitive(set_union2(iPr_def_10,sK18))
| in(sK1(iPr_def_11),sK18)
| in(sK1(set_union2(iPr_def_10,sK18)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3424,c_4024]) ).
tcf(c_15303,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X0,X1))
| in(sK1(set_union2(X1,X0)),X0)
| in(sK1(set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_58,c_4024]) ).
tcf(c_15305,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,X0))
| in(sK1(X0),X0)
| in(sK1(set_union2(X0,X0)),X0) ),
inference(superposition,[status(thm)],[c_97,c_4024]) ).
tcf(c_15306,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,empty_set))
| in(sK1(X0),X0)
| in(sK1(set_union2(X0,empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_126,c_4024]) ).
tcf(c_15307,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(empty_set,X0))
| in(sK1(X0),empty_set)
| in(sK1(set_union2(empty_set,X0)),X0) ),
inference(superposition,[status(thm)],[c_3423,c_4024]) ).
tcf(c_15308,plain,
( epsilon_transitive(set_union2(iPr_def_10,sK18))
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(set_union2(iPr_def_10,sK18)),sK18) ),
inference(superposition,[status(thm)],[c_3424,c_4024]) ).
tcf(c_15309,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X2,X0))
| element(sK1(set_union2(X2,X0)),X1)
| in(sK1(set_union2(X2,X0)),X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4024,c_358]) ).
tcf(c_15310,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X2,X1))
| in(X0,sK1(set_union2(X2,X1)))
| in(sK1(set_union2(X2,X1)),X2)
| in(sK1(set_union2(X2,X1)),X0)
| ( sK1(set_union2(X2,X1)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4024,c_77]) ).
tcf(c_15311,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X1,X0))
| subset(sK1(set_union2(X1,X0)),X0)
| in(sK1(set_union2(X1,X0)),X1)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4024,c_65]) ).
tcf(c_15312,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X1,X0))
| in(sK1(set_union2(X1,X0)),X1)
| ~ in(X0,sK1(set_union2(X1,X0))) ),
inference(superposition,[status(thm)],[c_4024,c_49]) ).
tcf(c_15313,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X1,X0))
| in(sK1(set_union2(X1,X0)),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4024,c_137]) ).
tcf(c_15314,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X0,X1))
| element(sK1(set_union2(X0,X1)),X1)
| in(sK1(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_127]) ).
tcf(c_15315,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X0,singleton(X1)))
| in(sK1(set_union2(X0,singleton(X1))),X0)
| ( sK1(set_union2(X0,singleton(X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_4024,c_62]) ).
tcf(c_15316,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X0,set_union2(X1,X2)))
| in(sK1(set_union2(X0,set_union2(X1,X2))),X2)
| in(sK1(set_union2(X0,set_union2(X1,X2))),X1)
| in(sK1(set_union2(X0,set_union2(X1,X2))),X0) ),
inference(superposition,[status(thm)],[c_4024,c_71]) ).
tcf(c_15317,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,empty_set))
| in(sK1(set_union2(X0,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_7097]) ).
tcf(c_15318,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,sK18))
| subset(sK1(set_union2(X0,sK18)),iPr_def_11)
| in(sK1(set_union2(X0,sK18)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_12813]) ).
tcf(c_15319,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,sK18))
| in(sK1(set_union2(X0,sK18)),X0)
| ~ in(iPr_def_11,sK1(set_union2(X0,sK18))) ),
inference(superposition,[status(thm)],[c_4024,c_6841]) ).
tcf(c_15320,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,sK18))
| element(sK1(set_union2(X0,sK18)),iPr_def_11)
| in(sK1(set_union2(X0,sK18)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_5047]) ).
tcf(c_15321,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,sK18))
| in(sK1(set_union2(X0,sK18)),iPr_def_11)
| in(sK1(set_union2(X0,sK18)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_3640]) ).
tcf(c_15322,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,iPr_def_10))
| subset(sK1(set_union2(X0,iPr_def_10)),iPr_def_11)
| in(sK1(set_union2(X0,iPr_def_10)),X0)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4024,c_9540]) ).
tcf(c_15323,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,iPr_def_10))
| in(sK1(set_union2(X0,iPr_def_10)),X0)
| ~ in(iPr_def_11,sK1(set_union2(X0,iPr_def_10))) ),
inference(superposition,[status(thm)],[c_4024,c_6289]) ).
tcf(c_15324,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,iPr_def_10))
| element(sK1(set_union2(X0,iPr_def_10)),iPr_def_11)
| in(sK1(set_union2(X0,iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_4912]) ).
tcf(c_15325,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,iPr_def_10))
| in(sK1(set_union2(X0,iPr_def_10)),X0)
| ( sK1(set_union2(X0,iPr_def_10)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4024,c_3592]) ).
tcf(c_15326,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,iPr_def_10))
| in(sK1(set_union2(X0,iPr_def_10)),iPr_def_11)
| in(sK1(set_union2(X0,iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_3614]) ).
tcf(c_15327,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,iPr_def_11))
| in(sK1(set_union2(X0,iPr_def_11)),iPr_def_10)
| in(sK1(set_union2(X0,iPr_def_11)),sK18)
| in(sK1(set_union2(X0,iPr_def_11)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_4035]) ).
tcf(c_15328,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X0,X2))
| element(sK1(set_union2(X0,X2)),X1)
| in(sK1(set_union2(X0,X2)),X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4024,c_358]) ).
tcf(c_15329,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X1,X2))
| in(X0,sK1(set_union2(X1,X2)))
| in(sK1(set_union2(X1,X2)),X2)
| in(sK1(set_union2(X1,X2)),X0)
| ( sK1(set_union2(X1,X2)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4024,c_77]) ).
tcf(c_15330,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X0,X1))
| subset(sK1(set_union2(X0,X1)),X0)
| in(sK1(set_union2(X0,X1)),X1)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4024,c_65]) ).
tcf(c_15331,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X0,X1))
| in(sK1(set_union2(X0,X1)),X1)
| ~ in(X0,sK1(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_4024,c_49]) ).
tcf(c_15332,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X0,X1))
| in(sK1(set_union2(X0,X1)),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4024,c_137]) ).
tcf(c_15333,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X0,X1))
| element(sK1(set_union2(X0,X1)),X0)
| in(sK1(set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_4024,c_127]) ).
tcf(c_15334,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(singleton(X0),X1))
| in(sK1(set_union2(singleton(X0),X1)),X1)
| ( sK1(set_union2(singleton(X0),X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_4024,c_62]) ).
tcf(c_15335,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(set_union2(X0,X1),X2))
| in(sK1(set_union2(set_union2(X0,X1),X2)),X2)
| in(sK1(set_union2(set_union2(X0,X1),X2)),X1)
| in(sK1(set_union2(set_union2(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_71]) ).
tcf(c_15336,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(empty_set,X0))
| in(sK1(set_union2(empty_set,X0)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_7097]) ).
tcf(c_15337,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(sK18,X0))
| subset(sK1(set_union2(sK18,X0)),iPr_def_11)
| in(sK1(set_union2(sK18,X0)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_12813]) ).
tcf(c_15338,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(sK18,X0))
| in(sK1(set_union2(sK18,X0)),X0)
| ~ in(iPr_def_11,sK1(set_union2(sK18,X0))) ),
inference(superposition,[status(thm)],[c_4024,c_6841]) ).
tcf(c_15339,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(sK18,X0))
| element(sK1(set_union2(sK18,X0)),iPr_def_11)
| in(sK1(set_union2(sK18,X0)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_5047]) ).
tcf(c_15340,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(sK18,X0))
| in(sK1(set_union2(sK18,X0)),iPr_def_11)
| in(sK1(set_union2(sK18,X0)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_3640]) ).
tcf(c_15341,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(iPr_def_10,X0))
| subset(sK1(set_union2(iPr_def_10,X0)),iPr_def_11)
| in(sK1(set_union2(iPr_def_10,X0)),X0)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4024,c_9540]) ).
tcf(c_15342,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(iPr_def_10,X0))
| in(sK1(set_union2(iPr_def_10,X0)),X0)
| ~ in(iPr_def_11,sK1(set_union2(iPr_def_10,X0))) ),
inference(superposition,[status(thm)],[c_4024,c_6289]) ).
tcf(c_15343,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(iPr_def_10,X0))
| element(sK1(set_union2(iPr_def_10,X0)),iPr_def_11)
| in(sK1(set_union2(iPr_def_10,X0)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_4912]) ).
tcf(c_15344,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(iPr_def_10,X0))
| in(sK1(set_union2(iPr_def_10,X0)),X0)
| ( sK1(set_union2(iPr_def_10,X0)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4024,c_3592]) ).
tcf(c_15345,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(iPr_def_10,X0))
| in(sK1(set_union2(iPr_def_10,X0)),iPr_def_11)
| in(sK1(set_union2(iPr_def_10,X0)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_3614]) ).
tcf(c_15346,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(iPr_def_11,X0))
| in(sK1(set_union2(iPr_def_11,X0)),iPr_def_10)
| in(sK1(set_union2(iPr_def_11,X0)),sK18)
| in(sK1(set_union2(iPr_def_11,X0)),X0) ),
inference(superposition,[status(thm)],[c_4024,c_4035]) ).
tcf(c_15347,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,X0))
| in(sK1(set_union2(X0,X0)),X0) ),
inference(equality_factoring,[status(thm)],[c_4024]) ).
tcf(c_15359,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK1(X0),empty_set)
| in(sK1(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_15307,c_3423]) ).
tcf(c_15641,plain,
! [X0: $i,X1: $i] :
( element(sK18,X1)
| empty(set_union2(iPr_def_10,X0))
| ~ subset(set_union2(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_14990,c_358]) ).
tcf(c_15642,plain,
! [X0: $i,X1: $i] :
( in(sK18,X0)
| in(X0,sK18)
| empty(set_union2(iPr_def_10,X1))
| ( X0 = sK18 )
| ~ epsilon_connected(set_union2(X1,iPr_def_10))
| ~ in(X0,set_union2(X1,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_14990,c_77]) ).
tcf(c_15643,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_10,X0))
| subset(sK18,set_union2(X0,iPr_def_10))
| ~ epsilon_transitive(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_14990,c_65]) ).
tcf(c_15644,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_10,X0))
| ~ in(set_union2(X0,iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_14990,c_49]) ).
tcf(c_15645,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_10,X0))
| ~ empty(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_14990,c_137]) ).
tcf(c_15689,plain,
! [X0: $i,X1: $i] :
( element(sK18,X1)
| empty(set_union2(X0,iPr_def_10))
| ~ subset(set_union2(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_15027,c_358]) ).
tcf(c_15690,plain,
! [X0: $i,X1: $i] :
( in(sK18,X0)
| in(X0,sK18)
| empty(set_union2(X1,iPr_def_10))
| ( X0 = sK18 )
| ~ epsilon_connected(set_union2(iPr_def_10,X1))
| ~ in(X0,set_union2(iPr_def_10,X1)) ),
inference(superposition,[status(thm)],[c_15027,c_77]) ).
tcf(c_15691,plain,
! [X0: $i] :
( empty(set_union2(X0,iPr_def_10))
| subset(sK18,set_union2(iPr_def_10,X0))
| ~ epsilon_transitive(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_15027,c_65]) ).
tcf(c_15692,plain,
! [X0: $i] :
( empty(set_union2(X0,iPr_def_10))
| ~ in(set_union2(iPr_def_10,X0),sK18) ),
inference(superposition,[status(thm)],[c_15027,c_49]) ).
tcf(c_15693,plain,
! [X0: $i] :
( empty(set_union2(X0,iPr_def_10))
| ~ empty(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_15027,c_137]) ).
tcf(c_15733,plain,
! [X0: $i] :
( empty(X0)
| in(sK5(iPr_def_11),X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_13662,c_131]) ).
tcf(c_15734,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),X0)
| ~ subset(iPr_def_11,powerset(X0)) ),
inference(superposition,[status(thm)],[c_13662,c_133]) ).
tcf(c_15756,plain,
( empty(singleton(iPr_def_10))
| in(sK18,singleton(iPr_def_10))
| ~ epsilon_transitive(singleton(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_14355,c_131]) ).
tcf(c_15757,plain,
( in(sK18,singleton(iPr_def_10))
| ~ epsilon_transitive(singleton(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15756,c_3513]) ).
tcf(c_15764,plain,
( empty(singleton(iPr_def_11))
| in(sK18,singleton(iPr_def_11))
| ~ epsilon_transitive(singleton(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_14380,c_131]) ).
tcf(c_15765,plain,
( in(sK18,singleton(iPr_def_11))
| ~ epsilon_transitive(singleton(iPr_def_11)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15764,c_3513]) ).
tcf(c_15772,plain,
! [X0: $i] :
( element(sK18,X0)
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ subset(singleton(iPr_def_10),X0) ),
inference(superposition,[status(thm)],[c_15757,c_358]) ).
tcf(c_15773,plain,
! [X0: $i] :
( in(sK18,X0)
| in(X0,sK18)
| ( X0 = sK18 )
| ~ epsilon_connected(singleton(iPr_def_10))
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ in(X0,singleton(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_15757,c_77]) ).
tcf(c_15774,plain,
( subset(sK18,singleton(iPr_def_10))
| ~ epsilon_transitive(singleton(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_15757,c_65]) ).
tcf(c_15775,plain,
( ~ epsilon_transitive(singleton(iPr_def_10))
| ~ in(singleton(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_15757,c_49]) ).
tcf(c_15776,plain,
( ~ epsilon_transitive(singleton(iPr_def_10))
| ~ empty(singleton(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_15757,c_137]) ).
tcf(c_15778,plain,
( ( sK18 = iPr_def_10 )
| ~ epsilon_transitive(singleton(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_15757,c_62]) ).
tcf(c_15808,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(X1,X0)
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_9904,c_358]) ).
tcf(c_15809,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK3(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X1 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9904,c_77]) ).
tcf(c_15810,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9904,c_65]) ).
tcf(c_15813,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9904,c_127]) ).
tcf(c_15814,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),sK2(sK3(iPr_def_11),X0,X1))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(sK3(iPr_def_11),X0) = X1 )
| ( sK2(sK3(iPr_def_11),X0,X1) = sK3(iPr_def_11) )
| ~ in(sK2(sK3(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK3(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_9904,c_66]) ).
tcf(c_15815,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),sK2(X0,X1,sK3(iPr_def_11)))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( sK2(X0,X1,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_9904,c_67]) ).
tcf(c_15816,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_76]) ).
tcf(c_15817,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(sK3(iPr_def_11)))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(singleton(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_3522]) ).
tcf(c_15819,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),set_union2(X0,X1))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(sK3(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_3641]) ).
tcf(c_15820,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),set_union2(X0,X1))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(sK3(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_3615]) ).
tcf(c_15821,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_3618]) ).
tcf(c_15822,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_3644]) ).
tcf(c_15823,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_3944]) ).
tcf(c_15824,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_3945]) ).
tcf(c_15825,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_4131]) ).
tcf(c_15826,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_4132]) ).
tcf(c_15829,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X1)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_9904,c_358]) ).
tcf(c_15830,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_9904,c_77]) ).
tcf(c_15831,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),X0)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9904,c_65]) ).
tcf(c_15834,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X0)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9904,c_127]) ).
tcf(c_15835,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(singleton(X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_62]) ).
tcf(c_15836,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_71]) ).
tcf(c_15837,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_74]) ).
tcf(c_15839,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9904,c_12813]) ).
tcf(c_15840,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9904,c_6841]) ).
tcf(c_15841,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9904,c_5047]) ).
tcf(c_15842,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_11)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9904,c_3640]) ).
tcf(c_15843,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK3(iPr_def_11))
| in(sK1(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK1(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK1(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_3523]) ).
tcf(c_15844,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| in(sK3(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK3(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_3524]) ).
tcf(c_15845,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| in(sK4(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK4(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK4(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_3525]) ).
tcf(c_15852,plain,
( epsilon_connected(iPr_def_11)
| empty(sK3(iPr_def_11))
| in(sK5(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK5(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK5(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_3900]) ).
tcf(c_15853,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9904,c_11771]) ).
tcf(c_16229,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(X1,X0)
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_11188,c_358]) ).
tcf(c_16230,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK4(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X1 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11188,c_77]) ).
tcf(c_16231,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11188,c_65]) ).
tcf(c_16234,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11188,c_127]) ).
tcf(c_16235,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),sK2(sK4(iPr_def_11),X0,X1))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(sK4(iPr_def_11),X0) = X1 )
| ( sK2(sK4(iPr_def_11),X0,X1) = sK4(iPr_def_11) )
| ~ in(sK2(sK4(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK4(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_11188,c_66]) ).
tcf(c_16236,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),sK2(X0,X1,sK4(iPr_def_11)))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ( sK2(X0,X1,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_11188,c_67]) ).
tcf(c_16237,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_74]) ).
tcf(c_16238,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(sK4(iPr_def_11)))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(singleton(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_3522]) ).
tcf(c_16240,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),set_union2(X0,X1))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_3641]) ).
tcf(c_16241,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),set_union2(X0,X1))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_3615]) ).
tcf(c_16242,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_3618]) ).
tcf(c_16243,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_3644]) ).
tcf(c_16244,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_3944]) ).
tcf(c_16245,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_3945]) ).
tcf(c_16246,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_4131]) ).
tcf(c_16247,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_4132]) ).
tcf(c_16250,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X1)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_11188,c_358]) ).
tcf(c_16251,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,sK4(iPr_def_11))
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_11188,c_77]) ).
tcf(c_16252,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),X0)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11188,c_65]) ).
tcf(c_16255,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X0)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11188,c_127]) ).
tcf(c_16256,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(singleton(X0),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_62]) ).
tcf(c_16257,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_71]) ).
tcf(c_16258,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_76]) ).
tcf(c_16260,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11188,c_12813]) ).
tcf(c_16261,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ in(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11188,c_6841]) ).
tcf(c_16262,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11188,c_5047]) ).
tcf(c_16263,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_11)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11188,c_3640]) ).
tcf(c_16264,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK4(iPr_def_11))
| in(sK1(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK1(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK1(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_3523]) ).
tcf(c_16265,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| in(sK3(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK3(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK3(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_3524]) ).
tcf(c_16266,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| in(sK4(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK4(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_3525]) ).
tcf(c_16273,plain,
( epsilon_connected(iPr_def_11)
| empty(sK4(iPr_def_11))
| in(sK5(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK5(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK5(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_3900]) ).
tcf(c_16274,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11188,c_10578]) ).
tcf(c_16522,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| in(sK3(set_union2(X1,X0)),X1)
| in(sK3(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_58,c_4027]) ).
tcf(c_16525,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,empty_set))
| in(sK3(X0),empty_set)
| in(sK3(set_union2(X0,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_126,c_4027]) ).
tcf(c_16526,plain,
! [X0: $i] :
( epsilon_connected(set_union2(empty_set,X0))
| in(sK3(X0),X0)
| in(sK3(set_union2(empty_set,X0)),empty_set) ),
inference(superposition,[status(thm)],[c_3423,c_4027]) ).
tcf(c_16527,plain,
( epsilon_connected(set_union2(iPr_def_10,sK18))
| in(sK3(iPr_def_11),sK18)
| in(sK3(set_union2(iPr_def_10,sK18)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3424,c_4027]) ).
tcf(c_16528,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| in(sK3(set_union2(X1,X0)),X0)
| in(sK3(set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_58,c_4027]) ).
tcf(c_16530,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,X0))
| in(sK3(X0),X0)
| in(sK3(set_union2(X0,X0)),X0) ),
inference(superposition,[status(thm)],[c_97,c_4027]) ).
tcf(c_16531,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,empty_set))
| in(sK3(X0),X0)
| in(sK3(set_union2(X0,empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_126,c_4027]) ).
tcf(c_16532,plain,
! [X0: $i] :
( epsilon_connected(set_union2(empty_set,X0))
| in(sK3(X0),empty_set)
| in(sK3(set_union2(empty_set,X0)),X0) ),
inference(superposition,[status(thm)],[c_3423,c_4027]) ).
tcf(c_16533,plain,
( epsilon_connected(set_union2(iPr_def_10,sK18))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(set_union2(iPr_def_10,sK18)),sK18) ),
inference(superposition,[status(thm)],[c_3424,c_4027]) ).
tcf(c_16534,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(X2,X0))
| element(sK3(set_union2(X2,X0)),X1)
| in(sK3(set_union2(X2,X0)),X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4027,c_358]) ).
tcf(c_16535,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(X2,X1))
| in(X0,sK3(set_union2(X2,X1)))
| in(sK3(set_union2(X2,X1)),X2)
| in(sK3(set_union2(X2,X1)),X0)
| ( sK3(set_union2(X2,X1)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4027,c_77]) ).
tcf(c_16536,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X1,X0))
| subset(sK3(set_union2(X1,X0)),X0)
| in(sK3(set_union2(X1,X0)),X1)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4027,c_65]) ).
tcf(c_16537,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X1,X0))
| in(sK3(set_union2(X1,X0)),X1)
| ~ in(X0,sK3(set_union2(X1,X0))) ),
inference(superposition,[status(thm)],[c_4027,c_49]) ).
tcf(c_16538,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X1,X0))
| in(sK3(set_union2(X1,X0)),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4027,c_137]) ).
tcf(c_16539,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| element(sK3(set_union2(X0,X1)),X1)
| in(sK3(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_127]) ).
tcf(c_16540,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,singleton(X1)))
| in(sK3(set_union2(X0,singleton(X1))),X0)
| ( sK3(set_union2(X0,singleton(X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_4027,c_62]) ).
tcf(c_16541,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(X0,set_union2(X1,X2)))
| in(sK3(set_union2(X0,set_union2(X1,X2))),X2)
| in(sK3(set_union2(X0,set_union2(X1,X2))),X1)
| in(sK3(set_union2(X0,set_union2(X1,X2))),X0) ),
inference(superposition,[status(thm)],[c_4027,c_71]) ).
tcf(c_16542,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,empty_set))
| in(sK3(set_union2(X0,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_7097]) ).
tcf(c_16543,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,sK18))
| subset(sK3(set_union2(X0,sK18)),iPr_def_11)
| in(sK3(set_union2(X0,sK18)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_12813]) ).
tcf(c_16544,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,sK18))
| in(sK3(set_union2(X0,sK18)),X0)
| ~ in(iPr_def_11,sK3(set_union2(X0,sK18))) ),
inference(superposition,[status(thm)],[c_4027,c_6841]) ).
tcf(c_16545,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,sK18))
| element(sK3(set_union2(X0,sK18)),iPr_def_11)
| in(sK3(set_union2(X0,sK18)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_5047]) ).
tcf(c_16546,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,sK18))
| in(sK3(set_union2(X0,sK18)),iPr_def_11)
| in(sK3(set_union2(X0,sK18)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_3640]) ).
tcf(c_16547,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,iPr_def_10))
| subset(sK3(set_union2(X0,iPr_def_10)),iPr_def_11)
| in(sK3(set_union2(X0,iPr_def_10)),X0)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4027,c_9540]) ).
tcf(c_16548,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,iPr_def_10))
| in(sK3(set_union2(X0,iPr_def_10)),X0)
| ~ in(iPr_def_11,sK3(set_union2(X0,iPr_def_10))) ),
inference(superposition,[status(thm)],[c_4027,c_6289]) ).
tcf(c_16549,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,iPr_def_10))
| element(sK3(set_union2(X0,iPr_def_10)),iPr_def_11)
| in(sK3(set_union2(X0,iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_4912]) ).
tcf(c_16550,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,iPr_def_10))
| in(sK3(set_union2(X0,iPr_def_10)),X0)
| ( sK3(set_union2(X0,iPr_def_10)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4027,c_3592]) ).
tcf(c_16551,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,iPr_def_10))
| in(sK3(set_union2(X0,iPr_def_10)),iPr_def_11)
| in(sK3(set_union2(X0,iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_3614]) ).
tcf(c_16552,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,iPr_def_11))
| in(sK3(set_union2(X0,iPr_def_11)),iPr_def_10)
| in(sK3(set_union2(X0,iPr_def_11)),sK18)
| in(sK3(set_union2(X0,iPr_def_11)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_4035]) ).
tcf(c_16553,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(X0,X2))
| element(sK3(set_union2(X0,X2)),X1)
| in(sK3(set_union2(X0,X2)),X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4027,c_358]) ).
tcf(c_16554,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(X1,X2))
| in(X0,sK3(set_union2(X1,X2)))
| in(sK3(set_union2(X1,X2)),X2)
| in(sK3(set_union2(X1,X2)),X0)
| ( sK3(set_union2(X1,X2)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4027,c_77]) ).
tcf(c_16555,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| subset(sK3(set_union2(X0,X1)),X0)
| in(sK3(set_union2(X0,X1)),X1)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4027,c_65]) ).
tcf(c_16556,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| in(sK3(set_union2(X0,X1)),X1)
| ~ in(X0,sK3(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_4027,c_49]) ).
tcf(c_16557,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| in(sK3(set_union2(X0,X1)),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4027,c_137]) ).
tcf(c_16558,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| element(sK3(set_union2(X0,X1)),X0)
| in(sK3(set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_4027,c_127]) ).
tcf(c_16559,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(singleton(X0),X1))
| in(sK3(set_union2(singleton(X0),X1)),X1)
| ( sK3(set_union2(singleton(X0),X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_4027,c_62]) ).
tcf(c_16560,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(set_union2(X0,X1),X2))
| in(sK3(set_union2(set_union2(X0,X1),X2)),X2)
| in(sK3(set_union2(set_union2(X0,X1),X2)),X1)
| in(sK3(set_union2(set_union2(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_71]) ).
tcf(c_16561,plain,
! [X0: $i] :
( epsilon_connected(set_union2(empty_set,X0))
| in(sK3(set_union2(empty_set,X0)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_7097]) ).
tcf(c_16562,plain,
! [X0: $i] :
( epsilon_connected(set_union2(sK18,X0))
| subset(sK3(set_union2(sK18,X0)),iPr_def_11)
| in(sK3(set_union2(sK18,X0)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_12813]) ).
tcf(c_16563,plain,
! [X0: $i] :
( epsilon_connected(set_union2(sK18,X0))
| in(sK3(set_union2(sK18,X0)),X0)
| ~ in(iPr_def_11,sK3(set_union2(sK18,X0))) ),
inference(superposition,[status(thm)],[c_4027,c_6841]) ).
tcf(c_16564,plain,
! [X0: $i] :
( epsilon_connected(set_union2(sK18,X0))
| element(sK3(set_union2(sK18,X0)),iPr_def_11)
| in(sK3(set_union2(sK18,X0)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_5047]) ).
tcf(c_16565,plain,
! [X0: $i] :
( epsilon_connected(set_union2(sK18,X0))
| in(sK3(set_union2(sK18,X0)),iPr_def_11)
| in(sK3(set_union2(sK18,X0)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_3640]) ).
tcf(c_16566,plain,
! [X0: $i] :
( epsilon_connected(set_union2(iPr_def_10,X0))
| subset(sK3(set_union2(iPr_def_10,X0)),iPr_def_11)
| in(sK3(set_union2(iPr_def_10,X0)),X0)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4027,c_9540]) ).
tcf(c_16567,plain,
! [X0: $i] :
( epsilon_connected(set_union2(iPr_def_10,X0))
| in(sK3(set_union2(iPr_def_10,X0)),X0)
| ~ in(iPr_def_11,sK3(set_union2(iPr_def_10,X0))) ),
inference(superposition,[status(thm)],[c_4027,c_6289]) ).
tcf(c_16568,plain,
! [X0: $i] :
( epsilon_connected(set_union2(iPr_def_10,X0))
| element(sK3(set_union2(iPr_def_10,X0)),iPr_def_11)
| in(sK3(set_union2(iPr_def_10,X0)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_4912]) ).
tcf(c_16569,plain,
! [X0: $i] :
( epsilon_connected(set_union2(iPr_def_10,X0))
| in(sK3(set_union2(iPr_def_10,X0)),X0)
| ( sK3(set_union2(iPr_def_10,X0)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4027,c_3592]) ).
tcf(c_16570,plain,
! [X0: $i] :
( epsilon_connected(set_union2(iPr_def_10,X0))
| in(sK3(set_union2(iPr_def_10,X0)),iPr_def_11)
| in(sK3(set_union2(iPr_def_10,X0)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_3614]) ).
tcf(c_16571,plain,
! [X0: $i] :
( epsilon_connected(set_union2(iPr_def_11,X0))
| in(sK3(set_union2(iPr_def_11,X0)),iPr_def_10)
| in(sK3(set_union2(iPr_def_11,X0)),sK18)
| in(sK3(set_union2(iPr_def_11,X0)),X0) ),
inference(superposition,[status(thm)],[c_4027,c_4035]) ).
tcf(c_16572,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,X0))
| in(sK3(set_union2(X0,X0)),X0) ),
inference(equality_factoring,[status(thm)],[c_4027]) ).
tcf(c_16584,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK3(X0),empty_set)
| in(sK3(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_16532,c_3423]) ).
tcf(c_16899,plain,
! [X0: $i] :
( element(sK18,X0)
| ~ epsilon_transitive(singleton(iPr_def_11))
| ~ subset(singleton(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_15765,c_358]) ).
tcf(c_16900,plain,
! [X0: $i] :
( in(sK18,X0)
| in(X0,sK18)
| ( X0 = sK18 )
| ~ epsilon_connected(singleton(iPr_def_11))
| ~ epsilon_transitive(singleton(iPr_def_11))
| ~ in(X0,singleton(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15765,c_77]) ).
tcf(c_16901,plain,
( subset(sK18,singleton(iPr_def_11))
| ~ epsilon_transitive(singleton(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15765,c_65]) ).
tcf(c_16903,plain,
( ~ epsilon_transitive(singleton(iPr_def_11))
| ~ empty(singleton(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15765,c_137]) ).
tcf(c_16905,plain,
( ( sK18 = iPr_def_11 )
| ~ epsilon_transitive(singleton(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15765,c_62]) ).
tcf(c_16995,plain,
! [X0: $i] :
( subset(X0,singleton(iPr_def_10))
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ subset(X0,sK18) ),
inference(superposition,[status(thm)],[c_15774,c_128]) ).
tcf(c_17004,plain,
( ( sK18 = iPr_def_10 )
| ( sK1(singleton(iPr_def_10)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3589,c_15778]) ).
tcf(c_17011,plain,
! [X0: $i] :
( subset(X0,singleton(iPr_def_11))
| ~ epsilon_transitive(singleton(iPr_def_11))
| ~ subset(X0,sK18) ),
inference(superposition,[status(thm)],[c_16901,c_128]) ).
tcf(c_17020,plain,
( ( sK18 = iPr_def_11 )
| ( sK1(singleton(iPr_def_11)) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_3589,c_16905]) ).
tcf(c_17031,plain,
! [X0: $i] :
( element(sK18,X0)
| ~ subset(iPr_def_10,empty_set) ),
inference(superposition,[status(thm)],[c_3423,c_14356]) ).
tcf(c_17033,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,X1))
| in(sK18,set_union2(X0,X1))
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_14356,c_131]) ).
tcf(c_17054,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X1,X0))
| in(sK18,set_union2(X1,X0))
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_14359,c_131]) ).
tcf(c_17071,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7244,c_128]) ).
tcf(c_17072,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),singleton(X0))
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7244,c_13617]) ).
tcf(c_17074,plain,
! [X0: $i] :
( subset(X0,sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_7199]) ).
tcf(c_17106,plain,
( in(iPr_def_10,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(sK18) = sK5(iPr_def_11) )
| ~ in(singleton(sK18),sK18) ),
inference(superposition,[status(thm)],[c_2420,c_7265]) ).
tcf(c_17107,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(singleton(X0),X1)
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ subset(sK5(iPr_def_11),X1)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_358]) ).
tcf(c_17108,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X1,singleton(X0))
| in(singleton(X0),X1)
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = X1 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK5(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_77]) ).
tcf(c_17109,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(singleton(X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_65]) ).
tcf(c_17110,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ in(singleton(X0),sK18)
| ~ in(sK5(iPr_def_11),singleton(X0)) ),
inference(superposition,[status(thm)],[c_7265,c_49]) ).
tcf(c_17112,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(singleton(X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_127]) ).
tcf(c_17114,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(sK5(iPr_def_11),X0) = sK5(iPr_def_11) )
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_3618]) ).
tcf(c_17115,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_3644]) ).
tcf(c_17116,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(sK5(iPr_def_11),X0),X1) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_3944]) ).
tcf(c_17117,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(X0,sK5(iPr_def_11)),X1) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_3945]) ).
tcf(c_17118,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(sK5(iPr_def_11),X1)) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_4131]) ).
tcf(c_17119,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(X1,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_4132]) ).
tcf(c_17120,plain,
( in(iPr_def_10,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = iPr_def_10 )
| ( sK5(iPr_def_11) = sK18 )
| ~ in(iPr_def_10,sK18) ),
inference(light_normalisation,[status(thm)],[c_17106,c_2420]) ).
tcf(c_17210,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13652,c_131]) ).
tcf(c_17211,plain,
! [X0: $i,X1: $i] :
( subset(sK5(iPr_def_11),X0)
| in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(iPr_def_10,powerset(X0)) ),
inference(superposition,[status(thm)],[c_13652,c_133]) ).
tcf(c_17212,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X1,X0)
| element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_13652,c_358]) ).
tcf(c_17213,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X0)
| in(X0,X1)
| element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK5(iPr_def_11) = X1 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ in(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_13652,c_77]) ).
tcf(c_17214,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| subset(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13652,c_65]) ).
tcf(c_17217,plain,
! [X0: $i,X1: $i] :
( element(X0,sK5(iPr_def_11))
| element(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13652,c_127]) ).
tcf(c_17218,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),sK2(sK5(iPr_def_11),X0,X1))
| ( set_union2(sK5(iPr_def_11),X0) = X1 )
| ( sK2(sK5(iPr_def_11),X0,X1) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK2(sK5(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK5(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_13652,c_66]) ).
tcf(c_17219,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),sK2(X0,X1,sK5(iPr_def_11)))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_13652,c_67]) ).
tcf(c_17220,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),X0)
| in(sK5(iPr_def_11),singleton(sK5(iPr_def_11)))
| ( singleton(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(singleton(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_3522]) ).
tcf(c_17221,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK5(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_3641]) ).
tcf(c_17222,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK5(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_3615]) ).
tcf(c_17223,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_3618]) ).
tcf(c_17224,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_3644]) ).
tcf(c_17226,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_3944]) ).
tcf(c_17227,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_3945]) ).
tcf(c_17228,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_4131]) ).
tcf(c_17229,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_4132]) ).
tcf(c_17234,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| element(sK5(iPr_def_11),X1)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X2)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_13652,c_358]) ).
tcf(c_17235,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_13652,c_77]) ).
tcf(c_17236,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| subset(sK5(iPr_def_11),X0)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13652,c_65]) ).
tcf(c_17239,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| element(sK5(iPr_def_11),X0)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13652,c_127]) ).
tcf(c_17240,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| in(singleton(X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_62]) ).
tcf(c_17241,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_71]) ).
tcf(c_17243,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| element(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_13652,c_12813]) ).
tcf(c_17245,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| element(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_13652,c_5047]) ).
tcf(c_17247,plain,
! [X0: $i] :
( epsilon_transitive(sK5(iPr_def_11))
| element(sK5(iPr_def_11),X0)
| in(sK1(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK1(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK1(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_3523]) ).
tcf(c_17248,plain,
! [X0: $i] :
( epsilon_connected(sK5(iPr_def_11))
| element(sK5(iPr_def_11),X0)
| in(sK3(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK3(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK3(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_3524]) ).
tcf(c_17249,plain,
! [X0: $i] :
( epsilon_connected(sK5(iPr_def_11))
| element(sK5(iPr_def_11),X0)
| in(sK4(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK4(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK4(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_3525]) ).
tcf(c_17256,plain,
! [X0: $i] :
( empty(sK5(iPr_def_11))
| element(sK5(iPr_def_11),X0)
| in(sK5(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK5(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_3900]) ).
tcf(c_17544,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| element(sK5(iPr_def_11),set_union2(X0,X1))
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_138,c_13657]) ).
tcf(c_17545,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK5(powerset(X0)),sK5(iPr_def_11))
| ( sK5(powerset(X0)) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3564,c_13657]) ).
tcf(c_17546,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| element(sK5(iPr_def_11),set_union2(X1,X0))
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3397,c_13657]) ).
tcf(c_17547,plain,
! [X0: $i] :
( in(empty_set,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_3420,c_13657]) ).
tcf(c_17550,plain,
! [X0: $i] :
( epsilon_transitive(powerset(X0))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK1(powerset(X0)),sK5(iPr_def_11))
| ( sK1(powerset(X0)) = sK5(iPr_def_11) )
| ~ in(sK1(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3566,c_13657]) ).
tcf(c_17551,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK3(powerset(X0)),sK5(iPr_def_11))
| ( sK3(powerset(X0)) = sK5(iPr_def_11) )
| ~ in(sK3(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3567,c_13657]) ).
tcf(c_17552,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK4(powerset(X0)),sK5(iPr_def_11))
| ( sK4(powerset(X0)) = sK5(iPr_def_11) )
| ~ in(sK4(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3568,c_13657]) ).
tcf(c_17553,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| element(sK5(iPr_def_11),singleton(X0))
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(singleton(X0))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3803,c_13657]) ).
tcf(c_17554,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| element(sK5(iPr_def_11),set_union2(X1,X2))
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3863,c_13657]) ).
tcf(c_17555,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| element(sK5(iPr_def_11),set_union2(X0,X1))
| ( sK5(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(X2,X1)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_13657]) ).
tcf(c_17556,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| element(sK5(iPr_def_11),set_union2(X0,X1))
| ( sK5(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(X2,X0)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_13657]) ).
tcf(c_17557,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| element(sK5(iPr_def_11),set_union2(X2,X1))
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3865,c_13657]) ).
tcf(c_17558,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK3(X0),sK5(iPr_def_11))
| ( sK3(X0) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ in(sK3(X0),sK18) ),
inference(superposition,[status(thm)],[c_3807,c_13657]) ).
tcf(c_17559,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK4(X0),sK5(iPr_def_11))
| ( sK4(X0) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ in(sK4(X0),sK18) ),
inference(superposition,[status(thm)],[c_3808,c_13657]) ).
tcf(c_17560,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_3809,c_13657]) ).
tcf(c_17561,plain,
( epsilon_transitive(iPr_def_10)
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_10),sK5(iPr_def_11))
| ( sK1(iPr_def_10) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(sK1(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_3810,c_13657]) ).
tcf(c_17562,plain,
( epsilon_connected(iPr_def_10)
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_10),sK5(iPr_def_11))
| ( sK3(iPr_def_10) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK3(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_5100,c_13657]) ).
tcf(c_17563,plain,
( epsilon_connected(iPr_def_10)
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_10),sK5(iPr_def_11))
| ( sK3(iPr_def_10) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(sK3(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_3811,c_13657]) ).
tcf(c_17564,plain,
( epsilon_connected(iPr_def_10)
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_10),sK5(iPr_def_11))
| ( sK4(iPr_def_10) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK4(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_5120,c_13657]) ).
tcf(c_17565,plain,
( epsilon_connected(iPr_def_10)
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_10),sK5(iPr_def_11))
| ( sK4(iPr_def_10) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(sK4(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_3812,c_13657]) ).
tcf(c_17566,plain,
! [X0: $i] :
( empty(X0)
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK5(X0),sK5(iPr_def_11))
| ( sK5(X0) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ in(sK5(X0),sK18) ),
inference(superposition,[status(thm)],[c_3899,c_13657]) ).
tcf(c_17567,plain,
( empty(sK18)
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK5(iPr_def_11))
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_5311,c_13657]) ).
tcf(c_17568,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK5(powerset(empty_set)),sK5(iPr_def_11))
| ( sK5(powerset(empty_set)) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4163,c_13657]) ).
tcf(c_17569,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK18)),sK5(iPr_def_11))
| ( sK5(powerset(sK18)) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_4174,c_13657]) ).
tcf(c_17570,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(iPr_def_10)),sK5(iPr_def_11))
| ( sK5(powerset(iPr_def_10)) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(iPr_def_10)),sK18) ),
inference(superposition,[status(thm)],[c_4186,c_13657]) ).
tcf(c_17571,plain,
( epsilon_transitive(powerset(sK18))
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK1(powerset(sK18)),sK5(iPr_def_11))
| ( sK1(powerset(sK18)) = sK5(iPr_def_11) )
| ~ in(sK1(powerset(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_4588,c_13657]) ).
tcf(c_17572,plain,
( epsilon_transitive(powerset(iPr_def_10))
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK1(powerset(iPr_def_10)),sK5(iPr_def_11))
| ( sK1(powerset(iPr_def_10)) = sK5(iPr_def_11) )
| ~ in(sK1(powerset(iPr_def_10)),sK18) ),
inference(superposition,[status(thm)],[c_4589,c_13657]) ).
tcf(c_17573,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK3(powerset(empty_set)),sK5(iPr_def_11))
| ( sK3(powerset(empty_set)) = sK5(iPr_def_11) )
| ~ in(sK3(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4620,c_13657]) ).
tcf(c_17574,plain,
( epsilon_connected(powerset(sK18))
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(powerset(sK18)),sK5(iPr_def_11))
| ( sK3(powerset(sK18)) = sK5(iPr_def_11) )
| ~ in(sK3(powerset(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_4621,c_13657]) ).
tcf(c_17575,plain,
( epsilon_connected(powerset(iPr_def_10))
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(powerset(iPr_def_10)),sK5(iPr_def_11))
| ( sK3(powerset(iPr_def_10)) = sK5(iPr_def_11) )
| ~ in(sK3(powerset(iPr_def_10)),sK18) ),
inference(superposition,[status(thm)],[c_4622,c_13657]) ).
tcf(c_17576,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK4(powerset(empty_set)),sK5(iPr_def_11))
| ( sK4(powerset(empty_set)) = sK5(iPr_def_11) )
| ~ in(sK4(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4637,c_13657]) ).
tcf(c_17577,plain,
( epsilon_connected(powerset(sK18))
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(powerset(sK18)),sK5(iPr_def_11))
| ( sK4(powerset(sK18)) = sK5(iPr_def_11) )
| ~ in(sK4(powerset(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_4638,c_13657]) ).
tcf(c_17578,plain,
( epsilon_connected(powerset(iPr_def_10))
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(powerset(iPr_def_10)),sK5(iPr_def_11))
| ( sK4(powerset(iPr_def_10)) = sK5(iPr_def_11) )
| ~ in(sK4(powerset(iPr_def_10)),sK18) ),
inference(superposition,[status(thm)],[c_4639,c_13657]) ).
tcf(c_17579,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(X0)))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(X0)))) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(X0)))),sK18) ),
inference(superposition,[status(thm)],[c_5196,c_13657]) ).
tcf(c_17580,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(empty_set)))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(empty_set)))) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(empty_set)))),sK18) ),
inference(superposition,[status(thm)],[c_5250,c_13657]) ).
tcf(c_17581,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK18)))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK18)))) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK18)))),sK18) ),
inference(superposition,[status(thm)],[c_5251,c_13657]) ).
tcf(c_17582,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(X0)))))) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),sK18) ),
inference(superposition,[status(thm)],[c_5252,c_13657]) ).
tcf(c_17583,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(iPr_def_10)))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(iPr_def_10)))) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(iPr_def_10)))),sK18) ),
inference(superposition,[status(thm)],[c_5253,c_13657]) ).
tcf(c_17584,plain,
( empty(sK18)
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(sK18))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(sK18))) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_5418,c_13657]) ).
tcf(c_17585,plain,
( empty(sK18)
| element(sK5(iPr_def_11),iPr_def_11)
| epsilon_transitive(powerset(sK5(sK18)))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK1(powerset(sK5(sK18))),sK5(iPr_def_11))
| ( sK1(powerset(sK5(sK18))) = sK5(iPr_def_11) )
| ~ in(sK1(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_5420,c_13657]) ).
tcf(c_17586,plain,
( empty(sK18)
| element(sK5(iPr_def_11),iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(powerset(sK5(sK18))),sK5(iPr_def_11))
| ( sK3(powerset(sK5(sK18))) = sK5(iPr_def_11) )
| ~ in(sK3(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_5421,c_13657]) ).
tcf(c_17587,plain,
( empty(sK18)
| element(sK5(iPr_def_11),iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(powerset(sK5(sK18))),sK5(iPr_def_11))
| ( sK4(powerset(sK5(sK18))) = sK5(iPr_def_11) )
| ~ in(sK4(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_5422,c_13657]) ).
tcf(c_17588,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(sK5(sK18)),sK5(iPr_def_11))
| ( sK3(sK5(sK18)) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ in(sK3(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_5423,c_13657]) ).
tcf(c_17589,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(sK5(sK18)),sK5(iPr_def_11))
| ( sK4(sK5(sK18)) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ in(sK4(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_5424,c_13657]) ).
tcf(c_17590,plain,
( empty(sK18)
| empty(sK5(sK18))
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(sK5(sK18)),sK5(iPr_def_11))
| ( sK5(sK5(sK18)) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ in(sK5(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_5425,c_13657]) ).
tcf(c_17591,plain,
( empty(sK18)
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(sK18))))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(sK18))))) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(sK18))))),sK18) ),
inference(superposition,[status(thm)],[c_5429,c_13657]) ).
tcf(c_17592,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),sK18) ),
inference(superposition,[status(thm)],[c_5727,c_13657]) ).
tcf(c_17593,plain,
( empty(sK18)
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))),sK18) ),
inference(superposition,[status(thm)],[c_5849,c_13657]) ).
tcf(c_17594,plain,
( empty(sK18)
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))))) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))))),sK18) ),
inference(superposition,[status(thm)],[c_5909,c_13657]) ).
tcf(c_17595,plain,
( empty(sK18)
| element(sK5(iPr_def_11),iPr_def_11)
| epsilon_transitive(powerset(sK5(sK18)))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK1(powerset(sK5(sK18))))),sK5(iPr_def_11))
| ( sK5(powerset(sK1(powerset(sK5(sK18))))) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(sK1(powerset(sK5(sK18))))),sK18) ),
inference(superposition,[status(thm)],[c_5967,c_13657]) ).
tcf(c_17596,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(powerset(sK18)))))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(sK18)))))) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(sK18)))))),sK18) ),
inference(superposition,[status(thm)],[c_6204,c_13657]) ).
tcf(c_17597,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(powerset(iPr_def_10)))))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(iPr_def_10)))))) = sK5(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(iPr_def_10)))))),sK18) ),
inference(superposition,[status(thm)],[c_6245,c_13657]) ).
tcf(c_17598,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK18)),sK5(iPr_def_11))
| ( sK5(powerset(sK18)) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(powerset(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_6924,c_13657]) ).
tcf(c_17599,plain,
( empty(sK18)
| element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK5(iPr_def_11))
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_6956,c_13657]) ).
tcf(c_17600,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK18)))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK18)))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(powerset(sK5(powerset(sK18)))),sK18) ),
inference(superposition,[status(thm)],[c_6935,c_13657]) ).
tcf(c_17603,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| element(sK5(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_13657]) ).
tcf(c_17609,plain,
( epsilon_connected(iPr_def_11)
| element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_10383,c_13657]) ).
tcf(c_17610,plain,
( epsilon_connected(iPr_def_11)
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_10394,c_13657]) ).
tcf(c_17611,plain,
( epsilon_connected(iPr_def_11)
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9864,c_13657]) ).
tcf(c_17613,plain,
( epsilon_connected(iPr_def_11)
| element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11588,c_13657]) ).
tcf(c_17614,plain,
( epsilon_connected(iPr_def_11)
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11599,c_13657]) ).
tcf(c_17615,plain,
( epsilon_connected(iPr_def_11)
| element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11156,c_13657]) ).
tcf(c_17616,plain,
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),singleton(iPr_def_10))
| ( sK5(iPr_def_11) = sK18 )
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_15774,c_13657]) ).
tcf(c_17617,plain,
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),singleton(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ~ epsilon_transitive(singleton(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_16901,c_13657]) ).
tcf(c_17890,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| element(X0,set_union2(sK5(iPr_def_11),X1))
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_138,c_13661]) ).
tcf(c_17891,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| element(X0,set_union2(X1,sK5(iPr_def_11)))
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3397,c_13661]) ).
tcf(c_17892,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| element(X0,singleton(sK5(iPr_def_11)))
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ epsilon_transitive(singleton(sK5(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_3803,c_13661]) ).
tcf(c_17893,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| element(X1,set_union2(X0,X2))
| ( sK5(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_3863,c_13661]) ).
tcf(c_17894,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X2)
| element(X2,set_union2(X0,X1))
| ( sK5(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(sK5(iPr_def_11),X1)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_13661]) ).
tcf(c_17895,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X2)
| element(X2,set_union2(X0,X1))
| ( sK5(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(sK5(iPr_def_11),X0)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_13661]) ).
tcf(c_17896,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| element(X1,set_union2(X2,X0))
| ( sK5(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_3865,c_13661]) ).
tcf(c_17898,plain,
! [X0: $i] :
( element(X0,sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7152,c_13661]) ).
tcf(c_17899,plain,
! [X0: $i] :
( element(X0,iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7563,c_13661]) ).
tcf(c_17901,plain,
! [X0: $i] :
( element(X0,iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7911,c_13661]) ).
tcf(c_17902,plain,
! [X0: $i] :
( element(X0,iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7571,c_13661]) ).
tcf(c_17903,plain,
! [X0: $i] :
( element(X0,iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7201,c_13661]) ).
tcf(c_17904,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7261,c_13661]) ).
tcf(c_18067,plain,
( epsilon_transitive(singleton(iPr_def_10))
| ( sK18 = iPr_def_10 )
| ~ in(singleton(iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_17004,c_3523]) ).
tcf(c_18068,plain,
( epsilon_transitive(singleton(iPr_def_10))
| element(iPr_def_10,singleton(iPr_def_10))
| ( sK18 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_17004,c_3454]) ).
tcf(c_18069,plain,
( epsilon_transitive(singleton(iPr_def_10))
| ( sK18 = iPr_def_10 )
| ~ subset(iPr_def_10,singleton(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_17004,c_63]) ).
tcf(c_18070,plain,
( epsilon_transitive(singleton(iPr_def_10))
| in(iPr_def_10,singleton(iPr_def_10))
| ( sK18 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_17004,c_64]) ).
tcf(c_18107,plain,
! [X0: $i] :
( element(sK18,X0)
| ~ subset(iPr_def_11,empty_set) ),
inference(superposition,[status(thm)],[c_3423,c_14381]) ).
tcf(c_18109,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,X1))
| in(sK18,set_union2(X0,X1))
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_14381,c_131]) ).
tcf(c_18116,plain,
~ subset(iPr_def_11,empty_set),
inference(global_subsumption_just,[status(thm)],[c_18107,c_95,c_3672,c_5471]) ).
tcf(c_18128,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X1,X0))
| in(sK18,set_union2(X1,X0))
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_14384,c_131]) ).
tcf(c_18137,plain,
! [X0: $i,X1: $i] : element(sK18,set_union2(set_union2(iPr_def_11,X0),X1)),
inference(superposition,[status(thm)],[c_138,c_15066]) ).
tcf(c_18138,plain,
! [X0: $i,X1: $i] : element(sK18,set_union2(X0,set_union2(iPr_def_11,X1))),
inference(superposition,[status(thm)],[c_3397,c_15066]) ).
tcf(c_18139,plain,
! [X0: $i] :
( element(sK18,singleton(set_union2(iPr_def_11,X0)))
| ~ epsilon_transitive(singleton(set_union2(iPr_def_11,X0))) ),
inference(superposition,[status(thm)],[c_3803,c_15066]) ).
tcf(c_18140,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X1,X2))
| ~ subset(set_union2(iPr_def_11,X0),X1) ),
inference(superposition,[status(thm)],[c_3863,c_15066]) ).
tcf(c_18141,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X2,X1))
| ~ epsilon_transitive(set_union2(X2,X1))
| ~ in(set_union2(iPr_def_11,X0),X1) ),
inference(superposition,[status(thm)],[c_3806,c_15066]) ).
tcf(c_18142,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X1,X2))
| ~ epsilon_transitive(set_union2(X1,X2))
| ~ in(set_union2(iPr_def_11,X0),X1) ),
inference(superposition,[status(thm)],[c_3805,c_15066]) ).
tcf(c_18143,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X2,X1))
| ~ subset(set_union2(iPr_def_11,X0),X1) ),
inference(superposition,[status(thm)],[c_3865,c_15066]) ).
tcf(c_18238,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_13657]) ).
tcf(c_18239,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,X1)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ~ epsilon_transitive(X1)
| ~ in(X1,sK18)
| ~ subset(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9925,c_128]) ).
tcf(c_18240,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(empty_set,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = empty_set )
| ~ epsilon_transitive(empty_set)
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_9925,c_3866]) ).
tcf(c_18241,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_10)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9925,c_3931]) ).
tcf(c_18242,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ epsilon_transitive(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9925,c_3867]) ).
tcf(c_18243,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),X0)
| in(sK5(powerset(X0)),sK3(iPr_def_11))
| ( sK5(powerset(X0)) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK5(powerset(X0)))
| ~ in(sK5(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_3864]) ).
tcf(c_18245,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),X0)
| in(sK5(powerset(empty_set)),sK3(iPr_def_11))
| ( sK5(powerset(empty_set)) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK5(powerset(empty_set)))
| ~ in(sK5(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_4165]) ).
tcf(c_18248,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| subset(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18))
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_7217]) ).
tcf(c_18249,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| subset(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(sK5(sK18))
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_5354]) ).
tcf(c_18250,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| subset(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(sK18))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(sK18))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK5(powerset(sK5(sK18))))
| ~ in(sK5(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_5478]) ).
tcf(c_18251,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| subset(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(sK18))))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(sK18))))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK5(sK18))))))
| ~ in(sK5(powerset(sK5(powerset(sK5(sK18))))),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_5491]) ).
tcf(c_18252,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| subset(sK3(iPr_def_11),iPr_def_11)
| epsilon_transitive(powerset(sK5(sK18)))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK1(powerset(sK5(sK18))),sK3(iPr_def_11))
| ( sK1(powerset(sK5(sK18))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK1(powerset(sK5(sK18))))
| ~ in(sK1(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_5502]) ).
tcf(c_18253,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| subset(sK3(iPr_def_11),iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(powerset(sK5(sK18))),sK3(iPr_def_11))
| ( sK3(powerset(sK5(sK18))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK3(powerset(sK5(sK18))))
| ~ in(sK3(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_5516]) ).
tcf(c_18254,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| subset(sK3(iPr_def_11),iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(powerset(sK5(sK18))),sK3(iPr_def_11))
| ( sK4(powerset(sK5(sK18))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK4(powerset(sK5(sK18))))
| ~ in(sK4(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_5528]) ).
tcf(c_18255,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(sK5(sK18)),sK3(iPr_def_11))
| ( sK3(sK5(sK18)) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK3(sK5(sK18)))
| ~ in(sK3(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_5794]) ).
tcf(c_18256,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(sK5(sK18)),sK3(iPr_def_11))
| ( sK4(sK5(sK18)) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK4(sK5(sK18)))
| ~ in(sK4(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_5809]) ).
tcf(c_18257,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| empty(sK5(sK18))
| subset(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(sK5(sK18)),sK3(iPr_def_11))
| ( sK5(sK5(sK18)) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK5(sK5(sK18)))
| ~ in(sK5(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_5824]) ).
tcf(c_18258,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_7199]) ).
tcf(c_18260,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),sK18)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_11154]) ).
tcf(c_18262,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(empty_set,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18240,c_89]) ).
tcf(c_18269,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_10)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18241,c_2426]) ).
tcf(c_18424,plain,
( epsilon_transitive(singleton(iPr_def_11))
| ( sK18 = iPr_def_11 )
| ~ in(singleton(iPr_def_11),iPr_def_11) ),
inference(superposition,[status(thm)],[c_17020,c_3523]) ).
tcf(c_18425,plain,
( epsilon_transitive(singleton(iPr_def_11))
| element(iPr_def_11,singleton(iPr_def_11))
| ( sK18 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_17020,c_3454]) ).
tcf(c_18426,plain,
( epsilon_transitive(singleton(iPr_def_11))
| ( sK18 = iPr_def_11 )
| ~ subset(iPr_def_11,singleton(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_17020,c_63]) ).
tcf(c_18427,plain,
( epsilon_transitive(singleton(iPr_def_11))
| in(iPr_def_11,singleton(iPr_def_11))
| ( sK18 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_17020,c_64]) ).
tcf(c_18435,plain,
! [X0: $i,X1: $i] : element(sK18,set_union2(set_union2(X0,iPr_def_11),X1)),
inference(superposition,[status(thm)],[c_58,c_18137]) ).
tcf(c_18439,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(set_union2(iPr_def_11,X0),X1))
| in(sK18,set_union2(set_union2(iPr_def_11,X0),X1)) ),
inference(superposition,[status(thm)],[c_18137,c_131]) ).
tcf(c_18444,plain,
! [X0: $i,X1: $i] : element(sK18,set_union2(X0,set_union2(X1,iPr_def_11))),
inference(superposition,[status(thm)],[c_58,c_18435]) ).
tcf(c_18452,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(set_union2(X0,iPr_def_11),X1))
| in(sK18,set_union2(set_union2(X0,iPr_def_11),X1)) ),
inference(superposition,[status(thm)],[c_18435,c_131]) ).
tcf(c_18465,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,set_union2(X1,iPr_def_11)))
| in(sK18,set_union2(X0,set_union2(X1,iPr_def_11))) ),
inference(superposition,[status(thm)],[c_18444,c_131]) ).
tcf(c_18475,plain,
! [X0: $i] :
( epsilon_transitive(singleton(iPr_def_10))
| element(iPr_def_10,X0)
| ( sK18 = iPr_def_10 )
| ~ subset(singleton(iPr_def_10),X0) ),
inference(superposition,[status(thm)],[c_17004,c_13618]) ).
tcf(c_18476,plain,
! [X0: $i] :
( epsilon_transitive(singleton(iPr_def_11))
| element(iPr_def_11,X0)
| ( sK18 = iPr_def_11 )
| ~ subset(singleton(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_17020,c_13618]) ).
tcf(c_18477,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| empty(X1)
| in(sK1(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_13618,c_131]) ).
tcf(c_18478,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| subset(sK1(X0),X1)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_13618,c_133]) ).
tcf(c_18547,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,set_union2(iPr_def_11,X1)))
| in(sK18,set_union2(X0,set_union2(iPr_def_11,X1))) ),
inference(superposition,[status(thm)],[c_18138,c_131]) ).
tcf(c_18558,plain,
! [X0: $i] :
( element(sK18,singleton(set_union2(X0,iPr_def_11)))
| ~ epsilon_transitive(singleton(set_union2(X0,iPr_def_11))) ),
inference(superposition,[status(thm)],[c_3803,c_15124]) ).
tcf(c_18559,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X1,X2))
| ~ subset(set_union2(X0,iPr_def_11),X1) ),
inference(superposition,[status(thm)],[c_3863,c_15124]) ).
tcf(c_18560,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X2,X1))
| ~ epsilon_transitive(set_union2(X2,X1))
| ~ in(set_union2(X0,iPr_def_11),X1) ),
inference(superposition,[status(thm)],[c_3806,c_15124]) ).
tcf(c_18561,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X1,X2))
| ~ epsilon_transitive(set_union2(X1,X2))
| ~ in(set_union2(X0,iPr_def_11),X1) ),
inference(superposition,[status(thm)],[c_3805,c_15124]) ).
tcf(c_18562,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X2,X1))
| ~ subset(set_union2(X0,iPr_def_11),X1) ),
inference(superposition,[status(thm)],[c_3865,c_15124]) ).
tcf(c_18597,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_13657]) ).
tcf(c_18598,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,X1)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X1,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X1 )
| ~ epsilon_transitive(X1)
| ~ in(X1,sK18)
| ~ subset(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11209,c_128]) ).
tcf(c_18599,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(empty_set,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = empty_set )
| ~ epsilon_transitive(empty_set)
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_11209,c_3866]) ).
tcf(c_18600,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_10)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11209,c_3931]) ).
tcf(c_18601,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ epsilon_transitive(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11209,c_3867]) ).
tcf(c_18602,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),X0)
| in(sK5(powerset(X0)),sK4(iPr_def_11))
| ( sK5(powerset(X0)) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK5(powerset(X0)))
| ~ in(sK5(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_3864]) ).
tcf(c_18604,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),X0)
| in(sK5(powerset(empty_set)),sK4(iPr_def_11))
| ( sK5(powerset(empty_set)) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK5(powerset(empty_set)))
| ~ in(sK5(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_4165]) ).
tcf(c_18607,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| subset(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18))
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_7217]) ).
tcf(c_18608,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| subset(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(sK5(sK18))
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_5354]) ).
tcf(c_18609,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| subset(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(sK18))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(sK18))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK5(powerset(sK5(sK18))))
| ~ in(sK5(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_5478]) ).
tcf(c_18610,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| subset(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(sK18))))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(sK18))))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK5(sK18))))))
| ~ in(sK5(powerset(sK5(powerset(sK5(sK18))))),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_5491]) ).
tcf(c_18611,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| subset(sK4(iPr_def_11),iPr_def_11)
| epsilon_transitive(powerset(sK5(sK18)))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK1(powerset(sK5(sK18))),sK4(iPr_def_11))
| ( sK1(powerset(sK5(sK18))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK1(powerset(sK5(sK18))))
| ~ in(sK1(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_5502]) ).
tcf(c_18612,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| subset(sK4(iPr_def_11),iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(powerset(sK5(sK18))),sK4(iPr_def_11))
| ( sK3(powerset(sK5(sK18))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK3(powerset(sK5(sK18))))
| ~ in(sK3(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_5516]) ).
tcf(c_18613,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| subset(sK4(iPr_def_11),iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(powerset(sK5(sK18))),sK4(iPr_def_11))
| ( sK4(powerset(sK5(sK18))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK4(powerset(sK5(sK18))))
| ~ in(sK4(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_5528]) ).
tcf(c_18614,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(sK5(sK18)),sK4(iPr_def_11))
| ( sK3(sK5(sK18)) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK3(sK5(sK18)))
| ~ in(sK3(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_5794]) ).
tcf(c_18615,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(sK5(sK18)),sK4(iPr_def_11))
| ( sK4(sK5(sK18)) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK4(sK5(sK18)))
| ~ in(sK4(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_5809]) ).
tcf(c_18616,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| empty(sK5(sK18))
| subset(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(sK5(sK18)),sK4(iPr_def_11))
| ( sK5(sK5(sK18)) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK5(sK5(sK18)))
| ~ in(sK5(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_5824]) ).
tcf(c_18617,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_7199]) ).
tcf(c_18621,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(empty_set,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18599,c_89]) ).
tcf(c_18628,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_10)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18600,c_2426]) ).
tcf(c_18857,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| element(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9907,c_13657]) ).
tcf(c_18858,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_9907,c_128]) ).
tcf(c_18859,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),singleton(X0))
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_9907,c_13617]) ).
tcf(c_18861,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| element(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9907,c_13661]) ).
tcf(c_18864,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,sK18)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9907,c_9862]) ).
tcf(c_18924,plain,
( epsilon_connected(iPr_def_11)
| in(iPr_def_10,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(sK18) = sK3(iPr_def_11) )
| ~ in(singleton(sK18),sK18) ),
inference(superposition,[status(thm)],[c_2420,c_9929]) ).
tcf(c_18925,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(singleton(X0),X1)
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ subset(sK3(iPr_def_11),X1)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_358]) ).
tcf(c_18926,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X1,singleton(X0))
| in(singleton(X0),X1)
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = X1 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK3(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_77]) ).
tcf(c_18927,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(singleton(X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_65]) ).
tcf(c_18928,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ in(singleton(X0),sK18)
| ~ in(sK3(iPr_def_11),singleton(X0)) ),
inference(superposition,[status(thm)],[c_9929,c_49]) ).
tcf(c_18930,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(singleton(X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_127]) ).
tcf(c_18932,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(sK3(iPr_def_11),X0) = sK3(iPr_def_11) )
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_3618]) ).
tcf(c_18933,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_3644]) ).
tcf(c_18934,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(sK3(iPr_def_11),X0),X1) = sK3(iPr_def_11) )
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_3944]) ).
tcf(c_18935,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(X0,sK3(iPr_def_11)),X1) = sK3(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_3945]) ).
tcf(c_18936,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(sK3(iPr_def_11),X1)) = sK3(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_4131]) ).
tcf(c_18937,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(X1,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_4132]) ).
tcf(c_18938,plain,
( epsilon_connected(iPr_def_11)
| in(iPr_def_10,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = iPr_def_10 )
| ( sK3(iPr_def_11) = sK18 )
| ~ in(iPr_def_10,sK18) ),
inference(light_normalisation,[status(thm)],[c_18924,c_2420]) ).
tcf(c_19097,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| in(sK4(set_union2(X1,X0)),X1)
| in(sK4(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_58,c_4028]) ).
tcf(c_19100,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,empty_set))
| in(sK4(X0),empty_set)
| in(sK4(set_union2(X0,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_126,c_4028]) ).
tcf(c_19101,plain,
! [X0: $i] :
( epsilon_connected(set_union2(empty_set,X0))
| in(sK4(X0),X0)
| in(sK4(set_union2(empty_set,X0)),empty_set) ),
inference(superposition,[status(thm)],[c_3423,c_4028]) ).
tcf(c_19102,plain,
( epsilon_connected(set_union2(iPr_def_10,sK18))
| in(sK4(iPr_def_11),sK18)
| in(sK4(set_union2(iPr_def_10,sK18)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3424,c_4028]) ).
tcf(c_19103,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| in(sK4(set_union2(X1,X0)),X0)
| in(sK4(set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_58,c_4028]) ).
tcf(c_19105,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,X0))
| in(sK4(X0),X0)
| in(sK4(set_union2(X0,X0)),X0) ),
inference(superposition,[status(thm)],[c_97,c_4028]) ).
tcf(c_19106,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,empty_set))
| in(sK4(X0),X0)
| in(sK4(set_union2(X0,empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_126,c_4028]) ).
tcf(c_19107,plain,
! [X0: $i] :
( epsilon_connected(set_union2(empty_set,X0))
| in(sK4(X0),empty_set)
| in(sK4(set_union2(empty_set,X0)),X0) ),
inference(superposition,[status(thm)],[c_3423,c_4028]) ).
tcf(c_19108,plain,
( epsilon_connected(set_union2(iPr_def_10,sK18))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(set_union2(iPr_def_10,sK18)),sK18) ),
inference(superposition,[status(thm)],[c_3424,c_4028]) ).
tcf(c_19109,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(X2,X0))
| element(sK4(set_union2(X2,X0)),X1)
| in(sK4(set_union2(X2,X0)),X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4028,c_358]) ).
tcf(c_19110,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(X2,X1))
| in(X0,sK4(set_union2(X2,X1)))
| in(sK4(set_union2(X2,X1)),X2)
| in(sK4(set_union2(X2,X1)),X0)
| ( sK4(set_union2(X2,X1)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4028,c_77]) ).
tcf(c_19111,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X1,X0))
| subset(sK4(set_union2(X1,X0)),X0)
| in(sK4(set_union2(X1,X0)),X1)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4028,c_65]) ).
tcf(c_19112,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X1,X0))
| in(sK4(set_union2(X1,X0)),X1)
| ~ in(X0,sK4(set_union2(X1,X0))) ),
inference(superposition,[status(thm)],[c_4028,c_49]) ).
tcf(c_19113,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X1,X0))
| in(sK4(set_union2(X1,X0)),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4028,c_137]) ).
tcf(c_19114,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| element(sK4(set_union2(X0,X1)),X1)
| in(sK4(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_127]) ).
tcf(c_19115,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,singleton(X1)))
| in(sK4(set_union2(X0,singleton(X1))),X0)
| ( sK4(set_union2(X0,singleton(X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_4028,c_62]) ).
tcf(c_19116,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(X0,set_union2(X1,X2)))
| in(sK4(set_union2(X0,set_union2(X1,X2))),X2)
| in(sK4(set_union2(X0,set_union2(X1,X2))),X1)
| in(sK4(set_union2(X0,set_union2(X1,X2))),X0) ),
inference(superposition,[status(thm)],[c_4028,c_71]) ).
tcf(c_19117,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,empty_set))
| in(sK4(set_union2(X0,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_7097]) ).
tcf(c_19118,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,sK18))
| subset(sK4(set_union2(X0,sK18)),iPr_def_11)
| in(sK4(set_union2(X0,sK18)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_12813]) ).
tcf(c_19119,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,sK18))
| in(sK4(set_union2(X0,sK18)),X0)
| ~ in(iPr_def_11,sK4(set_union2(X0,sK18))) ),
inference(superposition,[status(thm)],[c_4028,c_6841]) ).
tcf(c_19120,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,sK18))
| element(sK4(set_union2(X0,sK18)),iPr_def_11)
| in(sK4(set_union2(X0,sK18)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_5047]) ).
tcf(c_19121,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,sK18))
| in(sK4(set_union2(X0,sK18)),iPr_def_11)
| in(sK4(set_union2(X0,sK18)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_3640]) ).
tcf(c_19122,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,iPr_def_10))
| subset(sK4(set_union2(X0,iPr_def_10)),iPr_def_11)
| in(sK4(set_union2(X0,iPr_def_10)),X0)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4028,c_9540]) ).
tcf(c_19123,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,iPr_def_10))
| in(sK4(set_union2(X0,iPr_def_10)),X0)
| ~ in(iPr_def_11,sK4(set_union2(X0,iPr_def_10))) ),
inference(superposition,[status(thm)],[c_4028,c_6289]) ).
tcf(c_19124,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,iPr_def_10))
| element(sK4(set_union2(X0,iPr_def_10)),iPr_def_11)
| in(sK4(set_union2(X0,iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_4912]) ).
tcf(c_19125,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,iPr_def_10))
| in(sK4(set_union2(X0,iPr_def_10)),X0)
| ( sK4(set_union2(X0,iPr_def_10)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4028,c_3592]) ).
tcf(c_19126,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,iPr_def_10))
| in(sK4(set_union2(X0,iPr_def_10)),iPr_def_11)
| in(sK4(set_union2(X0,iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_3614]) ).
tcf(c_19127,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,iPr_def_11))
| in(sK4(set_union2(X0,iPr_def_11)),iPr_def_10)
| in(sK4(set_union2(X0,iPr_def_11)),sK18)
| in(sK4(set_union2(X0,iPr_def_11)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_4035]) ).
tcf(c_19128,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(X0,X2))
| element(sK4(set_union2(X0,X2)),X1)
| in(sK4(set_union2(X0,X2)),X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4028,c_358]) ).
tcf(c_19129,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(X1,X2))
| in(X0,sK4(set_union2(X1,X2)))
| in(sK4(set_union2(X1,X2)),X2)
| in(sK4(set_union2(X1,X2)),X0)
| ( sK4(set_union2(X1,X2)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4028,c_77]) ).
tcf(c_19130,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| subset(sK4(set_union2(X0,X1)),X0)
| in(sK4(set_union2(X0,X1)),X1)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4028,c_65]) ).
tcf(c_19131,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| in(sK4(set_union2(X0,X1)),X1)
| ~ in(X0,sK4(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_4028,c_49]) ).
tcf(c_19132,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| in(sK4(set_union2(X0,X1)),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4028,c_137]) ).
tcf(c_19133,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| element(sK4(set_union2(X0,X1)),X0)
| in(sK4(set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_4028,c_127]) ).
tcf(c_19134,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(singleton(X0),X1))
| in(sK4(set_union2(singleton(X0),X1)),X1)
| ( sK4(set_union2(singleton(X0),X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_4028,c_62]) ).
tcf(c_19135,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(set_union2(X0,X1),X2))
| in(sK4(set_union2(set_union2(X0,X1),X2)),X2)
| in(sK4(set_union2(set_union2(X0,X1),X2)),X1)
| in(sK4(set_union2(set_union2(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_71]) ).
tcf(c_19136,plain,
! [X0: $i] :
( epsilon_connected(set_union2(empty_set,X0))
| in(sK4(set_union2(empty_set,X0)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_7097]) ).
tcf(c_19137,plain,
! [X0: $i] :
( epsilon_connected(set_union2(sK18,X0))
| subset(sK4(set_union2(sK18,X0)),iPr_def_11)
| in(sK4(set_union2(sK18,X0)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_12813]) ).
tcf(c_19138,plain,
! [X0: $i] :
( epsilon_connected(set_union2(sK18,X0))
| in(sK4(set_union2(sK18,X0)),X0)
| ~ in(iPr_def_11,sK4(set_union2(sK18,X0))) ),
inference(superposition,[status(thm)],[c_4028,c_6841]) ).
tcf(c_19139,plain,
! [X0: $i] :
( epsilon_connected(set_union2(sK18,X0))
| element(sK4(set_union2(sK18,X0)),iPr_def_11)
| in(sK4(set_union2(sK18,X0)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_5047]) ).
tcf(c_19140,plain,
! [X0: $i] :
( epsilon_connected(set_union2(sK18,X0))
| in(sK4(set_union2(sK18,X0)),iPr_def_11)
| in(sK4(set_union2(sK18,X0)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_3640]) ).
tcf(c_19141,plain,
! [X0: $i] :
( epsilon_connected(set_union2(iPr_def_10,X0))
| subset(sK4(set_union2(iPr_def_10,X0)),iPr_def_11)
| in(sK4(set_union2(iPr_def_10,X0)),X0)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4028,c_9540]) ).
tcf(c_19142,plain,
! [X0: $i] :
( epsilon_connected(set_union2(iPr_def_10,X0))
| in(sK4(set_union2(iPr_def_10,X0)),X0)
| ~ in(iPr_def_11,sK4(set_union2(iPr_def_10,X0))) ),
inference(superposition,[status(thm)],[c_4028,c_6289]) ).
tcf(c_19143,plain,
! [X0: $i] :
( epsilon_connected(set_union2(iPr_def_10,X0))
| element(sK4(set_union2(iPr_def_10,X0)),iPr_def_11)
| in(sK4(set_union2(iPr_def_10,X0)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_4912]) ).
tcf(c_19144,plain,
! [X0: $i] :
( epsilon_connected(set_union2(iPr_def_10,X0))
| in(sK4(set_union2(iPr_def_10,X0)),X0)
| ( sK4(set_union2(iPr_def_10,X0)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4028,c_3592]) ).
tcf(c_19145,plain,
! [X0: $i] :
( epsilon_connected(set_union2(iPr_def_10,X0))
| in(sK4(set_union2(iPr_def_10,X0)),iPr_def_11)
| in(sK4(set_union2(iPr_def_10,X0)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_3614]) ).
tcf(c_19146,plain,
! [X0: $i] :
( epsilon_connected(set_union2(iPr_def_11,X0))
| in(sK4(set_union2(iPr_def_11,X0)),iPr_def_10)
| in(sK4(set_union2(iPr_def_11,X0)),sK18)
| in(sK4(set_union2(iPr_def_11,X0)),X0) ),
inference(superposition,[status(thm)],[c_4028,c_4035]) ).
tcf(c_19147,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,X0))
| in(sK4(set_union2(X0,X0)),X0) ),
inference(equality_factoring,[status(thm)],[c_4028]) ).
tcf(c_19159,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK4(X0),empty_set)
| in(sK4(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_19107,c_3423]) ).
tcf(c_19388,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| empty(X1)
| in(sK3(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_13624,c_131]) ).
tcf(c_19389,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| subset(sK3(X0),X1)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_13624,c_133]) ).
tcf(c_19403,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| empty(X1)
| in(sK4(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_13625,c_131]) ).
tcf(c_19404,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| subset(sK4(X0),X1)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_13625,c_133]) ).
tcf(c_19434,plain,
! [X0: $i] :
( subset(X0,sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| ~ subset(X0,sK5(powerset(sK5(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_7587,c_128]) ).
tcf(c_19435,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(iPr_def_11))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_7587,c_3931]) ).
tcf(c_19436,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(iPr_def_11))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_7587,c_3867]) ).
tcf(c_19465,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| element(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11191,c_13657]) ).
tcf(c_19466,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_11191,c_128]) ).
tcf(c_19467,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),singleton(X0))
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_11191,c_13617]) ).
tcf(c_19469,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| element(X0,sK4(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11191,c_13661]) ).
tcf(c_19472,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,sK18)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11191,c_11154]) ).
tcf(c_19532,plain,
( epsilon_connected(iPr_def_11)
| in(iPr_def_10,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(sK18) = sK4(iPr_def_11) )
| ~ in(singleton(sK18),sK18) ),
inference(superposition,[status(thm)],[c_2420,c_11213]) ).
tcf(c_19533,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(singleton(X0),X1)
| ( sK4(iPr_def_11) = X0 )
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ subset(sK4(iPr_def_11),X1)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_358]) ).
tcf(c_19534,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X1,singleton(X0))
| in(singleton(X0),X1)
| ( sK4(iPr_def_11) = X0 )
| ( singleton(X0) = X1 )
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK4(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_77]) ).
tcf(c_19535,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(singleton(X0),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_65]) ).
tcf(c_19536,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = X0 )
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ in(singleton(X0),sK18)
| ~ in(sK4(iPr_def_11),singleton(X0)) ),
inference(superposition,[status(thm)],[c_11213,c_49]) ).
tcf(c_19538,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(singleton(X0),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_127]) ).
tcf(c_19540,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(sK4(iPr_def_11),X0) = sK4(iPr_def_11) )
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_3618]) ).
tcf(c_19541,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_3644]) ).
tcf(c_19542,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(sK4(iPr_def_11),X0),X1) = sK4(iPr_def_11) )
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_3944]) ).
tcf(c_19543,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(X0,sK4(iPr_def_11)),X1) = sK4(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_3945]) ).
tcf(c_19544,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(sK4(iPr_def_11),X1)) = sK4(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_4131]) ).
tcf(c_19545,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(X1,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_4132]) ).
tcf(c_19546,plain,
( epsilon_connected(iPr_def_11)
| in(iPr_def_10,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = iPr_def_10 )
| ( sK4(iPr_def_11) = sK18 )
| ~ in(iPr_def_10,sK18) ),
inference(light_normalisation,[status(thm)],[c_19532,c_2420]) ).
tcf(c_19697,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| empty(X1)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13640,c_131]) ).
tcf(c_19698,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),X0)
| in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(iPr_def_10,powerset(X0)) ),
inference(superposition,[status(thm)],[c_13640,c_133]) ).
tcf(c_19699,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(X1,X0)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_13640,c_358]) ).
tcf(c_19700,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK3(iPr_def_11) = X1 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ in(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_13640,c_77]) ).
tcf(c_19701,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X1)
| subset(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13640,c_65]) ).
tcf(c_19704,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,sK3(iPr_def_11))
| element(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13640,c_127]) ).
tcf(c_19705,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),sK2(sK3(iPr_def_11),X0,X1))
| ( set_union2(sK3(iPr_def_11),X0) = X1 )
| ( sK2(sK3(iPr_def_11),X0,X1) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK2(sK3(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK3(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_13640,c_66]) ).
tcf(c_19706,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),sK2(X0,X1,sK3(iPr_def_11)))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( sK2(X0,X1,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_13640,c_67]) ).
tcf(c_19707,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_76]) ).
tcf(c_19708,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),singleton(sK3(iPr_def_11)))
| ( singleton(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(singleton(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_3522]) ).
tcf(c_19710,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK3(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_3641]) ).
tcf(c_19711,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK3(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_3615]) ).
tcf(c_19712,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_3618]) ).
tcf(c_19713,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_3644]) ).
tcf(c_19714,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_3944]) ).
tcf(c_19715,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_3945]) ).
tcf(c_19716,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_4131]) ).
tcf(c_19717,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_4132]) ).
tcf(c_19720,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| element(sK3(iPr_def_11),X1)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X2)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_13640,c_358]) ).
tcf(c_19721,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_13640,c_77]) ).
tcf(c_19722,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X1)
| subset(sK3(iPr_def_11),X0)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13640,c_65]) ).
tcf(c_19725,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X1)
| element(sK3(iPr_def_11),X0)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13640,c_127]) ).
tcf(c_19726,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X1)
| in(singleton(X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_62]) ).
tcf(c_19727,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_71]) ).
tcf(c_19728,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_74]) ).
tcf(c_19730,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| element(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_13640,c_12813]) ).
tcf(c_19731,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| element(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ subset(iPr_def_10,X0)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_13640,c_6841]) ).
tcf(c_19732,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| element(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_13640,c_5047]) ).
tcf(c_19733,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_11)
| element(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_13640,c_3640]) ).
tcf(c_19734,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK3(iPr_def_11))
| element(sK3(iPr_def_11),X0)
| in(sK1(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK1(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK1(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_3523]) ).
tcf(c_19735,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| element(sK3(iPr_def_11),X0)
| in(sK3(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK3(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_3524]) ).
tcf(c_19736,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| element(sK3(iPr_def_11),X0)
| in(sK4(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK4(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK4(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_3525]) ).
tcf(c_19743,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(sK3(iPr_def_11))
| element(sK3(iPr_def_11),X0)
| in(sK5(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK5(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK5(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_3900]) ).
tcf(c_19744,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_13640,c_11771]) ).
tcf(c_20077,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| empty(X1)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13646,c_131]) ).
tcf(c_20078,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),X0)
| in(X1,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(iPr_def_10,powerset(X0)) ),
inference(superposition,[status(thm)],[c_13646,c_133]) ).
tcf(c_20079,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(X1,X0)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_13646,c_358]) ).
tcf(c_20080,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK4(iPr_def_11) = X1 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ in(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_13646,c_77]) ).
tcf(c_20081,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X1)
| subset(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13646,c_65]) ).
tcf(c_20084,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,sK4(iPr_def_11))
| element(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13646,c_127]) ).
tcf(c_20085,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),sK2(sK4(iPr_def_11),X0,X1))
| ( set_union2(sK4(iPr_def_11),X0) = X1 )
| ( sK2(sK4(iPr_def_11),X0,X1) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK2(sK4(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK4(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_13646,c_66]) ).
tcf(c_20086,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),sK2(X0,X1,sK4(iPr_def_11)))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ( sK2(X0,X1,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_13646,c_67]) ).
tcf(c_20087,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_74]) ).
tcf(c_20088,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),singleton(sK4(iPr_def_11)))
| ( singleton(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(singleton(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_3522]) ).
tcf(c_20090,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK4(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_3641]) ).
tcf(c_20091,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK4(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_3615]) ).
tcf(c_20092,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_3618]) ).
tcf(c_20093,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_3644]) ).
tcf(c_20094,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_3944]) ).
tcf(c_20095,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_3945]) ).
tcf(c_20096,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_4131]) ).
tcf(c_20097,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_4132]) ).
tcf(c_20100,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| element(sK4(iPr_def_11),X1)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X2)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_13646,c_358]) ).
tcf(c_20101,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(X1,sK4(iPr_def_11))
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_13646,c_77]) ).
tcf(c_20102,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X1)
| subset(sK4(iPr_def_11),X0)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13646,c_65]) ).
tcf(c_20105,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X1)
| element(sK4(iPr_def_11),X0)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13646,c_127]) ).
tcf(c_20106,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X1)
| in(singleton(X0),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_62]) ).
tcf(c_20107,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_71]) ).
tcf(c_20108,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_76]) ).
tcf(c_20110,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| element(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_13646,c_12813]) ).
tcf(c_20111,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| element(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ subset(iPr_def_10,X0)
| ~ in(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_13646,c_6841]) ).
tcf(c_20112,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| element(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_13646,c_5047]) ).
tcf(c_20113,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_11)
| element(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_13646,c_3640]) ).
tcf(c_20114,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK4(iPr_def_11))
| element(sK4(iPr_def_11),X0)
| in(sK1(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK1(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK1(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_3523]) ).
tcf(c_20115,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| element(sK4(iPr_def_11),X0)
| in(sK3(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK3(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK3(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_3524]) ).
tcf(c_20116,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| element(sK4(iPr_def_11),X0)
| in(sK4(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK4(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK4(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_3525]) ).
tcf(c_20123,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(sK4(iPr_def_11))
| element(sK4(iPr_def_11),X0)
| in(sK5(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK5(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ in(sK5(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_3900]) ).
tcf(c_20124,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_13646,c_10578]) ).
tcf(c_20494,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| element(sK3(iPr_def_11),set_union2(X0,X1))
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_138,c_13665]) ).
tcf(c_20495,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK5(powerset(X0)),sK3(iPr_def_11))
| ( sK5(powerset(X0)) = sK3(iPr_def_11) )
| ~ in(sK5(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3564,c_13665]) ).
tcf(c_20496,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| element(sK3(iPr_def_11),set_union2(X1,X0))
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3397,c_13665]) ).
tcf(c_20497,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(empty_set,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_3420,c_13665]) ).
tcf(c_20500,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_transitive(powerset(X0))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK1(powerset(X0)),sK3(iPr_def_11))
| ( sK1(powerset(X0)) = sK3(iPr_def_11) )
| ~ in(sK1(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3566,c_13665]) ).
tcf(c_20501,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(X0))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK3(powerset(X0)),sK3(iPr_def_11))
| ( sK3(powerset(X0)) = sK3(iPr_def_11) )
| ~ in(sK3(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3567,c_13665]) ).
tcf(c_20502,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(X0))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK4(powerset(X0)),sK3(iPr_def_11))
| ( sK4(powerset(X0)) = sK3(iPr_def_11) )
| ~ in(sK4(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3568,c_13665]) ).
tcf(c_20503,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| element(sK3(iPr_def_11),singleton(X0))
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(singleton(X0))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3803,c_13665]) ).
tcf(c_20504,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| element(sK3(iPr_def_11),set_union2(X1,X2))
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3863,c_13665]) ).
tcf(c_20505,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| element(sK3(iPr_def_11),set_union2(X0,X1))
| ( sK3(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(X2,X1)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_13665]) ).
tcf(c_20506,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| element(sK3(iPr_def_11),set_union2(X0,X1))
| ( sK3(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(X2,X0)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_13665]) ).
tcf(c_20507,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| element(sK3(iPr_def_11),set_union2(X2,X1))
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3865,c_13665]) ).
tcf(c_20508,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(X0)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK3(X0),sK3(iPr_def_11))
| ( sK3(X0) = sK3(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ in(sK3(X0),sK18) ),
inference(superposition,[status(thm)],[c_3807,c_13665]) ).
tcf(c_20509,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(X0)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK4(X0),sK3(iPr_def_11))
| ( sK4(X0) = sK3(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ in(sK4(X0),sK18) ),
inference(superposition,[status(thm)],[c_3808,c_13665]) ).
tcf(c_20510,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_3809,c_13665]) ).
tcf(c_20511,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(iPr_def_10)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_10),sK3(iPr_def_11))
| ( sK1(iPr_def_10) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(sK1(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_3810,c_13665]) ).
tcf(c_20512,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(iPr_def_10)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_10),sK3(iPr_def_11))
| ( sK3(iPr_def_10) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK3(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_5100,c_13665]) ).
tcf(c_20513,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(iPr_def_10)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_10),sK3(iPr_def_11))
| ( sK3(iPr_def_10) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(sK3(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_3811,c_13665]) ).
tcf(c_20514,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(iPr_def_10)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_10),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_10) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK4(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_5120,c_13665]) ).
tcf(c_20515,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(iPr_def_10)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_10),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_10) )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(sK4(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_3812,c_13665]) ).
tcf(c_20516,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(X0)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK5(X0),sK3(iPr_def_11))
| ( sK5(X0) = sK3(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ in(sK5(X0),sK18) ),
inference(superposition,[status(thm)],[c_3899,c_13665]) ).
tcf(c_20517,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_5311,c_13665]) ).
tcf(c_20518,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK5(powerset(empty_set)),sK3(iPr_def_11))
| ( sK5(powerset(empty_set)) = sK3(iPr_def_11) )
| ~ in(sK5(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4163,c_13665]) ).
tcf(c_20521,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(powerset(sK18))
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK1(powerset(sK18)),sK3(iPr_def_11))
| ( sK1(powerset(sK18)) = sK3(iPr_def_11) )
| ~ in(sK1(powerset(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_4588,c_13665]) ).
tcf(c_20522,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(powerset(iPr_def_10))
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK1(powerset(iPr_def_10)),sK3(iPr_def_11))
| ( sK1(powerset(iPr_def_10)) = sK3(iPr_def_11) )
| ~ in(sK1(powerset(iPr_def_10)),sK18) ),
inference(superposition,[status(thm)],[c_4589,c_13665]) ).
tcf(c_20523,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(empty_set))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK3(powerset(empty_set)),sK3(iPr_def_11))
| ( sK3(powerset(empty_set)) = sK3(iPr_def_11) )
| ~ in(sK3(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4620,c_13665]) ).
tcf(c_20524,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(sK18))
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(powerset(sK18)),sK3(iPr_def_11))
| ( sK3(powerset(sK18)) = sK3(iPr_def_11) )
| ~ in(sK3(powerset(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_4621,c_13665]) ).
tcf(c_20525,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(iPr_def_10))
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(powerset(iPr_def_10)),sK3(iPr_def_11))
| ( sK3(powerset(iPr_def_10)) = sK3(iPr_def_11) )
| ~ in(sK3(powerset(iPr_def_10)),sK18) ),
inference(superposition,[status(thm)],[c_4622,c_13665]) ).
tcf(c_20526,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(empty_set))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK4(powerset(empty_set)),sK3(iPr_def_11))
| ( sK4(powerset(empty_set)) = sK3(iPr_def_11) )
| ~ in(sK4(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4637,c_13665]) ).
tcf(c_20527,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(sK18))
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(powerset(sK18)),sK3(iPr_def_11))
| ( sK4(powerset(sK18)) = sK3(iPr_def_11) )
| ~ in(sK4(powerset(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_4638,c_13665]) ).
tcf(c_20528,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(iPr_def_10))
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(powerset(iPr_def_10)),sK3(iPr_def_11))
| ( sK4(powerset(iPr_def_10)) = sK3(iPr_def_11) )
| ~ in(sK4(powerset(iPr_def_10)),sK18) ),
inference(superposition,[status(thm)],[c_4639,c_13665]) ).
tcf(c_20529,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(X0)))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(powerset(X0)))) = sK3(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(X0)))),sK18) ),
inference(superposition,[status(thm)],[c_5196,c_13665]) ).
tcf(c_20530,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(empty_set)))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(powerset(empty_set)))) = sK3(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(empty_set)))),sK18) ),
inference(superposition,[status(thm)],[c_5250,c_13665]) ).
tcf(c_20532,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(X0)))))) = sK3(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),sK18) ),
inference(superposition,[status(thm)],[c_5252,c_13665]) ).
tcf(c_20534,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(sK18))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(sK18))) = sK3(iPr_def_11) )
| ~ in(sK5(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_5418,c_13665]) ).
tcf(c_20535,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK3(iPr_def_11),iPr_def_11)
| epsilon_transitive(powerset(sK5(sK18)))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK1(powerset(sK5(sK18))),sK3(iPr_def_11))
| ( sK1(powerset(sK5(sK18))) = sK3(iPr_def_11) )
| ~ in(sK1(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_5420,c_13665]) ).
tcf(c_20536,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK3(iPr_def_11),iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(powerset(sK5(sK18))),sK3(iPr_def_11))
| ( sK3(powerset(sK5(sK18))) = sK3(iPr_def_11) )
| ~ in(sK3(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_5421,c_13665]) ).
tcf(c_20537,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK3(iPr_def_11),iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(powerset(sK5(sK18))),sK3(iPr_def_11))
| ( sK4(powerset(sK5(sK18))) = sK3(iPr_def_11) )
| ~ in(sK4(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_5422,c_13665]) ).
tcf(c_20538,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| epsilon_connected(sK5(sK18))
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(sK5(sK18)),sK3(iPr_def_11))
| ( sK3(sK5(sK18)) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ in(sK3(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_5423,c_13665]) ).
tcf(c_20539,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| epsilon_connected(sK5(sK18))
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(sK5(sK18)),sK3(iPr_def_11))
| ( sK4(sK5(sK18)) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ in(sK4(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_5424,c_13665]) ).
tcf(c_20540,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| empty(sK5(sK18))
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(sK5(sK18)),sK3(iPr_def_11))
| ( sK5(sK5(sK18)) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ in(sK5(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_5425,c_13665]) ).
tcf(c_20541,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(sK18))))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(sK18))))) = sK3(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(sK18))))),sK18) ),
inference(superposition,[status(thm)],[c_5429,c_13665]) ).
tcf(c_20542,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))) = sK3(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),sK18) ),
inference(superposition,[status(thm)],[c_5727,c_13665]) ).
tcf(c_20543,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))) = sK3(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))),sK18) ),
inference(superposition,[status(thm)],[c_5849,c_13665]) ).
tcf(c_20544,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))))) = sK3(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))))),sK18) ),
inference(superposition,[status(thm)],[c_5909,c_13665]) ).
tcf(c_20545,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK3(iPr_def_11),iPr_def_11)
| epsilon_transitive(powerset(sK5(sK18)))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK1(powerset(sK5(sK18))))),sK3(iPr_def_11))
| ( sK5(powerset(sK1(powerset(sK5(sK18))))) = sK3(iPr_def_11) )
| ~ in(sK5(powerset(sK1(powerset(sK5(sK18))))),sK18) ),
inference(superposition,[status(thm)],[c_5967,c_13665]) ).
tcf(c_20548,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK18)),sK3(iPr_def_11))
| ( sK5(powerset(sK18)) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(powerset(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_6924,c_13665]) ).
tcf(c_20549,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_6956,c_13665]) ).
tcf(c_20550,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK18)))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK18)))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(powerset(sK5(powerset(sK18)))),sK18) ),
inference(superposition,[status(thm)],[c_6935,c_13665]) ).
tcf(c_20551,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7152,c_13665]) ).
tcf(c_20552,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7563,c_13665]) ).
tcf(c_20553,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| element(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_13665]) ).
tcf(c_20556,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7201,c_13665]) ).
tcf(c_20557,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_13665]) ).
tcf(c_20558,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(iPr_def_11))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(sK5(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7587,c_13665]) ).
tcf(c_20561,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| element(sK3(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9907,c_13665]) ).
tcf(c_20565,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),sK18)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11031,c_13665]) ).
tcf(c_20566,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11588,c_13665]) ).
tcf(c_20569,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11156,c_13665]) ).
tcf(c_20571,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),singleton(iPr_def_10))
| ( sK3(iPr_def_11) = sK18 )
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_15774,c_13665]) ).
tcf(c_20572,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),singleton(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ~ epsilon_transitive(singleton(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_16901,c_13665]) ).
tcf(c_21321,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| element(X0,set_union2(sK3(iPr_def_11),X1))
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_138,c_13668]) ).
tcf(c_21322,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| element(X0,set_union2(X1,sK3(iPr_def_11)))
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3397,c_13668]) ).
tcf(c_21323,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| element(X0,singleton(sK3(iPr_def_11)))
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ epsilon_transitive(singleton(sK3(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_3803,c_13668]) ).
tcf(c_21324,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| element(X1,set_union2(X0,X2))
| ( sK3(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_3863,c_13668]) ).
tcf(c_21325,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X2)
| element(X2,set_union2(X0,X1))
| ( sK3(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(sK3(iPr_def_11),X1)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_13668]) ).
tcf(c_21326,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X2)
| element(X2,set_union2(X0,X1))
| ( sK3(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(sK3(iPr_def_11),X0)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_13668]) ).
tcf(c_21327,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| element(X1,set_union2(X2,X0))
| ( sK3(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_3865,c_13668]) ).
tcf(c_21328,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3807,c_13668]) ).
tcf(c_21329,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| element(X0,sK5(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7244,c_13668]) ).
tcf(c_21330,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,sK18)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9591,c_13668]) ).
tcf(c_21331,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_10383,c_13668]) ).
tcf(c_21333,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_10394,c_13668]) ).
tcf(c_21334,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9864,c_13668]) ).
tcf(c_21335,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(X1,X0)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9925,c_13668]) ).
tcf(c_21510,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| element(sK4(iPr_def_11),set_union2(X0,X1))
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_138,c_13671]) ).
tcf(c_21511,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK5(powerset(X0)),sK4(iPr_def_11))
| ( sK5(powerset(X0)) = sK4(iPr_def_11) )
| ~ in(sK5(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3564,c_13671]) ).
tcf(c_21512,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| element(sK4(iPr_def_11),set_union2(X1,X0))
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3397,c_13671]) ).
tcf(c_21513,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(empty_set,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_3420,c_13671]) ).
tcf(c_21516,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_transitive(powerset(X0))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK1(powerset(X0)),sK4(iPr_def_11))
| ( sK1(powerset(X0)) = sK4(iPr_def_11) )
| ~ in(sK1(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3566,c_13671]) ).
tcf(c_21517,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(X0))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK3(powerset(X0)),sK4(iPr_def_11))
| ( sK3(powerset(X0)) = sK4(iPr_def_11) )
| ~ in(sK3(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3567,c_13671]) ).
tcf(c_21518,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(X0))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK4(powerset(X0)),sK4(iPr_def_11))
| ( sK4(powerset(X0)) = sK4(iPr_def_11) )
| ~ in(sK4(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3568,c_13671]) ).
tcf(c_21519,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| element(sK4(iPr_def_11),singleton(X0))
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(singleton(X0))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3803,c_13671]) ).
tcf(c_21520,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| element(sK4(iPr_def_11),set_union2(X1,X2))
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3863,c_13671]) ).
tcf(c_21521,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| element(sK4(iPr_def_11),set_union2(X0,X1))
| ( sK4(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(X2,X1)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_13671]) ).
tcf(c_21522,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| element(sK4(iPr_def_11),set_union2(X0,X1))
| ( sK4(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(X2,X0)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_13671]) ).
tcf(c_21523,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| element(sK4(iPr_def_11),set_union2(X2,X1))
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3865,c_13671]) ).
tcf(c_21524,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(X0)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK3(X0),sK4(iPr_def_11))
| ( sK3(X0) = sK4(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ in(sK3(X0),sK18) ),
inference(superposition,[status(thm)],[c_3807,c_13671]) ).
tcf(c_21525,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(X0)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK4(X0),sK4(iPr_def_11))
| ( sK4(X0) = sK4(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ in(sK4(X0),sK18) ),
inference(superposition,[status(thm)],[c_3808,c_13671]) ).
tcf(c_21526,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_3809,c_13671]) ).
tcf(c_21527,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(iPr_def_10)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_10),sK4(iPr_def_11))
| ( sK1(iPr_def_10) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(sK1(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_3810,c_13671]) ).
tcf(c_21528,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(iPr_def_10)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_10),sK4(iPr_def_11))
| ( sK3(iPr_def_10) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK3(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_5100,c_13671]) ).
tcf(c_21529,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(iPr_def_10)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_10),sK4(iPr_def_11))
| ( sK3(iPr_def_10) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(sK3(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_3811,c_13671]) ).
tcf(c_21530,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(iPr_def_10)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_10),sK4(iPr_def_11))
| ( sK4(iPr_def_10) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK4(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_5120,c_13671]) ).
tcf(c_21531,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(iPr_def_10)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_10),sK4(iPr_def_11))
| ( sK4(iPr_def_10) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(sK4(iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_3812,c_13671]) ).
tcf(c_21532,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(X0)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK5(X0),sK4(iPr_def_11))
| ( sK5(X0) = sK4(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ in(sK5(X0),sK18) ),
inference(superposition,[status(thm)],[c_3899,c_13671]) ).
tcf(c_21533,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_5311,c_13671]) ).
tcf(c_21534,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK5(powerset(empty_set)),sK4(iPr_def_11))
| ( sK5(powerset(empty_set)) = sK4(iPr_def_11) )
| ~ in(sK5(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4163,c_13671]) ).
tcf(c_21537,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(powerset(sK18))
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK1(powerset(sK18)),sK4(iPr_def_11))
| ( sK1(powerset(sK18)) = sK4(iPr_def_11) )
| ~ in(sK1(powerset(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_4588,c_13671]) ).
tcf(c_21538,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(powerset(iPr_def_10))
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK1(powerset(iPr_def_10)),sK4(iPr_def_11))
| ( sK1(powerset(iPr_def_10)) = sK4(iPr_def_11) )
| ~ in(sK1(powerset(iPr_def_10)),sK18) ),
inference(superposition,[status(thm)],[c_4589,c_13671]) ).
tcf(c_21539,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(empty_set))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK3(powerset(empty_set)),sK4(iPr_def_11))
| ( sK3(powerset(empty_set)) = sK4(iPr_def_11) )
| ~ in(sK3(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4620,c_13671]) ).
tcf(c_21540,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(sK18))
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(powerset(sK18)),sK4(iPr_def_11))
| ( sK3(powerset(sK18)) = sK4(iPr_def_11) )
| ~ in(sK3(powerset(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_4621,c_13671]) ).
tcf(c_21541,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(iPr_def_10))
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(powerset(iPr_def_10)),sK4(iPr_def_11))
| ( sK3(powerset(iPr_def_10)) = sK4(iPr_def_11) )
| ~ in(sK3(powerset(iPr_def_10)),sK18) ),
inference(superposition,[status(thm)],[c_4622,c_13671]) ).
tcf(c_21542,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(empty_set))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK4(powerset(empty_set)),sK4(iPr_def_11))
| ( sK4(powerset(empty_set)) = sK4(iPr_def_11) )
| ~ in(sK4(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4637,c_13671]) ).
tcf(c_21543,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(sK18))
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(powerset(sK18)),sK4(iPr_def_11))
| ( sK4(powerset(sK18)) = sK4(iPr_def_11) )
| ~ in(sK4(powerset(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_4638,c_13671]) ).
tcf(c_21544,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(iPr_def_10))
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(powerset(iPr_def_10)),sK4(iPr_def_11))
| ( sK4(powerset(iPr_def_10)) = sK4(iPr_def_11) )
| ~ in(sK4(powerset(iPr_def_10)),sK18) ),
inference(superposition,[status(thm)],[c_4639,c_13671]) ).
tcf(c_21545,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(X0)))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(powerset(X0)))) = sK4(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(X0)))),sK18) ),
inference(superposition,[status(thm)],[c_5196,c_13671]) ).
tcf(c_21546,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(empty_set)))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(powerset(empty_set)))) = sK4(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(empty_set)))),sK18) ),
inference(superposition,[status(thm)],[c_5250,c_13671]) ).
tcf(c_21548,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(X0)))))) = sK4(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),sK18) ),
inference(superposition,[status(thm)],[c_5252,c_13671]) ).
tcf(c_21550,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(sK18))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(sK18))) = sK4(iPr_def_11) )
| ~ in(sK5(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_5418,c_13671]) ).
tcf(c_21551,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK4(iPr_def_11),iPr_def_11)
| epsilon_transitive(powerset(sK5(sK18)))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK1(powerset(sK5(sK18))),sK4(iPr_def_11))
| ( sK1(powerset(sK5(sK18))) = sK4(iPr_def_11) )
| ~ in(sK1(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_5420,c_13671]) ).
tcf(c_21552,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK4(iPr_def_11),iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(powerset(sK5(sK18))),sK4(iPr_def_11))
| ( sK3(powerset(sK5(sK18))) = sK4(iPr_def_11) )
| ~ in(sK3(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_5421,c_13671]) ).
tcf(c_21553,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK4(iPr_def_11),iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(powerset(sK5(sK18))),sK4(iPr_def_11))
| ( sK4(powerset(sK5(sK18))) = sK4(iPr_def_11) )
| ~ in(sK4(powerset(sK5(sK18))),sK18) ),
inference(superposition,[status(thm)],[c_5422,c_13671]) ).
tcf(c_21554,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| epsilon_connected(sK5(sK18))
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(sK5(sK18)),sK4(iPr_def_11))
| ( sK3(sK5(sK18)) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ in(sK3(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_5423,c_13671]) ).
tcf(c_21555,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| epsilon_connected(sK5(sK18))
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(sK5(sK18)),sK4(iPr_def_11))
| ( sK4(sK5(sK18)) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ in(sK4(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_5424,c_13671]) ).
tcf(c_21556,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| empty(sK5(sK18))
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(sK5(sK18)),sK4(iPr_def_11))
| ( sK5(sK5(sK18)) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK5(sK18))
| ~ in(sK5(sK5(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_5425,c_13671]) ).
tcf(c_21557,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(sK18))))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(sK18))))) = sK4(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(sK18))))),sK18) ),
inference(superposition,[status(thm)],[c_5429,c_13671]) ).
tcf(c_21558,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))) = sK4(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),sK18) ),
inference(superposition,[status(thm)],[c_5727,c_13671]) ).
tcf(c_21559,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))) = sK4(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))),sK18) ),
inference(superposition,[status(thm)],[c_5849,c_13671]) ).
tcf(c_21560,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))))) = sK4(iPr_def_11) )
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(sK18))))))))),sK18) ),
inference(superposition,[status(thm)],[c_5909,c_13671]) ).
tcf(c_21561,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK4(iPr_def_11),iPr_def_11)
| epsilon_transitive(powerset(sK5(sK18)))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK1(powerset(sK5(sK18))))),sK4(iPr_def_11))
| ( sK5(powerset(sK1(powerset(sK5(sK18))))) = sK4(iPr_def_11) )
| ~ in(sK5(powerset(sK1(powerset(sK5(sK18))))),sK18) ),
inference(superposition,[status(thm)],[c_5967,c_13671]) ).
tcf(c_21564,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK18)),sK4(iPr_def_11))
| ( sK5(powerset(sK18)) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(powerset(sK18)),sK18) ),
inference(superposition,[status(thm)],[c_6924,c_13671]) ).
tcf(c_21565,plain,
( epsilon_connected(iPr_def_11)
| empty(sK18)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_6956,c_13671]) ).
tcf(c_21566,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK18)))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK18)))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(powerset(sK5(powerset(sK18)))),sK18) ),
inference(superposition,[status(thm)],[c_6935,c_13671]) ).
tcf(c_21567,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7152,c_13671]) ).
tcf(c_21568,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7563,c_13671]) ).
tcf(c_21569,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| element(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_13671]) ).
tcf(c_21572,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7201,c_13671]) ).
tcf(c_21573,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_13671]) ).
tcf(c_21574,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(iPr_def_11))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(sK5(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7587,c_13671]) ).
tcf(c_21576,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_10383,c_13671]) ).
tcf(c_21583,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| element(sK4(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11191,c_13671]) ).
tcf(c_21587,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),singleton(iPr_def_10))
| ( sK4(iPr_def_11) = sK18 )
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_15774,c_13671]) ).
tcf(c_21588,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),singleton(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ~ epsilon_transitive(singleton(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_16901,c_13671]) ).
tcf(c_22252,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,X1))
| in(sK5(set_union2(X1,X0)),X1)
| in(sK5(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_58,c_4029]) ).
tcf(c_22255,plain,
! [X0: $i] :
( empty(set_union2(X0,empty_set))
| in(sK5(X0),empty_set)
| in(sK5(set_union2(X0,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_126,c_4029]) ).
tcf(c_22256,plain,
! [X0: $i] :
( empty(set_union2(empty_set,X0))
| in(sK5(X0),X0)
| in(sK5(set_union2(empty_set,X0)),empty_set) ),
inference(superposition,[status(thm)],[c_3423,c_4029]) ).
tcf(c_22257,plain,
( empty(set_union2(iPr_def_10,sK18))
| in(sK5(iPr_def_11),sK18)
| in(sK5(set_union2(iPr_def_10,sK18)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3424,c_4029]) ).
tcf(c_22258,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,X1))
| in(sK5(set_union2(X1,X0)),X0)
| in(sK5(set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_58,c_4029]) ).
tcf(c_22260,plain,
! [X0: $i] :
( empty(set_union2(X0,X0))
| in(sK5(X0),X0)
| in(sK5(set_union2(X0,X0)),X0) ),
inference(superposition,[status(thm)],[c_97,c_4029]) ).
tcf(c_22261,plain,
! [X0: $i] :
( empty(set_union2(X0,empty_set))
| in(sK5(X0),X0)
| in(sK5(set_union2(X0,empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_126,c_4029]) ).
tcf(c_22262,plain,
! [X0: $i] :
( empty(set_union2(empty_set,X0))
| in(sK5(X0),empty_set)
| in(sK5(set_union2(empty_set,X0)),X0) ),
inference(superposition,[status(thm)],[c_3423,c_4029]) ).
tcf(c_22263,plain,
( empty(set_union2(iPr_def_10,sK18))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(set_union2(iPr_def_10,sK18)),sK18) ),
inference(superposition,[status(thm)],[c_3424,c_4029]) ).
tcf(c_22264,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_union2(X2,X0))
| element(sK5(set_union2(X2,X0)),X1)
| in(sK5(set_union2(X2,X0)),X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4029,c_358]) ).
tcf(c_22265,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_union2(X2,X1))
| in(X0,sK5(set_union2(X2,X1)))
| in(sK5(set_union2(X2,X1)),X2)
| in(sK5(set_union2(X2,X1)),X0)
| ( sK5(set_union2(X2,X1)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4029,c_77]) ).
tcf(c_22266,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X1,X0))
| subset(sK5(set_union2(X1,X0)),X0)
| in(sK5(set_union2(X1,X0)),X1)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4029,c_65]) ).
tcf(c_22267,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X1,X0))
| in(sK5(set_union2(X1,X0)),X1)
| ~ in(X0,sK5(set_union2(X1,X0))) ),
inference(superposition,[status(thm)],[c_4029,c_49]) ).
tcf(c_22268,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X1,X0))
| in(sK5(set_union2(X1,X0)),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4029,c_137]) ).
tcf(c_22269,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,X1))
| element(sK5(set_union2(X0,X1)),X1)
| in(sK5(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_127]) ).
tcf(c_22270,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,singleton(X1)))
| in(sK5(set_union2(X0,singleton(X1))),X0)
| ( sK5(set_union2(X0,singleton(X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_4029,c_62]) ).
tcf(c_22271,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_union2(X0,set_union2(X1,X2)))
| in(sK5(set_union2(X0,set_union2(X1,X2))),X2)
| in(sK5(set_union2(X0,set_union2(X1,X2))),X1)
| in(sK5(set_union2(X0,set_union2(X1,X2))),X0) ),
inference(superposition,[status(thm)],[c_4029,c_71]) ).
tcf(c_22272,plain,
! [X0: $i] :
( empty(set_union2(X0,empty_set))
| in(sK5(set_union2(X0,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_7097]) ).
tcf(c_22273,plain,
! [X0: $i] :
( empty(set_union2(X0,sK18))
| subset(sK5(set_union2(X0,sK18)),iPr_def_11)
| in(sK5(set_union2(X0,sK18)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_12813]) ).
tcf(c_22274,plain,
! [X0: $i] :
( empty(set_union2(X0,sK18))
| in(sK5(set_union2(X0,sK18)),X0)
| ~ in(iPr_def_11,sK5(set_union2(X0,sK18))) ),
inference(superposition,[status(thm)],[c_4029,c_6841]) ).
tcf(c_22275,plain,
! [X0: $i] :
( empty(set_union2(X0,sK18))
| element(sK5(set_union2(X0,sK18)),iPr_def_11)
| in(sK5(set_union2(X0,sK18)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_5047]) ).
tcf(c_22276,plain,
! [X0: $i] :
( empty(set_union2(X0,sK18))
| in(sK5(set_union2(X0,sK18)),iPr_def_11)
| in(sK5(set_union2(X0,sK18)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_3640]) ).
tcf(c_22277,plain,
! [X0: $i] :
( empty(set_union2(X0,iPr_def_10))
| subset(sK5(set_union2(X0,iPr_def_10)),iPr_def_11)
| in(sK5(set_union2(X0,iPr_def_10)),X0)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4029,c_9540]) ).
tcf(c_22278,plain,
! [X0: $i] :
( empty(set_union2(X0,iPr_def_10))
| in(sK5(set_union2(X0,iPr_def_10)),X0)
| ~ in(iPr_def_11,sK5(set_union2(X0,iPr_def_10))) ),
inference(superposition,[status(thm)],[c_4029,c_6289]) ).
tcf(c_22279,plain,
! [X0: $i] :
( empty(set_union2(X0,iPr_def_10))
| element(sK5(set_union2(X0,iPr_def_10)),iPr_def_11)
| in(sK5(set_union2(X0,iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_4912]) ).
tcf(c_22280,plain,
! [X0: $i] :
( empty(set_union2(X0,iPr_def_10))
| in(sK5(set_union2(X0,iPr_def_10)),X0)
| ( sK5(set_union2(X0,iPr_def_10)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4029,c_3592]) ).
tcf(c_22281,plain,
! [X0: $i] :
( empty(set_union2(X0,iPr_def_10))
| in(sK5(set_union2(X0,iPr_def_10)),iPr_def_11)
| in(sK5(set_union2(X0,iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_3614]) ).
tcf(c_22282,plain,
! [X0: $i] :
( empty(set_union2(X0,iPr_def_11))
| in(sK5(set_union2(X0,iPr_def_11)),iPr_def_10)
| in(sK5(set_union2(X0,iPr_def_11)),sK18)
| in(sK5(set_union2(X0,iPr_def_11)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_4035]) ).
tcf(c_22283,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_union2(X0,X2))
| element(sK5(set_union2(X0,X2)),X1)
| in(sK5(set_union2(X0,X2)),X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4029,c_358]) ).
tcf(c_22284,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_union2(X1,X2))
| in(X0,sK5(set_union2(X1,X2)))
| in(sK5(set_union2(X1,X2)),X2)
| in(sK5(set_union2(X1,X2)),X0)
| ( sK5(set_union2(X1,X2)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4029,c_77]) ).
tcf(c_22285,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,X1))
| subset(sK5(set_union2(X0,X1)),X0)
| in(sK5(set_union2(X0,X1)),X1)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4029,c_65]) ).
tcf(c_22286,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,X1))
| in(sK5(set_union2(X0,X1)),X1)
| ~ in(X0,sK5(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_4029,c_49]) ).
tcf(c_22287,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,X1))
| in(sK5(set_union2(X0,X1)),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4029,c_137]) ).
tcf(c_22288,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,X1))
| element(sK5(set_union2(X0,X1)),X0)
| in(sK5(set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_4029,c_127]) ).
tcf(c_22289,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(singleton(X0),X1))
| in(sK5(set_union2(singleton(X0),X1)),X1)
| ( sK5(set_union2(singleton(X0),X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_4029,c_62]) ).
tcf(c_22290,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_union2(set_union2(X0,X1),X2))
| in(sK5(set_union2(set_union2(X0,X1),X2)),X2)
| in(sK5(set_union2(set_union2(X0,X1),X2)),X1)
| in(sK5(set_union2(set_union2(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_71]) ).
tcf(c_22291,plain,
! [X0: $i] :
( empty(set_union2(empty_set,X0))
| in(sK5(set_union2(empty_set,X0)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_7097]) ).
tcf(c_22292,plain,
! [X0: $i] :
( empty(set_union2(sK18,X0))
| subset(sK5(set_union2(sK18,X0)),iPr_def_11)
| in(sK5(set_union2(sK18,X0)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_12813]) ).
tcf(c_22293,plain,
! [X0: $i] :
( empty(set_union2(sK18,X0))
| in(sK5(set_union2(sK18,X0)),X0)
| ~ in(iPr_def_11,sK5(set_union2(sK18,X0))) ),
inference(superposition,[status(thm)],[c_4029,c_6841]) ).
tcf(c_22294,plain,
! [X0: $i] :
( empty(set_union2(sK18,X0))
| element(sK5(set_union2(sK18,X0)),iPr_def_11)
| in(sK5(set_union2(sK18,X0)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_5047]) ).
tcf(c_22295,plain,
! [X0: $i] :
( empty(set_union2(sK18,X0))
| in(sK5(set_union2(sK18,X0)),iPr_def_11)
| in(sK5(set_union2(sK18,X0)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_3640]) ).
tcf(c_22296,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_10,X0))
| subset(sK5(set_union2(iPr_def_10,X0)),iPr_def_11)
| in(sK5(set_union2(iPr_def_10,X0)),X0)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4029,c_9540]) ).
tcf(c_22297,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_10,X0))
| in(sK5(set_union2(iPr_def_10,X0)),X0)
| ~ in(iPr_def_11,sK5(set_union2(iPr_def_10,X0))) ),
inference(superposition,[status(thm)],[c_4029,c_6289]) ).
tcf(c_22298,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_10,X0))
| element(sK5(set_union2(iPr_def_10,X0)),iPr_def_11)
| in(sK5(set_union2(iPr_def_10,X0)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_4912]) ).
tcf(c_22299,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_10,X0))
| in(sK5(set_union2(iPr_def_10,X0)),X0)
| ( sK5(set_union2(iPr_def_10,X0)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4029,c_3592]) ).
tcf(c_22300,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_10,X0))
| in(sK5(set_union2(iPr_def_10,X0)),iPr_def_11)
| in(sK5(set_union2(iPr_def_10,X0)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_3614]) ).
tcf(c_22301,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_11,X0))
| in(sK5(set_union2(iPr_def_11,X0)),iPr_def_10)
| in(sK5(set_union2(iPr_def_11,X0)),sK18)
| in(sK5(set_union2(iPr_def_11,X0)),X0) ),
inference(superposition,[status(thm)],[c_4029,c_4035]) ).
tcf(c_22302,plain,
! [X0: $i] :
( empty(set_union2(X0,X0))
| in(sK5(set_union2(X0,X0)),X0) ),
inference(equality_factoring,[status(thm)],[c_4029]) ).
tcf(c_22315,plain,
! [X0: $i] :
( empty(X0)
| in(sK5(X0),empty_set)
| in(sK5(X0),X0) ),
inference(light_normalisation,[status(thm)],[c_22262,c_3423]) ).
tcf(c_22422,plain,
! [X0: $i] :
( in(sK5(set_union2(iPr_def_11,X0)),iPr_def_10)
| in(sK5(set_union2(iPr_def_11,X0)),sK18)
| in(sK5(set_union2(iPr_def_11,X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22301,c_15070]) ).
tcf(c_22426,plain,
! [X0: $i] :
( in(sK5(set_union2(X0,iPr_def_11)),iPr_def_10)
| in(sK5(set_union2(X0,iPr_def_11)),sK18)
| in(sK5(set_union2(X0,iPr_def_11)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22282,c_15128]) ).
tcf(c_22587,plain,
! [X0: $i] :
( subset(sK18,set_union2(X0,iPr_def_11))
| ~ epsilon_transitive(set_union2(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_58,c_15068]) ).
tcf(c_22591,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),set_union2(iPr_def_11,X0))
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_15068,c_13671]) ).
tcf(c_22592,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),set_union2(iPr_def_11,X0))
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_15068,c_13665]) ).
tcf(c_22593,plain,
! [X0: $i] :
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),set_union2(iPr_def_11,X0))
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_15068,c_13657]) ).
tcf(c_22594,plain,
! [X0: $i,X1: $i] :
( subset(X1,set_union2(iPr_def_11,X0))
| ~ subset(X1,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_15068,c_128]) ).
tcf(c_22629,plain,
! [X0: $i] :
( subset(sK18,set_union2(iPr_def_11,X0))
| ~ epsilon_transitive(set_union2(X0,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_58,c_15126]) ).
tcf(c_22633,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),set_union2(X0,iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15126,c_13671]) ).
tcf(c_22634,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),set_union2(X0,iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15126,c_13665]) ).
tcf(c_22635,plain,
! [X0: $i] :
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),set_union2(X0,iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15126,c_13657]) ).
tcf(c_22636,plain,
! [X0: $i,X1: $i] :
( subset(X1,set_union2(X0,iPr_def_11))
| ~ subset(X1,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15126,c_128]) ).
tcf(c_22780,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| element(X0,set_union2(sK4(iPr_def_11),X1))
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_138,c_13674]) ).
tcf(c_22781,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| element(X0,set_union2(X1,sK4(iPr_def_11)))
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3397,c_13674]) ).
tcf(c_22782,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| element(X0,singleton(sK4(iPr_def_11)))
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ epsilon_transitive(singleton(sK4(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_3803,c_13674]) ).
tcf(c_22783,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| element(X1,set_union2(X0,X2))
| ( sK4(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_3863,c_13674]) ).
tcf(c_22784,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X2)
| element(X2,set_union2(X0,X1))
| ( sK4(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(sK4(iPr_def_11),X1)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_13674]) ).
tcf(c_22785,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X2)
| element(X2,set_union2(X0,X1))
| ( sK4(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(sK4(iPr_def_11),X0)
| ~ epsilon_transitive(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_13674]) ).
tcf(c_22786,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| element(X1,set_union2(X2,X0))
| ( sK4(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_3865,c_13674]) ).
tcf(c_22787,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3808,c_13674]) ).
tcf(c_22788,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| element(X0,sK5(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7244,c_13674]) ).
tcf(c_22790,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,sK18)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11031,c_13674]) ).
tcf(c_22791,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11588,c_13674]) ).
tcf(c_22793,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11599,c_13674]) ).
tcf(c_22794,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11156,c_13674]) ).
tcf(c_22795,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(X1,X0)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11209,c_13674]) ).
tcf(c_22948,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_union2(X0,X1),X2,X0),X2)
| in(sK2(set_union2(X0,X1),X2,X0),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = X0 )
| ~ in(sK2(set_union2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_68,c_4078]) ).
tcf(c_22950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_union2(set_union2(set_union2(X0,X1),X2),X3) = X4 )
| ~ in(sK2(set_union2(set_union2(X0,X1),X2),X3,X4),X4)
| ~ in(sK2(set_union2(set_union2(X0,X1),X2),X3,X4),X0) ),
inference(superposition,[status(thm)],[c_69,c_4078]) ).
tcf(c_22951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_union2(set_union2(set_union2(X0,X1),X2),X3) = X4 )
| ~ in(sK2(set_union2(set_union2(X0,X1),X2),X3,X4),X4)
| ~ in(sK2(set_union2(set_union2(X0,X1),X2),X3,X4),X1) ),
inference(superposition,[status(thm)],[c_70,c_4078]) ).
tcf(c_22952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),sK2(set_union2(sK5(iPr_def_11),X0),X1,X2))
| ( set_union2(set_union2(sK5(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK5(iPr_def_11),X0),X1,X2) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_13652,c_4078]) ).
tcf(c_22953,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),sK2(set_union2(sK5(iPr_def_11),X0),X1,X2))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(set_union2(sK5(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK5(iPr_def_11),X0),X1,X2) = sK5(iPr_def_11) )
| ~ in(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_7241,c_4078]) ).
tcf(c_22954,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK2(set_union2(sK5(iPr_def_11),X0),X1,X2))
| ( set_union2(set_union2(sK5(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK5(iPr_def_11),X0),X1,X2) = sK5(iPr_def_11) )
| ~ in(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_7238,c_4078]) ).
tcf(c_22955,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(sK5(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK5(iPr_def_11),X0),X1,X2) = sK5(iPr_def_11) )
| ~ empty(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2))
| ~ in(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_7263,c_4078]) ).
tcf(c_22956,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK2(set_union2(sK5(iPr_def_11),X0),X1,X2))
| ( set_union2(set_union2(sK5(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK5(iPr_def_11),X0),X1,X2) = sK5(iPr_def_11) )
| ~ in(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_7155,c_4078]) ).
tcf(c_22957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),sK2(set_union2(sK3(iPr_def_11),X0),X1,X2))
| ( set_union2(set_union2(sK3(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK3(iPr_def_11),X0),X1,X2) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_13640,c_4078]) ).
tcf(c_22958,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),sK2(set_union2(sK3(iPr_def_11),X0),X1,X2))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(set_union2(sK3(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK3(iPr_def_11),X0),X1,X2) = sK3(iPr_def_11) )
| ~ in(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_9904,c_4078]) ).
tcf(c_22959,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK2(set_union2(sK3(iPr_def_11),X0),X1,X2))
| ( set_union2(set_union2(sK3(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK3(iPr_def_11),X0),X1,X2) = sK3(iPr_def_11) )
| ~ in(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_9901,c_4078]) ).
tcf(c_22960,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(sK3(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK3(iPr_def_11),X0),X1,X2) = sK3(iPr_def_11) )
| ~ empty(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2))
| ~ in(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_9927,c_4078]) ).
tcf(c_22961,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK2(set_union2(sK3(iPr_def_11),X0),X1,X2))
| ( set_union2(set_union2(sK3(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK3(iPr_def_11),X0),X1,X2) = sK3(iPr_def_11) )
| ~ in(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_9595,c_4078]) ).
tcf(c_22962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X3)
| in(sK4(iPr_def_11),sK2(set_union2(sK4(iPr_def_11),X0),X1,X2))
| ( set_union2(set_union2(sK4(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK4(iPr_def_11),X0),X1,X2) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(sK2(set_union2(sK4(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK4(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_13646,c_4078]) ).
tcf(c_22963,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),sK2(set_union2(sK4(iPr_def_11),X0),X1,X2))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(set_union2(sK4(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK4(iPr_def_11),X0),X1,X2) = sK4(iPr_def_11) )
| ~ in(sK2(set_union2(sK4(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK4(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_11188,c_4078]) ).
tcf(c_22964,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(set_union2(sK4(iPr_def_11),X0),X1,X2))
| ( set_union2(set_union2(sK4(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK4(iPr_def_11),X0),X1,X2) = sK4(iPr_def_11) )
| ~ in(sK2(set_union2(sK4(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK4(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_11185,c_4078]) ).
tcf(c_22965,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(sK4(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK4(iPr_def_11),X0),X1,X2) = sK4(iPr_def_11) )
| ~ empty(sK2(set_union2(sK4(iPr_def_11),X0),X1,X2))
| ~ in(sK2(set_union2(sK4(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK4(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_11211,c_4078]) ).
tcf(c_22966,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(set_union2(sK4(iPr_def_11),X0),X1,X2))
| ( set_union2(set_union2(sK4(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK4(iPr_def_11),X0),X1,X2) = sK4(iPr_def_11) )
| ~ in(sK2(set_union2(sK4(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK4(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_11035,c_4078]) ).
tcf(c_22967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_union2(set_union2(X0,X1),X2) = X3 )
| ~ in(sK2(set_union2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_union2(X0,X1),X2,X3),X3) ),
inference(superposition,[status(thm)],[c_58,c_4078]) ).
tcf(c_22969,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(set_union2(X0,X0),X1) = X2 )
| ~ in(sK2(X0,X1,X2),X0)
| ~ in(sK2(set_union2(X0,X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_97,c_4078]) ).
tcf(c_22970,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(set_union2(X0,empty_set),X1) = X2 )
| ~ in(sK2(X0,X1,X2),X0)
| ~ in(sK2(set_union2(X0,empty_set),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_126,c_4078]) ).
tcf(c_22971,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(set_union2(empty_set,X0),X1) = X2 )
| ~ in(sK2(X0,X1,X2),empty_set)
| ~ in(sK2(set_union2(empty_set,X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_3423,c_4078]) ).
tcf(c_22972,plain,
! [X0: $i,X1: $i] :
( ( set_union2(set_union2(iPr_def_10,sK18),X0) = X1 )
| ~ in(sK2(iPr_def_11,X0,X1),iPr_def_10)
| ~ in(sK2(set_union2(iPr_def_10,sK18),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_3424,c_4078]) ).
tcf(c_22973,plain,
! [X0: $i,X1: $i] :
( ( set_union2(iPr_def_11,X0) = X1 )
| ~ in(sK2(iPr_def_11,X0,X1),iPr_def_10)
| ~ in(sK2(iPr_def_11,X0,X1),X1) ),
inference(light_normalisation,[status(thm)],[c_22972,c_3424]) ).
tcf(c_22977,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK2(X0,X1,X2),empty_set)
| ~ in(sK2(X0,X1,X2),X2) ),
inference(light_normalisation,[status(thm)],[c_22971,c_3423]) ).
tcf(c_23180,plain,
! [X0: $i] :
( ~ subset(iPr_def_11,X0)
| in(sK5(iPr_def_11),X0) ),
inference(global_subsumption_just,[status(thm)],[c_15733,c_3672,c_5463,c_15733]) ).
tcf(c_23181,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),X0)
| ~ subset(iPr_def_11,X0) ),
inference(renaming,[status(thm)],[c_23180]) ).
tcf(c_23186,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| ~ subset(iPr_def_11,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_23181,c_358]) ).
tcf(c_23187,plain,
! [X0: $i,X1: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ subset(iPr_def_11,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_23181,c_77]) ).
tcf(c_23188,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),X0)
| ~ epsilon_transitive(X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_23181,c_65]) ).
tcf(c_23189,plain,
! [X0: $i] :
( ~ subset(iPr_def_11,X0)
| ~ in(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_23181,c_49]) ).
tcf(c_23190,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_23181,c_137]) ).
tcf(c_23192,plain,
! [X0: $i] :
( ( sK5(iPr_def_11) = X0 )
| ~ subset(iPr_def_11,singleton(X0)) ),
inference(superposition,[status(thm)],[c_23181,c_62]) ).
tcf(c_23193,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ~ subset(iPr_def_11,set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_23181,c_71]) ).
tcf(c_23195,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| ~ subset(iPr_def_11,sK18) ),
inference(superposition,[status(thm)],[c_23181,c_12813]) ).
tcf(c_23197,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| ~ subset(iPr_def_11,sK18) ),
inference(superposition,[status(thm)],[c_23181,c_5047]) ).
tcf(c_23199,plain,
( epsilon_transitive(sK5(iPr_def_11))
| ~ subset(iPr_def_11,sK1(sK5(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_23181,c_3523]) ).
tcf(c_23200,plain,
( epsilon_connected(sK5(iPr_def_11))
| ~ subset(iPr_def_11,sK3(sK5(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_23181,c_3524]) ).
tcf(c_23201,plain,
( epsilon_connected(sK5(iPr_def_11))
| ~ subset(iPr_def_11,sK4(sK5(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_23181,c_3525]) ).
tcf(c_23204,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| ~ subset(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_23181,c_4912]) ).
tcf(c_23205,plain,
( ( sK5(iPr_def_11) = sK18 )
| ~ subset(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_23181,c_3592]) ).
tcf(c_23208,plain,
( empty(sK5(iPr_def_11))
| ~ subset(iPr_def_11,sK5(sK5(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_23181,c_3900]) ).
tcf(c_23252,plain,
! [X0: $i,X1: $i] :
( ~ subset(iPr_def_11,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_23190]) ).
tcf(c_23253,plain,
! [X0: $i,X1: $i] :
( ~ in(iPr_def_11,X1)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_23190]) ).
tcf(c_23254,plain,
! [X0: $i,X1: $i] :
( ~ in(iPr_def_11,X0)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_23190]) ).
tcf(c_23255,plain,
! [X0: $i,X1: $i] :
( ~ subset(iPr_def_11,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_23190]) ).
tcf(c_23273,plain,
! [X0: $i] :
( ( singleton(X0) = sK5(iPr_def_11) )
| ( sK0(X0,sK5(iPr_def_11)) = X0 )
| ~ subset(iPr_def_11,sK0(X0,sK5(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_60,c_23189]) ).
tcf(c_23275,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK5(iPr_def_11),X0,X1),X1)
| in(sK2(sK5(iPr_def_11),X0,X1),X0)
| ( set_union2(sK5(iPr_def_11),X0) = X1 )
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,X1)) ),
inference(superposition,[status(thm)],[c_68,c_23189]) ).
tcf(c_23276,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK5(iPr_def_11)),X1)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ subset(iPr_def_11,sK2(X0,X1,sK5(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_68,c_23189]) ).
tcf(c_23277,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ~ subset(iPr_def_11,sK2(X0,sK5(iPr_def_11),X1)) ),
inference(superposition,[status(thm)],[c_68,c_23189]) ).
tcf(c_23281,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(sK5(iPr_def_11),X1)),X1)
| ( set_union2(sK5(iPr_def_11),X1) = singleton(X0) )
| ( sK0(X0,set_union2(sK5(iPr_def_11),X1)) = X0 )
| ~ subset(iPr_def_11,sK0(X0,set_union2(sK5(iPr_def_11),X1))) ),
inference(superposition,[status(thm)],[c_4023,c_23189]) ).
tcf(c_23282,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(X1,sK5(iPr_def_11))),X1)
| ( set_union2(X1,sK5(iPr_def_11)) = singleton(X0) )
| ( sK0(X0,set_union2(X1,sK5(iPr_def_11))) = X0 )
| ~ subset(iPr_def_11,sK0(X0,set_union2(X1,sK5(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_4023,c_23189]) ).
tcf(c_23283,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(sK5(iPr_def_11),X0))
| in(sK1(set_union2(sK5(iPr_def_11),X0)),X0)
| ~ subset(iPr_def_11,sK1(set_union2(sK5(iPr_def_11),X0))) ),
inference(superposition,[status(thm)],[c_4024,c_23189]) ).
tcf(c_23284,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,sK5(iPr_def_11)))
| in(sK1(set_union2(X0,sK5(iPr_def_11))),X0)
| ~ subset(iPr_def_11,sK1(set_union2(X0,sK5(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_4024,c_23189]) ).
tcf(c_23285,plain,
! [X0: $i] :
( epsilon_connected(set_union2(sK5(iPr_def_11),X0))
| in(sK3(set_union2(sK5(iPr_def_11),X0)),X0)
| ~ subset(iPr_def_11,sK3(set_union2(sK5(iPr_def_11),X0))) ),
inference(superposition,[status(thm)],[c_4027,c_23189]) ).
tcf(c_23286,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,sK5(iPr_def_11)))
| in(sK3(set_union2(X0,sK5(iPr_def_11))),X0)
| ~ subset(iPr_def_11,sK3(set_union2(X0,sK5(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_4027,c_23189]) ).
tcf(c_23287,plain,
! [X0: $i] :
( epsilon_connected(set_union2(sK5(iPr_def_11),X0))
| in(sK4(set_union2(sK5(iPr_def_11),X0)),X0)
| ~ subset(iPr_def_11,sK4(set_union2(sK5(iPr_def_11),X0))) ),
inference(superposition,[status(thm)],[c_4028,c_23189]) ).
tcf(c_23288,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,sK5(iPr_def_11)))
| in(sK4(set_union2(X0,sK5(iPr_def_11))),X0)
| ~ subset(iPr_def_11,sK4(set_union2(X0,sK5(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_4028,c_23189]) ).
tcf(c_23289,plain,
! [X0: $i] :
( empty(set_union2(sK5(iPr_def_11),X0))
| in(sK5(set_union2(sK5(iPr_def_11),X0)),X0)
| ~ subset(iPr_def_11,sK5(set_union2(sK5(iPr_def_11),X0))) ),
inference(superposition,[status(thm)],[c_4029,c_23189]) ).
tcf(c_23290,plain,
! [X0: $i] :
( empty(set_union2(X0,sK5(iPr_def_11)))
| in(sK5(set_union2(X0,sK5(iPr_def_11))),X0)
| ~ subset(iPr_def_11,sK5(set_union2(X0,sK5(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_4029,c_23189]) ).
tcf(c_23291,plain,
~ subset(iPr_def_11,sK5(iPr_def_11)),
inference(superposition,[status(thm)],[c_23181,c_23189]) ).
tcf(c_23297,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ subset(iPr_def_11,X0)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13652,c_23189]) ).
tcf(c_23298,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ subset(iPr_def_11,X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7241,c_23189]) ).
tcf(c_23299,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ subset(iPr_def_11,X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7238,c_23189]) ).
tcf(c_23301,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ subset(iPr_def_11,X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_23189]) ).
tcf(c_23302,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ subset(iPr_def_11,singleton(X0))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_23189]) ).
tcf(c_23303,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ subset(iPr_def_11,sK3(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_23189]) ).
tcf(c_23304,plain,
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ subset(iPr_def_11,sK3(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_23189]) ).
tcf(c_23305,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ subset(iPr_def_11,sK3(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_23189]) ).
tcf(c_23306,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ subset(iPr_def_11,sK3(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_23189]) ).
tcf(c_23307,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ subset(iPr_def_11,sK3(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_23189]) ).
tcf(c_23308,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ subset(iPr_def_11,sK4(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_23189]) ).
tcf(c_23309,plain,
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ subset(iPr_def_11,sK4(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_23189]) ).
tcf(c_23310,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK4(iPr_def_11))
| ~ subset(iPr_def_11,sK4(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11193,c_23189]) ).
tcf(c_23311,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ subset(iPr_def_11,sK4(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_23189]) ).
tcf(c_23312,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ subset(iPr_def_11,sK4(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_23189]) ).
tcf(c_23705,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),set_union2(X0,iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_22587,c_13671]) ).
tcf(c_23706,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),set_union2(X0,iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_22587,c_13665]) ).
tcf(c_23707,plain,
! [X0: $i] :
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),set_union2(X0,iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_22587,c_13657]) ).
tcf(c_23708,plain,
! [X0: $i,X1: $i] :
( subset(X1,set_union2(X0,iPr_def_11))
| ~ subset(X1,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_22587,c_128]) ).
tcf(c_23786,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ subset(iPr_def_11,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_23195,c_13665]) ).
tcf(c_23788,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ subset(iPr_def_11,sK18)
| ~ subset(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_23195,c_128]) ).
tcf(c_23789,plain,
! [X0: $i] :
( element(X0,iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ subset(iPr_def_11,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_23195,c_13661]) ).
tcf(c_23823,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X2)
| in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = set_union2(X0,X1) )
| ~ in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_68,c_4079]) ).
tcf(c_23824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_union2(X0,X1),X2,X3),X2)
| in(sK2(set_union2(X0,X1),X2,X3),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = X3 )
| ~ in(sK2(set_union2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_68,c_4079]) ).
tcf(c_23826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_union2(set_union2(X0,X1),X2) = set_union2(X3,X4) )
| ~ in(sK2(set_union2(X0,X1),X2,set_union2(X3,X4)),X3)
| ~ in(sK2(set_union2(X0,X1),X2,set_union2(X3,X4)),X1) ),
inference(superposition,[status(thm)],[c_69,c_4079]) ).
tcf(c_23827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_union2(set_union2(X0,X1),X2) = set_union2(X3,X4) )
| ~ in(sK2(set_union2(X0,X1),X2,set_union2(X3,X4)),X4)
| ~ in(sK2(set_union2(X0,X1),X2,set_union2(X3,X4)),X1) ),
inference(superposition,[status(thm)],[c_70,c_4079]) ).
tcf(c_23828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)))
| ( set_union2(set_union2(X0,X1),X2) = sK5(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_13652,c_4079]) ).
tcf(c_23829,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(set_union2(X0,X1),X2) = sK5(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_7241,c_4079]) ).
tcf(c_23830,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)))
| ( set_union2(set_union2(X0,X1),X2) = sK5(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_7238,c_4079]) ).
tcf(c_23831,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(X0,X1),X2) = sK5(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ empty(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)))
| ~ in(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_7263,c_4079]) ).
tcf(c_23832,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)))
| ( set_union2(set_union2(X0,X1),X2) = sK5(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_7155,c_4079]) ).
tcf(c_23833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)))
| ( set_union2(set_union2(X0,X1),X2) = sK3(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_13640,c_4079]) ).
tcf(c_23834,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(set_union2(X0,X1),X2) = sK3(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_9904,c_4079]) ).
tcf(c_23835,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)))
| ( set_union2(set_union2(X0,X1),X2) = sK3(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_9901,c_4079]) ).
tcf(c_23836,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(X0,X1),X2) = sK3(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ empty(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)))
| ~ in(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_9927,c_4079]) ).
tcf(c_23837,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)))
| ( set_union2(set_union2(X0,X1),X2) = sK3(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_9595,c_4079]) ).
tcf(c_23838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X3)
| in(sK4(iPr_def_11),sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)))
| ( set_union2(set_union2(X0,X1),X2) = sK4(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_13646,c_4079]) ).
tcf(c_23839,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(set_union2(X0,X1),X2) = sK4(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_11188,c_4079]) ).
tcf(c_23840,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)))
| ( set_union2(set_union2(X0,X1),X2) = sK4(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_11185,c_4079]) ).
tcf(c_23841,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(X0,X1),X2) = sK4(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ empty(sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)))
| ~ in(sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_11211,c_4079]) ).
tcf(c_23842,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)))
| ( set_union2(set_union2(X0,X1),X2) = sK4(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_11035,c_4079]) ).
tcf(c_23843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_union2(set_union2(X0,X1),X2) = X3 )
| ~ in(sK2(set_union2(X1,X0),X2,X3),X3)
| ~ in(sK2(set_union2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_58,c_4079]) ).
tcf(c_23845,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(set_union2(X0,X0),X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(set_union2(X0,X0),X1,X2),X0) ),
inference(superposition,[status(thm)],[c_97,c_4079]) ).
tcf(c_23846,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(set_union2(X0,empty_set),X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(set_union2(X0,empty_set),X1,X2),empty_set) ),
inference(superposition,[status(thm)],[c_126,c_4079]) ).
tcf(c_23847,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(set_union2(empty_set,X0),X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(set_union2(empty_set,X0),X1,X2),X0) ),
inference(superposition,[status(thm)],[c_3423,c_4079]) ).
tcf(c_23848,plain,
! [X0: $i,X1: $i] :
( ( set_union2(set_union2(iPr_def_10,sK18),X0) = X1 )
| ~ in(sK2(iPr_def_11,X0,X1),X1)
| ~ in(sK2(set_union2(iPr_def_10,sK18),X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_3424,c_4079]) ).
tcf(c_23849,plain,
! [X0: $i,X1: $i] :
( ( set_union2(iPr_def_11,X0) = X1 )
| ~ in(sK2(iPr_def_11,X0,X1),sK18)
| ~ in(sK2(iPr_def_11,X0,X1),X1) ),
inference(light_normalisation,[status(thm)],[c_23848,c_3424]) ).
tcf(c_24037,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),set_union2(iPr_def_11,X0))
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_22629,c_13671]) ).
tcf(c_24038,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),set_union2(iPr_def_11,X0))
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_22629,c_13665]) ).
tcf(c_24039,plain,
! [X0: $i] :
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),set_union2(iPr_def_11,X0))
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_22629,c_13657]) ).
tcf(c_24040,plain,
! [X0: $i,X1: $i] :
( subset(X1,set_union2(iPr_def_11,X0))
| ~ subset(X1,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_22629,c_128]) ).
tcf(c_24072,plain,
( ( sK5(iPr_def_11) = iPr_def_11 )
| ~ epsilon_transitive(singleton(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3803,c_23192]) ).
tcf(c_24082,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( singleton(X2) = X0 )
| ( sK0(X2,X0) = X2 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_60,c_359]) ).
tcf(c_24083,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ subset(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_61,c_359]) ).
tcf(c_24084,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_359]) ).
tcf(c_24085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X2,X3),X3)
| in(sK2(X0,X2,X3),X2)
| ( set_union2(X0,X2) = X3 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_359]) ).
tcf(c_24086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X3)
| in(sK2(X2,X3,X0),X2)
| ( set_union2(X2,X3) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_359]) ).
tcf(c_24087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X0,X3),X3)
| in(sK2(X2,X0,X3),X2)
| ( set_union2(X2,X0) = X3 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_359]) ).
tcf(c_24088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X2)
| ~ in(X3,X0)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_69,c_359]) ).
tcf(c_24089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X2)
| ~ in(X3,X1)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_70,c_359]) ).
tcf(c_24090,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_72,c_359]) ).
tcf(c_24092,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3768,c_359]) ).
tcf(c_24093,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_3400,c_359]) ).
tcf(c_24101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,set_union2(X0,X3)),X3)
| ( set_union2(X0,X3) = singleton(X2) )
| ( sK0(X2,set_union2(X0,X3)) = X2 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4023,c_359]) ).
tcf(c_24102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK0(X2,set_union2(X3,X0)),X3)
| ( set_union2(X3,X0) = singleton(X2) )
| ( sK0(X2,set_union2(X3,X0)) = X2 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4023,c_359]) ).
tcf(c_24103,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X0,X2))
| in(sK1(set_union2(X0,X2)),X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4024,c_359]) ).
tcf(c_24104,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X2,X0))
| in(sK1(set_union2(X2,X0)),X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4024,c_359]) ).
tcf(c_24105,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(X0,X2))
| in(sK3(set_union2(X0,X2)),X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4027,c_359]) ).
tcf(c_24106,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(X2,X0))
| in(sK3(set_union2(X2,X0)),X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4027,c_359]) ).
tcf(c_24107,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(X0,X2))
| in(sK4(set_union2(X0,X2)),X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4028,c_359]) ).
tcf(c_24108,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(set_union2(X2,X0))
| in(sK4(set_union2(X2,X0)),X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4028,c_359]) ).
tcf(c_24109,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_union2(X0,X2))
| in(sK5(set_union2(X0,X2)),X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4029,c_359]) ).
tcf(c_24110,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_union2(X2,X0))
| in(sK5(set_union2(X2,X0)),X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4029,c_359]) ).
tcf(c_24111,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ subset(set_union2(X0,iPr_def_11),X1) ),
inference(superposition,[status(thm)],[c_15062,c_359]) ).
tcf(c_24112,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ subset(set_union2(iPr_def_11,X0),X1) ),
inference(superposition,[status(thm)],[c_15059,c_359]) ).
tcf(c_24114,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ~ empty(X0)
| ~ subset(sK18,X0) ),
inference(superposition,[status(thm)],[c_6994,c_359]) ).
tcf(c_24115,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ empty(sK3(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9909,c_359]) ).
tcf(c_24116,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ empty(X0)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9927,c_359]) ).
tcf(c_24117,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(empty_set,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = empty_set )
| ~ empty(X0)
| ~ in(empty_set,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_9932,c_359]) ).
tcf(c_24118,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_359]) ).
tcf(c_24120,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ empty(X0)
| ~ subset(sK18,X0) ),
inference(superposition,[status(thm)],[c_6995,c_359]) ).
tcf(c_24121,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ empty(sK4(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11193,c_359]) ).
tcf(c_24122,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ empty(X0)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11211,c_359]) ).
tcf(c_24123,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(empty_set,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = empty_set )
| ~ empty(X0)
| ~ in(empty_set,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_11216,c_359]) ).
tcf(c_24124,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_359]) ).
tcf(c_24126,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ~ empty(X0)
| ~ subset(sK18,X0) ),
inference(superposition,[status(thm)],[c_7014,c_359]) ).
tcf(c_24127,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ empty(sK5(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7246,c_359]) ).
tcf(c_24128,plain,
! [X0: $i,X1: $i] :
( in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ empty(X0)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7263,c_359]) ).
tcf(c_24129,plain,
! [X0: $i] :
( in(empty_set,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = empty_set )
| ~ empty(X0)
| ~ in(empty_set,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_7267,c_359]) ).
tcf(c_24130,plain,
! [X0: $i,X1: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_359]) ).
tcf(c_24132,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ subset(iPr_def_11,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_23181,c_359]) ).
tcf(c_24133,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ subset(iPr_def_10,X2)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_13652,c_359]) ).
tcf(c_24134,plain,
! [X0: $i,X1: $i] :
( in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7241,c_359]) ).
tcf(c_24135,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7246,c_359]) ).
tcf(c_24136,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7238,c_359]) ).
tcf(c_24137,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7155,c_359]) ).
tcf(c_24138,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ~ empty(X0)
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_13652,c_359]) ).
tcf(c_24139,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X1 )
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_7241,c_359]) ).
tcf(c_24140,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_7238,c_359]) ).
tcf(c_24141,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = X1 )
| ~ empty(X1)
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_7263,c_359]) ).
tcf(c_24142,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_7155,c_359]) ).
tcf(c_24144,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ empty(X1)
| ~ subset(sK5(iPr_def_11),X1)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_359]) ).
tcf(c_24145,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ subset(iPr_def_10,X2)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_13640,c_359]) ).
tcf(c_24146,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_9904,c_359]) ).
tcf(c_24147,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_9909,c_359]) ).
tcf(c_24148,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_9901,c_359]) ).
tcf(c_24149,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_9595,c_359]) ).
tcf(c_24150,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ~ empty(X0)
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_13640,c_359]) ).
tcf(c_24151,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X1 )
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_9904,c_359]) ).
tcf(c_24152,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_9901,c_359]) ).
tcf(c_24153,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = X1 )
| ~ empty(X1)
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_9927,c_359]) ).
tcf(c_24154,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_9595,c_359]) ).
tcf(c_24155,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ empty(X1)
| ~ subset(sK3(iPr_def_11),X1)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_359]) ).
tcf(c_24156,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ subset(iPr_def_10,X2)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_13646,c_359]) ).
tcf(c_24157,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_11188,c_359]) ).
tcf(c_24158,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_11193,c_359]) ).
tcf(c_24159,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_11185,c_359]) ).
tcf(c_24160,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_11035,c_359]) ).
tcf(c_24161,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ~ empty(X0)
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_13646,c_359]) ).
tcf(c_24162,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X1 )
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_11188,c_359]) ).
tcf(c_24163,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_11185,c_359]) ).
tcf(c_24164,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = X1 )
| ~ empty(X1)
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_11211,c_359]) ).
tcf(c_24165,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_11035,c_359]) ).
tcf(c_24166,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = X0 )
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ empty(X1)
| ~ subset(sK4(iPr_def_11),X1)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_359]) ).
tcf(c_24167,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,iPr_def_10))
| ~ empty(X1)
| ~ subset(set_union2(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_15027,c_359]) ).
tcf(c_24168,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(iPr_def_10,X0))
| ~ empty(X1)
| ~ subset(set_union2(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_14317,c_359]) ).
tcf(c_24169,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(iPr_def_10,X0))
| ~ empty(X1)
| ~ subset(set_union2(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_14990,c_359]) ).
tcf(c_24170,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,iPr_def_10))
| ~ empty(X1)
| ~ subset(set_union2(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_14326,c_359]) ).
tcf(c_24171,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ subset(singleton(iPr_def_10),X0) ),
inference(superposition,[status(thm)],[c_15757,c_359]) ).
tcf(c_24172,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ epsilon_transitive(singleton(iPr_def_11))
| ~ subset(singleton(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_15765,c_359]) ).
tcf(c_24592,plain,
( ~ empty(empty_set)
| ~ subset(iPr_def_10,empty_set) ),
inference(instantiation,[status(thm)],[c_24093]) ).
tcf(c_25063,plain,
! [X0: $i,X1: $i] : ~ empty(set_union2(singleton(X0),X1)),
inference(superposition,[status(thm)],[c_138,c_24083]) ).
tcf(c_25064,plain,
! [X0: $i,X1: $i] : ~ empty(set_union2(X0,singleton(X1))),
inference(superposition,[status(thm)],[c_3397,c_24083]) ).
tcf(c_25065,plain,
! [X0: $i] :
( ~ epsilon_transitive(singleton(singleton(X0)))
| ~ empty(singleton(singleton(X0))) ),
inference(superposition,[status(thm)],[c_3803,c_24083]) ).
tcf(c_25066,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(singleton(X2),X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_24083]) ).
tcf(c_25067,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ epsilon_transitive(set_union2(X2,X1))
| ~ empty(set_union2(X2,X1))
| ~ in(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_3806,c_24083]) ).
tcf(c_25068,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ epsilon_transitive(set_union2(X1,X2))
| ~ empty(set_union2(X1,X2))
| ~ in(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_3805,c_24083]) ).
tcf(c_25069,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(singleton(X2),X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_24083]) ).
tcf(c_25070,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(X0))
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ empty(sK5(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7244,c_24083]) ).
tcf(c_25071,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(X0))
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ empty(sK3(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_9907,c_24083]) ).
tcf(c_25072,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(X0))
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ empty(sK4(iPr_def_11))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_11191,c_24083]) ).
tcf(c_25140,plain,
! [X0: $i] : ~ empty(set_union2(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_2420,c_25063]) ).
tcf(c_25141,plain,
! [X0: $i] : ~ empty(set_union2(X0,iPr_def_10)),
inference(backward_subsumption_resolution,[status(thm)],[c_15645,c_25140]) ).
tcf(c_25146,plain,
! [X0: $i] : ~ in(set_union2(iPr_def_10,X0),sK18),
inference(backward_subsumption_resolution,[status(thm)],[c_15692,c_25141]) ).
tcf(c_25147,plain,
! [X0: $i] : ~ in(set_union2(X0,iPr_def_10),sK18),
inference(backward_subsumption_resolution,[status(thm)],[c_15034,c_25141]) ).
tcf(c_25148,plain,
! [X0: $i] : in(sK18,set_union2(iPr_def_10,X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_15027,c_25141]) ).
tcf(c_25149,plain,
! [X0: $i] : in(sK18,set_union2(X0,iPr_def_10)),
inference(backward_subsumption_resolution,[status(thm)],[c_14326,c_25141]) ).
tcf(c_25170,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ subset(set_union2(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_25148,c_359]) ).
tcf(c_25171,plain,
! [X0: $i,X1: $i] :
( element(sK18,X1)
| ~ subset(set_union2(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_25148,c_358]) ).
tcf(c_25172,plain,
! [X0: $i,X1: $i] :
( in(sK18,X0)
| in(X0,sK18)
| ( X0 = sK18 )
| ~ epsilon_connected(set_union2(iPr_def_10,X1))
| ~ in(X0,set_union2(iPr_def_10,X1)) ),
inference(superposition,[status(thm)],[c_25148,c_77]) ).
tcf(c_25173,plain,
! [X0: $i] :
( subset(sK18,set_union2(iPr_def_10,X0))
| ~ epsilon_transitive(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_25148,c_65]) ).
tcf(c_25209,plain,
! [X0: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ empty(singleton(iPr_def_10))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3803,c_24130]) ).
tcf(c_25210,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ~ subset(iPr_def_10,X0)
| ~ in(X2,sK18)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_24130]) ).
tcf(c_25211,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ~ in(iPr_def_10,X1)
| ~ in(X2,sK18)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_24130]) ).
tcf(c_25212,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ~ in(iPr_def_10,X0)
| ~ in(X2,sK18)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_24130]) ).
tcf(c_25213,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ~ subset(iPr_def_10,X1)
| ~ in(X2,sK18)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_24130]) ).
tcf(c_25257,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_138,c_24137]) ).
tcf(c_25258,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(X0)),sK5(iPr_def_11))
| ( sK5(powerset(X0)) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3564,c_24137]) ).
tcf(c_25259,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3397,c_24137]) ).
tcf(c_25260,plain,
! [X0: $i] :
( in(empty_set,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = empty_set )
| ~ empty(X0)
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_3420,c_24137]) ).
tcf(c_25263,plain,
! [X0: $i] :
( epsilon_transitive(powerset(X0))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK1(powerset(X0)),sK5(iPr_def_11))
| ( sK1(powerset(X0)) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK1(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3566,c_24137]) ).
tcf(c_25264,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(powerset(X0)),sK5(iPr_def_11))
| ( sK3(powerset(X0)) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK3(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3567,c_24137]) ).
tcf(c_25265,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(powerset(X0)),sK5(iPr_def_11))
| ( sK4(powerset(X0)) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK4(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3568,c_24137]) ).
tcf(c_25267,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ subset(X2,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_24137]) ).
tcf(c_25268,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(X2,X1)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_24137]) ).
tcf(c_25269,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(X2,X0)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_24137]) ).
tcf(c_25270,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ subset(X2,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_24137]) ).
tcf(c_25271,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(X0),sK5(iPr_def_11))
| ( sK3(X0) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(sK3(X0),sK18) ),
inference(superposition,[status(thm)],[c_3807,c_24137]) ).
tcf(c_25272,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(X0),sK5(iPr_def_11))
| ( sK4(X0) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(sK4(X0),sK18) ),
inference(superposition,[status(thm)],[c_3808,c_24137]) ).
tcf(c_25281,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(empty_set)),sK5(iPr_def_11))
| ( sK5(powerset(empty_set)) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4163,c_24137]) ).
tcf(c_25286,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(powerset(empty_set)),sK5(iPr_def_11))
| ( sK3(powerset(empty_set)) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK3(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4620,c_24137]) ).
tcf(c_25289,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(powerset(empty_set)),sK5(iPr_def_11))
| ( sK4(powerset(empty_set)) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK4(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4637,c_24137]) ).
tcf(c_25292,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(X0)))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(X0)))) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(sK5(powerset(X0)))),sK18) ),
inference(superposition,[status(thm)],[c_5196,c_24137]) ).
tcf(c_25293,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(empty_set)))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(empty_set)))) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(sK5(powerset(empty_set)))),sK18) ),
inference(superposition,[status(thm)],[c_5250,c_24137]) ).
tcf(c_25295,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(X0)))))) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),sK18) ),
inference(superposition,[status(thm)],[c_5252,c_24137]) ).
tcf(c_25305,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),sK18) ),
inference(superposition,[status(thm)],[c_5727,c_24137]) ).
tcf(c_25316,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_24137]) ).
tcf(c_25322,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(iPr_def_11))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ empty(sK18)
| ~ in(sK5(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7587,c_24137]) ).
tcf(c_25323,plain,
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9591,c_24137]) ).
tcf(c_25325,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9907,c_24137]) ).
tcf(c_25328,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_24137]) ).
tcf(c_25329,plain,
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11031,c_24137]) ).
tcf(c_25331,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11191,c_24137]) ).
tcf(c_25334,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_24137]) ).
tcf(c_25339,plain,
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = sK18 )
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ empty(singleton(iPr_def_10))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_15774,c_24137]) ).
tcf(c_25340,plain,
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = sK18 )
| ~ epsilon_transitive(singleton(iPr_def_11))
| ~ empty(singleton(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_16901,c_24137]) ).
tcf(c_25602,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ empty(set_union2(sK5(iPr_def_11),X0)) ),
inference(superposition,[status(thm)],[c_138,c_24142]) ).
tcf(c_25603,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ empty(set_union2(X0,sK5(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_3397,c_24142]) ).
tcf(c_25604,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ epsilon_transitive(singleton(sK5(iPr_def_11)))
| ~ empty(singleton(sK5(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_3803,c_24142]) ).
tcf(c_25605,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ subset(sK5(iPr_def_11),X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_24142]) ).
tcf(c_25606,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(sK5(iPr_def_11),X1)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_24142]) ).
tcf(c_25607,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(sK5(iPr_def_11),X0)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_24142]) ).
tcf(c_25608,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ subset(sK5(iPr_def_11),X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_24142]) ).
tcf(c_25610,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ empty(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7152,c_24142]) ).
tcf(c_25617,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7261,c_24142]) ).
tcf(c_25618,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9907,c_24142]) ).
tcf(c_25619,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11191,c_24142]) ).
tcf(c_25717,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ empty(singleton(iPr_def_10))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3803,c_24118]) ).
tcf(c_25718,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ~ subset(iPr_def_10,X0)
| ~ in(X2,sK18)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_24118]) ).
tcf(c_25719,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ~ in(iPr_def_10,X1)
| ~ in(X2,sK18)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_24118]) ).
tcf(c_25720,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ~ in(iPr_def_10,X0)
| ~ in(X2,sK18)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_24118]) ).
tcf(c_25721,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ~ subset(iPr_def_10,X1)
| ~ in(X2,sK18)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_24118]) ).
tcf(c_25797,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ empty(singleton(iPr_def_10))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3803,c_24124]) ).
tcf(c_25798,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ~ subset(iPr_def_10,X0)
| ~ in(X2,sK18)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_24124]) ).
tcf(c_25799,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ~ in(iPr_def_10,X1)
| ~ in(X2,sK18)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_24124]) ).
tcf(c_25800,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ~ in(iPr_def_10,X0)
| ~ in(X2,sK18)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_24124]) ).
tcf(c_25801,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ~ subset(iPr_def_10,X1)
| ~ in(X2,sK18)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_24124]) ).
tcf(c_25851,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_138,c_24149]) ).
tcf(c_25852,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(X0)),sK3(iPr_def_11))
| ( sK5(powerset(X0)) = sK3(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3564,c_24149]) ).
tcf(c_25853,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3397,c_24149]) ).
tcf(c_25854,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(empty_set,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = empty_set )
| ~ empty(X0)
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_3420,c_24149]) ).
tcf(c_25857,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_transitive(powerset(X0))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK1(powerset(X0)),sK3(iPr_def_11))
| ( sK1(powerset(X0)) = sK3(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK1(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3566,c_24149]) ).
tcf(c_25858,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(X0))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(powerset(X0)),sK3(iPr_def_11))
| ( sK3(powerset(X0)) = sK3(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK3(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3567,c_24149]) ).
tcf(c_25859,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(X0))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(powerset(X0)),sK3(iPr_def_11))
| ( sK4(powerset(X0)) = sK3(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK4(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3568,c_24149]) ).
tcf(c_25861,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ subset(X2,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_24149]) ).
tcf(c_25862,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(X2,X1)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_24149]) ).
tcf(c_25863,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(X2,X0)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_24149]) ).
tcf(c_25864,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ subset(X2,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_24149]) ).
tcf(c_25865,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(X0)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(X0),sK3(iPr_def_11))
| ( sK3(X0) = sK3(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(sK3(X0),sK18) ),
inference(superposition,[status(thm)],[c_3807,c_24149]) ).
tcf(c_25866,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(X0)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(X0),sK3(iPr_def_11))
| ( sK4(X0) = sK3(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(sK4(X0),sK18) ),
inference(superposition,[status(thm)],[c_3808,c_24149]) ).
tcf(c_25875,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(empty_set)),sK3(iPr_def_11))
| ( sK5(powerset(empty_set)) = sK3(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4163,c_24149]) ).
tcf(c_25880,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(empty_set))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(powerset(empty_set)),sK3(iPr_def_11))
| ( sK3(powerset(empty_set)) = sK3(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK3(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4620,c_24149]) ).
tcf(c_25883,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(empty_set))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(powerset(empty_set)),sK3(iPr_def_11))
| ( sK4(powerset(empty_set)) = sK3(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK4(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4637,c_24149]) ).
tcf(c_25886,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(X0)))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(powerset(X0)))) = sK3(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(sK5(powerset(X0)))),sK18) ),
inference(superposition,[status(thm)],[c_5196,c_24149]) ).
tcf(c_25887,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(empty_set)))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(powerset(empty_set)))) = sK3(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(sK5(powerset(empty_set)))),sK18) ),
inference(superposition,[status(thm)],[c_5250,c_24149]) ).
tcf(c_25889,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(X0)))))) = sK3(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),sK18) ),
inference(superposition,[status(thm)],[c_5252,c_24149]) ).
tcf(c_25899,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))) = sK3(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),sK18) ),
inference(superposition,[status(thm)],[c_5727,c_24149]) ).
tcf(c_25908,plain,
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7152,c_24149]) ).
tcf(c_25910,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_24149]) ).
tcf(c_25915,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_24149]) ).
tcf(c_25916,plain,
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(iPr_def_11))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(iPr_def_11))) = sK3(iPr_def_11) )
| ~ empty(sK18)
| ~ in(sK5(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7587,c_24149]) ).
tcf(c_25919,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9907,c_24149]) ).
tcf(c_25933,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ empty(singleton(iPr_def_10))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_15774,c_24149]) ).
tcf(c_25934,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ epsilon_transitive(singleton(iPr_def_11))
| ~ empty(singleton(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_16901,c_24149]) ).
tcf(c_26128,plain,
( ( iPr_def_11 = sK18 )
| ( iPr_def_11 != iPr_def_11 )
| ( sK18 != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_4142]) ).
tcf(c_26202,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_138,c_24160]) ).
tcf(c_26203,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(X0)),sK4(iPr_def_11))
| ( sK5(powerset(X0)) = sK4(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3564,c_24160]) ).
tcf(c_26204,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X1,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3397,c_24160]) ).
tcf(c_26205,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(empty_set,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = empty_set )
| ~ empty(X0)
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_3420,c_24160]) ).
tcf(c_26208,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_transitive(powerset(X0))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK1(powerset(X0)),sK4(iPr_def_11))
| ( sK1(powerset(X0)) = sK4(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK1(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3566,c_24160]) ).
tcf(c_26209,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(X0))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(powerset(X0)),sK4(iPr_def_11))
| ( sK3(powerset(X0)) = sK4(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK3(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3567,c_24160]) ).
tcf(c_26210,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(X0))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(powerset(X0)),sK4(iPr_def_11))
| ( sK4(powerset(X0)) = sK4(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK4(powerset(X0)),sK18) ),
inference(superposition,[status(thm)],[c_3568,c_24160]) ).
tcf(c_26212,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ subset(X2,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_24160]) ).
tcf(c_26213,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(X2,X1)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_24160]) ).
tcf(c_26214,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(X2,X0)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_24160]) ).
tcf(c_26215,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ subset(X2,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_24160]) ).
tcf(c_26216,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(X0)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(X0),sK4(iPr_def_11))
| ( sK3(X0) = sK4(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(sK3(X0),sK18) ),
inference(superposition,[status(thm)],[c_3807,c_24160]) ).
tcf(c_26217,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(X0)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(X0),sK4(iPr_def_11))
| ( sK4(X0) = sK4(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(sK4(X0),sK18) ),
inference(superposition,[status(thm)],[c_3808,c_24160]) ).
tcf(c_26226,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(empty_set)),sK4(iPr_def_11))
| ( sK5(powerset(empty_set)) = sK4(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4163,c_24160]) ).
tcf(c_26231,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(empty_set))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(powerset(empty_set)),sK4(iPr_def_11))
| ( sK3(powerset(empty_set)) = sK4(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK3(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4620,c_24160]) ).
tcf(c_26234,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(powerset(empty_set))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(powerset(empty_set)),sK4(iPr_def_11))
| ( sK4(powerset(empty_set)) = sK4(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK4(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4637,c_24160]) ).
tcf(c_26237,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(X0)))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(powerset(X0)))) = sK4(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(sK5(powerset(X0)))),sK18) ),
inference(superposition,[status(thm)],[c_5196,c_24160]) ).
tcf(c_26238,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(empty_set)))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(powerset(empty_set)))) = sK4(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(sK5(powerset(empty_set)))),sK18) ),
inference(superposition,[status(thm)],[c_5250,c_24160]) ).
tcf(c_26240,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(X0)))))) = sK4(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),sK18) ),
inference(superposition,[status(thm)],[c_5252,c_24160]) ).
tcf(c_26250,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))) = sK4(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))),sK18) ),
inference(superposition,[status(thm)],[c_5727,c_24160]) ).
tcf(c_26259,plain,
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7152,c_24160]) ).
tcf(c_26261,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_24160]) ).
tcf(c_26266,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_24160]) ).
tcf(c_26267,plain,
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(iPr_def_11))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(iPr_def_11))) = sK4(iPr_def_11) )
| ~ empty(sK18)
| ~ in(sK5(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7587,c_24160]) ).
tcf(c_26276,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11191,c_24160]) ).
tcf(c_26284,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ empty(singleton(iPr_def_10))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_15774,c_24160]) ).
tcf(c_26285,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ epsilon_transitive(singleton(iPr_def_11))
| ~ empty(singleton(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_16901,c_24160]) ).
tcf(c_26554,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X1,X2)),X0)
| in(sK2(X0,X1,set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X0,X1) = set_union2(X1,X2) )
| ~ in(sK2(X0,X1,set_union2(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_68,c_4095]) ).
tcf(c_26555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_union2(set_union2(X2,X3),X4) = set_union2(X0,X1) )
| ~ in(sK2(X0,X1,set_union2(set_union2(X2,X3),X4)),X2)
| ~ in(sK2(X0,X1,set_union2(set_union2(X2,X3),X4)),X1) ),
inference(superposition,[status(thm)],[c_69,c_4095]) ).
tcf(c_26556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_union2(set_union2(X2,X3),X4) = set_union2(X0,X1) )
| ~ in(sK2(X0,X1,set_union2(set_union2(X2,X3),X4)),X3)
| ~ in(sK2(X0,X1,set_union2(set_union2(X2,X3),X4)),X1) ),
inference(superposition,[status(thm)],[c_70,c_4095]) ).
tcf(c_26557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)))
| ( set_union2(sK5(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_13652,c_4095]) ).
tcf(c_26558,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(sK5(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)) = sK5(iPr_def_11) )
| ~ in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_7241,c_4095]) ).
tcf(c_26559,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)))
| ( set_union2(sK5(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)) = sK5(iPr_def_11) )
| ~ in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_7238,c_4095]) ).
tcf(c_26560,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(sK5(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)) = sK5(iPr_def_11) )
| ~ empty(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)))
| ~ in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_7263,c_4095]) ).
tcf(c_26561,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)))
| ( set_union2(sK5(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)) = sK5(iPr_def_11) )
| ~ in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_7155,c_4095]) ).
tcf(c_26562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)))
| ( set_union2(sK3(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_13640,c_4095]) ).
tcf(c_26563,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(sK3(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)) = sK3(iPr_def_11) )
| ~ in(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_9904,c_4095]) ).
tcf(c_26564,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)))
| ( set_union2(sK3(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)) = sK3(iPr_def_11) )
| ~ in(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_9901,c_4095]) ).
tcf(c_26565,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(sK3(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)) = sK3(iPr_def_11) )
| ~ empty(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)))
| ~ in(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_9927,c_4095]) ).
tcf(c_26566,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)))
| ( set_union2(sK3(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)) = sK3(iPr_def_11) )
| ~ in(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_9595,c_4095]) ).
tcf(c_26567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X3)
| in(sK4(iPr_def_11),sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)))
| ( set_union2(sK4(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_13646,c_4095]) ).
tcf(c_26568,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(sK4(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_11188,c_4095]) ).
tcf(c_26569,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)))
| ( set_union2(sK4(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_11185,c_4095]) ).
tcf(c_26570,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(sK4(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)) = sK4(iPr_def_11) )
| ~ empty(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)))
| ~ in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_11211,c_4095]) ).
tcf(c_26571,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)))
| ( set_union2(sK4(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_11035,c_4095]) ).
tcf(c_26572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_union2(X0,X1) = set_union2(X2,X3) )
| ~ in(sK2(X0,X1,set_union2(X3,X2)),X2)
| ~ in(sK2(X0,X1,set_union2(X2,X3)),X1) ),
inference(superposition,[status(thm)],[c_58,c_4095]) ).
tcf(c_26574,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = set_union2(X2,X2) )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,set_union2(X2,X2)),X1) ),
inference(superposition,[status(thm)],[c_97,c_4095]) ).
tcf(c_26575,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = set_union2(X2,empty_set) )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,set_union2(X2,empty_set)),X1) ),
inference(superposition,[status(thm)],[c_126,c_4095]) ).
tcf(c_26576,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = set_union2(empty_set,X2) )
| ~ in(sK2(X0,X1,X2),empty_set)
| ~ in(sK2(X0,X1,set_union2(empty_set,X2)),X1) ),
inference(superposition,[status(thm)],[c_3423,c_4095]) ).
tcf(c_26577,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = set_union2(iPr_def_10,sK18) )
| ~ in(sK2(X0,X1,iPr_def_11),iPr_def_10)
| ~ in(sK2(X0,X1,set_union2(iPr_def_10,sK18)),X1) ),
inference(superposition,[status(thm)],[c_3424,c_4095]) ).
tcf(c_26578,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = iPr_def_11 )
| ~ in(sK2(X0,X1,iPr_def_11),iPr_def_10)
| ~ in(sK2(X0,X1,iPr_def_11),X1) ),
inference(light_normalisation,[status(thm)],[c_26577,c_3424]) ).
tcf(c_26770,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ subset(set_union2(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_25149,c_359]) ).
tcf(c_26771,plain,
! [X0: $i,X1: $i] :
( element(sK18,X1)
| ~ subset(set_union2(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_25149,c_358]) ).
tcf(c_26772,plain,
! [X0: $i,X1: $i] :
( in(sK18,X0)
| in(X0,sK18)
| ( X0 = sK18 )
| ~ epsilon_connected(set_union2(X1,iPr_def_10))
| ~ in(X0,set_union2(X1,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_25149,c_77]) ).
tcf(c_26773,plain,
! [X0: $i] :
( subset(sK18,set_union2(X0,iPr_def_10))
| ~ epsilon_transitive(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_25149,c_65]) ).
tcf(c_26809,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_138,c_24084]) ).
tcf(c_26810,plain,
! [X0: $i] :
( epsilon_transitive(sK5(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3564,c_24084]) ).
tcf(c_26811,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3397,c_24084]) ).
tcf(c_26815,plain,
! [X0: $i] :
( epsilon_transitive(powerset(X0))
| epsilon_transitive(sK1(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3566,c_24084]) ).
tcf(c_26816,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| epsilon_transitive(sK3(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3567,c_24084]) ).
tcf(c_26817,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| epsilon_transitive(sK4(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3568,c_24084]) ).
tcf(c_26819,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(X2)
| ~ subset(X2,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_24084]) ).
tcf(c_26820,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(X2)
| ~ in(X2,X1)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_24084]) ).
tcf(c_26821,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(X2)
| ~ in(X2,X0)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_24084]) ).
tcf(c_26822,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(X2)
| ~ subset(X2,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_24084]) ).
tcf(c_26823,plain,
! [X0: $i] :
( epsilon_connected(X0)
| epsilon_transitive(sK3(X0))
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3807,c_24084]) ).
tcf(c_26824,plain,
! [X0: $i] :
( epsilon_connected(X0)
| epsilon_transitive(sK4(X0))
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3808,c_24084]) ).
tcf(c_26833,plain,
! [X0: $i] :
( epsilon_transitive(sK5(powerset(empty_set)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4163,c_24084]) ).
tcf(c_26838,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| epsilon_transitive(sK3(powerset(empty_set)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4620,c_24084]) ).
tcf(c_26841,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| epsilon_transitive(sK4(powerset(empty_set)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4637,c_24084]) ).
tcf(c_26844,plain,
! [X0: $i] :
( epsilon_transitive(sK5(powerset(sK5(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5196,c_24084]) ).
tcf(c_26845,plain,
! [X0: $i] :
( epsilon_transitive(sK5(powerset(sK5(powerset(empty_set)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5250,c_24084]) ).
tcf(c_26847,plain,
! [X0: $i] :
( epsilon_transitive(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5252,c_24084]) ).
tcf(c_26857,plain,
! [X0: $i] :
( epsilon_transitive(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5727,c_24084]) ).
tcf(c_26868,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_24084]) ).
tcf(c_26873,plain,
! [X0: $i] :
( epsilon_transitive(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7261,c_24084]) ).
tcf(c_26874,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| epsilon_transitive(sK5(powerset(sK5(iPr_def_11))))
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_7587,c_24084]) ).
tcf(c_26875,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_9591,c_24084]) ).
tcf(c_26877,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_transitive(X0)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9907,c_24084]) ).
tcf(c_26880,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9925,c_24084]) ).
tcf(c_26881,plain,
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_11031,c_24084]) ).
tcf(c_26883,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_transitive(X0)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11191,c_24084]) ).
tcf(c_26886,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11209,c_24084]) ).
tcf(c_27003,plain,
( epsilon_transitive(sK5(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_26833]) ).
tcf(c_27004,plain,
( epsilon_transitive(sK5(powerset(sK5(powerset(empty_set)))))
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_26845]) ).
tcf(c_27084,plain,
! [X0: $i,X1: $i] :
( ~ subset(iPr_def_10,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_24093]) ).
tcf(c_27085,plain,
! [X0: $i,X1: $i] :
( ~ in(iPr_def_10,X1)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_24093]) ).
tcf(c_27086,plain,
! [X0: $i,X1: $i] :
( ~ in(iPr_def_10,X0)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_24093]) ).
tcf(c_27087,plain,
! [X0: $i,X1: $i] :
( ~ subset(iPr_def_10,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_24093]) ).
tcf(c_27143,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ empty(set_union2(sK3(iPr_def_11),X0)) ),
inference(superposition,[status(thm)],[c_138,c_24154]) ).
tcf(c_27144,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ empty(set_union2(X0,sK3(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_3397,c_24154]) ).
tcf(c_27145,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ epsilon_transitive(singleton(sK3(iPr_def_11)))
| ~ empty(singleton(sK3(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_3803,c_24154]) ).
tcf(c_27146,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ subset(sK3(iPr_def_11),X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_24154]) ).
tcf(c_27147,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(sK3(iPr_def_11),X1)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_24154]) ).
tcf(c_27148,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(sK3(iPr_def_11),X0)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_24154]) ).
tcf(c_27149,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ subset(sK3(iPr_def_11),X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_24154]) ).
tcf(c_27151,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7244,c_24154]) ).
tcf(c_27152,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ empty(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9591,c_24154]) ).
tcf(c_27157,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9925,c_24154]) ).
tcf(c_27306,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ empty(set_union2(sK4(iPr_def_11),X0)) ),
inference(superposition,[status(thm)],[c_138,c_24165]) ).
tcf(c_27307,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ empty(set_union2(X0,sK4(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_3397,c_24165]) ).
tcf(c_27308,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ epsilon_transitive(singleton(sK4(iPr_def_11)))
| ~ empty(singleton(sK4(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_3803,c_24165]) ).
tcf(c_27309,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ subset(sK4(iPr_def_11),X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_24165]) ).
tcf(c_27310,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(sK4(iPr_def_11),X1)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_24165]) ).
tcf(c_27311,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ in(sK4(iPr_def_11),X0)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_24165]) ).
tcf(c_27312,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ~ in(X2,sK18)
| ~ subset(sK4(iPr_def_11),X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_24165]) ).
tcf(c_27314,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7244,c_24165]) ).
tcf(c_27316,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11031,c_24165]) ).
tcf(c_27321,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11209,c_24165]) ).
tcf(c_27439,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_union2(X1,X2)),X0)
| in(sK2(X0,X0,set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X0,X0) = set_union2(X1,X2) )
| ~ in(sK2(X0,X0,set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_68,c_4096]) ).
tcf(c_27440,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_union2(X1,X2),set_union2(X1,X2)),X0)
| in(sK2(X0,set_union2(X1,X2),set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X0,set_union2(X1,X2)) = set_union2(X1,X2) )
| ~ in(sK2(X0,set_union2(X1,X2),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_68,c_4096]) ).
tcf(c_27441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_union2(X2,X3)),X0)
| in(sK2(X0,X1,set_union2(X2,X3)),set_union2(X2,X3))
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ~ in(sK2(X0,X1,set_union2(X2,X3)),X3) ),
inference(superposition,[status(thm)],[c_68,c_4096]) ).
tcf(c_27442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_union2(X0,set_union2(X1,X2)) = set_union2(X3,X4) )
| ~ in(sK2(X0,set_union2(X1,X2),set_union2(X3,X4)),X4)
| ~ in(sK2(X0,set_union2(X1,X2),set_union2(X3,X4)),X1) ),
inference(superposition,[status(thm)],[c_69,c_4096]) ).
tcf(c_27443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_union2(X0,set_union2(X1,X2)) = set_union2(X3,X4) )
| ~ in(sK2(X0,set_union2(X1,X2),set_union2(X3,X4)),X4)
| ~ in(sK2(X0,set_union2(X1,X2),set_union2(X3,X4)),X2) ),
inference(superposition,[status(thm)],[c_70,c_4096]) ).
tcf(c_27444,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)))
| ( set_union2(X0,sK5(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_13652,c_4096]) ).
tcf(c_27445,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,sK5(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)) = sK5(iPr_def_11) )
| ~ in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_7241,c_4096]) ).
tcf(c_27446,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)))
| ( set_union2(X0,sK5(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)) = sK5(iPr_def_11) )
| ~ in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_7238,c_4096]) ).
tcf(c_27447,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,sK5(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)) = sK5(iPr_def_11) )
| ~ empty(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)))
| ~ in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_7263,c_4096]) ).
tcf(c_27448,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)))
| ( set_union2(X0,sK5(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)) = sK5(iPr_def_11) )
| ~ in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_7155,c_4096]) ).
tcf(c_27449,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)))
| ( set_union2(X0,sK3(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_13640,c_4096]) ).
tcf(c_27450,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(X0,sK3(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)) = sK3(iPr_def_11) )
| ~ in(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_9904,c_4096]) ).
tcf(c_27451,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)))
| ( set_union2(X0,sK3(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)) = sK3(iPr_def_11) )
| ~ in(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_9901,c_4096]) ).
tcf(c_27452,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,sK3(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)) = sK3(iPr_def_11) )
| ~ empty(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)))
| ~ in(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_9927,c_4096]) ).
tcf(c_27453,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)))
| ( set_union2(X0,sK3(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)) = sK3(iPr_def_11) )
| ~ in(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_9595,c_4096]) ).
tcf(c_27454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X3)
| in(sK4(iPr_def_11),sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)))
| ( set_union2(X0,sK4(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_13646,c_4096]) ).
tcf(c_27455,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(X0,sK4(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_11188,c_4096]) ).
tcf(c_27456,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)))
| ( set_union2(X0,sK4(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_11185,c_4096]) ).
tcf(c_27457,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,sK4(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)) = sK4(iPr_def_11) )
| ~ empty(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)))
| ~ in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_11211,c_4096]) ).
tcf(c_27458,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)))
| ( set_union2(X0,sK4(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_11035,c_4096]) ).
tcf(c_27459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_union2(X0,X1) = set_union2(X2,X3) )
| ~ in(sK2(X0,X1,set_union2(X3,X2)),X1)
| ~ in(sK2(X0,X1,set_union2(X2,X3)),X3) ),
inference(superposition,[status(thm)],[c_58,c_4096]) ).
tcf(c_27461,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = set_union2(X2,X2) )
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,set_union2(X2,X2)),X2) ),
inference(superposition,[status(thm)],[c_97,c_4096]) ).
tcf(c_27462,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = set_union2(X2,empty_set) )
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,set_union2(X2,empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_126,c_4096]) ).
tcf(c_27463,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = set_union2(empty_set,X2) )
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,set_union2(empty_set,X2)),X2) ),
inference(superposition,[status(thm)],[c_3423,c_4096]) ).
tcf(c_27464,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = set_union2(iPr_def_10,sK18) )
| ~ in(sK2(X0,X1,iPr_def_11),X1)
| ~ in(sK2(X0,X1,set_union2(iPr_def_10,sK18)),sK18) ),
inference(superposition,[status(thm)],[c_3424,c_4096]) ).
tcf(c_27465,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = iPr_def_11 )
| ~ in(sK2(X0,X1,iPr_def_11),sK18)
| ~ in(sK2(X0,X1,iPr_def_11),X1) ),
inference(light_normalisation,[status(thm)],[c_27464,c_3424]) ).
tcf(c_27488,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_union2(X1,X2)),X0)
| in(sK2(X0,X0,set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X1,X2) = X0 )
| ~ in(sK2(X0,X0,set_union2(X1,X2)),X2) ),
inference(light_normalisation,[status(thm)],[c_27439,c_97]) ).
tcf(c_27653,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_138,c_24090]) ).
tcf(c_27654,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3564,c_24090]) ).
tcf(c_27655,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3397,c_24090]) ).
tcf(c_27659,plain,
! [X0: $i] :
( epsilon_transitive(powerset(X0))
| epsilon_connected(sK1(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3566,c_24090]) ).
tcf(c_27660,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| epsilon_connected(sK3(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3567,c_24090]) ).
tcf(c_27661,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| epsilon_connected(sK4(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3568,c_24090]) ).
tcf(c_27663,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(X2)
| ~ subset(X2,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_24090]) ).
tcf(c_27664,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(X2)
| ~ in(X2,X1)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_24090]) ).
tcf(c_27665,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(X2)
| ~ in(X2,X0)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_24090]) ).
tcf(c_27666,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(X2)
| ~ subset(X2,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_24090]) ).
tcf(c_27667,plain,
! [X0: $i] :
( epsilon_connected(X0)
| epsilon_connected(sK3(X0))
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3807,c_24090]) ).
tcf(c_27668,plain,
! [X0: $i] :
( epsilon_connected(X0)
| epsilon_connected(sK4(X0))
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3808,c_24090]) ).
tcf(c_27677,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(empty_set)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4163,c_24090]) ).
tcf(c_27682,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| epsilon_connected(sK3(powerset(empty_set)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4620,c_24090]) ).
tcf(c_27685,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| epsilon_connected(sK4(powerset(empty_set)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4637,c_24090]) ).
tcf(c_27688,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(sK5(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5196,c_24090]) ).
tcf(c_27689,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(sK5(powerset(empty_set)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5250,c_24090]) ).
tcf(c_27691,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5252,c_24090]) ).
tcf(c_27701,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5727,c_24090]) ).
tcf(c_27712,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_24090]) ).
tcf(c_27717,plain,
! [X0: $i] :
( epsilon_connected(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7261,c_24090]) ).
tcf(c_27718,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| epsilon_connected(sK5(powerset(sK5(iPr_def_11))))
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_7587,c_24090]) ).
tcf(c_27719,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_9591,c_24090]) ).
tcf(c_27721,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(X0)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9907,c_24090]) ).
tcf(c_27724,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9925,c_24090]) ).
tcf(c_27725,plain,
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_11031,c_24090]) ).
tcf(c_27727,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(X0)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11191,c_24090]) ).
tcf(c_27730,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11209,c_24090]) ).
tcf(c_27847,plain,
( epsilon_connected(sK5(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_27677]) ).
tcf(c_27848,plain,
( epsilon_connected(sK5(powerset(sK5(powerset(empty_set)))))
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_27689]) ).
tcf(c_28105,plain,
! [X0: $i] :
( subset(sK18,set_union2(X0,iPr_def_10))
| ~ epsilon_transitive(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_58,c_25173]) ).
tcf(c_28107,plain,
( subset(sK18,iPr_def_10)
| ~ epsilon_transitive(set_union2(iPr_def_10,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_97,c_25173]) ).
tcf(c_28108,plain,
( subset(sK18,iPr_def_10)
| ~ epsilon_transitive(set_union2(iPr_def_10,empty_set)) ),
inference(superposition,[status(thm)],[c_126,c_25173]) ).
tcf(c_28115,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),set_union2(iPr_def_10,X0))
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_25173,c_13671]) ).
tcf(c_28116,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),set_union2(iPr_def_10,X0))
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_25173,c_13665]) ).
tcf(c_28117,plain,
! [X0: $i] :
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),set_union2(iPr_def_10,X0))
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_25173,c_13657]) ).
tcf(c_28118,plain,
! [X0: $i,X1: $i] :
( subset(X1,set_union2(iPr_def_10,X0))
| ~ subset(X1,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_25173,c_128]) ).
tcf(c_28165,plain,
epsilon_transitive(sK5(powerset(empty_set))),
inference(global_subsumption_just,[status(thm)],[c_26833,c_95,c_27003]) ).
tcf(c_28210,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_7253]) ).
tcf(c_28212,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(sK5(iPr_def_11)))
| ( singleton(set_union2(sK5(iPr_def_11),sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(sK5(iPr_def_11),sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_7253]) ).
tcf(c_28213,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(sK5(iPr_def_11)))
| ( singleton(set_union2(sK5(iPr_def_11),empty_set)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(sK5(iPr_def_11),empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_126,c_7253]) ).
tcf(c_28214,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ empty(X1)
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK18)
| ~ subset(singleton(set_union2(sK5(iPr_def_11),X0)),X1) ),
inference(superposition,[status(thm)],[c_7253,c_359]) ).
tcf(c_28215,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X1)
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK18)
| ~ subset(singleton(set_union2(sK5(iPr_def_11),X0)),X1) ),
inference(superposition,[status(thm)],[c_7253,c_358]) ).
tcf(c_28216,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( singleton(set_union2(sK5(iPr_def_11),X1)) = sK5(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(sK5(iPr_def_11),X1)))
| ~ in(singleton(set_union2(sK5(iPr_def_11),X1)),sK18)
| ~ in(X0,singleton(set_union2(sK5(iPr_def_11),X1))) ),
inference(superposition,[status(thm)],[c_7253,c_77]) ).
tcf(c_28217,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(sK5(iPr_def_11),X0)))
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_7253,c_65]) ).
tcf(c_28218,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK18)
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7253,c_49]) ).
tcf(c_28220,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_7253,c_127]) ).
tcf(c_28259,plain,
( subset(sK1(set_union2(sK18,singleton(sK18))),sK18)
| ~ epsilon_transitive(sK18)
| ~ in(sK1(set_union2(sK18,singleton(sK18))),sK18) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_28273,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_7254]) ).
tcf(c_28276,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(sK5(iPr_def_11)))
| ( singleton(set_union2(empty_set,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(empty_set,sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_7254]) ).
tcf(c_28277,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ empty(X1)
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK18)
| ~ subset(singleton(set_union2(X0,sK5(iPr_def_11))),X1) ),
inference(superposition,[status(thm)],[c_7254,c_359]) ).
tcf(c_28278,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X1)
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK18)
| ~ subset(singleton(set_union2(X0,sK5(iPr_def_11))),X1) ),
inference(superposition,[status(thm)],[c_7254,c_358]) ).
tcf(c_28279,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( singleton(set_union2(X1,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X1,sK5(iPr_def_11))))
| ~ in(singleton(set_union2(X1,sK5(iPr_def_11))),sK18)
| ~ in(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_7254,c_77]) ).
tcf(c_28280,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(X0,sK5(iPr_def_11))))
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7254,c_65]) ).
tcf(c_28281,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK18)
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7254,c_49]) ).
tcf(c_28283,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7254,c_127]) ).
tcf(c_28359,plain,
( ~ in(sK5(sK18),sK18)
| ~ epsilon_transitive(iPr_def_10)
| ( sK5(sK18) = sK5(iPr_def_11) )
| in(sK5(sK18),sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_17599,c_7170,c_17599]) ).
tcf(c_28360,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK5(iPr_def_11))
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18) ),
inference(renaming,[status(thm)],[c_28359]) ).
tcf(c_28367,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK5(iPr_def_11))
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28360,c_127]) ).
tcf(c_28383,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(sK5(sK18),sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_28367,c_359]) ).
tcf(c_28384,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| element(sK5(sK18),X0)
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_28367,c_358]) ).
tcf(c_28385,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(sK18))
| in(sK5(sK18),X0)
| ( sK5(sK18) = X0 )
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(sK5(sK18),sK18)
| ~ in(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_28367,c_77]) ).
tcf(c_28386,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(sK18),sK5(iPr_def_11))
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_28367,c_65]) ).
tcf(c_28387,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18)
| ~ in(sK5(iPr_def_11),sK5(sK18)) ),
inference(superposition,[status(thm)],[c_28367,c_49]) ).
tcf(c_28388,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK5(iPr_def_11))
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_28367,c_137]) ).
tcf(c_28389,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| element(sK5(sK18),sK5(iPr_def_11))
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_28367,c_127]) ).
tcf(c_28390,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK5(sK18))
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_28367,c_23189]) ).
tcf(c_28448,plain,
! [X0: $i] :
( subset(sK18,set_union2(iPr_def_10,X0))
| ~ epsilon_transitive(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_58,c_26773]) ).
tcf(c_28451,plain,
( subset(sK18,iPr_def_10)
| ~ epsilon_transitive(set_union2(empty_set,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_3423,c_26773]) ).
tcf(c_28457,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),set_union2(X0,iPr_def_10))
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_26773,c_13671]) ).
tcf(c_28458,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),set_union2(X0,iPr_def_10))
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_26773,c_13665]) ).
tcf(c_28459,plain,
! [X0: $i] :
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),set_union2(X0,iPr_def_10))
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_26773,c_13657]) ).
tcf(c_28460,plain,
! [X0: $i,X1: $i] :
( subset(X1,set_union2(X0,iPr_def_10))
| ~ subset(X1,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_26773,c_128]) ).
tcf(c_28506,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),set_union2(X0,iPr_def_10))
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_28105,c_13671]) ).
tcf(c_28507,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),set_union2(X0,iPr_def_10))
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_28105,c_13665]) ).
tcf(c_28508,plain,
! [X0: $i] :
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),set_union2(X0,iPr_def_10))
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_28105,c_13657]) ).
tcf(c_28509,plain,
! [X0: $i,X1: $i] :
( subset(X1,set_union2(X0,iPr_def_10))
| ~ subset(X1,sK18)
| ~ epsilon_transitive(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_28105,c_128]) ).
tcf(c_28551,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),set_union2(iPr_def_10,X0))
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_28448,c_13671]) ).
tcf(c_28552,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),set_union2(iPr_def_10,X0))
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_28448,c_13665]) ).
tcf(c_28553,plain,
! [X0: $i] :
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),set_union2(iPr_def_10,X0))
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_28448,c_13657]) ).
tcf(c_28554,plain,
! [X0: $i,X1: $i] :
( subset(X1,set_union2(iPr_def_10,X0))
| ~ subset(X1,sK18)
| ~ epsilon_transitive(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_28448,c_128]) ).
tcf(c_28779,plain,
epsilon_connected(sK5(powerset(empty_set))),
inference(global_subsumption_just,[status(thm)],[c_27677,c_95,c_27847]) ).
tcf(c_28810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,sK0(X3,set_union2(X0,X1)))
| in(sK0(X3,set_union2(X0,X1)),X2)
| ( set_union2(X0,X1) = singleton(X3) )
| ( sK0(X3,set_union2(X0,X1)) = X3 )
| ( sK0(X3,set_union2(X0,X1)) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_60,c_4212]) ).
tcf(c_28811,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X0,X1))
| in(X2,sK1(set_union2(X0,X1)))
| in(sK1(set_union2(X0,X1)),X2)
| ( sK1(set_union2(X0,X1)) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_64,c_4212]) ).
tcf(c_28812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(set_union2(X0,X1),X3,X4))
| in(sK2(set_union2(X0,X1),X3,X4),X4)
| in(sK2(set_union2(X0,X1),X3,X4),X3)
| in(sK2(set_union2(X0,X1),X3,X4),X2)
| ( set_union2(set_union2(X0,X1),X3) = X4 )
| ( sK2(set_union2(X0,X1),X3,X4) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_68,c_4212]) ).
tcf(c_28813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(X3,X4,set_union2(X0,X1)))
| in(sK2(X3,X4,set_union2(X0,X1)),X4)
| in(sK2(X3,X4,set_union2(X0,X1)),X3)
| in(sK2(X3,X4,set_union2(X0,X1)),X2)
| ( set_union2(X0,X1) = set_union2(X3,X4) )
| ( sK2(X3,X4,set_union2(X0,X1)) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_68,c_4212]) ).
tcf(c_28814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(X3,set_union2(X0,X1),X4))
| in(sK2(X3,set_union2(X0,X1),X4),X4)
| in(sK2(X3,set_union2(X0,X1),X4),X3)
| in(sK2(X3,set_union2(X0,X1),X4),X2)
| ( set_union2(X3,set_union2(X0,X1)) = X4 )
| ( sK2(X3,set_union2(X0,X1),X4) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_68,c_4212]) ).
tcf(c_28815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| in(X2,X3)
| ( X2 = X3 )
| ~ in(X3,X0)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_69,c_4212]) ).
tcf(c_28816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| in(X2,X3)
| ( X2 = X3 )
| ~ in(X3,X0)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_70,c_4212]) ).
tcf(c_28819,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_union2(X0,X1))
| in(X2,sK5(set_union2(X0,X1)))
| in(sK5(set_union2(X0,X1)),X2)
| ( sK5(set_union2(X0,X1)) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3768,c_4212]) ).
tcf(c_28820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK0(X3,set_union2(set_union2(X0,X1),X4)))
| in(sK0(X3,set_union2(set_union2(X0,X1),X4)),X4)
| in(sK0(X3,set_union2(set_union2(X0,X1),X4)),X2)
| ( set_union2(set_union2(X0,X1),X4) = singleton(X3) )
| ( sK0(X3,set_union2(set_union2(X0,X1),X4)) = X3 )
| ( sK0(X3,set_union2(set_union2(X0,X1),X4)) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4023,c_4212]) ).
tcf(c_28821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK0(X3,set_union2(X4,set_union2(X0,X1))))
| in(sK0(X3,set_union2(X4,set_union2(X0,X1))),X4)
| in(sK0(X3,set_union2(X4,set_union2(X0,X1))),X2)
| ( set_union2(X4,set_union2(X0,X1)) = singleton(X3) )
| ( sK0(X3,set_union2(X4,set_union2(X0,X1))) = X3 )
| ( sK0(X3,set_union2(X4,set_union2(X0,X1))) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4023,c_4212]) ).
tcf(c_28822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(set_union2(set_union2(X0,X1),X3))
| in(X2,sK1(set_union2(set_union2(X0,X1),X3)))
| in(sK1(set_union2(set_union2(X0,X1),X3)),X3)
| in(sK1(set_union2(set_union2(X0,X1),X3)),X2)
| ( sK1(set_union2(set_union2(X0,X1),X3)) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4024,c_4212]) ).
tcf(c_28823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(set_union2(X3,set_union2(X0,X1)))
| in(X2,sK1(set_union2(X3,set_union2(X0,X1))))
| in(sK1(set_union2(X3,set_union2(X0,X1))),X3)
| in(sK1(set_union2(X3,set_union2(X0,X1))),X2)
| ( sK1(set_union2(X3,set_union2(X0,X1))) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4024,c_4212]) ).
tcf(c_28824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(set_union2(set_union2(X0,X1),X3))
| in(X2,sK3(set_union2(set_union2(X0,X1),X3)))
| in(sK3(set_union2(set_union2(X0,X1),X3)),X3)
| in(sK3(set_union2(set_union2(X0,X1),X3)),X2)
| ( sK3(set_union2(set_union2(X0,X1),X3)) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4027,c_4212]) ).
tcf(c_28825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(set_union2(X3,set_union2(X0,X1)))
| in(X2,sK3(set_union2(X3,set_union2(X0,X1))))
| in(sK3(set_union2(X3,set_union2(X0,X1))),X3)
| in(sK3(set_union2(X3,set_union2(X0,X1))),X2)
| ( sK3(set_union2(X3,set_union2(X0,X1))) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4027,c_4212]) ).
tcf(c_28826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(set_union2(set_union2(X0,X1),X3))
| in(X2,sK4(set_union2(set_union2(X0,X1),X3)))
| in(sK4(set_union2(set_union2(X0,X1),X3)),X3)
| in(sK4(set_union2(set_union2(X0,X1),X3)),X2)
| ( sK4(set_union2(set_union2(X0,X1),X3)) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4028,c_4212]) ).
tcf(c_28827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(set_union2(X3,set_union2(X0,X1)))
| in(X2,sK4(set_union2(X3,set_union2(X0,X1))))
| in(sK4(set_union2(X3,set_union2(X0,X1))),X3)
| in(sK4(set_union2(X3,set_union2(X0,X1))),X2)
| ( sK4(set_union2(X3,set_union2(X0,X1))) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4028,c_4212]) ).
tcf(c_28828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(set_union2(set_union2(X0,X1),X3))
| in(X2,sK5(set_union2(set_union2(X0,X1),X3)))
| in(sK5(set_union2(set_union2(X0,X1),X3)),X3)
| in(sK5(set_union2(set_union2(X0,X1),X3)),X2)
| ( sK5(set_union2(set_union2(X0,X1),X3)) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4029,c_4212]) ).
tcf(c_28829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(set_union2(X3,set_union2(X0,X1)))
| in(X2,sK5(set_union2(X3,set_union2(X0,X1))))
| in(sK5(set_union2(X3,set_union2(X0,X1))),X3)
| in(sK5(set_union2(X3,set_union2(X0,X1))),X2)
| ( sK5(set_union2(X3,set_union2(X0,X1))) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4029,c_4212]) ).
tcf(c_28830,plain,
! [X0: $i,X1: $i] :
( in(sK18,X1)
| in(X1,sK18)
| ( X1 = sK18 )
| ~ in(X1,X0)
| ~ epsilon_connected(set_union2(X0,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15062,c_4212]) ).
tcf(c_28831,plain,
! [X0: $i,X1: $i] :
( in(sK18,X1)
| in(X1,sK18)
| ( X1 = sK18 )
| ~ in(X1,iPr_def_11)
| ~ epsilon_connected(set_union2(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_15059,c_4212]) ).
tcf(c_28832,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ subset(iPr_def_11,set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_23181,c_4212]) ).
tcf(c_28833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK5(iPr_def_11),X3)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_4212]) ).
tcf(c_28834,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_4212]) ).
tcf(c_28835,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ empty(sK5(iPr_def_11))
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7246,c_4212]) ).
tcf(c_28836,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_4212]) ).
tcf(c_28837,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_4212]) ).
tcf(c_28838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X3)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_4212]) ).
tcf(c_28839,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_4212]) ).
tcf(c_28840,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_4212]) ).
tcf(c_28841,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_4212]) ).
tcf(c_28842,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_4212]) ).
tcf(c_28843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X3)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_4212]) ).
tcf(c_28844,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_4212]) ).
tcf(c_28845,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ empty(sK4(iPr_def_11))
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11193,c_4212]) ).
tcf(c_28846,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_4212]) ).
tcf(c_28847,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_4212]) ).
tcf(c_28848,plain,
! [X0: $i,X1: $i] :
( in(sK18,X1)
| in(X1,sK18)
| ( X1 = sK18 )
| ~ in(X1,iPr_def_10)
| ~ epsilon_connected(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_25148,c_4212]) ).
tcf(c_28849,plain,
! [X0: $i,X1: $i] :
( in(sK18,X1)
| in(X1,sK18)
| ( X1 = sK18 )
| ~ in(X1,X0)
| ~ epsilon_connected(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_25149,c_4212]) ).
tcf(c_28850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X0)
| in(X0,X3)
| ( X0 = X3 )
| ~ in(X3,X2)
| ~ epsilon_connected(set_union2(X2,X1))
| ~ in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_58,c_4212]) ).
tcf(c_28852,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| in(X1,X2)
| ( X1 = X2 )
| ~ in(X2,X0)
| ~ in(X1,X0)
| ~ epsilon_connected(set_union2(X0,X0)) ),
inference(superposition,[status(thm)],[c_97,c_4212]) ).
tcf(c_28853,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| in(X1,X2)
| ( X1 = X2 )
| ~ in(X2,X0)
| ~ in(X1,X0)
| ~ epsilon_connected(set_union2(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_126,c_4212]) ).
tcf(c_28854,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| in(X1,X2)
| ( X1 = X2 )
| ~ in(X2,empty_set)
| ~ in(X1,X0)
| ~ epsilon_connected(set_union2(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_3423,c_4212]) ).
tcf(c_28855,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ in(X1,iPr_def_10)
| ~ in(X0,iPr_def_11)
| ~ epsilon_connected(set_union2(iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_3424,c_4212]) ).
tcf(c_28876,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X1,iPr_def_10)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_28855,c_3424]) ).
tcf(c_28883,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X0,X2)
| ( X0 = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,empty_set)
| ~ in(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_28854,c_3423]) ).
tcf(c_29286,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X0))
| ~ empty(X1)
| ~ subset(X2,X0)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_3769,c_359]) ).
tcf(c_29287,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X0))
| element(X2,X1)
| ~ subset(X2,X0)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_3769,c_358]) ).
tcf(c_29288,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X1))
| in(X2,X0)
| in(X0,X2)
| ( X0 = X2 )
| ~ epsilon_connected(powerset(X1))
| ~ subset(X2,X1)
| ~ in(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_3769,c_77]) ).
tcf(c_29289,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| subset(X0,powerset(X1))
| ~ epsilon_transitive(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3769,c_65]) ).
tcf(c_29290,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_3769,c_49]) ).
tcf(c_29293,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X0))
| ( set_union2(powerset(X0),X1) = X2 )
| ~ subset(sK2(powerset(X0),X1,X2),X0)
| ~ in(sK2(powerset(X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_3769,c_66]) ).
tcf(c_29294,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| ( set_union2(X0,X1) = powerset(X2) )
| ~ subset(sK2(X0,X1,powerset(X2)),X2)
| ~ in(sK2(X0,X1,powerset(X2)),X1) ),
inference(superposition,[status(thm)],[c_3769,c_67]) ).
tcf(c_29295,plain,
! [X0: $i] :
( empty(powerset(X0))
| ~ subset(singleton(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_3769,c_3522]) ).
tcf(c_29296,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| ~ in(powerset(X2),X1)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_3769,c_3641]) ).
tcf(c_29297,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| ~ in(powerset(X2),X0)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_3769,c_3615]) ).
tcf(c_29298,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X0))
| ~ subset(singleton(set_union2(powerset(X0),X1)),X0) ),
inference(superposition,[status(thm)],[c_3769,c_3618]) ).
tcf(c_29299,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ subset(singleton(set_union2(X0,powerset(X1))),X1) ),
inference(superposition,[status(thm)],[c_3769,c_3644]) ).
tcf(c_29300,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X0))
| ~ subset(singleton(set_union2(set_union2(powerset(X0),X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_3769,c_3944]) ).
tcf(c_29301,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X1))
| ~ subset(singleton(set_union2(set_union2(X0,powerset(X1)),X2)),X1) ),
inference(superposition,[status(thm)],[c_3769,c_3945]) ).
tcf(c_29302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(powerset(X0))
| ( set_union2(set_union2(powerset(X0),X1),X2) = X3 )
| ~ subset(sK2(set_union2(powerset(X0),X1),X2,X3),X0)
| ~ in(sK2(set_union2(powerset(X0),X1),X2,X3),X3) ),
inference(superposition,[status(thm)],[c_3769,c_4078]) ).
tcf(c_29303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(powerset(X3))
| ( set_union2(set_union2(X0,X1),X2) = powerset(X3) )
| ~ subset(sK2(set_union2(X0,X1),X2,powerset(X3)),X3)
| ~ in(sK2(set_union2(X0,X1),X2,powerset(X3)),X1) ),
inference(superposition,[status(thm)],[c_3769,c_4079]) ).
tcf(c_29304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(powerset(X2))
| ( set_union2(powerset(X2),X3) = set_union2(X0,X1) )
| ~ subset(sK2(X0,X1,set_union2(powerset(X2),X3)),X2)
| ~ in(sK2(X0,X1,set_union2(powerset(X2),X3)),X1) ),
inference(superposition,[status(thm)],[c_3769,c_4095]) ).
tcf(c_29305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(powerset(X1))
| ( set_union2(X0,powerset(X1)) = set_union2(X2,X3) )
| ~ subset(sK2(X0,powerset(X1),set_union2(X2,X3)),X1)
| ~ in(sK2(X0,powerset(X1),set_union2(X2,X3)),X3) ),
inference(superposition,[status(thm)],[c_3769,c_4096]) ).
tcf(c_29306,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X1))
| ~ subset(singleton(set_union2(X0,set_union2(powerset(X1),X2))),X1) ),
inference(superposition,[status(thm)],[c_3769,c_4131]) ).
tcf(c_29307,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| ~ subset(singleton(set_union2(X0,set_union2(X1,powerset(X2)))),X2) ),
inference(superposition,[status(thm)],[c_3769,c_4132]) ).
tcf(c_29450,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(set_union2(X0,X1),X2))
| ~ subset(sK1(set_union2(set_union2(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_3863,c_5183]) ).
tcf(c_29451,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(set_union2(X0,X1),X2))
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ in(sK1(set_union2(set_union2(X0,X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_3806,c_5183]) ).
tcf(c_29452,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(set_union2(X0,X1),X2))
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ in(sK1(set_union2(set_union2(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_3805,c_5183]) ).
tcf(c_29453,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(set_union2(X0,X1),X2))
| ~ subset(sK1(set_union2(set_union2(X0,X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_3865,c_5183]) ).
tcf(c_29454,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| epsilon_transitive(set_union2(sK5(iPr_def_11),X0))
| in(sK5(iPr_def_11),sK1(set_union2(sK5(iPr_def_11),X0)))
| ( sK1(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(sK1(set_union2(sK5(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_7244,c_5183]) ).
tcf(c_29455,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| epsilon_transitive(set_union2(sK3(iPr_def_11),X0))
| in(sK3(iPr_def_11),sK1(set_union2(sK3(iPr_def_11),X0)))
| ( sK1(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(sK1(set_union2(sK3(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_9907,c_5183]) ).
tcf(c_29456,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| epsilon_transitive(set_union2(sK4(iPr_def_11),X0))
| in(sK4(iPr_def_11),sK1(set_union2(sK4(iPr_def_11),X0)))
| ( sK1(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(sK1(set_union2(sK4(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_11191,c_5183]) ).
tcf(c_29457,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X1,X0))
| ~ subset(sK1(set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_58,c_5183]) ).
tcf(c_29459,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,X0))
| ~ subset(sK1(X0),X0) ),
inference(superposition,[status(thm)],[c_97,c_5183]) ).
tcf(c_29460,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,empty_set))
| ~ subset(sK1(X0),X0) ),
inference(superposition,[status(thm)],[c_126,c_5183]) ).
tcf(c_29461,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(empty_set,X0))
| ~ subset(sK1(X0),empty_set) ),
inference(superposition,[status(thm)],[c_3423,c_5183]) ).
tcf(c_29462,plain,
( epsilon_transitive(set_union2(iPr_def_10,sK18))
| ~ subset(sK1(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3424,c_5183]) ).
tcf(c_29463,plain,
( epsilon_transitive(iPr_def_11)
| ~ subset(sK1(iPr_def_11),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_29462,c_3424]) ).
tcf(c_29466,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ subset(sK1(X0),empty_set) ),
inference(light_normalisation,[status(thm)],[c_29461,c_3423]) ).
tcf(c_29519,plain,
! [X0: $i] :
( epsilon_transitive(powerset(sK5(powerset(sK5(powerset(X0))))))
| subset(sK1(powerset(sK5(powerset(sK5(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_3566,c_5249]) ).
tcf(c_29520,plain,
! [X0: $i] :
( epsilon_connected(powerset(sK5(powerset(sK5(powerset(X0))))))
| subset(sK3(powerset(sK5(powerset(sK5(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_3567,c_5249]) ).
tcf(c_29521,plain,
! [X0: $i] :
( epsilon_connected(powerset(sK5(powerset(sK5(powerset(X0))))))
| subset(sK4(powerset(sK5(powerset(sK5(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_3568,c_5249]) ).
tcf(c_29522,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(sK5(powerset(X0)))))
| subset(sK3(sK5(powerset(sK5(powerset(X0))))),X0)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_3807,c_5249]) ).
tcf(c_29523,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(sK5(powerset(X0)))))
| subset(sK4(sK5(powerset(sK5(powerset(X0))))),X0)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_3808,c_5249]) ).
tcf(c_29524,plain,
! [X0: $i] :
( empty(sK5(powerset(sK5(powerset(X0)))))
| subset(sK5(sK5(powerset(sK5(powerset(X0))))),X0)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_3899,c_5249]) ).
tcf(c_29530,plain,
! [X0: $i] : subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))))))),X0),
inference(superposition,[status(thm)],[c_5252,c_5249]) ).
tcf(c_29532,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(X0)))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(powerset(X0)))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(X0)))))
| ~ in(sK5(powerset(sK5(powerset(X0)))),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_5249]) ).
tcf(c_29533,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(X0)))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(powerset(X0)))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(X0)))))
| ~ in(sK5(powerset(sK5(powerset(X0)))),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_5249]) ).
tcf(c_29534,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),X0)
| in(sK5(powerset(sK5(powerset(X0)))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(powerset(X0)))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(X0)))))
| ~ in(sK5(powerset(sK5(powerset(X0)))),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_5249]) ).
tcf(c_29745,plain,
( epsilon_transitive(singleton(iPr_def_10))
| ( sK18 = iPr_def_10 )
| ~ subset(iPr_def_10,empty_set) ),
inference(superposition,[status(thm)],[c_17004,c_29466]) ).
tcf(c_29792,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| in(set_union2(X1,X0),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_7266]) ).
tcf(c_29794,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( set_union2(X0,X0) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,X0),sK18) ),
inference(superposition,[status(thm)],[c_97,c_7266]) ).
tcf(c_29795,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),empty_set)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( set_union2(X0,empty_set) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,empty_set),sK18) ),
inference(superposition,[status(thm)],[c_126,c_7266]) ).
tcf(c_29796,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),empty_set)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( set_union2(empty_set,X0) = sK5(iPr_def_11) )
| ~ in(set_union2(empty_set,X0),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_7266]) ).
tcf(c_29798,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ empty(X2)
| ~ subset(sK5(iPr_def_11),X2)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7266,c_359]) ).
tcf(c_29799,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| element(set_union2(X0,X1),X2)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ subset(sK5(iPr_def_11),X2)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7266,c_358]) ).
tcf(c_29800,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| in(X2,set_union2(X0,X1))
| in(set_union2(X0,X1),X2)
| ( set_union2(X0,X1) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X2,sK5(iPr_def_11))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7266,c_77]) ).
tcf(c_29801,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| subset(set_union2(X0,X1),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7266,c_65]) ).
tcf(c_29802,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18)
| ~ in(sK5(iPr_def_11),set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_7266,c_49]) ).
tcf(c_29804,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| element(set_union2(X0,X1),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7266,c_127]) ).
tcf(c_29807,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ subset(iPr_def_11,set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7266,c_23189]) ).
tcf(c_29809,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),empty_set)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(light_normalisation,[status(thm)],[c_29796,c_3423]) ).
tcf(c_29886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,sK0(X3,set_union2(X0,X1)))
| in(sK0(X3,set_union2(X0,X1)),X2)
| ( set_union2(X0,X1) = singleton(X3) )
| ( sK0(X3,set_union2(X0,X1)) = X3 )
| ( sK0(X3,set_union2(X0,X1)) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_60,c_4213]) ).
tcf(c_29887,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X0,X1))
| in(X2,sK1(set_union2(X0,X1)))
| in(sK1(set_union2(X0,X1)),X2)
| ( sK1(set_union2(X0,X1)) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_64,c_4213]) ).
tcf(c_29888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(set_union2(X0,X1),X3,X4))
| in(sK2(set_union2(X0,X1),X3,X4),X4)
| in(sK2(set_union2(X0,X1),X3,X4),X3)
| in(sK2(set_union2(X0,X1),X3,X4),X2)
| ( set_union2(set_union2(X0,X1),X3) = X4 )
| ( sK2(set_union2(X0,X1),X3,X4) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_68,c_4213]) ).
tcf(c_29889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(X3,X4,set_union2(X0,X1)))
| in(sK2(X3,X4,set_union2(X0,X1)),X4)
| in(sK2(X3,X4,set_union2(X0,X1)),X3)
| in(sK2(X3,X4,set_union2(X0,X1)),X2)
| ( set_union2(X0,X1) = set_union2(X3,X4) )
| ( sK2(X3,X4,set_union2(X0,X1)) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_68,c_4213]) ).
tcf(c_29890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(X3,set_union2(X0,X1),X4))
| in(sK2(X3,set_union2(X0,X1),X4),X4)
| in(sK2(X3,set_union2(X0,X1),X4),X3)
| in(sK2(X3,set_union2(X0,X1),X4),X2)
| ( set_union2(X3,set_union2(X0,X1)) = X4 )
| ( sK2(X3,set_union2(X0,X1),X4) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_68,c_4213]) ).
tcf(c_29891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| in(X2,X3)
| ( X2 = X3 )
| ~ in(X3,X1)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_69,c_4213]) ).
tcf(c_29892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| in(X2,X3)
| ( X2 = X3 )
| ~ in(X3,X1)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_70,c_4213]) ).
tcf(c_29895,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_union2(X0,X1))
| in(X2,sK5(set_union2(X0,X1)))
| in(sK5(set_union2(X0,X1)),X2)
| ( sK5(set_union2(X0,X1)) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3768,c_4213]) ).
tcf(c_29896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK0(X3,set_union2(set_union2(X0,X1),X4)))
| in(sK0(X3,set_union2(set_union2(X0,X1),X4)),X4)
| in(sK0(X3,set_union2(set_union2(X0,X1),X4)),X2)
| ( set_union2(set_union2(X0,X1),X4) = singleton(X3) )
| ( sK0(X3,set_union2(set_union2(X0,X1),X4)) = X3 )
| ( sK0(X3,set_union2(set_union2(X0,X1),X4)) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4023,c_4213]) ).
tcf(c_29897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK0(X3,set_union2(X4,set_union2(X0,X1))))
| in(sK0(X3,set_union2(X4,set_union2(X0,X1))),X4)
| in(sK0(X3,set_union2(X4,set_union2(X0,X1))),X2)
| ( set_union2(X4,set_union2(X0,X1)) = singleton(X3) )
| ( sK0(X3,set_union2(X4,set_union2(X0,X1))) = X3 )
| ( sK0(X3,set_union2(X4,set_union2(X0,X1))) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4023,c_4213]) ).
tcf(c_29898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(set_union2(set_union2(X0,X1),X3))
| in(X2,sK1(set_union2(set_union2(X0,X1),X3)))
| in(sK1(set_union2(set_union2(X0,X1),X3)),X3)
| in(sK1(set_union2(set_union2(X0,X1),X3)),X2)
| ( sK1(set_union2(set_union2(X0,X1),X3)) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4024,c_4213]) ).
tcf(c_29899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(set_union2(X3,set_union2(X0,X1)))
| in(X2,sK1(set_union2(X3,set_union2(X0,X1))))
| in(sK1(set_union2(X3,set_union2(X0,X1))),X3)
| in(sK1(set_union2(X3,set_union2(X0,X1))),X2)
| ( sK1(set_union2(X3,set_union2(X0,X1))) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4024,c_4213]) ).
tcf(c_29900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(set_union2(set_union2(X0,X1),X3))
| in(X2,sK3(set_union2(set_union2(X0,X1),X3)))
| in(sK3(set_union2(set_union2(X0,X1),X3)),X3)
| in(sK3(set_union2(set_union2(X0,X1),X3)),X2)
| ( sK3(set_union2(set_union2(X0,X1),X3)) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4027,c_4213]) ).
tcf(c_29901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(set_union2(X3,set_union2(X0,X1)))
| in(X2,sK3(set_union2(X3,set_union2(X0,X1))))
| in(sK3(set_union2(X3,set_union2(X0,X1))),X3)
| in(sK3(set_union2(X3,set_union2(X0,X1))),X2)
| ( sK3(set_union2(X3,set_union2(X0,X1))) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4027,c_4213]) ).
tcf(c_29902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(set_union2(set_union2(X0,X1),X3))
| in(X2,sK4(set_union2(set_union2(X0,X1),X3)))
| in(sK4(set_union2(set_union2(X0,X1),X3)),X3)
| in(sK4(set_union2(set_union2(X0,X1),X3)),X2)
| ( sK4(set_union2(set_union2(X0,X1),X3)) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4028,c_4213]) ).
tcf(c_29903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(set_union2(X3,set_union2(X0,X1)))
| in(X2,sK4(set_union2(X3,set_union2(X0,X1))))
| in(sK4(set_union2(X3,set_union2(X0,X1))),X3)
| in(sK4(set_union2(X3,set_union2(X0,X1))),X2)
| ( sK4(set_union2(X3,set_union2(X0,X1))) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4028,c_4213]) ).
tcf(c_29904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(set_union2(set_union2(X0,X1),X3))
| in(X2,sK5(set_union2(set_union2(X0,X1),X3)))
| in(sK5(set_union2(set_union2(X0,X1),X3)),X3)
| in(sK5(set_union2(set_union2(X0,X1),X3)),X2)
| ( sK5(set_union2(set_union2(X0,X1),X3)) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4029,c_4213]) ).
tcf(c_29905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(set_union2(X3,set_union2(X0,X1)))
| in(X2,sK5(set_union2(X3,set_union2(X0,X1))))
| in(sK5(set_union2(X3,set_union2(X0,X1))),X3)
| in(sK5(set_union2(X3,set_union2(X0,X1))),X2)
| ( sK5(set_union2(X3,set_union2(X0,X1))) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4029,c_4213]) ).
tcf(c_29906,plain,
! [X0: $i,X1: $i] :
( in(sK18,X1)
| in(X1,sK18)
| ( X1 = sK18 )
| ~ in(X1,iPr_def_11)
| ~ epsilon_connected(set_union2(X0,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_15062,c_4213]) ).
tcf(c_29907,plain,
! [X0: $i,X1: $i] :
( in(sK18,X1)
| in(X1,sK18)
| ( X1 = sK18 )
| ~ in(X1,X0)
| ~ epsilon_connected(set_union2(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_15059,c_4213]) ).
tcf(c_29908,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ subset(iPr_def_11,set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_23181,c_4213]) ).
tcf(c_29909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK5(iPr_def_11),X3)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_4213]) ).
tcf(c_29910,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_4213]) ).
tcf(c_29911,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ empty(sK5(iPr_def_11))
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7246,c_4213]) ).
tcf(c_29912,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_4213]) ).
tcf(c_29913,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_4213]) ).
tcf(c_29914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X3)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_4213]) ).
tcf(c_29915,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_4213]) ).
tcf(c_29916,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_4213]) ).
tcf(c_29917,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_4213]) ).
tcf(c_29918,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_4213]) ).
tcf(c_29919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X3)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_4213]) ).
tcf(c_29920,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_4213]) ).
tcf(c_29921,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ empty(sK4(iPr_def_11))
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11193,c_4213]) ).
tcf(c_29922,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_4213]) ).
tcf(c_29923,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_4213]) ).
tcf(c_29924,plain,
! [X0: $i,X1: $i] :
( in(sK18,X1)
| in(X1,sK18)
| ( X1 = sK18 )
| ~ in(X1,X0)
| ~ epsilon_connected(set_union2(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_25148,c_4213]) ).
tcf(c_29925,plain,
! [X0: $i,X1: $i] :
( in(sK18,X1)
| in(X1,sK18)
| ( X1 = sK18 )
| ~ in(X1,iPr_def_10)
| ~ epsilon_connected(set_union2(X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_25149,c_4213]) ).
tcf(c_29926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X0)
| in(X0,X3)
| ( X0 = X3 )
| ~ in(X3,X1)
| ~ epsilon_connected(set_union2(X2,X1))
| ~ in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_58,c_4213]) ).
tcf(c_29929,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| in(X1,X2)
| ( X1 = X2 )
| ~ in(X2,empty_set)
| ~ in(X1,X0)
| ~ epsilon_connected(set_union2(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_126,c_4213]) ).
tcf(c_29930,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| in(X1,X2)
| ( X1 = X2 )
| ~ in(X2,X0)
| ~ in(X1,X0)
| ~ epsilon_connected(set_union2(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_3423,c_4213]) ).
tcf(c_29931,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ in(X1,sK18)
| ~ in(X0,iPr_def_11)
| ~ epsilon_connected(set_union2(iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_3424,c_4213]) ).
tcf(c_29952,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X1,sK18)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_29931,c_3424]) ).
tcf(c_30445,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X0,set_union2(X1,X2)))
| ~ subset(sK1(set_union2(X0,set_union2(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_3863,c_5290]) ).
tcf(c_30446,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X0,set_union2(X1,X2)))
| ~ epsilon_transitive(set_union2(X1,X2))
| ~ in(sK1(set_union2(X0,set_union2(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_3806,c_5290]) ).
tcf(c_30447,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X0,set_union2(X1,X2)))
| ~ epsilon_transitive(set_union2(X1,X2))
| ~ in(sK1(set_union2(X0,set_union2(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_3805,c_5290]) ).
tcf(c_30448,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X0,set_union2(X1,X2)))
| ~ subset(sK1(set_union2(X0,set_union2(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_3865,c_5290]) ).
tcf(c_30449,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| epsilon_transitive(set_union2(X0,sK5(iPr_def_11)))
| in(sK5(iPr_def_11),sK1(set_union2(X0,sK5(iPr_def_11))))
| ( sK1(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(sK1(set_union2(X0,sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7244,c_5290]) ).
tcf(c_30450,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| epsilon_transitive(set_union2(X0,sK3(iPr_def_11)))
| in(sK3(iPr_def_11),sK1(set_union2(X0,sK3(iPr_def_11))))
| ( sK1(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(sK1(set_union2(X0,sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9907,c_5290]) ).
tcf(c_30451,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| epsilon_transitive(set_union2(X0,sK4(iPr_def_11)))
| in(sK4(iPr_def_11),sK1(set_union2(X0,sK4(iPr_def_11))))
| ( sK1(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(sK1(set_union2(X0,sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11191,c_5290]) ).
tcf(c_30452,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X1,X0))
| ~ subset(sK1(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_58,c_5290]) ).
tcf(c_30455,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,empty_set))
| ~ subset(sK1(X0),empty_set) ),
inference(superposition,[status(thm)],[c_126,c_5290]) ).
tcf(c_30456,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(empty_set,X0))
| ~ subset(sK1(X0),X0) ),
inference(superposition,[status(thm)],[c_3423,c_5290]) ).
tcf(c_30457,plain,
( epsilon_transitive(set_union2(iPr_def_10,sK18))
| ~ subset(sK1(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_3424,c_5290]) ).
tcf(c_30458,plain,
( epsilon_transitive(iPr_def_11)
| ~ subset(sK1(iPr_def_11),sK18) ),
inference(light_normalisation,[status(thm)],[c_30457,c_3424]) ).
tcf(c_30504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(set_union2(set_union2(set_union2(X0,X1),X2),X3),X4)),X0),
inference(superposition,[status(thm)],[c_69,c_5325]) ).
tcf(c_30505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(set_union2(set_union2(set_union2(X0,X1),X2),X3),X4)),X1),
inference(superposition,[status(thm)],[c_70,c_5325]) ).
tcf(c_30506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(powerset(X0))
| ~ subset(singleton(set_union2(set_union2(set_union2(powerset(X0),X1),X2),X3)),X0) ),
inference(superposition,[status(thm)],[c_3769,c_5325]) ).
tcf(c_30507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_5325]) ).
tcf(c_30508,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_5325]) ).
tcf(c_30509,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_5325]) ).
tcf(c_30510,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)) = sK5(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)))
| ~ in(singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_5325]) ).
tcf(c_30511,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_5325]) ).
tcf(c_30512,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_5325]) ).
tcf(c_30513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_5325]) ).
tcf(c_30514,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_5325]) ).
tcf(c_30515,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_5325]) ).
tcf(c_30516,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)) = sK3(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)))
| ~ in(singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_5325]) ).
tcf(c_30517,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_5325]) ).
tcf(c_30518,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2) = sK3(iPr_def_11) )
| ( singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_5325]) ).
tcf(c_30519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X3)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_5325]) ).
tcf(c_30520,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_5325]) ).
tcf(c_30521,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_5325]) ).
tcf(c_30522,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)) = sK4(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)))
| ~ in(singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_5325]) ).
tcf(c_30523,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_5325]) ).
tcf(c_30524,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2) = sK4(iPr_def_11) )
| ( singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_5325]) ).
tcf(c_30537,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(singleton(set_union2(set_union2(X0,X1),X2)),empty_set),
inference(superposition,[status(thm)],[c_3423,c_5325]) ).
tcf(c_30538,plain,
! [X0: $i,X1: $i] : ~ in(singleton(set_union2(set_union2(iPr_def_11,X0),X1)),iPr_def_10),
inference(superposition,[status(thm)],[c_3424,c_5325]) ).
tcf(c_30673,plain,
! [X0: $i,X1: $i] : ~ in(singleton(set_union2(X0,set_union2(iPr_def_11,X1))),iPr_def_10),
inference(superposition,[status(thm)],[c_58,c_30538]) ).
tcf(c_30677,plain,
! [X0: $i,X1: $i] : ~ in(singleton(set_union2(set_union2(X0,iPr_def_11),X1)),iPr_def_10),
inference(superposition,[status(thm)],[c_58,c_30538]) ).
tcf(c_30755,plain,
~ epsilon_transitive(singleton(iPr_def_11)),
inference(global_subsumption_just,[status(thm)],[c_24072,c_2422,c_5262,c_16905,c_26128]) ).
tcf(c_30757,plain,
sK1(singleton(iPr_def_11)) = iPr_def_11,
inference(superposition,[status(thm)],[c_3589,c_30755]) ).
tcf(c_30759,plain,
! [X0: $i] :
( epsilon_transitive(singleton(iPr_def_11))
| element(iPr_def_11,X0)
| ~ subset(singleton(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_30757,c_13618]) ).
tcf(c_30760,plain,
( epsilon_transitive(singleton(iPr_def_11))
| ~ in(singleton(iPr_def_11),iPr_def_11) ),
inference(superposition,[status(thm)],[c_30757,c_3523]) ).
tcf(c_30761,plain,
( epsilon_transitive(singleton(iPr_def_11))
| element(iPr_def_11,singleton(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_30757,c_3454]) ).
tcf(c_30762,plain,
( epsilon_transitive(singleton(iPr_def_11))
| ~ subset(iPr_def_11,singleton(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_30757,c_63]) ).
tcf(c_30763,plain,
( epsilon_transitive(singleton(iPr_def_11))
| in(iPr_def_11,singleton(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_30757,c_64]) ).
tcf(c_30764,plain,
~ subset(iPr_def_11,singleton(iPr_def_11)),
inference(forward_subsumption_resolution,[status(thm)],[c_30762,c_30755]) ).
tcf(c_30765,plain,
! [X0: $i] :
( element(iPr_def_11,X0)
| ~ subset(singleton(iPr_def_11),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30759,c_30755]) ).
tcf(c_30780,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_9918]) ).
tcf(c_30782,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(sK3(iPr_def_11)))
| ( singleton(set_union2(sK3(iPr_def_11),sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(sK3(iPr_def_11),sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_9918]) ).
tcf(c_30783,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(sK3(iPr_def_11)))
| ( singleton(set_union2(sK3(iPr_def_11),empty_set)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(sK3(iPr_def_11),empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_126,c_9918]) ).
tcf(c_30784,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ empty(X1)
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK18)
| ~ subset(singleton(set_union2(sK3(iPr_def_11),X0)),X1) ),
inference(superposition,[status(thm)],[c_9918,c_359]) ).
tcf(c_30785,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X1)
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK18)
| ~ subset(singleton(set_union2(sK3(iPr_def_11),X0)),X1) ),
inference(superposition,[status(thm)],[c_9918,c_358]) ).
tcf(c_30786,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ( singleton(set_union2(sK3(iPr_def_11),X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(sK3(iPr_def_11),X1)))
| ~ in(singleton(set_union2(sK3(iPr_def_11),X1)),sK18)
| ~ in(X0,singleton(set_union2(sK3(iPr_def_11),X1))) ),
inference(superposition,[status(thm)],[c_9918,c_77]) ).
tcf(c_30787,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(sK3(iPr_def_11),X0)))
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_9918,c_65]) ).
tcf(c_30788,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK18)
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9918,c_49]) ).
tcf(c_30790,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_9918,c_127]) ).
tcf(c_30845,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_9919]) ).
tcf(c_30848,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(sK3(iPr_def_11)))
| ( singleton(set_union2(empty_set,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(empty_set,sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_9919]) ).
tcf(c_30849,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ empty(X1)
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK18)
| ~ subset(singleton(set_union2(X0,sK3(iPr_def_11))),X1) ),
inference(superposition,[status(thm)],[c_9919,c_359]) ).
tcf(c_30850,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X1)
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK18)
| ~ subset(singleton(set_union2(X0,sK3(iPr_def_11))),X1) ),
inference(superposition,[status(thm)],[c_9919,c_358]) ).
tcf(c_30851,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ( singleton(set_union2(X1,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X1,sK3(iPr_def_11))))
| ~ in(singleton(set_union2(X1,sK3(iPr_def_11))),sK18)
| ~ in(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_9919,c_77]) ).
tcf(c_30852,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(X0,sK3(iPr_def_11))))
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9919,c_65]) ).
tcf(c_30853,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK18)
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9919,c_49]) ).
tcf(c_30855,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9919,c_127]) ).
tcf(c_30910,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_11202]) ).
tcf(c_30912,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(sK4(iPr_def_11)))
| ( singleton(set_union2(sK4(iPr_def_11),sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(sK4(iPr_def_11),sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_11202]) ).
tcf(c_30913,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(sK4(iPr_def_11)))
| ( singleton(set_union2(sK4(iPr_def_11),empty_set)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(sK4(iPr_def_11),empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_126,c_11202]) ).
tcf(c_30914,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ empty(X1)
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK18)
| ~ subset(singleton(set_union2(sK4(iPr_def_11),X0)),X1) ),
inference(superposition,[status(thm)],[c_11202,c_359]) ).
tcf(c_30915,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X1)
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK18)
| ~ subset(singleton(set_union2(sK4(iPr_def_11),X0)),X1) ),
inference(superposition,[status(thm)],[c_11202,c_358]) ).
tcf(c_30916,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ( singleton(set_union2(sK4(iPr_def_11),X1)) = sK4(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(sK4(iPr_def_11),X1)))
| ~ in(singleton(set_union2(sK4(iPr_def_11),X1)),sK18)
| ~ in(X0,singleton(set_union2(sK4(iPr_def_11),X1))) ),
inference(superposition,[status(thm)],[c_11202,c_77]) ).
tcf(c_30917,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(sK4(iPr_def_11),X0)))
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_11202,c_65]) ).
tcf(c_30918,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK18)
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11202,c_49]) ).
tcf(c_30920,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_11202,c_127]) ).
tcf(c_31011,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_11203]) ).
tcf(c_31014,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(sK4(iPr_def_11)))
| ( singleton(set_union2(empty_set,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(empty_set,sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_11203]) ).
tcf(c_31015,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ empty(X1)
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK18)
| ~ subset(singleton(set_union2(X0,sK4(iPr_def_11))),X1) ),
inference(superposition,[status(thm)],[c_11203,c_359]) ).
tcf(c_31016,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X1)
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK18)
| ~ subset(singleton(set_union2(X0,sK4(iPr_def_11))),X1) ),
inference(superposition,[status(thm)],[c_11203,c_358]) ).
tcf(c_31017,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ( singleton(set_union2(X1,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X1,sK4(iPr_def_11))))
| ~ in(singleton(set_union2(X1,sK4(iPr_def_11))),sK18)
| ~ in(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_11203,c_77]) ).
tcf(c_31018,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(X0,sK4(iPr_def_11))))
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11203,c_65]) ).
tcf(c_31019,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK18)
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11203,c_49]) ).
tcf(c_31021,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11203,c_127]) ).
tcf(c_31178,plain,
( epsilon_connected(iPr_def_11)
| ~ in(sK5(sK18),sK18)
| ~ epsilon_transitive(iPr_def_10)
| ( sK3(iPr_def_11) = sK5(sK18) )
| in(sK5(sK18),sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_20549,c_9639,c_20549]) ).
tcf(c_31179,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18) ),
inference(renaming,[status(thm)],[c_31178]) ).
tcf(c_31187,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31179,c_127]) ).
tcf(c_31206,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(sK5(sK18),sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_31187,c_359]) ).
tcf(c_31207,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| element(sK5(sK18),X0)
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_31187,c_358]) ).
tcf(c_31208,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(sK18))
| in(sK5(sK18),X0)
| ( sK5(sK18) = X0 )
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(sK5(sK18),sK18)
| ~ in(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_31187,c_77]) ).
tcf(c_31209,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| subset(sK5(sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_31187,c_65]) ).
tcf(c_31210,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18)
| ~ in(sK3(iPr_def_11),sK5(sK18)) ),
inference(superposition,[status(thm)],[c_31187,c_49]) ).
tcf(c_31211,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK3(iPr_def_11))
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_31187,c_137]) ).
tcf(c_31212,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| element(sK5(sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_31187,c_127]) ).
tcf(c_31289,plain,
( epsilon_connected(iPr_def_11)
| ~ in(sK5(sK18),sK18)
| ~ epsilon_transitive(iPr_def_10)
| ( sK4(iPr_def_11) = sK5(sK18) )
| in(sK5(sK18),sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_21565,c_11004,c_21565]) ).
tcf(c_31290,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18) ),
inference(renaming,[status(thm)],[c_31289]) ).
tcf(c_31298,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31290,c_127]) ).
tcf(c_31317,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(sK5(sK18),sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_31298,c_359]) ).
tcf(c_31318,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| element(sK5(sK18),X0)
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_31298,c_358]) ).
tcf(c_31319,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(sK18))
| in(sK5(sK18),X0)
| ( sK5(sK18) = X0 )
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(sK5(sK18),sK18)
| ~ in(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_31298,c_77]) ).
tcf(c_31320,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| subset(sK5(sK18),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_31298,c_65]) ).
tcf(c_31321,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18)
| ~ in(sK4(iPr_def_11),sK5(sK18)) ),
inference(superposition,[status(thm)],[c_31298,c_49]) ).
tcf(c_31322,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK4(iPr_def_11))
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_31298,c_137]) ).
tcf(c_31323,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| element(sK5(sK18),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_31298,c_127]) ).
tcf(c_31443,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| in(set_union2(X1,X0),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_9930]) ).
tcf(c_31445,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( set_union2(X0,X0) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,X0),sK18) ),
inference(superposition,[status(thm)],[c_97,c_9930]) ).
tcf(c_31446,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),empty_set)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( set_union2(X0,empty_set) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,empty_set),sK18) ),
inference(superposition,[status(thm)],[c_126,c_9930]) ).
tcf(c_31447,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),empty_set)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( set_union2(empty_set,X0) = sK3(iPr_def_11) )
| ~ in(set_union2(empty_set,X0),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_9930]) ).
tcf(c_31448,plain,
( epsilon_connected(iPr_def_11)
| in(iPr_def_11,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK18)
| ( set_union2(iPr_def_10,sK18) = sK3(iPr_def_11) )
| ~ in(set_union2(iPr_def_10,sK18),sK18) ),
inference(superposition,[status(thm)],[c_3424,c_9930]) ).
tcf(c_31449,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ empty(X2)
| ~ subset(sK3(iPr_def_11),X2)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9930,c_359]) ).
tcf(c_31450,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| element(set_union2(X0,X1),X2)
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ subset(sK3(iPr_def_11),X2)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9930,c_358]) ).
tcf(c_31451,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| in(X2,set_union2(X0,X1))
| in(set_union2(X0,X1),X2)
| ( set_union2(X0,X1) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X2,sK3(iPr_def_11))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9930,c_77]) ).
tcf(c_31452,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| subset(set_union2(X0,X1),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9930,c_65]) ).
tcf(c_31453,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18)
| ~ in(sK3(iPr_def_11),set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_9930,c_49]) ).
tcf(c_31455,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| element(set_union2(X0,X1),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9930,c_127]) ).
tcf(c_31458,plain,
( epsilon_connected(iPr_def_11)
| in(iPr_def_11,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK18)
| ( sK3(iPr_def_11) = iPr_def_11 )
| ~ in(iPr_def_11,sK18) ),
inference(light_normalisation,[status(thm)],[c_31448,c_3424]) ).
tcf(c_31460,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),empty_set)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(light_normalisation,[status(thm)],[c_31447,c_3423]) ).
tcf(c_31531,plain,
! [X0: $i,X1: $i] : ~ in(singleton(set_union2(X0,set_union2(X1,iPr_def_11))),iPr_def_10),
inference(superposition,[status(thm)],[c_58,c_30673]) ).
tcf(c_31552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(set_union2(set_union2(X0,set_union2(X1,X2)),X3),X4)),X1),
inference(superposition,[status(thm)],[c_69,c_5326]) ).
tcf(c_31553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(set_union2(set_union2(X0,set_union2(X1,X2)),X3),X4)),X2),
inference(superposition,[status(thm)],[c_70,c_5326]) ).
tcf(c_31554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(powerset(X1))
| ~ subset(singleton(set_union2(set_union2(set_union2(X0,powerset(X1)),X2),X3)),X1) ),
inference(superposition,[status(thm)],[c_3769,c_5326]) ).
tcf(c_31555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_5326]) ).
tcf(c_31556,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_5326]) ).
tcf(c_31557,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_5326]) ).
tcf(c_31558,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)) = sK5(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)))
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_5326]) ).
tcf(c_31559,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_5326]) ).
tcf(c_31560,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_5326]) ).
tcf(c_31561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_5326]) ).
tcf(c_31562,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_5326]) ).
tcf(c_31563,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_5326]) ).
tcf(c_31564,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)) = sK3(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)))
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_5326]) ).
tcf(c_31565,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_5326]) ).
tcf(c_31566,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2) = sK3(iPr_def_11) )
| ( singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_5326]) ).
tcf(c_31567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X3)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_5326]) ).
tcf(c_31568,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_5326]) ).
tcf(c_31569,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_5326]) ).
tcf(c_31570,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)) = sK4(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)))
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_5326]) ).
tcf(c_31571,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_5326]) ).
tcf(c_31572,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2) = sK4(iPr_def_11) )
| ( singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_5326]) ).
tcf(c_31586,plain,
! [X0: $i,X1: $i] : ~ in(singleton(set_union2(set_union2(iPr_def_11,X0),X1)),sK18),
inference(superposition,[status(thm)],[c_3424,c_5326]) ).
tcf(c_31868,plain,
! [X0: $i] :
( empty(sK5(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3564,c_24092]) ).
tcf(c_31873,plain,
! [X0: $i] :
( epsilon_transitive(powerset(X0))
| empty(sK1(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3566,c_24092]) ).
tcf(c_31874,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| empty(sK3(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3567,c_24092]) ).
tcf(c_31875,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| empty(sK4(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3568,c_24092]) ).
tcf(c_31877,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| ~ subset(X2,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_24092]) ).
tcf(c_31878,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| ~ in(X2,X1)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_24092]) ).
tcf(c_31879,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| ~ in(X2,X0)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_24092]) ).
tcf(c_31880,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| ~ subset(X2,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_24092]) ).
tcf(c_31881,plain,
! [X0: $i] :
( epsilon_connected(X0)
| empty(sK3(X0))
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3807,c_24092]) ).
tcf(c_31882,plain,
! [X0: $i] :
( epsilon_connected(X0)
| empty(sK4(X0))
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3808,c_24092]) ).
tcf(c_31891,plain,
! [X0: $i] :
( empty(sK5(powerset(empty_set)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4163,c_24092]) ).
tcf(c_31896,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| empty(sK3(powerset(empty_set)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4620,c_24092]) ).
tcf(c_31899,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| empty(sK4(powerset(empty_set)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4637,c_24092]) ).
tcf(c_31902,plain,
! [X0: $i] :
( empty(sK5(powerset(sK5(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5196,c_24092]) ).
tcf(c_31903,plain,
! [X0: $i] :
( empty(sK5(powerset(sK5(powerset(empty_set)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5250,c_24092]) ).
tcf(c_31905,plain,
! [X0: $i] :
( empty(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5252,c_24092]) ).
tcf(c_31915,plain,
! [X0: $i] :
( empty(sK5(powerset(sK5(powerset(sK5(powerset(empty_set)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5727,c_24092]) ).
tcf(c_31926,plain,
! [X0: $i] :
( empty(X0)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_24092]) ).
tcf(c_31931,plain,
! [X0: $i] :
( empty(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7261,c_24092]) ).
tcf(c_31932,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| empty(sK5(powerset(sK5(iPr_def_11))))
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_7587,c_24092]) ).
tcf(c_31933,plain,
( epsilon_connected(iPr_def_11)
| empty(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_9591,c_24092]) ).
tcf(c_31935,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(X0)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9907,c_24092]) ).
tcf(c_31938,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9925,c_24092]) ).
tcf(c_31939,plain,
( epsilon_connected(iPr_def_11)
| empty(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_11031,c_24092]) ).
tcf(c_31941,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(X0)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11191,c_24092]) ).
tcf(c_31944,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11209,c_24092]) ).
tcf(c_31953,plain,
( empty(sK18)
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ empty(singleton(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_15774,c_24092]) ).
tcf(c_32060,plain,
( empty(sK5(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_31891]) ).
tcf(c_32061,plain,
( empty(sK5(powerset(sK5(powerset(empty_set)))))
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_31903]) ).
tcf(c_32110,plain,
! [X0: $i,X1: $i] :
( ( sK5(powerset(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_31868,c_139]) ).
tcf(c_32111,plain,
! [X0: $i] :
( ( sK5(powerset(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_31868,c_136]) ).
tcf(c_32120,plain,
empty(sK5(powerset(empty_set))),
inference(global_subsumption_just,[status(thm)],[c_31891,c_95,c_32060]) ).
tcf(c_32122,plain,
! [X0: $i] :
( ( sK5(powerset(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32120,c_139]) ).
tcf(c_32123,plain,
sK5(powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_32120,c_136]) ).
tcf(c_32135,plain,
( empty(powerset(empty_set))
| subset(empty_set,powerset(empty_set))
| ~ epsilon_transitive(powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_32123,c_3899]) ).
tcf(c_32136,plain,
( empty(powerset(empty_set))
| ~ in(powerset(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_32123,c_3900]) ).
tcf(c_32137,plain,
( empty(powerset(empty_set))
| in(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_32123,c_3768]) ).
tcf(c_32138,plain,
element(empty_set,powerset(empty_set)),
inference(superposition,[status(thm)],[c_32123,c_81]) ).
tcf(c_32142,plain,
subset(empty_set,empty_set),
inference(superposition,[status(thm)],[c_32123,c_5252]) ).
tcf(c_32167,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| in(set_union2(X1,X0),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_11214]) ).
tcf(c_32169,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( set_union2(X0,X0) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,X0),sK18) ),
inference(superposition,[status(thm)],[c_97,c_11214]) ).
tcf(c_32170,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),empty_set)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( set_union2(X0,empty_set) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,empty_set),sK18) ),
inference(superposition,[status(thm)],[c_126,c_11214]) ).
tcf(c_32171,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),empty_set)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( set_union2(empty_set,X0) = sK4(iPr_def_11) )
| ~ in(set_union2(empty_set,X0),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_11214]) ).
tcf(c_32172,plain,
( epsilon_connected(iPr_def_11)
| in(iPr_def_11,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK18)
| ( set_union2(iPr_def_10,sK18) = sK4(iPr_def_11) )
| ~ in(set_union2(iPr_def_10,sK18),sK18) ),
inference(superposition,[status(thm)],[c_3424,c_11214]) ).
tcf(c_32173,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ empty(X2)
| ~ subset(sK4(iPr_def_11),X2)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11214,c_359]) ).
tcf(c_32174,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| element(set_union2(X0,X1),X2)
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ subset(sK4(iPr_def_11),X2)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11214,c_358]) ).
tcf(c_32175,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| in(X2,set_union2(X0,X1))
| in(set_union2(X0,X1),X2)
| ( set_union2(X0,X1) = X2 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X2,sK4(iPr_def_11))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11214,c_77]) ).
tcf(c_32176,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| subset(set_union2(X0,X1),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11214,c_65]) ).
tcf(c_32177,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18)
| ~ in(sK4(iPr_def_11),set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_11214,c_49]) ).
tcf(c_32179,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| element(set_union2(X0,X1),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11214,c_127]) ).
tcf(c_32182,plain,
( epsilon_connected(iPr_def_11)
| in(iPr_def_11,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK18)
| ( sK4(iPr_def_11) = iPr_def_11 )
| ~ in(iPr_def_11,sK18) ),
inference(light_normalisation,[status(thm)],[c_32172,c_3424]) ).
tcf(c_32184,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),empty_set)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(light_normalisation,[status(thm)],[c_32171,c_3423]) ).
tcf(c_32257,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X1,set_union2(sK5(iPr_def_11),X0))))
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_7256]) ).
tcf(c_32259,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),set_union2(sK5(iPr_def_11),X0))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),set_union2(sK5(iPr_def_11),X0))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_7256]) ).
tcf(c_32260,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),empty_set)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_126,c_7256]) ).
tcf(c_32261,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_7256]) ).
tcf(c_32263,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),sK5(iPr_def_11)),X0)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),sK5(iPr_def_11)),X0)),sK18) ),
inference(superposition,[status(thm)],[c_97,c_7256]) ).
tcf(c_32264,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),empty_set),X0)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),empty_set),X0)),sK18) ),
inference(superposition,[status(thm)],[c_126,c_7256]) ).
tcf(c_32265,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ empty(X2)
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18)
| ~ subset(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),X2) ),
inference(superposition,[status(thm)],[c_7256,c_359]) ).
tcf(c_32266,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X2)
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18)
| ~ subset(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),X2) ),
inference(superposition,[status(thm)],[c_7256,c_358]) ).
tcf(c_32267,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X1),X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(set_union2(sK5(iPr_def_11),X1),X2)))
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X1),X2)),sK18)
| ~ in(X0,singleton(set_union2(set_union2(sK5(iPr_def_11),X1),X2))) ),
inference(superposition,[status(thm)],[c_7256,c_77]) ).
tcf(c_32268,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)))
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7256,c_65]) ).
tcf(c_32269,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18)
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7256,c_49]) ).
tcf(c_32271,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7256,c_127]) ).
tcf(c_32362,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X1,set_union2(X0,sK5(iPr_def_11)))))
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_7257]) ).
tcf(c_32364,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),set_union2(X0,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),set_union2(X0,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_7257]) ).
tcf(c_32365,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),empty_set)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_126,c_7257]) ).
tcf(c_32366,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_7257]) ).
tcf(c_32369,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(empty_set,sK5(iPr_def_11)),X0)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(empty_set,sK5(iPr_def_11)),X0)),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_7257]) ).
tcf(c_32370,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ empty(X2)
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18)
| ~ subset(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),X2) ),
inference(superposition,[status(thm)],[c_7257,c_359]) ).
tcf(c_32371,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X2)
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18)
| ~ subset(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),X2) ),
inference(superposition,[status(thm)],[c_7257,c_358]) ).
tcf(c_32372,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( singleton(set_union2(set_union2(X1,sK5(iPr_def_11)),X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(set_union2(X1,sK5(iPr_def_11)),X2)))
| ~ in(singleton(set_union2(set_union2(X1,sK5(iPr_def_11)),X2)),sK18)
| ~ in(X0,singleton(set_union2(set_union2(X1,sK5(iPr_def_11)),X2))) ),
inference(superposition,[status(thm)],[c_7257,c_77]) ).
tcf(c_32373,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)))
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7257,c_65]) ).
tcf(c_32374,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18)
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7257,c_49]) ).
tcf(c_32376,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7257,c_127]) ).
tcf(c_32553,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(sK5(iPr_def_11),X1),X0)))
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_7258]) ).
tcf(c_32556,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( singleton(set_union2(empty_set,set_union2(sK5(iPr_def_11),X0))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(empty_set,set_union2(sK5(iPr_def_11),X0))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_7258]) ).
tcf(c_32557,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_7258]) ).
tcf(c_32559,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_7258]) ).
tcf(c_32560,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),empty_set))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),empty_set))),sK18) ),
inference(superposition,[status(thm)],[c_126,c_7258]) ).
tcf(c_32561,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ empty(X2)
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18)
| ~ subset(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),X2) ),
inference(superposition,[status(thm)],[c_7258,c_359]) ).
tcf(c_32562,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X2)
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18)
| ~ subset(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),X2) ),
inference(superposition,[status(thm)],[c_7258,c_358]) ).
tcf(c_32563,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( singleton(set_union2(X1,set_union2(sK5(iPr_def_11),X2))) = sK5(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X1,set_union2(sK5(iPr_def_11),X2))))
| ~ in(singleton(set_union2(X1,set_union2(sK5(iPr_def_11),X2))),sK18)
| ~ in(X0,singleton(set_union2(X1,set_union2(sK5(iPr_def_11),X2)))) ),
inference(superposition,[status(thm)],[c_7258,c_77]) ).
tcf(c_32564,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))))
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7258,c_65]) ).
tcf(c_32565,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18)
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7258,c_49]) ).
tcf(c_32567,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7258,c_127]) ).
tcf(c_32642,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X1,sK5(iPr_def_11)),X0)))
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_7259]) ).
tcf(c_32645,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( singleton(set_union2(empty_set,set_union2(X0,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(empty_set,set_union2(X0,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_7259]) ).
tcf(c_32646,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_7259]) ).
tcf(c_32649,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( singleton(set_union2(X0,set_union2(empty_set,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(empty_set,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_7259]) ).
tcf(c_32650,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ empty(X2)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18)
| ~ subset(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),X2) ),
inference(superposition,[status(thm)],[c_7259,c_359]) ).
tcf(c_32651,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X2)
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18)
| ~ subset(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),X2) ),
inference(superposition,[status(thm)],[c_7259,c_358]) ).
tcf(c_32652,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( singleton(set_union2(X1,set_union2(X2,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X1,set_union2(X2,sK5(iPr_def_11)))))
| ~ in(singleton(set_union2(X1,set_union2(X2,sK5(iPr_def_11)))),sK18)
| ~ in(X0,singleton(set_union2(X1,set_union2(X2,sK5(iPr_def_11))))) ),
inference(superposition,[status(thm)],[c_7259,c_77]) ).
tcf(c_32653,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))))
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7259,c_65]) ).
tcf(c_32654,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7259,c_49]) ).
tcf(c_32656,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7259,c_127]) ).
tcf(c_32852,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK0(X1,sK5(iPr_def_11)))
| in(sK0(X1,sK5(iPr_def_11)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X1) = sK5(iPr_def_11) )
| ( sK0(X1,sK5(iPr_def_11)) = X1 )
| ( sK0(X1,sK5(iPr_def_11)) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_60,c_7243]) ).
tcf(c_32853,plain,
! [X0: $i] :
( epsilon_transitive(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK1(sK5(iPr_def_11)))
| in(sK1(sK5(iPr_def_11)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK1(sK5(iPr_def_11)) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_64,c_7243]) ).
tcf(c_32854,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK2(sK5(iPr_def_11),X1,X2))
| in(sK2(sK5(iPr_def_11),X1,X2),X2)
| in(sK2(sK5(iPr_def_11),X1,X2),X1)
| in(sK2(sK5(iPr_def_11),X1,X2),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X1) = X2 )
| ( sK2(sK5(iPr_def_11),X1,X2) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_7243]) ).
tcf(c_32855,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK2(X1,X2,sK5(iPr_def_11)))
| in(sK2(X1,X2,sK5(iPr_def_11)),X2)
| in(sK2(X1,X2,sK5(iPr_def_11)),X1)
| in(sK2(X1,X2,sK5(iPr_def_11)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,X2) = sK5(iPr_def_11) )
| ( sK2(X1,X2,sK5(iPr_def_11)) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_7243]) ).
tcf(c_32856,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK2(X1,sK5(iPr_def_11),X2))
| in(sK2(X1,sK5(iPr_def_11),X2),X2)
| in(sK2(X1,sK5(iPr_def_11),X2),X1)
| in(sK2(X1,sK5(iPr_def_11),X2),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,sK5(iPr_def_11)) = X2 )
| ( sK2(X1,sK5(iPr_def_11),X2) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_7243]) ).
tcf(c_32859,plain,
! [X0: $i] :
( empty(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK5(sK5(iPr_def_11)))
| in(sK5(sK5(iPr_def_11)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK5(sK5(iPr_def_11)) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3768,c_7243]) ).
tcf(c_32860,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK0(X1,set_union2(sK5(iPr_def_11),X2)))
| in(sK0(X1,set_union2(sK5(iPr_def_11),X2)),X2)
| in(sK0(X1,set_union2(sK5(iPr_def_11),X2)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X2) = singleton(X1) )
| ( sK0(X1,set_union2(sK5(iPr_def_11),X2)) = X1 )
| ( sK0(X1,set_union2(sK5(iPr_def_11),X2)) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4023,c_7243]) ).
tcf(c_32861,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK0(X1,set_union2(X2,sK5(iPr_def_11))))
| in(sK0(X1,set_union2(X2,sK5(iPr_def_11))),X2)
| in(sK0(X1,set_union2(X2,sK5(iPr_def_11))),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X2,sK5(iPr_def_11)) = singleton(X1) )
| ( sK0(X1,set_union2(X2,sK5(iPr_def_11))) = X1 )
| ( sK0(X1,set_union2(X2,sK5(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4023,c_7243]) ).
tcf(c_32862,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| epsilon_transitive(set_union2(sK5(iPr_def_11),X1))
| in(X0,sK1(set_union2(sK5(iPr_def_11),X1)))
| in(sK1(set_union2(sK5(iPr_def_11),X1)),X1)
| in(sK1(set_union2(sK5(iPr_def_11),X1)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK1(set_union2(sK5(iPr_def_11),X1)) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4024,c_7243]) ).
tcf(c_32863,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| epsilon_transitive(set_union2(X1,sK5(iPr_def_11)))
| in(X0,sK1(set_union2(X1,sK5(iPr_def_11))))
| in(sK1(set_union2(X1,sK5(iPr_def_11))),X1)
| in(sK1(set_union2(X1,sK5(iPr_def_11))),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK1(set_union2(X1,sK5(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4024,c_7243]) ).
tcf(c_32864,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| epsilon_connected(set_union2(sK5(iPr_def_11),X1))
| in(X0,sK3(set_union2(sK5(iPr_def_11),X1)))
| in(sK3(set_union2(sK5(iPr_def_11),X1)),X1)
| in(sK3(set_union2(sK5(iPr_def_11),X1)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK3(set_union2(sK5(iPr_def_11),X1)) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4027,c_7243]) ).
tcf(c_32865,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| epsilon_connected(set_union2(X1,sK5(iPr_def_11)))
| in(X0,sK3(set_union2(X1,sK5(iPr_def_11))))
| in(sK3(set_union2(X1,sK5(iPr_def_11))),X1)
| in(sK3(set_union2(X1,sK5(iPr_def_11))),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK3(set_union2(X1,sK5(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4027,c_7243]) ).
tcf(c_32866,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| epsilon_connected(set_union2(sK5(iPr_def_11),X1))
| in(X0,sK4(set_union2(sK5(iPr_def_11),X1)))
| in(sK4(set_union2(sK5(iPr_def_11),X1)),X1)
| in(sK4(set_union2(sK5(iPr_def_11),X1)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK4(set_union2(sK5(iPr_def_11),X1)) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4028,c_7243]) ).
tcf(c_32867,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| epsilon_connected(set_union2(X1,sK5(iPr_def_11)))
| in(X0,sK4(set_union2(X1,sK5(iPr_def_11))))
| in(sK4(set_union2(X1,sK5(iPr_def_11))),X1)
| in(sK4(set_union2(X1,sK5(iPr_def_11))),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK4(set_union2(X1,sK5(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4028,c_7243]) ).
tcf(c_32868,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| empty(set_union2(sK5(iPr_def_11),X1))
| in(X0,sK5(set_union2(sK5(iPr_def_11),X1)))
| in(sK5(set_union2(sK5(iPr_def_11),X1)),X1)
| in(sK5(set_union2(sK5(iPr_def_11),X1)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK5(set_union2(sK5(iPr_def_11),X1)) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4029,c_7243]) ).
tcf(c_32869,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| empty(set_union2(X1,sK5(iPr_def_11)))
| in(X0,sK5(set_union2(X1,sK5(iPr_def_11))))
| in(sK5(set_union2(X1,sK5(iPr_def_11))),X1)
| in(sK5(set_union2(X1,sK5(iPr_def_11))),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK5(set_union2(X1,sK5(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4029,c_7243]) ).
tcf(c_32876,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X0)
| in(X0,X1)
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( X0 = X1 )
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13652,c_7243]) ).
tcf(c_32877,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( X0 = X1 )
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7241,c_7243]) ).
tcf(c_32878,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( X0 = X1 )
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7238,c_7243]) ).
tcf(c_32879,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7263,c_7243]) ).
tcf(c_32880,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( X0 = X1 )
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_7243]) ).
tcf(c_32881,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(X1,singleton(X0))
| in(singleton(X0),X1)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = X1 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_7243]) ).
tcf(c_32882,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| in(X2,set_union2(X0,X1))
| in(set_union2(X0,X1),X2)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7266,c_7243]) ).
tcf(c_32883,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X1)
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_7243]) ).
tcf(c_32884,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_7243]) ).
tcf(c_32885,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_7243]) ).
tcf(c_32886,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_7243]) ).
tcf(c_32887,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_7243]) ).
tcf(c_32888,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X1)
| in(X0,sK4(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_7243]) ).
tcf(c_32889,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_7243]) ).
tcf(c_32890,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11193,c_7243]) ).
tcf(c_32891,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_7243]) ).
tcf(c_32892,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_7243]) ).
tcf(c_32893,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(sK18))
| in(sK5(iPr_def_11),X0)
| in(sK5(sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK5(sK18) = X0 )
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_28367,c_7243]) ).
tcf(c_33456,plain,
! [X0: $i] :
( ~ in(X0,iPr_def_11)
| ( X0 = sK18 )
| in(X0,sK18) ),
inference(global_subsumption_just,[status(thm)],[c_4221,c_3592,c_4035]) ).
tcf(c_33457,plain,
! [X0: $i] :
( in(X0,sK18)
| ( X0 = sK18 )
| ~ in(X0,iPr_def_11) ),
inference(renaming,[status(thm)],[c_33456]) ).
tcf(c_33465,plain,
! [X0: $i] :
( in(sK0(X0,iPr_def_11),sK18)
| ( singleton(X0) = iPr_def_11 )
| ( sK0(X0,iPr_def_11) = sK18 )
| ( sK0(X0,iPr_def_11) = X0 ) ),
inference(superposition,[status(thm)],[c_60,c_33457]) ).
tcf(c_33466,plain,
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),sK18)
| ( sK1(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_64,c_33457]) ).
tcf(c_33467,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_11,X0,X1),sK18)
| in(sK2(iPr_def_11,X0,X1),X1)
| in(sK2(iPr_def_11,X0,X1),X0)
| ( set_union2(iPr_def_11,X0) = X1 )
| ( sK2(iPr_def_11,X0,X1) = sK18 ) ),
inference(superposition,[status(thm)],[c_68,c_33457]) ).
tcf(c_33468,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_11),sK18)
| in(sK2(X0,X1,iPr_def_11),X1)
| in(sK2(X0,X1,iPr_def_11),X0)
| ( set_union2(X0,X1) = iPr_def_11 )
| ( sK2(X0,X1,iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_68,c_33457]) ).
tcf(c_33469,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_11,X1),sK18)
| in(sK2(X0,iPr_def_11,X1),X1)
| in(sK2(X0,iPr_def_11,X1),X0)
| ( set_union2(X0,iPr_def_11) = X1 )
| ( sK2(X0,iPr_def_11,X1) = sK18 ) ),
inference(superposition,[status(thm)],[c_68,c_33457]) ).
tcf(c_33470,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),sK18)
| ( sK3(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_72,c_33457]) ).
tcf(c_33471,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),sK18)
| ( sK4(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_73,c_33457]) ).
tcf(c_33473,plain,
( epsilon_transitive(iPr_def_10)
| in(sK1(iPr_def_10),sK18)
| ( sK1(iPr_def_10) = sK18 ) ),
inference(superposition,[status(thm)],[c_3669,c_33457]) ).
tcf(c_33474,plain,
( epsilon_connected(iPr_def_10)
| in(sK3(iPr_def_10),sK18)
| ( sK3(iPr_def_10) = sK18 ) ),
inference(superposition,[status(thm)],[c_3670,c_33457]) ).
tcf(c_33475,plain,
( epsilon_connected(iPr_def_10)
| in(sK4(iPr_def_10),sK18)
| ( sK4(iPr_def_10) = sK18 ) ),
inference(superposition,[status(thm)],[c_3671,c_33457]) ).
tcf(c_33478,plain,
! [X0: $i] :
( in(sK0(X0,sK18),sK18)
| ( singleton(X0) = sK18 )
| ( sK0(X0,sK18) = sK18 )
| ( sK0(X0,sK18) = X0 ) ),
inference(superposition,[status(thm)],[c_3959,c_33457]) ).
tcf(c_33479,plain,
( empty(sK18)
| in(sK5(sK18),sK18)
| ( sK5(sK18) = sK18 ) ),
inference(superposition,[status(thm)],[c_3963,c_33457]) ).
tcf(c_33480,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(iPr_def_11,X1)),sK18)
| in(sK0(X0,set_union2(iPr_def_11,X1)),X1)
| ( set_union2(iPr_def_11,X1) = singleton(X0) )
| ( sK0(X0,set_union2(iPr_def_11,X1)) = sK18 )
| ( sK0(X0,set_union2(iPr_def_11,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_33457]) ).
tcf(c_33481,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(X1,iPr_def_11)),sK18)
| in(sK0(X0,set_union2(X1,iPr_def_11)),X1)
| ( set_union2(X1,iPr_def_11) = singleton(X0) )
| ( sK0(X0,set_union2(X1,iPr_def_11)) = sK18 )
| ( sK0(X0,set_union2(X1,iPr_def_11)) = X0 ) ),
inference(superposition,[status(thm)],[c_4023,c_33457]) ).
tcf(c_33482,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(iPr_def_11,X0))
| in(sK1(set_union2(iPr_def_11,X0)),sK18)
| in(sK1(set_union2(iPr_def_11,X0)),X0)
| ( sK1(set_union2(iPr_def_11,X0)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4024,c_33457]) ).
tcf(c_33483,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,iPr_def_11))
| in(sK1(set_union2(X0,iPr_def_11)),sK18)
| in(sK1(set_union2(X0,iPr_def_11)),X0)
| ( sK1(set_union2(X0,iPr_def_11)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4024,c_33457]) ).
tcf(c_33484,plain,
! [X0: $i] :
( epsilon_connected(set_union2(iPr_def_11,X0))
| in(sK3(set_union2(iPr_def_11,X0)),sK18)
| in(sK3(set_union2(iPr_def_11,X0)),X0)
| ( sK3(set_union2(iPr_def_11,X0)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4027,c_33457]) ).
tcf(c_33485,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,iPr_def_11))
| in(sK3(set_union2(X0,iPr_def_11)),sK18)
| in(sK3(set_union2(X0,iPr_def_11)),X0)
| ( sK3(set_union2(X0,iPr_def_11)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4027,c_33457]) ).
tcf(c_33486,plain,
! [X0: $i] :
( epsilon_connected(set_union2(iPr_def_11,X0))
| in(sK4(set_union2(iPr_def_11,X0)),sK18)
| in(sK4(set_union2(iPr_def_11,X0)),X0)
| ( sK4(set_union2(iPr_def_11,X0)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4028,c_33457]) ).
tcf(c_33487,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,iPr_def_11))
| in(sK4(set_union2(X0,iPr_def_11)),sK18)
| in(sK4(set_union2(X0,iPr_def_11)),X0)
| ( sK4(set_union2(X0,iPr_def_11)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4028,c_33457]) ).
tcf(c_33488,plain,
! [X0: $i] :
( empty(set_union2(iPr_def_11,X0))
| in(sK5(set_union2(iPr_def_11,X0)),sK18)
| in(sK5(set_union2(iPr_def_11,X0)),X0)
| ( sK5(set_union2(iPr_def_11,X0)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4029,c_33457]) ).
tcf(c_33489,plain,
! [X0: $i] :
( empty(set_union2(X0,iPr_def_11))
| in(sK5(set_union2(X0,iPr_def_11)),sK18)
| in(sK5(set_union2(X0,iPr_def_11)),X0)
| ( sK5(set_union2(X0,iPr_def_11)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4029,c_33457]) ).
tcf(c_33496,plain,
( in(sK5(iPr_def_11),sK18)
| ( sK5(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_7909,c_33457]) ).
tcf(c_33538,plain,
! [X0: $i] :
( in(sK5(set_union2(X0,iPr_def_11)),sK18)
| in(sK5(set_union2(X0,iPr_def_11)),X0)
| ( sK5(set_union2(X0,iPr_def_11)) = sK18 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33489,c_15128]) ).
tcf(c_33542,plain,
! [X0: $i] :
( in(sK5(set_union2(iPr_def_11,X0)),sK18)
| in(sK5(set_union2(iPr_def_11,X0)),X0)
| ( sK5(set_union2(iPr_def_11,X0)) = sK18 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33488,c_15070]) ).
tcf(c_33662,plain,
! [X0: $i,X1: $i] : ~ in(singleton(set_union2(X0,set_union2(iPr_def_11,X1))),sK18),
inference(superposition,[status(thm)],[c_58,c_31586]) ).
tcf(c_33666,plain,
! [X0: $i,X1: $i] : ~ in(singleton(set_union2(set_union2(X0,iPr_def_11),X1)),sK18),
inference(superposition,[status(thm)],[c_58,c_31586]) ).
tcf(c_33677,plain,
! [X0: $i] :
( ( sK5(powerset(sK5(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_31868,c_32111]) ).
tcf(c_33686,plain,
! [X0: $i] :
( empty(powerset(empty_set))
| ~ empty(X0)
| ~ subset(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_32137,c_359]) ).
tcf(c_33687,plain,
! [X0: $i] :
( empty(powerset(empty_set))
| element(empty_set,X0)
| ~ subset(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_32137,c_358]) ).
tcf(c_33688,plain,
! [X0: $i] :
( empty(powerset(empty_set))
| in(empty_set,X0)
| in(X0,empty_set)
| ( X0 = empty_set )
| ~ epsilon_connected(powerset(empty_set))
| ~ in(X0,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_32137,c_77]) ).
tcf(c_33699,plain,
! [X0: $i] :
( empty(powerset(empty_set))
| in(empty_set,X0)
| ( X0 = empty_set )
| ~ epsilon_connected(powerset(empty_set))
| ~ in(X0,powerset(empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33688,c_7097]) ).
tcf(c_33712,plain,
! [X0: $i,X1: $i] : ~ empty(set_union2(set_union2(X0,iPr_def_11),X1)),
inference(superposition,[status(thm)],[c_138,c_24111]) ).
tcf(c_33713,plain,
! [X0: $i,X1: $i] : ~ empty(set_union2(X0,set_union2(X1,iPr_def_11))),
inference(superposition,[status(thm)],[c_3397,c_24111]) ).
tcf(c_33714,plain,
! [X0: $i] :
( ~ epsilon_transitive(singleton(set_union2(X0,iPr_def_11)))
| ~ empty(singleton(set_union2(X0,iPr_def_11))) ),
inference(superposition,[status(thm)],[c_3803,c_24111]) ).
tcf(c_33715,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(set_union2(X1,X2))
| ~ subset(set_union2(X0,iPr_def_11),X1) ),
inference(superposition,[status(thm)],[c_3863,c_24111]) ).
tcf(c_33716,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ epsilon_transitive(set_union2(X2,X1))
| ~ empty(set_union2(X2,X1))
| ~ in(set_union2(X0,iPr_def_11),X1) ),
inference(superposition,[status(thm)],[c_3806,c_24111]) ).
tcf(c_33717,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ epsilon_transitive(set_union2(X1,X2))
| ~ empty(set_union2(X1,X2))
| ~ in(set_union2(X0,iPr_def_11),X1) ),
inference(superposition,[status(thm)],[c_3805,c_24111]) ).
tcf(c_33718,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(set_union2(X2,X1))
| ~ subset(set_union2(X0,iPr_def_11),X1) ),
inference(superposition,[status(thm)],[c_3865,c_24111]) ).
tcf(c_33771,plain,
! [X0: $i,X1: $i] : ~ empty(set_union2(set_union2(iPr_def_11,X0),X1)),
inference(superposition,[status(thm)],[c_58,c_33712]) ).
tcf(c_33780,plain,
! [X0: $i,X1: $i] : ~ empty(set_union2(X0,set_union2(iPr_def_11,X1))),
inference(superposition,[status(thm)],[c_58,c_33713]) ).
tcf(c_33803,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X2 )
| ( sK5(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X0)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_7234,c_359]) ).
tcf(c_33804,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X0)
| in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X2 )
| ( sK5(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_7234,c_358]) ).
tcf(c_33805,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X0,X2)
| in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| ( X0 = X2 )
| ( sK5(iPr_def_11) = X2 )
| ( sK5(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7234,c_77]) ).
tcf(c_33806,plain,
! [X0: $i,X1: $i] :
( subset(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_65]) ).
tcf(c_33808,plain,
! [X0: $i,X1: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK5(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_137]) ).
tcf(c_33809,plain,
! [X0: $i,X1: $i] :
( element(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_127]) ).
tcf(c_33810,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),sK2(sK5(iPr_def_11),X0,X1))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(sK5(iPr_def_11),X0) = X1 )
| ( sK2(sK5(iPr_def_11),X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK2(sK5(iPr_def_11),X0,X1),iPr_def_10)
| ~ in(sK2(sK5(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_7234,c_66]) ).
tcf(c_33811,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),sK2(X0,X1,sK5(iPr_def_11)))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),iPr_def_10)
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_7234,c_67]) ).
tcf(c_33812,plain,
! [X0: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK5(iPr_def_11),singleton(sK5(iPr_def_11)))
| ( sK5(iPr_def_11) = X0 )
| ( singleton(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(singleton(sK5(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_3522]) ).
tcf(c_33813,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(X0,X1))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK5(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_3641]) ).
tcf(c_33814,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(X0,X1))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK5(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_3615]) ).
tcf(c_33815,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( sK5(iPr_def_11) = X1 )
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_3618]) ).
tcf(c_33816,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( sK5(iPr_def_11) = X1 )
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_3644]) ).
tcf(c_33818,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)))
| ( sK5(iPr_def_11) = X2 )
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_3944]) ).
tcf(c_33819,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)))
| ( sK5(iPr_def_11) = X2 )
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_3945]) ).
tcf(c_33820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),sK2(set_union2(sK5(iPr_def_11),X0),X1,X2))
| ( sK5(iPr_def_11) = X3 )
| ( set_union2(set_union2(sK5(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK5(iPr_def_11),X0),X1,X2) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2),iPr_def_10)
| ~ in(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_7234,c_4078]) ).
tcf(c_33821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)))
| ( sK5(iPr_def_11) = X3 )
| ( set_union2(set_union2(X0,X1),X2) = sK5(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)),iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_7234,c_4079]) ).
tcf(c_33822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)))
| ( sK5(iPr_def_11) = X3 )
| ( set_union2(sK5(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),iPr_def_10)
| ~ in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_7234,c_4095]) ).
tcf(c_33823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)))
| ( sK5(iPr_def_11) = X3 )
| ( set_union2(X0,sK5(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),iPr_def_10)
| ~ in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_7234,c_4096]) ).
tcf(c_33824,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))))
| ( sK5(iPr_def_11) = X2 )
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_4131]) ).
tcf(c_33825,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))))
| ( sK5(iPr_def_11) = X2 )
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_4132]) ).
tcf(c_33826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_5325]) ).
tcf(c_33827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_5326]) ).
tcf(c_33828,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| in(X1,X2)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( X1 = X2 )
| ( sK5(iPr_def_11) = X2 )
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_7243]) ).
tcf(c_33829,plain,
! [X0: $i,X1: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ subset(iPr_def_11,X1)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_23189]) ).
tcf(c_33832,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = iPr_def_10 )
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_7236]) ).
tcf(c_33833,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = iPr_def_10 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK18)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_7168]) ).
tcf(c_33834,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X2 )
| ( sK5(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X0)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_7234,c_359]) ).
tcf(c_33835,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X1,X0)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X2 )
| ( sK5(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ subset(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_7234,c_358]) ).
tcf(c_33836,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X0)
| in(X0,X1)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK5(iPr_def_11) = X2 )
| ( sK5(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_7234,c_77]) ).
tcf(c_33837,plain,
! [X0: $i,X1: $i] :
( subset(X0,sK5(iPr_def_11))
| in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_65]) ).
tcf(c_33840,plain,
! [X0: $i,X1: $i] :
( element(X0,sK5(iPr_def_11))
| in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_127]) ).
tcf(c_33841,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),sK2(sK5(iPr_def_11),X0,X1))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(sK5(iPr_def_11),X0) = X1 )
| ( sK2(sK5(iPr_def_11),X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK2(sK5(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK5(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_7234,c_66]) ).
tcf(c_33842,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),sK2(X0,X1,sK5(iPr_def_11)))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_7234,c_67]) ).
tcf(c_33843,plain,
! [X0: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK5(iPr_def_11),singleton(sK5(iPr_def_11)))
| ( sK5(iPr_def_11) = X0 )
| ( singleton(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(singleton(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_3522]) ).
tcf(c_33844,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(X0,X1))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK5(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_3641]) ).
tcf(c_33845,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(X0,X1))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK5(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_3615]) ).
tcf(c_33846,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( sK5(iPr_def_11) = X1 )
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_3618]) ).
tcf(c_33847,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( sK5(iPr_def_11) = X1 )
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_3644]) ).
tcf(c_33849,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)))
| ( sK5(iPr_def_11) = X2 )
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_3944]) ).
tcf(c_33850,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)))
| ( sK5(iPr_def_11) = X2 )
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_3945]) ).
tcf(c_33851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),sK2(set_union2(sK5(iPr_def_11),X0),X1,X2))
| ( sK5(iPr_def_11) = X3 )
| ( set_union2(set_union2(sK5(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK5(iPr_def_11),X0),X1,X2) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK5(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_7234,c_4078]) ).
tcf(c_33852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)))
| ( sK5(iPr_def_11) = X3 )
| ( set_union2(set_union2(X0,X1),X2) = sK5(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK5(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_7234,c_4079]) ).
tcf(c_33853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)))
| ( sK5(iPr_def_11) = X3 )
| ( set_union2(sK5(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_7234,c_4095]) ).
tcf(c_33854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)))
| ( sK5(iPr_def_11) = X3 )
| ( set_union2(X0,sK5(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_7234,c_4096]) ).
tcf(c_33855,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))))
| ( sK5(iPr_def_11) = X2 )
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_4131]) ).
tcf(c_33856,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))))
| ( sK5(iPr_def_11) = X2 )
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_4132]) ).
tcf(c_33857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(set_union2(sK5(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_5325]) ).
tcf(c_33858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK5(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_5326]) ).
tcf(c_33859,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X0,X2)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( X0 = X2 )
| ( sK5(iPr_def_11) = X2 )
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_7243]) ).
tcf(c_33860,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ subset(iPr_def_11,X0)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_23189]) ).
tcf(c_33865,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X1)
| ~ in(X2,sK18)
| ~ in(X0,iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7234,c_359]) ).
tcf(c_33866,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X1)
| in(X2,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(X0,iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7234,c_358]) ).
tcf(c_33867,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X2 )
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X2,sK18)
| ~ in(X1,iPr_def_10)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_7234,c_77]) ).
tcf(c_33868,plain,
! [X0: $i,X1: $i] :
( subset(sK5(iPr_def_11),X1)
| in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_65]) ).
tcf(c_33870,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X1)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_137]) ).
tcf(c_33871,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_127]) ).
tcf(c_33872,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(singleton(X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(singleton(X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_62]) ).
tcf(c_33873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),X2)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X3 )
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_4213]) ).
tcf(c_33874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),X2)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X3 )
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_4212]) ).
tcf(c_33875,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_71]) ).
tcf(c_33876,plain,
! [X0: $i] :
( in(empty_set,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = empty_set )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(empty_set,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_7097]) ).
tcf(c_33877,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_12813]) ).
tcf(c_33879,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_5047]) ).
tcf(c_33881,plain,
! [X0: $i] :
( epsilon_transitive(sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK1(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK1(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK1(sK5(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_3523]) ).
tcf(c_33882,plain,
! [X0: $i] :
( epsilon_connected(sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK3(sK5(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_3524]) ).
tcf(c_33883,plain,
! [X0: $i] :
( epsilon_connected(sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK4(sK5(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_3525]) ).
tcf(c_33884,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),iPr_def_11)
| in(iPr_def_10,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = iPr_def_10 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_11)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_9540]) ).
tcf(c_33886,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_11)
| in(iPr_def_10,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = iPr_def_10 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_4912]) ).
tcf(c_33887,plain,
! [X0: $i] :
( in(iPr_def_10,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = iPr_def_10 )
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_3592]) ).
tcf(c_33889,plain,
! [X0: $i] :
( in(iPr_def_11,sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK18)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = iPr_def_11 )
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_11,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_33457]) ).
tcf(c_33891,plain,
! [X0: $i] :
( empty(sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK5(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK5(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK5(sK5(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_3900]) ).
tcf(c_33894,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X1)
| ~ in(X2,iPr_def_10)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7234,c_359]) ).
tcf(c_33895,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X1)
| in(X2,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_7234,c_358]) ).
tcf(c_33896,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X2 )
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_7234,c_77]) ).
tcf(c_33897,plain,
! [X0: $i,X1: $i] :
( subset(sK5(iPr_def_11),X0)
| in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_65]) ).
tcf(c_33900,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X0)
| in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_127]) ).
tcf(c_33901,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(singleton(X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_62]) ).
tcf(c_33902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),X2)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X3 )
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_4213]) ).
tcf(c_33903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),X2)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X3 )
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_4212]) ).
tcf(c_33904,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_71]) ).
tcf(c_33906,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_12813]) ).
tcf(c_33908,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_5047]) ).
tcf(c_33910,plain,
! [X0: $i] :
( epsilon_transitive(sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK1(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK1(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(sK1(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_3523]) ).
tcf(c_33911,plain,
! [X0: $i] :
( epsilon_connected(sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(sK3(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_3524]) ).
tcf(c_33912,plain,
! [X0: $i] :
( epsilon_connected(sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(sK4(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_3525]) ).
tcf(c_33920,plain,
! [X0: $i] :
( empty(sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK5(sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK5(sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(sK5(sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_3900]) ).
tcf(c_33934,plain,
! [X0: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(X0,sK18) ),
inference(equality_factoring,[status(thm)],[c_7234]) ).
tcf(c_33985,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33877,c_3400]) ).
tcf(c_34250,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),sK18)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = iPr_def_11 )
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_11,iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33889,c_7912]) ).
tcf(c_35143,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK0(X1,X0))
| in(sK0(X1,X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X1) = X0 )
| ( sK0(X1,X0) = X1 )
| ( sK0(X1,X0) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_60,c_7260]) ).
tcf(c_35144,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(singleton(X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( singleton(X0) = sK5(iPr_def_11) )
| ~ epsilon_connected(singleton(X0))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_61,c_7260]) ).
tcf(c_35145,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK1(X0))
| in(sK1(X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK1(X0) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_64,c_7260]) ).
tcf(c_35146,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK5(iPr_def_11),sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_7260]) ).
tcf(c_35147,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| in(sK5(iPr_def_11),sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,X2) = X0 )
| ( sK2(X1,X2,X0) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_7260]) ).
tcf(c_35148,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| in(sK5(iPr_def_11),sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_7260]) ).
tcf(c_35153,plain,
! [X0: $i] :
( empty(X0)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK5(X0))
| in(sK5(X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK5(X0) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3768,c_7260]) ).
tcf(c_35154,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X0))
| in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(powerset(X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( powerset(X0) = sK5(iPr_def_11) )
| ~ epsilon_connected(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),sK18) ),
inference(superposition,[status(thm)],[c_3769,c_7260]) ).
tcf(c_35155,plain,
( empty(powerset(empty_set))
| in(empty_set,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),empty_set)
| in(powerset(empty_set),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = empty_set )
| ( sK5(iPr_def_11) = powerset(empty_set) )
| ~ epsilon_connected(powerset(empty_set))
| ~ in(powerset(empty_set),sK18) ),
inference(superposition,[status(thm)],[c_32137,c_7260]) ).
tcf(c_35164,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK0(X1,set_union2(X0,X2)),X2)
| in(sK5(iPr_def_11),sK0(X1,set_union2(X0,X2)))
| in(sK0(X1,set_union2(X0,X2)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X2) = singleton(X1) )
| ( sK0(X1,set_union2(X0,X2)) = X1 )
| ( sK0(X1,set_union2(X0,X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4023,c_7260]) ).
tcf(c_35165,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK0(X1,set_union2(X2,X0)),X2)
| in(sK5(iPr_def_11),sK0(X1,set_union2(X2,X0)))
| in(sK0(X1,set_union2(X2,X0)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X2,X0) = singleton(X1) )
| ( sK0(X1,set_union2(X2,X0)) = X1 )
| ( sK0(X1,set_union2(X2,X0)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4023,c_7260]) ).
tcf(c_35166,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| epsilon_transitive(set_union2(X0,X1))
| in(sK1(set_union2(X0,X1)),X1)
| in(sK5(iPr_def_11),sK1(set_union2(X0,X1)))
| in(sK1(set_union2(X0,X1)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK1(set_union2(X0,X1)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4024,c_7260]) ).
tcf(c_35167,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| epsilon_transitive(set_union2(X1,X0))
| in(sK1(set_union2(X1,X0)),X1)
| in(sK5(iPr_def_11),sK1(set_union2(X1,X0)))
| in(sK1(set_union2(X1,X0)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK1(set_union2(X1,X0)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4024,c_7260]) ).
tcf(c_35168,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| epsilon_connected(set_union2(X0,X1))
| in(sK3(set_union2(X0,X1)),X1)
| in(sK5(iPr_def_11),sK3(set_union2(X0,X1)))
| in(sK3(set_union2(X0,X1)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(set_union2(X0,X1)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4027,c_7260]) ).
tcf(c_35169,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| epsilon_connected(set_union2(X1,X0))
| in(sK3(set_union2(X1,X0)),X1)
| in(sK5(iPr_def_11),sK3(set_union2(X1,X0)))
| in(sK3(set_union2(X1,X0)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(set_union2(X1,X0)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4027,c_7260]) ).
tcf(c_35170,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| epsilon_connected(set_union2(X0,X1))
| in(sK4(set_union2(X0,X1)),X1)
| in(sK5(iPr_def_11),sK4(set_union2(X0,X1)))
| in(sK4(set_union2(X0,X1)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(set_union2(X0,X1)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4028,c_7260]) ).
tcf(c_35171,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| epsilon_connected(set_union2(X1,X0))
| in(sK4(set_union2(X1,X0)),X1)
| in(sK5(iPr_def_11),sK4(set_union2(X1,X0)))
| in(sK4(set_union2(X1,X0)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(set_union2(X1,X0)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4028,c_7260]) ).
tcf(c_35172,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| empty(set_union2(X0,X1))
| in(sK5(set_union2(X0,X1)),X1)
| in(sK5(iPr_def_11),sK5(set_union2(X0,X1)))
| in(sK5(set_union2(X0,X1)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK5(set_union2(X0,X1)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4029,c_7260]) ).
tcf(c_35173,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| empty(set_union2(X1,X0))
| in(sK5(set_union2(X1,X0)),X1)
| in(sK5(iPr_def_11),sK5(set_union2(X1,X0)))
| in(sK5(set_union2(X1,X0)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK5(set_union2(X1,X0)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4029,c_7260]) ).
tcf(c_35177,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_6994,c_7260]) ).
tcf(c_35183,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_6995,c_7260]) ).
tcf(c_35219,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X1)
| in(X0,sK5(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13640,c_7260]) ).
tcf(c_35220,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9904,c_7260]) ).
tcf(c_35221,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9909,c_7260]) ).
tcf(c_35222,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9901,c_7260]) ).
tcf(c_35223,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_7260]) ).
tcf(c_35224,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X1)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_7260]) ).
tcf(c_35225,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_7260]) ).
tcf(c_35226,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_7260]) ).
tcf(c_35227,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_7260]) ).
tcf(c_35228,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_7260]) ).
tcf(c_35229,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(sK3(iPr_def_11),X0)),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(sK3(iPr_def_11),X0)))
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_9918,c_7260]) ).
tcf(c_35230,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(X0,sK3(iPr_def_11))),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X0,sK3(iPr_def_11))))
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9919,c_7260]) ).
tcf(c_35231,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(sK5(iPr_def_11),singleton(X0))
| in(singleton(X0),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(X0) = sK5(iPr_def_11) )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(sK3(iPr_def_11),sK18)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_7260]) ).
tcf(c_35232,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(sK5(iPr_def_11),set_union2(X0,X1))
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(sK3(iPr_def_11),sK18)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9930,c_7260]) ).
tcf(c_35233,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X1)
| in(X0,sK5(iPr_def_11))
| in(X0,sK4(iPr_def_11))
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13646,c_7260]) ).
tcf(c_35234,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(X0,sK4(iPr_def_11))
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11188,c_7260]) ).
tcf(c_35235,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11193,c_7260]) ).
tcf(c_35236,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(X0,sK4(iPr_def_11))
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11185,c_7260]) ).
tcf(c_35237,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(X0,sK4(iPr_def_11))
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_7260]) ).
tcf(c_35238,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X1)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_7260]) ).
tcf(c_35239,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_7260]) ).
tcf(c_35240,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_7260]) ).
tcf(c_35241,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_7260]) ).
tcf(c_35242,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_7260]) ).
tcf(c_35243,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(sK4(iPr_def_11),X0)),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(sK4(iPr_def_11),X0)))
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_11202,c_7260]) ).
tcf(c_35244,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(X0,sK4(iPr_def_11))),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X0,sK4(iPr_def_11))))
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11203,c_7260]) ).
tcf(c_35245,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(sK5(iPr_def_11),singleton(X0))
| in(singleton(X0),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(X0) = sK5(iPr_def_11) )
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(sK4(iPr_def_11),sK18)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_7260]) ).
tcf(c_35246,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(sK5(iPr_def_11),set_union2(X0,X1))
| in(set_union2(X0,X1),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(sK4(iPr_def_11),sK18)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11214,c_7260]) ).
tcf(c_35251,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK5(sK18))
| in(sK5(sK18),sK5(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(sK18) = sK5(iPr_def_11) )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(sK5(sK18),sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_31187,c_7260]) ).
tcf(c_35252,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK5(sK18))
| in(sK5(sK18),sK5(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(sK18) = sK5(iPr_def_11) )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(sK5(sK18),sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_31298,c_7260]) ).
tcf(c_35279,plain,
( empty(powerset(empty_set))
| in(empty_set,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(powerset(empty_set),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = empty_set )
| ( sK5(iPr_def_11) = powerset(empty_set) )
| ~ epsilon_connected(powerset(empty_set))
| ~ in(powerset(empty_set),sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35155,c_7097]) ).
tcf(c_35288,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35183,c_2427]) ).
tcf(c_35298,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35177,c_2427]) ).
tcf(c_36266,plain,
( subset(sK1(set_union2(sK18,singleton(sK18))),set_union2(sK18,singleton(sK18)))
| ~ subset(sK18,set_union2(sK18,singleton(sK18)))
| ( set_union2(sK18,singleton(sK18)) != set_union2(sK18,singleton(sK18)) )
| ( sK1(set_union2(sK18,singleton(sK18))) != sK18 ) ),
inference(instantiation,[status(thm)],[c_11539]) ).
tcf(c_36375,plain,
( epsilon_connected(iPr_def_11)
| ~ in(sK18,sK18)
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( sK5(iPr_def_11) = sK18 )
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_35288,c_7136,c_35288]) ).
tcf(c_36376,plain,
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(renaming,[status(thm)],[c_36375]) ).
tcf(c_36385,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36376,c_3592]) ).
tcf(c_36408,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK18,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_36385,c_359]) ).
tcf(c_36409,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_36385,c_358]) ).
tcf(c_36410,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(sK18,sK18)
| ~ in(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_36385,c_77]) ).
tcf(c_36411,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_36385,c_65]) ).
tcf(c_36413,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK4(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_36385,c_137]) ).
tcf(c_36414,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_36385,c_127]) ).
tcf(c_36531,plain,
( epsilon_connected(iPr_def_11)
| ~ in(sK18,sK18)
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( sK5(iPr_def_11) = sK18 )
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_35298,c_7136,c_35298]) ).
tcf(c_36532,plain,
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(renaming,[status(thm)],[c_36531]) ).
tcf(c_36541,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36532,c_3592]) ).
tcf(c_36564,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK18,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_36541,c_359]) ).
tcf(c_36565,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_36541,c_358]) ).
tcf(c_36566,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(sK18,sK18)
| ~ in(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_36541,c_77]) ).
tcf(c_36567,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_36541,c_65]) ).
tcf(c_36569,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_36541,c_137]) ).
tcf(c_36570,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_36541,c_127]) ).
tcf(c_36643,plain,
! [X0: $i] :
( empty(sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK5(sK18),X0)
| in(sK5(sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK5(sK18) = X0 )
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_11)
| ~ epsilon_connected(sK5(sK18))
| ~ in(X0,iPr_def_11)
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_4222,c_7260]) ).
tcf(c_36644,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK5(sK18),X1)
| ( sK5(sK18) = X1 )
| ~ epsilon_connected(iPr_def_11)
| ~ empty(X0)
| ~ in(X1,iPr_def_11)
| ~ subset(sK5(sK18),X0) ),
inference(superposition,[status(thm)],[c_4222,c_359]) ).
tcf(c_36645,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| element(X1,X0)
| in(sK5(sK18),X1)
| ( sK5(sK18) = X1 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X1,iPr_def_11)
| ~ subset(sK5(sK18),X0) ),
inference(superposition,[status(thm)],[c_4222,c_358]) ).
tcf(c_36646,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(X1,X0)
| in(X0,X1)
| in(sK5(sK18),X1)
| ( X0 = X1 )
| ( sK5(sK18) = X1 )
| ~ epsilon_connected(iPr_def_11)
| ~ epsilon_connected(sK5(sK18))
| ~ in(X1,iPr_def_11)
| ~ in(X0,sK5(sK18)) ),
inference(superposition,[status(thm)],[c_4222,c_77]) ).
tcf(c_36647,plain,
! [X0: $i] :
( empty(sK18)
| subset(X0,sK5(sK18))
| in(sK5(sK18),X0)
| ( sK5(sK18) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_65]) ).
tcf(c_36649,plain,
! [X0: $i] :
( empty(sK18)
| in(sK5(sK18),X0)
| ( sK5(sK18) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ empty(sK5(sK18))
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_137]) ).
tcf(c_36650,plain,
! [X0: $i] :
( empty(sK18)
| element(X0,sK5(sK18))
| in(sK5(sK18),X0)
| ( sK5(sK18) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_127]) ).
tcf(c_36651,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK5(sK18),sK2(sK5(sK18),X0,X1))
| ( set_union2(sK5(sK18),X0) = X1 )
| ( sK2(sK5(sK18),X0,X1) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK2(sK5(sK18),X0,X1),iPr_def_11)
| ~ in(sK2(sK5(sK18),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_4222,c_66]) ).
tcf(c_36652,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK5(sK18),sK2(X0,X1,sK5(sK18)))
| ( set_union2(X0,X1) = sK5(sK18) )
| ( sK2(X0,X1,sK5(sK18)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK2(X0,X1,sK5(sK18)),iPr_def_11)
| ~ in(sK2(X0,X1,sK5(sK18)),X1) ),
inference(superposition,[status(thm)],[c_4222,c_67]) ).
tcf(c_36653,plain,
( empty(sK18)
| in(sK5(sK18),singleton(sK5(sK18)))
| ( singleton(sK5(sK18)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(sK5(sK18)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_3522]) ).
tcf(c_36654,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK5(sK18),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK5(sK18),X1)
| ~ in(set_union2(X0,X1),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_3641]) ).
tcf(c_36655,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK5(sK18),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK5(sK18),X0)
| ~ in(set_union2(X0,X1),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_3615]) ).
tcf(c_36656,plain,
! [X0: $i] :
( empty(sK18)
| in(sK5(sK18),singleton(set_union2(sK5(sK18),X0)))
| ( singleton(set_union2(sK5(sK18),X0)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(set_union2(sK5(sK18),X0)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_3618]) ).
tcf(c_36657,plain,
! [X0: $i] :
( empty(sK18)
| in(sK5(sK18),singleton(set_union2(X0,sK5(sK18))))
| ( singleton(set_union2(X0,sK5(sK18))) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(set_union2(X0,sK5(sK18))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_3644]) ).
tcf(c_36659,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK5(sK18),singleton(set_union2(set_union2(sK5(sK18),X0),X1)))
| ( singleton(set_union2(set_union2(sK5(sK18),X0),X1)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(set_union2(set_union2(sK5(sK18),X0),X1)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_3944]) ).
tcf(c_36660,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK5(sK18),singleton(set_union2(set_union2(X0,sK5(sK18)),X1)))
| ( singleton(set_union2(set_union2(X0,sK5(sK18)),X1)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(set_union2(set_union2(X0,sK5(sK18)),X1)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_3945]) ).
tcf(c_36661,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK18)
| in(sK5(sK18),sK2(set_union2(sK5(sK18),X0),X1,X2))
| ( set_union2(set_union2(sK5(sK18),X0),X1) = X2 )
| ( sK2(set_union2(sK5(sK18),X0),X1,X2) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK2(set_union2(sK5(sK18),X0),X1,X2),iPr_def_11)
| ~ in(sK2(set_union2(sK5(sK18),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_4222,c_4078]) ).
tcf(c_36662,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK18)
| in(sK5(sK18),sK2(set_union2(X0,X1),X2,sK5(sK18)))
| ( set_union2(set_union2(X0,X1),X2) = sK5(sK18) )
| ( sK2(set_union2(X0,X1),X2,sK5(sK18)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK2(set_union2(X0,X1),X2,sK5(sK18)),iPr_def_11)
| ~ in(sK2(set_union2(X0,X1),X2,sK5(sK18)),X1) ),
inference(superposition,[status(thm)],[c_4222,c_4079]) ).
tcf(c_36663,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK18)
| in(sK5(sK18),sK2(X0,X1,set_union2(sK5(sK18),X2)))
| ( set_union2(sK5(sK18),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK5(sK18),X2)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK2(X0,X1,set_union2(sK5(sK18),X2)),iPr_def_11)
| ~ in(sK2(X0,X1,set_union2(sK5(sK18),X2)),X1) ),
inference(superposition,[status(thm)],[c_4222,c_4095]) ).
tcf(c_36664,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK18)
| in(sK5(sK18),sK2(X0,sK5(sK18),set_union2(X1,X2)))
| ( set_union2(X0,sK5(sK18)) = set_union2(X1,X2) )
| ( sK2(X0,sK5(sK18),set_union2(X1,X2)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK2(X0,sK5(sK18),set_union2(X1,X2)),iPr_def_11)
| ~ in(sK2(X0,sK5(sK18),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4222,c_4096]) ).
tcf(c_36666,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK5(sK18),singleton(set_union2(X0,set_union2(sK5(sK18),X1))))
| ( singleton(set_union2(X0,set_union2(sK5(sK18),X1))) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(set_union2(X0,set_union2(sK5(sK18),X1))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_4131]) ).
tcf(c_36667,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK5(sK18),singleton(set_union2(X0,set_union2(X1,sK5(sK18)))))
| ( singleton(set_union2(X0,set_union2(X1,sK5(sK18)))) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(sK18)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_4132]) ).
tcf(c_36668,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK18)
| in(sK5(sK18),singleton(set_union2(set_union2(set_union2(sK5(sK18),X0),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(sK5(sK18),X0),X1),X2)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(set_union2(set_union2(set_union2(sK5(sK18),X0),X1),X2)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_5325]) ).
tcf(c_36669,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK18)
| in(sK5(sK18),singleton(set_union2(set_union2(set_union2(X0,sK5(sK18)),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(X0,sK5(sK18)),X1),X2)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK5(sK18)),X1),X2)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_5326]) ).
tcf(c_36670,plain,
! [X0: $i] :
( empty(sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(X0,sK5(sK18))
| in(sK5(iPr_def_11),sK5(sK18))
| in(sK5(sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK5(sK18) = X0 )
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_11)
| ~ epsilon_connected(X0)
| ~ in(X0,iPr_def_11)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4222,c_7260]) ).
tcf(c_36671,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(X0,sK5(sK18))
| ( sK5(sK18) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ empty(X1)
| ~ in(X0,iPr_def_11)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4222,c_359]) ).
tcf(c_36672,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| element(sK5(sK18),X1)
| in(X0,sK5(sK18))
| ( sK5(sK18) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X0,iPr_def_11)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4222,c_358]) ).
tcf(c_36673,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(X1,sK5(sK18))
| in(X0,sK5(sK18))
| in(sK5(sK18),X0)
| ( sK5(sK18) = X1 )
| ( sK5(sK18) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ epsilon_connected(X1)
| ~ in(X1,iPr_def_11)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4222,c_77]) ).
tcf(c_36674,plain,
! [X0: $i] :
( empty(sK18)
| subset(sK5(sK18),X0)
| in(X0,sK5(sK18))
| ( sK5(sK18) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ epsilon_transitive(X0)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_65]) ).
tcf(c_36676,plain,
! [X0: $i] :
( empty(sK18)
| in(X0,sK5(sK18))
| ( sK5(sK18) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ empty(X0)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_137]) ).
tcf(c_36677,plain,
! [X0: $i] :
( empty(sK18)
| element(sK5(sK18),X0)
| in(X0,sK5(sK18))
| ( sK5(sK18) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_127]) ).
tcf(c_36678,plain,
! [X0: $i] :
( empty(sK18)
| in(singleton(X0),sK5(sK18))
| ( sK5(sK18) = X0 )
| ( singleton(X0) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_62]) ).
tcf(c_36679,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK18)
| in(X2,sK5(sK18))
| in(sK5(sK18),X2)
| in(set_union2(X0,X1),sK5(sK18))
| ( sK5(sK18) = X2 )
| ( set_union2(X0,X1) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_4213]) ).
tcf(c_36680,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK18)
| in(X2,sK5(sK18))
| in(sK5(sK18),X2)
| in(set_union2(X0,X1),sK5(sK18))
| ( sK5(sK18) = X2 )
| ( set_union2(X0,X1) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_4212]) ).
tcf(c_36681,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK5(sK18),X1)
| in(sK5(sK18),X0)
| in(set_union2(X0,X1),sK5(sK18))
| ( set_union2(X0,X1) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(set_union2(X0,X1),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_71]) ).
tcf(c_36682,plain,
( empty(sK18)
| in(empty_set,sK5(sK18))
| ( sK5(sK18) = empty_set )
| ~ epsilon_connected(iPr_def_11)
| ~ in(empty_set,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_7097]) ).
tcf(c_36684,plain,
( empty(sK18)
| in(sK18,sK5(sK18))
| ( sK5(sK18) = sK18 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK18,iPr_def_11)
| ~ in(iPr_def_11,sK5(sK18)) ),
inference(superposition,[status(thm)],[c_4222,c_6841]) ).
tcf(c_36686,plain,
( empty(sK18)
| in(sK18,sK5(sK18))
| in(sK5(sK18),iPr_def_11)
| ( sK5(sK18) = sK18 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK18,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_3640]) ).
tcf(c_36687,plain,
( empty(sK18)
| epsilon_transitive(sK5(sK18))
| in(sK1(sK5(sK18)),sK5(sK18))
| ( sK1(sK5(sK18)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK1(sK5(sK18)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_3523]) ).
tcf(c_36688,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| in(sK3(sK5(sK18)),sK5(sK18))
| ( sK3(sK5(sK18)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK3(sK5(sK18)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_3524]) ).
tcf(c_36689,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| in(sK4(sK5(sK18)),sK5(sK18))
| ( sK4(sK5(sK18)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK4(sK5(sK18)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_3525]) ).
tcf(c_36691,plain,
( empty(sK18)
| in(iPr_def_10,sK5(sK18))
| ( sK5(sK18) = iPr_def_10 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(iPr_def_10,iPr_def_11)
| ~ in(iPr_def_11,sK5(sK18)) ),
inference(superposition,[status(thm)],[c_4222,c_6289]) ).
tcf(c_36693,plain,
( empty(sK18)
| in(iPr_def_10,sK5(sK18))
| ( sK5(sK18) = iPr_def_10 )
| ( sK5(sK18) = sK18 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_3592]) ).
tcf(c_36694,plain,
( empty(sK18)
| in(iPr_def_10,sK5(sK18))
| in(sK5(sK18),iPr_def_11)
| ( sK5(sK18) = iPr_def_10 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_3614]) ).
tcf(c_36695,plain,
( empty(sK18)
| in(iPr_def_11,sK5(sK18))
| in(sK5(sK18),sK18)
| ( sK5(sK18) = iPr_def_11 )
| ( sK5(sK18) = sK18 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(iPr_def_11,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_33457]) ).
tcf(c_36696,plain,
( empty(sK18)
| in(iPr_def_11,sK5(sK18))
| in(sK5(sK18),iPr_def_10)
| in(sK5(sK18),sK18)
| ( sK5(sK18) = iPr_def_11 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(iPr_def_11,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_4035]) ).
tcf(c_36697,plain,
( empty(sK18)
| empty(sK5(sK18))
| in(sK5(sK5(sK18)),sK5(sK18))
| ( sK5(sK5(sK18)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK5(sK5(sK18)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_3900]) ).
tcf(c_36698,plain,
! [X0: $i] :
( empty(sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(sK18))
| in(sK5(iPr_def_11),X0)
| in(sK5(sK18),X0)
| in(sK5(iPr_def_11),sK5(sK18))
| ( sK5(iPr_def_11) = X0 )
| ( sK5(sK18) = X0 )
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_11)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_7243]) ).
tcf(c_36699,plain,
( empty(sK18)
| in(sK5(iPr_def_11),sK5(sK18))
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_11)
| ~ subset(iPr_def_11,sK5(sK18))
| ~ in(sK5(iPr_def_11),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_23189]) ).
tcf(c_36719,plain,
( empty(sK18)
| in(sK18,sK5(sK18))
| in(sK5(sK18),iPr_def_11)
| ( sK5(sK18) = sK18 )
| ~ epsilon_connected(iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36686,c_3672]) ).
tcf(c_36755,plain,
( empty(sK18)
| in(sK18,sK5(sK18))
| ( sK5(sK18) = sK18 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(iPr_def_11,sK5(sK18)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36684,c_3672]) ).
tcf(c_36775,plain,
( empty(sK18)
| in(sK5(iPr_def_11),sK5(sK18))
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_11)
| ~ subset(iPr_def_11,sK5(sK18)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36699,c_7909]) ).
tcf(c_36979,plain,
! [X0: $i] :
( empty(sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(sK18))
| in(sK5(iPr_def_11),X0)
| in(sK5(sK18),X0)
| in(sK5(iPr_def_11),sK5(sK18))
| ( sK5(iPr_def_11) = X0 )
| ( sK5(sK18) = X0 )
| ( sK5(sK18) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_11)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36698,c_7909]) ).
tcf(c_37160,plain,
! [X0: $i,X1: $i] : ~ in(singleton(set_union2(X0,set_union2(X1,iPr_def_11))),sK18),
inference(superposition,[status(thm)],[c_58,c_33662]) ).
tcf(c_37180,plain,
! [X0: $i] :
( ~ epsilon_transitive(singleton(set_union2(iPr_def_11,X0)))
| ~ empty(singleton(set_union2(iPr_def_11,X0))) ),
inference(superposition,[status(thm)],[c_3803,c_24112]) ).
tcf(c_37181,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(set_union2(X1,X2))
| ~ subset(set_union2(iPr_def_11,X0),X1) ),
inference(superposition,[status(thm)],[c_3863,c_24112]) ).
tcf(c_37182,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ epsilon_transitive(set_union2(X2,X1))
| ~ empty(set_union2(X2,X1))
| ~ in(set_union2(iPr_def_11,X0),X1) ),
inference(superposition,[status(thm)],[c_3806,c_24112]) ).
tcf(c_37183,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ epsilon_transitive(set_union2(X1,X2))
| ~ empty(set_union2(X1,X2))
| ~ in(set_union2(iPr_def_11,X0),X1) ),
inference(superposition,[status(thm)],[c_3805,c_24112]) ).
tcf(c_37184,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(set_union2(X2,X1))
| ~ subset(set_union2(iPr_def_11,X0),X1) ),
inference(superposition,[status(thm)],[c_3865,c_24112]) ).
tcf(c_37209,plain,
! [X0: $i,X1: $i] : ~ empty(set_union2(set_union2(iPr_def_10,X0),X1)),
inference(superposition,[status(thm)],[c_138,c_25170]) ).
tcf(c_37210,plain,
! [X0: $i,X1: $i] : ~ empty(set_union2(X0,set_union2(iPr_def_10,X1))),
inference(superposition,[status(thm)],[c_3397,c_25170]) ).
tcf(c_37211,plain,
! [X0: $i] :
( ~ epsilon_transitive(singleton(set_union2(iPr_def_10,X0)))
| ~ empty(singleton(set_union2(iPr_def_10,X0))) ),
inference(superposition,[status(thm)],[c_3803,c_25170]) ).
tcf(c_37212,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(set_union2(X1,X2))
| ~ subset(set_union2(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_3863,c_25170]) ).
tcf(c_37213,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ epsilon_transitive(set_union2(X2,X1))
| ~ empty(set_union2(X2,X1))
| ~ in(set_union2(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_3806,c_25170]) ).
tcf(c_37214,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ epsilon_transitive(set_union2(X1,X2))
| ~ empty(set_union2(X1,X2))
| ~ in(set_union2(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_3805,c_25170]) ).
tcf(c_37215,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(set_union2(X2,X1))
| ~ subset(set_union2(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_3865,c_25170]) ).
tcf(c_37242,plain,
! [X0: $i,X1: $i] : ~ empty(set_union2(set_union2(X0,iPr_def_10),X1)),
inference(superposition,[status(thm)],[c_58,c_37209]) ).
tcf(c_37283,plain,
! [X0: $i,X1: $i] : ~ empty(set_union2(X0,set_union2(X1,iPr_def_10))),
inference(superposition,[status(thm)],[c_58,c_37210]) ).
tcf(c_37299,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X1,set_union2(sK3(iPr_def_11),X0))))
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_9920]) ).
tcf(c_37301,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),set_union2(sK3(iPr_def_11),X0))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),set_union2(sK3(iPr_def_11),X0))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_9920]) ).
tcf(c_37302,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),empty_set)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_126,c_9920]) ).
tcf(c_37303,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_9920]) ).
tcf(c_37305,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),sK3(iPr_def_11)),X0)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),sK3(iPr_def_11)),X0)),sK18) ),
inference(superposition,[status(thm)],[c_97,c_9920]) ).
tcf(c_37306,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),empty_set),X0)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),empty_set),X0)),sK18) ),
inference(superposition,[status(thm)],[c_126,c_9920]) ).
tcf(c_37307,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)))
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9920,c_7260]) ).
tcf(c_37308,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ empty(X2)
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18)
| ~ subset(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),X2) ),
inference(superposition,[status(thm)],[c_9920,c_359]) ).
tcf(c_37309,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X2)
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18)
| ~ subset(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),X2) ),
inference(superposition,[status(thm)],[c_9920,c_358]) ).
tcf(c_37310,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X1),X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(set_union2(sK3(iPr_def_11),X1),X2)))
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X1),X2)),sK18)
| ~ in(X0,singleton(set_union2(set_union2(sK3(iPr_def_11),X1),X2))) ),
inference(superposition,[status(thm)],[c_9920,c_77]) ).
tcf(c_37311,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)))
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9920,c_65]) ).
tcf(c_37312,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18)
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9920,c_49]) ).
tcf(c_37314,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9920,c_127]) ).
tcf(c_37433,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X1,set_union2(X0,sK3(iPr_def_11)))))
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_9921]) ).
tcf(c_37435,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),set_union2(X0,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),set_union2(X0,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_9921]) ).
tcf(c_37436,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),empty_set)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_126,c_9921]) ).
tcf(c_37437,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_9921]) ).
tcf(c_37440,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(empty_set,sK3(iPr_def_11)),X0)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(empty_set,sK3(iPr_def_11)),X0)),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_9921]) ).
tcf(c_37441,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)))
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9921,c_7260]) ).
tcf(c_37442,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ empty(X2)
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18)
| ~ subset(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),X2) ),
inference(superposition,[status(thm)],[c_9921,c_359]) ).
tcf(c_37443,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X2)
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18)
| ~ subset(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),X2) ),
inference(superposition,[status(thm)],[c_9921,c_358]) ).
tcf(c_37444,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ( singleton(set_union2(set_union2(X1,sK3(iPr_def_11)),X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(set_union2(X1,sK3(iPr_def_11)),X2)))
| ~ in(singleton(set_union2(set_union2(X1,sK3(iPr_def_11)),X2)),sK18)
| ~ in(X0,singleton(set_union2(set_union2(X1,sK3(iPr_def_11)),X2))) ),
inference(superposition,[status(thm)],[c_9921,c_77]) ).
tcf(c_37445,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)))
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9921,c_65]) ).
tcf(c_37446,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18)
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9921,c_49]) ).
tcf(c_37448,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_9921,c_127]) ).
tcf(c_37563,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(sK3(iPr_def_11),X1),X0)))
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_9922]) ).
tcf(c_37566,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( singleton(set_union2(empty_set,set_union2(sK3(iPr_def_11),X0))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(empty_set,set_union2(sK3(iPr_def_11),X0))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_9922]) ).
tcf(c_37567,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_9922]) ).
tcf(c_37569,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_9922]) ).
tcf(c_37570,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),empty_set))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),empty_set))),sK18) ),
inference(superposition,[status(thm)],[c_126,c_9922]) ).
tcf(c_37571,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))))
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_9922,c_7260]) ).
tcf(c_37572,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ empty(X2)
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18)
| ~ subset(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),X2) ),
inference(superposition,[status(thm)],[c_9922,c_359]) ).
tcf(c_37573,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X2)
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18)
| ~ subset(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),X2) ),
inference(superposition,[status(thm)],[c_9922,c_358]) ).
tcf(c_37574,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ( singleton(set_union2(X1,set_union2(sK3(iPr_def_11),X2))) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X1,set_union2(sK3(iPr_def_11),X2))))
| ~ in(singleton(set_union2(X1,set_union2(sK3(iPr_def_11),X2))),sK18)
| ~ in(X0,singleton(set_union2(X1,set_union2(sK3(iPr_def_11),X2)))) ),
inference(superposition,[status(thm)],[c_9922,c_77]) ).
tcf(c_37575,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))))
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_9922,c_65]) ).
tcf(c_37576,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18)
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9922,c_49]) ).
tcf(c_37578,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_9922,c_127]) ).
tcf(c_37669,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X1,sK3(iPr_def_11)),X0)))
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_9923]) ).
tcf(c_37672,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( singleton(set_union2(empty_set,set_union2(X0,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(empty_set,set_union2(X0,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_9923]) ).
tcf(c_37673,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_9923]) ).
tcf(c_37676,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( singleton(set_union2(X0,set_union2(empty_set,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(empty_set,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_9923]) ).
tcf(c_37677,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))))
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_9923,c_7260]) ).
tcf(c_37678,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ empty(X2)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18)
| ~ subset(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),X2) ),
inference(superposition,[status(thm)],[c_9923,c_359]) ).
tcf(c_37679,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X2)
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18)
| ~ subset(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),X2) ),
inference(superposition,[status(thm)],[c_9923,c_358]) ).
tcf(c_37680,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ( singleton(set_union2(X1,set_union2(X2,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X1,set_union2(X2,sK3(iPr_def_11)))))
| ~ in(singleton(set_union2(X1,set_union2(X2,sK3(iPr_def_11)))),sK18)
| ~ in(X0,singleton(set_union2(X1,set_union2(X2,sK3(iPr_def_11))))) ),
inference(superposition,[status(thm)],[c_9923,c_77]) ).
tcf(c_37681,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))))
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_9923,c_65]) ).
tcf(c_37682,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9923,c_49]) ).
tcf(c_37684,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_9923,c_127]) ).
tcf(c_37805,plain,
( ( sK1(set_union2(sK18,singleton(sK18))) = sK18 )
| ~ in(sK1(set_union2(sK18,singleton(sK18))),singleton(sK18)) ),
inference(instantiation,[status(thm)],[c_12898]) ).
tcf(c_37826,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X1,set_union2(sK4(iPr_def_11),X0))))
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_11204]) ).
tcf(c_37828,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),set_union2(sK4(iPr_def_11),X0))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),set_union2(sK4(iPr_def_11),X0))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_11204]) ).
tcf(c_37829,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),empty_set)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_126,c_11204]) ).
tcf(c_37830,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_11204]) ).
tcf(c_37832,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),sK4(iPr_def_11)),X0)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),sK4(iPr_def_11)),X0)),sK18) ),
inference(superposition,[status(thm)],[c_97,c_11204]) ).
tcf(c_37833,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),empty_set),X0)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),empty_set),X0)),sK18) ),
inference(superposition,[status(thm)],[c_126,c_11204]) ).
tcf(c_37834,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)))
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11204,c_7260]) ).
tcf(c_37835,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ empty(X2)
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18)
| ~ subset(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),X2) ),
inference(superposition,[status(thm)],[c_11204,c_359]) ).
tcf(c_37836,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X2)
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18)
| ~ subset(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),X2) ),
inference(superposition,[status(thm)],[c_11204,c_358]) ).
tcf(c_37837,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X1),X2)) = sK4(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(set_union2(sK4(iPr_def_11),X1),X2)))
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X1),X2)),sK18)
| ~ in(X0,singleton(set_union2(set_union2(sK4(iPr_def_11),X1),X2))) ),
inference(superposition,[status(thm)],[c_11204,c_77]) ).
tcf(c_37838,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)))
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11204,c_65]) ).
tcf(c_37839,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18)
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11204,c_49]) ).
tcf(c_37841,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11204,c_127]) ).
tcf(c_38049,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X1,set_union2(X0,sK4(iPr_def_11)))))
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_11205]) ).
tcf(c_38051,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),set_union2(X0,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),set_union2(X0,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_11205]) ).
tcf(c_38052,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),empty_set)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_126,c_11205]) ).
tcf(c_38053,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_58,c_11205]) ).
tcf(c_38056,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( singleton(set_union2(set_union2(empty_set,sK4(iPr_def_11)),X0)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(empty_set,sK4(iPr_def_11)),X0)),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_11205]) ).
tcf(c_38057,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)))
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11205,c_7260]) ).
tcf(c_38058,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ empty(X2)
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18)
| ~ subset(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),X2) ),
inference(superposition,[status(thm)],[c_11205,c_359]) ).
tcf(c_38059,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X2)
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18)
| ~ subset(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),X2) ),
inference(superposition,[status(thm)],[c_11205,c_358]) ).
tcf(c_38060,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ( singleton(set_union2(set_union2(X1,sK4(iPr_def_11)),X2)) = sK4(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(set_union2(X1,sK4(iPr_def_11)),X2)))
| ~ in(singleton(set_union2(set_union2(X1,sK4(iPr_def_11)),X2)),sK18)
| ~ in(X0,singleton(set_union2(set_union2(X1,sK4(iPr_def_11)),X2))) ),
inference(superposition,[status(thm)],[c_11205,c_77]) ).
tcf(c_38061,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)))
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11205,c_65]) ).
tcf(c_38062,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18)
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11205,c_49]) ).
tcf(c_38064,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_11205,c_127]) ).
tcf(c_38215,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(sK4(iPr_def_11),X1),X0)))
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_11206]) ).
tcf(c_38218,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( singleton(set_union2(empty_set,set_union2(sK4(iPr_def_11),X0))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(empty_set,set_union2(sK4(iPr_def_11),X0))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_11206]) ).
tcf(c_38219,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_11206]) ).
tcf(c_38221,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_11206]) ).
tcf(c_38222,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),empty_set))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),empty_set))),sK18) ),
inference(superposition,[status(thm)],[c_126,c_11206]) ).
tcf(c_38223,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))))
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_11206,c_7260]) ).
tcf(c_38224,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ empty(X2)
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18)
| ~ subset(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),X2) ),
inference(superposition,[status(thm)],[c_11206,c_359]) ).
tcf(c_38225,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X2)
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18)
| ~ subset(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),X2) ),
inference(superposition,[status(thm)],[c_11206,c_358]) ).
tcf(c_38226,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ( singleton(set_union2(X1,set_union2(sK4(iPr_def_11),X2))) = sK4(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X1,set_union2(sK4(iPr_def_11),X2))))
| ~ in(singleton(set_union2(X1,set_union2(sK4(iPr_def_11),X2))),sK18)
| ~ in(X0,singleton(set_union2(X1,set_union2(sK4(iPr_def_11),X2)))) ),
inference(superposition,[status(thm)],[c_11206,c_77]) ).
tcf(c_38227,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))))
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_11206,c_65]) ).
tcf(c_38228,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18)
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11206,c_49]) ).
tcf(c_38230,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_11206,c_127]) ).
tcf(c_38332,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X1,sK4(iPr_def_11)),X0)))
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_11207]) ).
tcf(c_38335,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( singleton(set_union2(empty_set,set_union2(X0,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(empty_set,set_union2(X0,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_11207]) ).
tcf(c_38336,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_11207]) ).
tcf(c_38339,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( singleton(set_union2(X0,set_union2(empty_set,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(empty_set,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_11207]) ).
tcf(c_38340,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))))
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_11207,c_7260]) ).
tcf(c_38341,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ empty(X2)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18)
| ~ subset(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),X2) ),
inference(superposition,[status(thm)],[c_11207,c_359]) ).
tcf(c_38342,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X2)
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18)
| ~ subset(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),X2) ),
inference(superposition,[status(thm)],[c_11207,c_358]) ).
tcf(c_38343,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ( singleton(set_union2(X1,set_union2(X2,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X1,set_union2(X2,sK4(iPr_def_11)))))
| ~ in(singleton(set_union2(X1,set_union2(X2,sK4(iPr_def_11)))),sK18)
| ~ in(X0,singleton(set_union2(X1,set_union2(X2,sK4(iPr_def_11))))) ),
inference(superposition,[status(thm)],[c_11207,c_77]) ).
tcf(c_38344,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))))
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_11207,c_65]) ).
tcf(c_38345,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_11207,c_49]) ).
tcf(c_38347,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_11207,c_127]) ).
tcf(c_38464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK2(X0,X1,X2),X3)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X3 )
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X3 )
| ( sK2(X0,X1,X2) = sK5(iPr_def_11) )
| ~ epsilon_connected(X2)
| ~ in(X3,X2)
| ~ epsilon_connected(sK2(X0,X1,X2))
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4329,c_7260]) ).
tcf(c_38465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X4)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X4 )
| ~ epsilon_connected(X2)
| ~ empty(X3)
| ~ in(X4,X2)
| ~ subset(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_4329,c_359]) ).
tcf(c_38466,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(X4,X3)
| in(sK2(X0,X1,X2),X4)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X4 )
| ~ epsilon_connected(X2)
| ~ in(X4,X2)
| ~ subset(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_4329,c_358]) ).
tcf(c_38467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X4,X0)
| in(X0,X4)
| in(sK2(X1,X2,X3),X4)
| in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X1)
| ( X0 = X4 )
| ( set_union2(X1,X2) = X3 )
| ( sK2(X1,X2,X3) = X4 )
| ~ epsilon_connected(X3)
| ~ in(X4,X3)
| ~ epsilon_connected(sK2(X1,X2,X3))
| ~ in(X0,sK2(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_4329,c_77]) ).
tcf(c_38468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X3)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X3 )
| ~ epsilon_connected(X2)
| ~ in(X3,X2)
| ~ epsilon_transitive(sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4329,c_65]) ).
tcf(c_38470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,X2),X3)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X3 )
| ~ epsilon_connected(X2)
| ~ in(X3,X2)
| ~ empty(sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4329,c_137]) ).
tcf(c_38471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X0,sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),X3)
| in(sK2(X2,X3,X1),X2)
| in(sK2(X2,X3,X1),X0)
| ( set_union2(X2,X3) = X1 )
| ( sK2(X2,X3,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_127]) ).
tcf(c_38472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK2(sK2(X0,X1,X2),X3,X4))
| ( set_union2(X0,X1) = X2 )
| ( set_union2(sK2(X0,X1,X2),X3) = X4 )
| ( sK2(sK2(X0,X1,X2),X3,X4) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X2)
| ~ in(sK2(sK2(X0,X1,X2),X3,X4),X4)
| ~ in(sK2(sK2(X0,X1,X2),X3,X4),X2) ),
inference(superposition,[status(thm)],[c_4329,c_66]) ).
tcf(c_38473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X4),X3)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X2,X3,X4),sK2(X0,X1,sK2(X2,X3,X4)))
| ( set_union2(X2,X3) = X4 )
| ( sK2(X2,X3,X4) = set_union2(X0,X1) )
| ( sK2(X0,X1,sK2(X2,X3,X4)) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X4)
| ~ in(sK2(X0,X1,sK2(X2,X3,X4)),X4)
| ~ in(sK2(X0,X1,sK2(X2,X3,X4)),X1) ),
inference(superposition,[status(thm)],[c_4329,c_67]) ).
tcf(c_38474,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),singleton(sK2(X0,X1,X2)))
| ( set_union2(X0,X1) = X2 )
| ( singleton(sK2(X0,X1,X2)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X2)
| ~ in(singleton(sK2(X0,X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4329,c_3522]) ).
tcf(c_38475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),set_union2(X4,X3))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = set_union2(X4,X3) )
| ~ epsilon_connected(X2)
| ~ in(set_union2(X4,X3),X2)
| ~ in(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_4329,c_3641]) ).
tcf(c_38476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),set_union2(X3,X4))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = set_union2(X3,X4) )
| ~ epsilon_connected(X2)
| ~ in(set_union2(X3,X4),X2)
| ~ in(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_4329,c_3615]) ).
tcf(c_38477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),singleton(set_union2(sK2(X0,X1,X2),X3)))
| ( set_union2(X0,X1) = X2 )
| ( singleton(set_union2(sK2(X0,X1,X2),X3)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X2)
| ~ in(singleton(set_union2(sK2(X0,X1,X2),X3)),X2) ),
inference(superposition,[status(thm)],[c_4329,c_3618]) ).
tcf(c_38478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),singleton(set_union2(X0,sK2(X1,X2,X3))))
| ( set_union2(X1,X2) = X3 )
| ( singleton(set_union2(X0,sK2(X1,X2,X3))) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X3)
| ~ in(singleton(set_union2(X0,sK2(X1,X2,X3))),X3) ),
inference(superposition,[status(thm)],[c_4329,c_3644]) ).
tcf(c_38479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),singleton(set_union2(set_union2(sK2(X0,X1,X2),X3),X4)))
| ( set_union2(X0,X1) = X2 )
| ( singleton(set_union2(set_union2(sK2(X0,X1,X2),X3),X4)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X2)
| ~ in(singleton(set_union2(set_union2(sK2(X0,X1,X2),X3),X4)),X2) ),
inference(superposition,[status(thm)],[c_4329,c_3944]) ).
tcf(c_38480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),singleton(set_union2(set_union2(X0,sK2(X1,X2,X3)),X4)))
| ( set_union2(X1,X2) = X3 )
| ( singleton(set_union2(set_union2(X0,sK2(X1,X2,X3)),X4)) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X3)
| ~ in(singleton(set_union2(set_union2(X0,sK2(X1,X2,X3)),X4)),X3) ),
inference(superposition,[status(thm)],[c_4329,c_3945]) ).
tcf(c_38481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK2(set_union2(sK2(X0,X1,X2),X3),X4,X5))
| ( set_union2(X0,X1) = X2 )
| ( set_union2(set_union2(sK2(X0,X1,X2),X3),X4) = X5 )
| ( sK2(set_union2(sK2(X0,X1,X2),X3),X4,X5) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X2)
| ~ in(sK2(set_union2(sK2(X0,X1,X2),X3),X4,X5),X5)
| ~ in(sK2(set_union2(sK2(X0,X1,X2),X3),X4,X5),X2) ),
inference(superposition,[status(thm)],[c_4329,c_4078]) ).
tcf(c_38482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,X4,X5),X4)
| in(sK2(X3,X4,X5),X3)
| in(sK2(X3,X4,X5),sK2(set_union2(X0,X1),X2,sK2(X3,X4,X5)))
| ( set_union2(X3,X4) = X5 )
| ( set_union2(set_union2(X0,X1),X2) = sK2(X3,X4,X5) )
| ( sK2(set_union2(X0,X1),X2,sK2(X3,X4,X5)) = sK2(X3,X4,X5) )
| ~ epsilon_connected(X5)
| ~ in(sK2(set_union2(X0,X1),X2,sK2(X3,X4,X5)),X5)
| ~ in(sK2(set_union2(X0,X1),X2,sK2(X3,X4,X5)),X1) ),
inference(superposition,[status(thm)],[c_4329,c_4079]) ).
tcf(c_38483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,X3,X4),X3)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X2,X3,X4),sK2(X0,X1,set_union2(sK2(X2,X3,X4),X5)))
| ( set_union2(X2,X3) = X4 )
| ( set_union2(sK2(X2,X3,X4),X5) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK2(X2,X3,X4),X5)) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X4)
| ~ in(sK2(X0,X1,set_union2(sK2(X2,X3,X4),X5)),X4)
| ~ in(sK2(X0,X1,set_union2(sK2(X2,X3,X4),X5)),X1) ),
inference(superposition,[status(thm)],[c_4329,c_4095]) ).
tcf(c_38484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),sK2(X0,sK2(X1,X2,X3),set_union2(X4,X5)))
| ( set_union2(X1,X2) = X3 )
| ( set_union2(X0,sK2(X1,X2,X3)) = set_union2(X4,X5) )
| ( sK2(X0,sK2(X1,X2,X3),set_union2(X4,X5)) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X3)
| ~ in(sK2(X0,sK2(X1,X2,X3),set_union2(X4,X5)),X5)
| ~ in(sK2(X0,sK2(X1,X2,X3),set_union2(X4,X5)),X3) ),
inference(superposition,[status(thm)],[c_4329,c_4096]) ).
tcf(c_38485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),singleton(set_union2(X0,set_union2(sK2(X1,X2,X3),X4))))
| ( set_union2(X1,X2) = X3 )
| ( singleton(set_union2(X0,set_union2(sK2(X1,X2,X3),X4))) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X3)
| ~ in(singleton(set_union2(X0,set_union2(sK2(X1,X2,X3),X4))),X3) ),
inference(superposition,[status(thm)],[c_4329,c_4131]) ).
tcf(c_38486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X4),X3)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X2,X3,X4),singleton(set_union2(X0,set_union2(X1,sK2(X2,X3,X4)))))
| ( set_union2(X2,X3) = X4 )
| ( singleton(set_union2(X0,set_union2(X1,sK2(X2,X3,X4)))) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X4)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK2(X2,X3,X4)))),X4) ),
inference(superposition,[status(thm)],[c_4329,c_4132]) ).
tcf(c_38487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),singleton(set_union2(set_union2(set_union2(sK2(X0,X1,X2),X3),X4),X5)))
| ( set_union2(X0,X1) = X2 )
| ( singleton(set_union2(set_union2(set_union2(sK2(X0,X1,X2),X3),X4),X5)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X2)
| ~ in(singleton(set_union2(set_union2(set_union2(sK2(X0,X1,X2),X3),X4),X5)),X2) ),
inference(superposition,[status(thm)],[c_4329,c_5325]) ).
tcf(c_38488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),singleton(set_union2(set_union2(set_union2(X0,sK2(X1,X2,X3)),X4),X5)))
| ( set_union2(X1,X2) = X3 )
| ( singleton(set_union2(set_union2(set_union2(X0,sK2(X1,X2,X3)),X4),X5)) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X3)
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK2(X1,X2,X3)),X4),X5)),X3) ),
inference(superposition,[status(thm)],[c_4329,c_5326]) ).
tcf(c_38489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(X0,sK2(X3,X2,X1))
| in(sK2(X3,X2,X1),X3)
| in(sK2(X3,X2,X1),X0)
| in(sK5(iPr_def_11),sK2(X3,X2,X1))
| in(sK2(X3,X2,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X3,X2) = X1 )
| ( sK2(X3,X2,X1) = X0 )
| ( sK2(X3,X2,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(X2)
| ~ epsilon_connected(X1)
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_7260]) ).
tcf(c_38490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,sK2(X4,X2,X1))
| in(sK2(X4,X2,X1),X4)
| in(sK2(X4,X2,X1),X0)
| ( set_union2(X4,X2) = X1 )
| ( sK2(X4,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_359]) ).
tcf(c_38491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X2,X1),X3)
| in(X0,sK2(X4,X2,X1))
| in(sK2(X4,X2,X1),X4)
| in(sK2(X4,X2,X1),X0)
| ( set_union2(X4,X2) = X1 )
| ( sK2(X4,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ subset(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_358]) ).
tcf(c_38492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(X4,X3,X1))
| in(X0,sK2(X4,X3,X1))
| in(sK2(X4,X3,X1),X4)
| in(sK2(X4,X3,X1),X2)
| in(sK2(X4,X3,X1),X0)
| ( set_union2(X4,X3) = X1 )
| ( sK2(X4,X3,X1) = X2 )
| ( sK2(X4,X3,X1) = X0 )
| ~ epsilon_connected(X3)
| ~ epsilon_connected(X1)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_77]) ).
tcf(c_38493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,X2,X1),X2)
| in(X0,sK2(X3,X2,X1))
| in(sK2(X3,X2,X1),X3)
| in(sK2(X3,X2,X1),X0)
| ( set_union2(X3,X2) = X1 )
| ( sK2(X3,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_65]) ).
tcf(c_38494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),X3)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = X3 )
| ~ epsilon_connected(X2)
| ~ in(X3,X2)
| ~ in(X0,sK2(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_4329,c_49]) ).
tcf(c_38495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X3,X2,X1))
| in(sK2(X3,X2,X1),X3)
| in(sK2(X3,X2,X1),X0)
| ( set_union2(X3,X2) = X1 )
| ( sK2(X3,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_137]) ).
tcf(c_38496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,X1),X3)
| in(X0,sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),X2)
| in(sK2(X2,X3,X1),X0)
| ( set_union2(X2,X3) = X1 )
| ( sK2(X2,X3,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_127]) ).
tcf(c_38497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X2,singleton(X3),X1))
| in(sK2(X2,singleton(X3),X1),X2)
| in(sK2(X2,singleton(X3),X1),X0)
| ( set_union2(X2,singleton(X3)) = X1 )
| ( sK2(X2,singleton(X3),X1) = X3 )
| ( sK2(X2,singleton(X3),X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_62]) ).
tcf(c_38498,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(X0,X0,X1))
| in(sK2(X0,X0,X1),X2)
| in(sK2(X0,X0,X1),X0)
| ( set_union2(X0,X0) = X1 )
| ( sK2(X0,X0,X1) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ in(sK2(X0,X0,X1),X1) ),
inference(superposition,[status(thm)],[c_4329,c_66]) ).
tcf(c_38499,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(X0,X1,X1))
| in(sK2(X0,X1,X1),X2)
| in(sK2(X0,X1,X1),X0)
| ( set_union2(X0,X1) = X1 )
| ( sK2(X0,X1,X1) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ in(sK2(X0,X1,X1),X1) ),
inference(superposition,[status(thm)],[c_4329,c_67]) ).
tcf(c_38500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X4,sK2(X5,set_union2(X0,X1),X3))
| in(X2,sK2(X5,set_union2(X0,X1),X3))
| in(sK2(X5,set_union2(X0,X1),X3),X5)
| in(sK2(X5,set_union2(X0,X1),X3),X4)
| in(sK2(X5,set_union2(X0,X1),X3),X2)
| ( set_union2(X5,set_union2(X0,X1)) = X3 )
| ( sK2(X5,set_union2(X0,X1),X3) = X4 )
| ( sK2(X5,set_union2(X0,X1),X3) = X2 )
| ~ epsilon_connected(X3)
| ~ in(X4,X1)
| ~ in(X2,X3)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4329,c_4213]) ).
tcf(c_38501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X4,sK2(X5,set_union2(X0,X1),X3))
| in(X2,sK2(X5,set_union2(X0,X1),X3))
| in(sK2(X5,set_union2(X0,X1),X3),X5)
| in(sK2(X5,set_union2(X0,X1),X3),X4)
| in(sK2(X5,set_union2(X0,X1),X3),X2)
| ( set_union2(X5,set_union2(X0,X1)) = X3 )
| ( sK2(X5,set_union2(X0,X1),X3) = X4 )
| ( sK2(X5,set_union2(X0,X1),X3) = X2 )
| ~ epsilon_connected(X3)
| ~ in(X4,X0)
| ~ in(X2,X3)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4329,c_4212]) ).
tcf(c_38502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,sK2(X2,set_union2(X3,X4),X1))
| in(sK2(X2,set_union2(X3,X4),X1),X4)
| in(sK2(X2,set_union2(X3,X4),X1),X3)
| in(sK2(X2,set_union2(X3,X4),X1),X2)
| in(sK2(X2,set_union2(X3,X4),X1),X0)
| ( set_union2(X2,set_union2(X3,X4)) = X1 )
| ( sK2(X2,set_union2(X3,X4),X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_71]) ).
tcf(c_38503,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X2,empty_set,X1))
| in(sK2(X2,empty_set,X1),X2)
| in(sK2(X2,empty_set,X1),X0)
| ( set_union2(X2,empty_set) = X1 )
| ( sK2(X2,empty_set,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_7097]) ).
tcf(c_38504,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,sK18,X1),iPr_def_11)
| in(X0,sK2(X2,sK18,X1))
| in(sK2(X2,sK18,X1),X2)
| in(sK2(X2,sK18,X1),X0)
| ( set_union2(X2,sK18) = X1 )
| ( sK2(X2,sK18,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_12813]) ).
tcf(c_38505,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(X0,sK18,X1))
| in(sK2(X0,sK18,X1),X2)
| in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 )
| ( sK2(X0,sK18,X1) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ in(iPr_def_11,sK2(X0,sK18,X1)) ),
inference(superposition,[status(thm)],[c_4329,c_6841]) ).
tcf(c_38506,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X2,sK18,X1),iPr_def_11)
| in(X0,sK2(X2,sK18,X1))
| in(sK2(X2,sK18,X1),X2)
| in(sK2(X2,sK18,X1),X0)
| ( set_union2(X2,sK18) = X1 )
| ( sK2(X2,sK18,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_5047]) ).
tcf(c_38507,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,sK18,X1),iPr_def_11)
| in(X0,sK2(X2,sK18,X1))
| in(sK2(X2,sK18,X1),X2)
| in(sK2(X2,sK18,X1),X0)
| ( set_union2(X2,sK18) = X1 )
| ( sK2(X2,sK18,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_3640]) ).
tcf(c_38508,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,iPr_def_10,X1),iPr_def_11)
| in(X0,sK2(X2,iPr_def_10,X1))
| in(sK2(X2,iPr_def_10,X1),X2)
| in(sK2(X2,iPr_def_10,X1),X0)
| ( set_union2(X2,iPr_def_10) = X1 )
| ( sK2(X2,iPr_def_10,X1) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_9540]) ).
tcf(c_38509,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(X0,iPr_def_10,X1))
| in(sK2(X0,iPr_def_10,X1),X2)
| in(sK2(X0,iPr_def_10,X1),X0)
| ( set_union2(X0,iPr_def_10) = X1 )
| ( sK2(X0,iPr_def_10,X1) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ in(iPr_def_11,sK2(X0,iPr_def_10,X1)) ),
inference(superposition,[status(thm)],[c_4329,c_6289]) ).
tcf(c_38510,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X2,iPr_def_10,X1),iPr_def_11)
| in(X0,sK2(X2,iPr_def_10,X1))
| in(sK2(X2,iPr_def_10,X1),X2)
| in(sK2(X2,iPr_def_10,X1),X0)
| ( set_union2(X2,iPr_def_10) = X1 )
| ( sK2(X2,iPr_def_10,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_4912]) ).
tcf(c_38511,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X2,iPr_def_10,X1))
| in(sK2(X2,iPr_def_10,X1),X2)
| in(sK2(X2,iPr_def_10,X1),X0)
| ( set_union2(X2,iPr_def_10) = X1 )
| ( sK2(X2,iPr_def_10,X1) = sK18 )
| ( sK2(X2,iPr_def_10,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_3592]) ).
tcf(c_38512,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,iPr_def_10,X1),iPr_def_11)
| in(X0,sK2(X2,iPr_def_10,X1))
| in(sK2(X2,iPr_def_10,X1),X2)
| in(sK2(X2,iPr_def_10,X1),X0)
| ( set_union2(X2,iPr_def_10) = X1 )
| ( sK2(X2,iPr_def_10,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_3614]) ).
tcf(c_38513,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,iPr_def_11,X1),sK18)
| in(X0,sK2(X2,iPr_def_11,X1))
| in(sK2(X2,iPr_def_11,X1),X2)
| in(sK2(X2,iPr_def_11,X1),X0)
| ( set_union2(X2,iPr_def_11) = X1 )
| ( sK2(X2,iPr_def_11,X1) = sK18 )
| ( sK2(X2,iPr_def_11,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_33457]) ).
tcf(c_38514,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,iPr_def_11,X1),iPr_def_10)
| in(sK2(X2,iPr_def_11,X1),sK18)
| in(X0,sK2(X2,iPr_def_11,X1))
| in(sK2(X2,iPr_def_11,X1),X2)
| in(sK2(X2,iPr_def_11,X1),X0)
| ( set_union2(X2,iPr_def_11) = X1 )
| ( sK2(X2,iPr_def_11,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_4035]) ).
tcf(c_38515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(set_union2(X0,X1),X0,X2))
| in(sK2(set_union2(X0,X1),X0,X2),X3)
| in(sK2(set_union2(X0,X1),X0,X2),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X0) = X2 )
| ( sK2(set_union2(X0,X1),X0,X2) = X3 )
| ~ epsilon_connected(X2)
| ~ in(X3,X2)
| ~ in(sK2(set_union2(X0,X1),X0,X2),X2) ),
inference(superposition,[status(thm)],[c_4329,c_4078]) ).
tcf(c_38516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(set_union2(X0,X1),X2,X2))
| in(sK2(set_union2(X0,X1),X2,X2),X3)
| in(sK2(set_union2(X0,X1),X2,X2),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = X2 )
| ( sK2(set_union2(X0,X1),X2,X2) = X3 )
| ~ epsilon_connected(X2)
| ~ in(X3,X2)
| ~ in(sK2(set_union2(X0,X1),X2,X2),X1) ),
inference(superposition,[status(thm)],[c_4329,c_4079]) ).
tcf(c_38517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(X0,X1,set_union2(X1,X2)))
| in(sK2(X0,X1,set_union2(X1,X2)),X3)
| in(sK2(X0,X1,set_union2(X1,X2)),X0)
| ( set_union2(X0,X1) = set_union2(X1,X2) )
| ( sK2(X0,X1,set_union2(X1,X2)) = X3 )
| ~ epsilon_connected(set_union2(X1,X2))
| ~ in(X3,set_union2(X1,X2))
| ~ in(sK2(X0,X1,set_union2(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_4329,c_4095]) ).
tcf(c_38518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X4,sK2(X0,X1,set_union2(X2,X3)))
| in(sK2(X0,X1,set_union2(X2,X3)),X4)
| in(sK2(X0,X1,set_union2(X2,X3)),X0)
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ( sK2(X0,X1,set_union2(X2,X3)) = X4 )
| ~ epsilon_connected(set_union2(X2,X3))
| ~ in(X4,set_union2(X2,X3))
| ~ in(sK2(X0,X1,set_union2(X2,X3)),X3) ),
inference(superposition,[status(thm)],[c_4329,c_4096]) ).
tcf(c_38519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X2)
| in(X2,sK2(X3,sK5(iPr_def_11),X1))
| in(X0,sK2(X3,sK5(iPr_def_11),X1))
| in(sK2(X3,sK5(iPr_def_11),X1),X3)
| in(sK2(X3,sK5(iPr_def_11),X1),X2)
| in(sK2(X3,sK5(iPr_def_11),X1),X0)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X3,sK5(iPr_def_11)) = X1 )
| ( sK2(X3,sK5(iPr_def_11),X1) = X2 )
| ( sK2(X3,sK5(iPr_def_11),X1) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_7243]) ).
tcf(c_38520,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(X0,sK5(iPr_def_11),X1))
| in(sK2(X0,sK5(iPr_def_11),X1),X2)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ( sK2(X0,sK5(iPr_def_11),X1) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ subset(iPr_def_11,sK2(X0,sK5(iPr_def_11),X1)) ),
inference(superposition,[status(thm)],[c_4329,c_23189]) ).
tcf(c_38521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(X0,sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),X3)
| in(sK2(X2,X3,X1),X0)
| in(sK5(iPr_def_11),sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X2,X3) = X1 )
| ( sK2(X2,X3,X1) = X0 )
| ( sK2(X2,X3,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(X2)
| ~ epsilon_connected(X1)
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_7260]) ).
tcf(c_38522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,sK2(X2,X4,X1))
| in(sK2(X2,X4,X1),X4)
| in(sK2(X2,X4,X1),X0)
| ( set_union2(X2,X4) = X1 )
| ( sK2(X2,X4,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_359]) ).
tcf(c_38523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,X4,X1),X3)
| in(X0,sK2(X2,X4,X1))
| in(sK2(X2,X4,X1),X4)
| in(sK2(X2,X4,X1),X0)
| ( set_union2(X2,X4) = X1 )
| ( sK2(X2,X4,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ subset(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_358]) ).
tcf(c_38524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(X3,X4,X1))
| in(X0,sK2(X3,X4,X1))
| in(sK2(X3,X4,X1),X4)
| in(sK2(X3,X4,X1),X2)
| in(sK2(X3,X4,X1),X0)
| ( set_union2(X3,X4) = X1 )
| ( sK2(X3,X4,X1) = X2 )
| ( sK2(X3,X4,X1) = X0 )
| ~ epsilon_connected(X3)
| ~ epsilon_connected(X1)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_77]) ).
tcf(c_38525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X3,X1),X2)
| in(X0,sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),X3)
| in(sK2(X2,X3,X1),X0)
| ( set_union2(X2,X3) = X1 )
| ( sK2(X2,X3,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_65]) ).
tcf(c_38526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X3)
| in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X3 )
| ~ epsilon_connected(X2)
| ~ in(X3,X2)
| ~ in(X0,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4329,c_49]) ).
tcf(c_38527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),X3)
| in(sK2(X2,X3,X1),X0)
| ( set_union2(X2,X3) = X1 )
| ( sK2(X2,X3,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_137]) ).
tcf(c_38528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,X1),X2)
| in(X0,sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),X3)
| in(sK2(X2,X3,X1),X0)
| ( set_union2(X2,X3) = X1 )
| ( sK2(X2,X3,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_127]) ).
tcf(c_38529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(singleton(X2),X3,X1))
| in(sK2(singleton(X2),X3,X1),X3)
| in(sK2(singleton(X2),X3,X1),X0)
| ( set_union2(singleton(X2),X3) = X1 )
| ( sK2(singleton(X2),X3,X1) = X2 )
| ( sK2(singleton(X2),X3,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_62]) ).
tcf(c_38530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X3)
| in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X3 )
| ~ epsilon_connected(X2)
| ~ in(X3,X2)
| ~ in(sK2(X0,X1,X2),X2) ),
inference(superposition,[status(thm)],[c_4329,c_66]) ).
tcf(c_38532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X4,sK2(set_union2(X0,X1),X5,X3))
| in(X2,sK2(set_union2(X0,X1),X5,X3))
| in(sK2(set_union2(X0,X1),X5,X3),X5)
| in(sK2(set_union2(X0,X1),X5,X3),X4)
| in(sK2(set_union2(X0,X1),X5,X3),X2)
| ( set_union2(set_union2(X0,X1),X5) = X3 )
| ( sK2(set_union2(X0,X1),X5,X3) = X4 )
| ( sK2(set_union2(X0,X1),X5,X3) = X2 )
| ~ epsilon_connected(X3)
| ~ in(X4,X1)
| ~ in(X2,X3)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4329,c_4213]) ).
tcf(c_38533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X4,sK2(set_union2(X0,X1),X5,X3))
| in(X2,sK2(set_union2(X0,X1),X5,X3))
| in(sK2(set_union2(X0,X1),X5,X3),X5)
| in(sK2(set_union2(X0,X1),X5,X3),X4)
| in(sK2(set_union2(X0,X1),X5,X3),X2)
| ( set_union2(set_union2(X0,X1),X5) = X3 )
| ( sK2(set_union2(X0,X1),X5,X3) = X4 )
| ( sK2(set_union2(X0,X1),X5,X3) = X2 )
| ~ epsilon_connected(X3)
| ~ in(X4,X0)
| ~ in(X2,X3)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4329,c_4212]) ).
tcf(c_38534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,sK2(set_union2(X2,X3),X4,X1))
| in(sK2(set_union2(X2,X3),X4,X1),X4)
| in(sK2(set_union2(X2,X3),X4,X1),X3)
| in(sK2(set_union2(X2,X3),X4,X1),X2)
| in(sK2(set_union2(X2,X3),X4,X1),X0)
| ( set_union2(set_union2(X2,X3),X4) = X1 )
| ( sK2(set_union2(X2,X3),X4,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_71]) ).
tcf(c_38535,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(empty_set,X2,X1))
| in(sK2(empty_set,X2,X1),X2)
| in(sK2(empty_set,X2,X1),X0)
| ( set_union2(empty_set,X2) = X1 )
| ( sK2(empty_set,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_7097]) ).
tcf(c_38536,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X2,X1),iPr_def_11)
| in(X0,sK2(sK18,X2,X1))
| in(sK2(sK18,X2,X1),X2)
| in(sK2(sK18,X2,X1),X0)
| ( set_union2(sK18,X2) = X1 )
| ( sK2(sK18,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_12813]) ).
tcf(c_38537,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(sK18,X0,X1))
| in(sK2(sK18,X0,X1),X2)
| in(sK2(sK18,X0,X1),X0)
| ( set_union2(sK18,X0) = X1 )
| ( sK2(sK18,X0,X1) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ in(iPr_def_11,sK2(sK18,X0,X1)) ),
inference(superposition,[status(thm)],[c_4329,c_6841]) ).
tcf(c_38538,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(sK18,X2,X1),iPr_def_11)
| in(X0,sK2(sK18,X2,X1))
| in(sK2(sK18,X2,X1),X2)
| in(sK2(sK18,X2,X1),X0)
| ( set_union2(sK18,X2) = X1 )
| ( sK2(sK18,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_5047]) ).
tcf(c_38539,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK18,X2,X1),iPr_def_11)
| in(X0,sK2(sK18,X2,X1))
| in(sK2(sK18,X2,X1),X2)
| in(sK2(sK18,X2,X1),X0)
| ( set_union2(sK18,X2) = X1 )
| ( sK2(sK18,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_3640]) ).
tcf(c_38540,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(iPr_def_10,X2,X1),iPr_def_11)
| in(X0,sK2(iPr_def_10,X2,X1))
| in(sK2(iPr_def_10,X2,X1),X2)
| in(sK2(iPr_def_10,X2,X1),X0)
| ( set_union2(iPr_def_10,X2) = X1 )
| ( sK2(iPr_def_10,X2,X1) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_9540]) ).
tcf(c_38541,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(iPr_def_10,X0,X1))
| in(sK2(iPr_def_10,X0,X1),X2)
| in(sK2(iPr_def_10,X0,X1),X0)
| ( set_union2(iPr_def_10,X0) = X1 )
| ( sK2(iPr_def_10,X0,X1) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ in(iPr_def_11,sK2(iPr_def_10,X0,X1)) ),
inference(superposition,[status(thm)],[c_4329,c_6289]) ).
tcf(c_38542,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(iPr_def_10,X2,X1),iPr_def_11)
| in(X0,sK2(iPr_def_10,X2,X1))
| in(sK2(iPr_def_10,X2,X1),X2)
| in(sK2(iPr_def_10,X2,X1),X0)
| ( set_union2(iPr_def_10,X2) = X1 )
| ( sK2(iPr_def_10,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_4912]) ).
tcf(c_38543,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(iPr_def_10,X2,X1))
| in(sK2(iPr_def_10,X2,X1),X2)
| in(sK2(iPr_def_10,X2,X1),X0)
| ( set_union2(iPr_def_10,X2) = X1 )
| ( sK2(iPr_def_10,X2,X1) = sK18 )
| ( sK2(iPr_def_10,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_3592]) ).
tcf(c_38544,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(iPr_def_10,X2,X1),iPr_def_11)
| in(X0,sK2(iPr_def_10,X2,X1))
| in(sK2(iPr_def_10,X2,X1),X2)
| in(sK2(iPr_def_10,X2,X1),X0)
| ( set_union2(iPr_def_10,X2) = X1 )
| ( sK2(iPr_def_10,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_3614]) ).
tcf(c_38545,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(iPr_def_11,X2,X1),sK18)
| in(X0,sK2(iPr_def_11,X2,X1))
| in(sK2(iPr_def_11,X2,X1),X2)
| in(sK2(iPr_def_11,X2,X1),X0)
| ( set_union2(iPr_def_11,X2) = X1 )
| ( sK2(iPr_def_11,X2,X1) = sK18 )
| ( sK2(iPr_def_11,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_33457]) ).
tcf(c_38546,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(iPr_def_11,X2,X1),iPr_def_10)
| in(sK2(iPr_def_11,X2,X1),sK18)
| in(X0,sK2(iPr_def_11,X2,X1))
| in(sK2(iPr_def_11,X2,X1),X2)
| in(sK2(iPr_def_11,X2,X1),X0)
| ( set_union2(iPr_def_11,X2) = X1 )
| ( sK2(iPr_def_11,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_4035]) ).
tcf(c_38547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(set_union2(X0,X1),X2,set_union2(X0,X1)))
| in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X3)
| in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X2)
| ( set_union2(set_union2(X0,X1),X2) = set_union2(X0,X1) )
| ( sK2(set_union2(X0,X1),X2,set_union2(X0,X1)) = X3 )
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(X3,set_union2(X0,X1))
| ~ in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_4329,c_4079]) ).
tcf(c_38549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(X0,X0,set_union2(X1,X2)))
| in(sK2(X0,X0,set_union2(X1,X2)),X3)
| in(sK2(X0,X0,set_union2(X1,X2)),X0)
| ( set_union2(X0,X0) = set_union2(X1,X2) )
| ( sK2(X0,X0,set_union2(X1,X2)) = X3 )
| ~ epsilon_connected(set_union2(X1,X2))
| ~ in(X3,set_union2(X1,X2))
| ~ in(sK2(X0,X0,set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4329,c_4096]) ).
tcf(c_38550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X2)
| in(X2,sK2(sK5(iPr_def_11),X3,X1))
| in(X0,sK2(sK5(iPr_def_11),X3,X1))
| in(sK2(sK5(iPr_def_11),X3,X1),X3)
| in(sK2(sK5(iPr_def_11),X3,X1),X2)
| in(sK2(sK5(iPr_def_11),X3,X1),X0)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(sK5(iPr_def_11),X3) = X1 )
| ( sK2(sK5(iPr_def_11),X3,X1) = X2 )
| ( sK2(sK5(iPr_def_11),X3,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_7243]) ).
tcf(c_38551,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(sK5(iPr_def_11),X0,X1))
| in(sK2(sK5(iPr_def_11),X0,X1),X2)
| in(sK2(sK5(iPr_def_11),X0,X1),X0)
| ( set_union2(sK5(iPr_def_11),X0) = X1 )
| ( sK2(sK5(iPr_def_11),X0,X1) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,X1)) ),
inference(superposition,[status(thm)],[c_4329,c_23189]) ).
tcf(c_38552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(X0,sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),X3)
| in(sK2(X2,X3,X1),X2)
| in(sK5(iPr_def_11),sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X2,X3) = X1 )
| ( sK2(X2,X3,X1) = X0 )
| ( sK2(X2,X3,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_7260]) ).
tcf(c_38553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,sK2(X3,X4,X1))
| in(sK2(X3,X4,X1),X4)
| in(sK2(X3,X4,X1),X3)
| ( set_union2(X3,X4) = X1 )
| ( sK2(X3,X4,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(X2)
| ~ subset(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_359]) ).
tcf(c_38554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,X1),X2)
| in(X0,sK2(X3,X4,X1))
| in(sK2(X3,X4,X1),X4)
| in(sK2(X3,X4,X1),X3)
| ( set_union2(X3,X4) = X1 )
| ( sK2(X3,X4,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ subset(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_358]) ).
tcf(c_38555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(X3,X4,X1))
| in(X0,sK2(X3,X4,X1))
| in(sK2(X3,X4,X1),X4)
| in(sK2(X3,X4,X1),X3)
| in(sK2(X3,X4,X1),X2)
| ( set_union2(X3,X4) = X1 )
| ( sK2(X3,X4,X1) = X2 )
| ( sK2(X3,X4,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(X0)
| ~ in(X2,X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_77]) ).
tcf(c_38556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X3,X1),X0)
| in(X0,sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),X3)
| in(sK2(X2,X3,X1),X2)
| ( set_union2(X2,X3) = X1 )
| ( sK2(X2,X3,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_65]) ).
tcf(c_38558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),X3)
| in(sK2(X2,X3,X1),X2)
| ( set_union2(X2,X3) = X1 )
| ( sK2(X2,X3,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_137]) ).
tcf(c_38559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,X1),X0)
| in(X0,sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),X3)
| in(sK2(X2,X3,X1),X2)
| ( set_union2(X2,X3) = X1 )
| ( sK2(X2,X3,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_127]) ).
tcf(c_38560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X1),X3)
| in(sK2(X2,X3,X1),X2)
| in(singleton(X0),sK2(X2,X3,X1))
| ( set_union2(X2,X3) = X1 )
| ( sK2(X2,X3,X1) = X0 )
| ( sK2(X2,X3,X1) = singleton(X0) )
| ~ epsilon_connected(X1)
| ~ in(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_4329,c_62]) ).
tcf(c_38563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X3,sK2(X4,X5,X2))
| in(sK2(X4,X5,X2),X5)
| in(sK2(X4,X5,X2),X4)
| in(sK2(X4,X5,X2),X3)
| in(set_union2(X0,X1),sK2(X4,X5,X2))
| ( set_union2(X4,X5) = X2 )
| ( sK2(X4,X5,X2) = X3 )
| ( sK2(X4,X5,X2) = set_union2(X0,X1) )
| ~ epsilon_connected(X2)
| ~ in(X3,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_4329,c_4213]) ).
tcf(c_38564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X3,sK2(X4,X5,X2))
| in(sK2(X4,X5,X2),X5)
| in(sK2(X4,X5,X2),X4)
| in(sK2(X4,X5,X2),X3)
| in(set_union2(X0,X1),sK2(X4,X5,X2))
| ( set_union2(X4,X5) = X2 )
| ( sK2(X4,X5,X2) = X3 )
| ( sK2(X4,X5,X2) = set_union2(X0,X1) )
| ~ epsilon_connected(X2)
| ~ in(X3,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_4329,c_4212]) ).
tcf(c_38565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X4)
| in(sK2(X3,X4,X2),X3)
| in(sK2(X3,X4,X2),X1)
| in(sK2(X3,X4,X2),X0)
| in(set_union2(X0,X1),sK2(X3,X4,X2))
| ( set_union2(X3,X4) = X2 )
| ( sK2(X3,X4,X2) = set_union2(X0,X1) )
| ~ epsilon_connected(X2)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_4329,c_71]) ).
tcf(c_38566,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(empty_set,sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ( sK2(X1,X2,X0) = empty_set )
| ~ epsilon_connected(X0)
| ~ in(empty_set,X0) ),
inference(superposition,[status(thm)],[c_4329,c_7097]) ).
tcf(c_38567,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X2,X0),iPr_def_11)
| in(sK18,sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ( sK2(X1,X2,X0) = sK18 )
| ~ epsilon_connected(X0)
| ~ in(sK18,X0) ),
inference(superposition,[status(thm)],[c_4329,c_12813]) ).
tcf(c_38568,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK18 )
| ~ epsilon_connected(X2)
| ~ in(sK18,X2)
| ~ in(iPr_def_11,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4329,c_6841]) ).
tcf(c_38569,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X2,X0),iPr_def_11)
| in(sK18,sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ( sK2(X1,X2,X0) = sK18 )
| ~ epsilon_connected(X0)
| ~ in(sK18,X0) ),
inference(superposition,[status(thm)],[c_4329,c_5047]) ).
tcf(c_38570,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),iPr_def_11)
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ( sK2(X1,X2,X0) = sK18 )
| ~ epsilon_connected(X0)
| ~ in(sK18,X0) ),
inference(superposition,[status(thm)],[c_4329,c_3640]) ).
tcf(c_38571,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK1(sK2(X0,X1,X2)),sK2(X0,X1,X2))
| ( set_union2(X0,X1) = X2 )
| ( sK1(sK2(X0,X1,X2)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X2)
| ~ in(sK1(sK2(X0,X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4329,c_3523]) ).
tcf(c_38572,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK3(sK2(X0,X1,X2)),sK2(X0,X1,X2))
| ( set_union2(X0,X1) = X2 )
| ( sK3(sK2(X0,X1,X2)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X2)
| ~ in(sK3(sK2(X0,X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4329,c_3524]) ).
tcf(c_38573,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK4(sK2(X0,X1,X2)),sK2(X0,X1,X2))
| ( set_union2(X0,X1) = X2 )
| ( sK4(sK2(X0,X1,X2)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X2)
| ~ in(sK4(sK2(X0,X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4329,c_3525]) ).
tcf(c_38574,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X2,X0),iPr_def_11)
| in(iPr_def_10,sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ( sK2(X1,X2,X0) = iPr_def_10 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_connected(X0)
| ~ in(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4329,c_9540]) ).
tcf(c_38575,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(iPr_def_10,sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = iPr_def_10 )
| ~ epsilon_connected(X2)
| ~ in(iPr_def_10,X2)
| ~ in(iPr_def_11,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4329,c_6289]) ).
tcf(c_38576,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X2,X0),iPr_def_11)
| in(iPr_def_10,sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ( sK2(X1,X2,X0) = iPr_def_10 )
| ~ epsilon_connected(X0)
| ~ in(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4329,c_4912]) ).
tcf(c_38577,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(iPr_def_10,sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ( sK2(X1,X2,X0) = iPr_def_10 )
| ( sK2(X1,X2,X0) = sK18 )
| ~ epsilon_connected(X0)
| ~ in(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4329,c_3592]) ).
tcf(c_38578,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(iPr_def_10,sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),iPr_def_11)
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ( sK2(X1,X2,X0) = iPr_def_10 )
| ~ epsilon_connected(X0)
| ~ in(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4329,c_3614]) ).
tcf(c_38579,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(iPr_def_11,sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),sK18)
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ( sK2(X1,X2,X0) = iPr_def_11 )
| ( sK2(X1,X2,X0) = sK18 )
| ~ epsilon_connected(X0)
| ~ in(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_4329,c_33457]) ).
tcf(c_38580,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(iPr_def_11,sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),iPr_def_10)
| in(sK2(X1,X2,X0),sK18)
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ( sK2(X1,X2,X0) = iPr_def_11 )
| ~ epsilon_connected(X0)
| ~ in(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_4329,c_4035]) ).
tcf(c_38581,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK5(sK2(X0,X1,X2)),sK2(X0,X1,X2))
| ( set_union2(X0,X1) = X2 )
| ( sK5(sK2(X0,X1,X2)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X2)
| ~ in(sK5(sK2(X0,X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4329,c_3900]) ).
tcf(c_38582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(set_union2(X0,X1),X2,X3))
| in(sK2(set_union2(X0,X1),X2,X3),X2)
| in(sK2(set_union2(X0,X1),X2,X3),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = X3 )
| ( sK2(set_union2(X0,X1),X2,X3) = X0 )
| ~ epsilon_connected(X3)
| ~ in(X0,X3)
| ~ in(sK2(set_union2(X0,X1),X2,X3),X3) ),
inference(superposition,[status(thm)],[c_4329,c_4078]) ).
tcf(c_38583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(set_union2(X0,X1),X2,X3))
| in(sK2(set_union2(X0,X1),X2,X3),X2)
| in(sK2(set_union2(X0,X1),X2,X3),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = X3 )
| ( sK2(set_union2(X0,X1),X2,X3) = X3 )
| ~ epsilon_connected(X3)
| ~ in(X3,X3)
| ~ in(sK2(set_union2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_4329,c_4079]) ).
tcf(c_38586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(X1,sK2(X2,X3,X0))
| in(sK2(X2,X3,X0),X3)
| in(sK2(X2,X3,X0),X2)
| in(sK2(X2,X3,X0),X1)
| in(sK5(iPr_def_11),sK2(X2,X3,X0))
| ( sK5(iPr_def_11) = X1 )
| ( set_union2(X2,X3) = X0 )
| ( sK2(X2,X3,X0) = X1 )
| ( sK2(X2,X3,X0) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_4329,c_7243]) ).
tcf(c_38587,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK5(iPr_def_11),sK2(X0,X1,X2))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK5(iPr_def_11) )
| ~ epsilon_connected(X2)
| ~ in(sK5(iPr_def_11),X2)
| ~ subset(iPr_def_11,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4329,c_23189]) ).
tcf(c_38591,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X2,X2,X1))
| in(sK2(X2,X2,X1),X2)
| in(sK2(X2,X2,X1),X0)
| ( set_union2(X2,X2) = X1 )
| ( sK2(X2,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_4329]) ).
tcf(c_38594,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X2,X0,X1))
| in(sK2(X2,X0,X1),X2)
| in(sK2(X2,X0,X1),X0)
| ( set_union2(X2,X0) = X1 )
| ( sK2(X2,X0,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_4329]) ).
tcf(c_38595,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X0,X2,X1))
| in(sK2(X0,X2,X1),X2)
| in(sK2(X0,X2,X1),X0)
| ( set_union2(X0,X2) = X1 )
| ( sK2(X0,X2,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_4329]) ).
tcf(c_38944,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(X0,X0,X1))
| in(sK2(X0,X0,X1),X2)
| in(sK2(X0,X0,X1),X0)
| ( X0 = X1 )
| ( sK2(X0,X0,X1) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ in(sK2(X0,X0,X1),X1) ),
inference(light_normalisation,[status(thm)],[c_38498,c_97]) ).
tcf(c_39291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(X0,X0,set_union2(X1,X2)))
| in(sK2(X0,X0,set_union2(X1,X2)),X3)
| in(sK2(X0,X0,set_union2(X1,X2)),X0)
| ( set_union2(X1,X2) = X0 )
| ( sK2(X0,X0,set_union2(X1,X2)) = X3 )
| ~ epsilon_connected(set_union2(X1,X2))
| ~ in(X3,set_union2(X1,X2))
| ~ in(sK2(X0,X0,set_union2(X1,X2)),X2) ),
inference(light_normalisation,[status(thm)],[c_38549,c_97]) ).
tcf(c_40242,plain,
! [X0: $i,X1: $i] : element(sK18,set_union2(set_union2(iPr_def_10,X0),X1)),
inference(superposition,[status(thm)],[c_138,c_25171]) ).
tcf(c_40243,plain,
! [X0: $i,X1: $i] : element(sK18,set_union2(X0,set_union2(iPr_def_10,X1))),
inference(superposition,[status(thm)],[c_3397,c_25171]) ).
tcf(c_40244,plain,
! [X0: $i] :
( element(sK18,singleton(set_union2(iPr_def_10,X0)))
| ~ epsilon_transitive(singleton(set_union2(iPr_def_10,X0))) ),
inference(superposition,[status(thm)],[c_3803,c_25171]) ).
tcf(c_40245,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X1,X2))
| ~ subset(set_union2(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_3863,c_25171]) ).
tcf(c_40246,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X2,X1))
| ~ epsilon_transitive(set_union2(X2,X1))
| ~ in(set_union2(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_3806,c_25171]) ).
tcf(c_40247,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X1,X2))
| ~ epsilon_transitive(set_union2(X1,X2))
| ~ in(set_union2(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_3805,c_25171]) ).
tcf(c_40248,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X2,X1))
| ~ subset(set_union2(iPr_def_10,X0),X1) ),
inference(superposition,[status(thm)],[c_3865,c_25171]) ).
tcf(c_40302,plain,
! [X0: $i,X1: $i] : element(sK18,set_union2(set_union2(X0,iPr_def_10),X1)),
inference(superposition,[status(thm)],[c_58,c_40242]) ).
tcf(c_40307,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(set_union2(iPr_def_10,X0),X1))
| in(sK18,set_union2(set_union2(iPr_def_10,X0),X1)) ),
inference(superposition,[status(thm)],[c_40242,c_131]) ).
tcf(c_40308,plain,
! [X0: $i,X1: $i] : in(sK18,set_union2(set_union2(iPr_def_10,X0),X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_40307,c_37209]) ).
tcf(c_40315,plain,
! [X0: $i,X1: $i] : element(sK18,set_union2(X0,set_union2(X1,iPr_def_10))),
inference(superposition,[status(thm)],[c_58,c_40243]) ).
tcf(c_40320,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,set_union2(iPr_def_10,X1)))
| in(sK18,set_union2(X0,set_union2(iPr_def_10,X1))) ),
inference(superposition,[status(thm)],[c_40243,c_131]) ).
tcf(c_40321,plain,
! [X0: $i,X1: $i] : in(sK18,set_union2(X0,set_union2(iPr_def_10,X1))),
inference(forward_subsumption_resolution,[status(thm)],[c_40320,c_37210]) ).
tcf(c_40332,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(set_union2(X0,iPr_def_10),X1))
| in(sK18,set_union2(set_union2(X0,iPr_def_10),X1)) ),
inference(superposition,[status(thm)],[c_40302,c_131]) ).
tcf(c_40333,plain,
! [X0: $i,X1: $i] : in(sK18,set_union2(set_union2(X0,iPr_def_10),X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_40332,c_37242]) ).
tcf(c_40357,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK0(X1,sK3(iPr_def_11)))
| in(sK0(X1,sK3(iPr_def_11)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X1) = sK3(iPr_def_11) )
| ( sK0(X1,sK3(iPr_def_11)) = X1 )
| ( sK0(X1,sK3(iPr_def_11)) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_60,c_9906]) ).
tcf(c_40358,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK1(sK3(iPr_def_11)))
| in(sK1(sK3(iPr_def_11)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( sK1(sK3(iPr_def_11)) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_64,c_9906]) ).
tcf(c_40359,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK2(sK3(iPr_def_11),X1,X2))
| in(sK2(sK3(iPr_def_11),X1,X2),X2)
| in(sK2(sK3(iPr_def_11),X1,X2),X1)
| in(sK2(sK3(iPr_def_11),X1,X2),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X1) = X2 )
| ( sK2(sK3(iPr_def_11),X1,X2) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_9906]) ).
tcf(c_40360,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK2(X1,X2,sK3(iPr_def_11)))
| in(sK2(X1,X2,sK3(iPr_def_11)),X2)
| in(sK2(X1,X2,sK3(iPr_def_11)),X1)
| in(sK2(X1,X2,sK3(iPr_def_11)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,X2) = sK3(iPr_def_11) )
| ( sK2(X1,X2,sK3(iPr_def_11)) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_9906]) ).
tcf(c_40361,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK2(X1,sK3(iPr_def_11),X2))
| in(sK2(X1,sK3(iPr_def_11),X2),X2)
| in(sK2(X1,sK3(iPr_def_11),X2),X1)
| in(sK2(X1,sK3(iPr_def_11),X2),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,sK3(iPr_def_11)) = X2 )
| ( sK2(X1,sK3(iPr_def_11),X2) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_9906]) ).
tcf(c_40364,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| empty(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK5(sK3(iPr_def_11)))
| in(sK5(sK3(iPr_def_11)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( sK5(sK3(iPr_def_11)) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3768,c_9906]) ).
tcf(c_40365,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK0(X1,set_union2(sK3(iPr_def_11),X2)))
| in(sK0(X1,set_union2(sK3(iPr_def_11),X2)),X2)
| in(sK0(X1,set_union2(sK3(iPr_def_11),X2)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X2) = singleton(X1) )
| ( sK0(X1,set_union2(sK3(iPr_def_11),X2)) = X1 )
| ( sK0(X1,set_union2(sK3(iPr_def_11),X2)) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4023,c_9906]) ).
tcf(c_40366,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK0(X1,set_union2(X2,sK3(iPr_def_11))))
| in(sK0(X1,set_union2(X2,sK3(iPr_def_11))),X2)
| in(sK0(X1,set_union2(X2,sK3(iPr_def_11))),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X2,sK3(iPr_def_11)) = singleton(X1) )
| ( sK0(X1,set_union2(X2,sK3(iPr_def_11))) = X1 )
| ( sK0(X1,set_union2(X2,sK3(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4023,c_9906]) ).
tcf(c_40367,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| epsilon_transitive(set_union2(sK3(iPr_def_11),X1))
| in(X0,sK1(set_union2(sK3(iPr_def_11),X1)))
| in(sK1(set_union2(sK3(iPr_def_11),X1)),X1)
| in(sK1(set_union2(sK3(iPr_def_11),X1)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( sK1(set_union2(sK3(iPr_def_11),X1)) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4024,c_9906]) ).
tcf(c_40368,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| epsilon_transitive(set_union2(X1,sK3(iPr_def_11)))
| in(X0,sK1(set_union2(X1,sK3(iPr_def_11))))
| in(sK1(set_union2(X1,sK3(iPr_def_11))),X1)
| in(sK1(set_union2(X1,sK3(iPr_def_11))),X0)
| ( sK3(iPr_def_11) = X0 )
| ( sK1(set_union2(X1,sK3(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4024,c_9906]) ).
tcf(c_40369,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| epsilon_connected(set_union2(sK3(iPr_def_11),X1))
| in(X0,sK3(set_union2(sK3(iPr_def_11),X1)))
| in(sK3(set_union2(sK3(iPr_def_11),X1)),X1)
| in(sK3(set_union2(sK3(iPr_def_11),X1)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( sK3(set_union2(sK3(iPr_def_11),X1)) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4027,c_9906]) ).
tcf(c_40370,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| epsilon_connected(set_union2(X1,sK3(iPr_def_11)))
| in(X0,sK3(set_union2(X1,sK3(iPr_def_11))))
| in(sK3(set_union2(X1,sK3(iPr_def_11))),X1)
| in(sK3(set_union2(X1,sK3(iPr_def_11))),X0)
| ( sK3(iPr_def_11) = X0 )
| ( sK3(set_union2(X1,sK3(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4027,c_9906]) ).
tcf(c_40371,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| epsilon_connected(set_union2(sK3(iPr_def_11),X1))
| in(X0,sK4(set_union2(sK3(iPr_def_11),X1)))
| in(sK4(set_union2(sK3(iPr_def_11),X1)),X1)
| in(sK4(set_union2(sK3(iPr_def_11),X1)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( sK4(set_union2(sK3(iPr_def_11),X1)) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4028,c_9906]) ).
tcf(c_40372,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| epsilon_connected(set_union2(X1,sK3(iPr_def_11)))
| in(X0,sK4(set_union2(X1,sK3(iPr_def_11))))
| in(sK4(set_union2(X1,sK3(iPr_def_11))),X1)
| in(sK4(set_union2(X1,sK3(iPr_def_11))),X0)
| ( sK3(iPr_def_11) = X0 )
| ( sK4(set_union2(X1,sK3(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4028,c_9906]) ).
tcf(c_40373,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| empty(set_union2(sK3(iPr_def_11),X1))
| in(X0,sK5(set_union2(sK3(iPr_def_11),X1)))
| in(sK5(set_union2(sK3(iPr_def_11),X1)),X1)
| in(sK5(set_union2(sK3(iPr_def_11),X1)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( sK5(set_union2(sK3(iPr_def_11),X1)) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4029,c_9906]) ).
tcf(c_40374,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| empty(set_union2(X1,sK3(iPr_def_11)))
| in(X0,sK5(set_union2(X1,sK3(iPr_def_11))))
| in(sK5(set_union2(X1,sK3(iPr_def_11))),X1)
| in(sK5(set_union2(X1,sK3(iPr_def_11))),X0)
| ( sK3(iPr_def_11) = X0 )
| ( sK5(set_union2(X1,sK3(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4029,c_9906]) ).
tcf(c_40376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X2)
| in(X2,sK2(sK3(iPr_def_11),X3,X1))
| in(X0,sK2(sK3(iPr_def_11),X3,X1))
| in(sK2(sK3(iPr_def_11),X3,X1),X3)
| in(sK2(sK3(iPr_def_11),X3,X1),X2)
| in(sK2(sK3(iPr_def_11),X3,X1),X0)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(sK3(iPr_def_11),X3) = X1 )
| ( sK2(sK3(iPr_def_11),X3,X1) = X2 )
| ( sK2(sK3(iPr_def_11),X3,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_9906]) ).
tcf(c_40377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X2)
| in(X2,sK2(X3,sK3(iPr_def_11),X1))
| in(X0,sK2(X3,sK3(iPr_def_11),X1))
| in(sK2(X3,sK3(iPr_def_11),X1),X3)
| in(sK2(X3,sK3(iPr_def_11),X1),X2)
| in(sK2(X3,sK3(iPr_def_11),X1),X0)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X3,sK3(iPr_def_11)) = X1 )
| ( sK2(X3,sK3(iPr_def_11),X1) = X2 )
| ( sK2(X3,sK3(iPr_def_11),X1) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_9906]) ).
tcf(c_40378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(X1,sK2(X2,X3,X0))
| in(sK2(X2,X3,X0),X3)
| in(sK2(X2,X3,X0),X2)
| in(sK2(X2,X3,X0),X1)
| in(sK3(iPr_def_11),sK2(X2,X3,X0))
| ( sK3(iPr_def_11) = X1 )
| ( set_union2(X2,X3) = X0 )
| ( sK2(X2,X3,X0) = X1 )
| ( sK2(X2,X3,X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_4329,c_9906]) ).
tcf(c_40379,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,iPr_def_10)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_9906]) ).
tcf(c_40380,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ subset(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_23181,c_9906]) ).
tcf(c_40381,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X1)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_9906]) ).
tcf(c_40382,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_9906]) ).
tcf(c_40383,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7246,c_9906]) ).
tcf(c_40384,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_9906]) ).
tcf(c_40392,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( X0 = X1 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13640,c_9906]) ).
tcf(c_40393,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( X0 = X1 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9904,c_9906]) ).
tcf(c_40394,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( X0 = X1 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9901,c_9906]) ).
tcf(c_40395,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9927,c_9906]) ).
tcf(c_40396,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( X0 = X1 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9595,c_9906]) ).
tcf(c_40397,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(X1,singleton(X0))
| in(singleton(X0),X1)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = X1 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_9906]) ).
tcf(c_40398,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| in(X2,set_union2(X0,X1))
| in(set_union2(X0,X1),X2)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_9930,c_9906]) ).
tcf(c_40399,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X1)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_9906]) ).
tcf(c_40400,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_9906]) ).
tcf(c_40402,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_9906]) ).
tcf(c_40404,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(sK18))
| in(sK5(sK18),X0)
| in(sK3(iPr_def_11),X0)
| ( sK5(sK18) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_31187,c_9906]) ).
tcf(c_40405,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(sK18,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_36541,c_9906]) ).
tcf(c_40994,plain,
set_union2(iPr_def_10,sK18) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2421,c_58]) ).
tcf(c_41256,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_70,c_127]) ).
tcf(c_41418,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| in(sK3(set_union2(X0,X1)),X1)
| in(sK3(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_72,c_71]) ).
tcf(c_41419,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| in(sK4(set_union2(X0,X1)),X1)
| in(sK4(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_73,c_71]) ).
tcf(c_41442,plain,
~ epsilon_connected(set_union2(sK18,singleton(sK18))),
inference(global_subsumption_just,[status(thm)],[c_1466,c_978,c_1066,c_1074,c_4548,c_9163,c_9164,c_11540,c_28259,c_36266,c_37805]) ).
tcf(c_41444,plain,
~ epsilon_connected(set_union2(sK18,iPr_def_10)),
inference(light_normalisation,[status(thm)],[c_41442,c_2420]) ).
tcf(c_41445,plain,
~ epsilon_connected(iPr_def_11),
inference(demodulation,[status(thm)],[c_41444,c_58,c_40994]) ).
tcf(c_41643,plain,
( epsilon_connected(set_union2(iPr_def_10,sK18))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(set_union2(iPr_def_10,sK18)),sK18) ),
inference(superposition,[status(thm)],[c_40994,c_41418]) ).
tcf(c_41671,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK18) ),
inference(light_normalisation,[status(thm)],[c_41643,c_40994]) ).
tcf(c_41672,plain,
( in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41671,c_41445]) ).
tcf(c_41839,plain,
( epsilon_connected(set_union2(iPr_def_10,sK18))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(set_union2(iPr_def_10,sK18)),sK18) ),
inference(superposition,[status(thm)],[c_40994,c_41419]) ).
tcf(c_41867,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK18) ),
inference(light_normalisation,[status(thm)],[c_41839,c_40994]) ).
tcf(c_41868,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41867,c_41445]) ).
tcf(c_43061,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_41672,c_77]) ).
tcf(c_43063,plain,
( in(sK3(iPr_def_11),iPr_def_10)
| ~ in(sK18,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_41672,c_49]) ).
tcf(c_43064,plain,
( in(sK3(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_41672,c_137]) ).
tcf(c_43078,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43061,c_2427]) ).
tcf(c_43123,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_41868,c_77]) ).
tcf(c_43125,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| ~ in(sK18,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_41868,c_49]) ).
tcf(c_43126,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_41868,c_137]) ).
tcf(c_43140,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43123,c_2427]) ).
tcf(c_43364,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_43078,c_77]) ).
tcf(c_43385,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_43078,c_77]) ).
tcf(c_43392,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_43078,c_74]) ).
tcf(c_43439,plain,
( in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43392,c_41445]) ).
tcf(c_43601,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK4(iPr_def_11) = X1 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_43140,c_77]) ).
tcf(c_45800,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ epsilon_connected(sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X1 )
| ( X0 = X1 )
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,X1)
| in(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_11190,c_43601]) ).
tcf(c_45801,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK4(iPr_def_11) = X1 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK4(iPr_def_11)) ),
inference(renaming,[status(thm)],[c_45800]) ).
tcf(c_45820,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK0(X1,sK4(iPr_def_11)))
| in(sK0(X1,sK4(iPr_def_11)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( singleton(X1) = sK4(iPr_def_11) )
| ( sK0(X1,sK4(iPr_def_11)) = X1 )
| ( sK0(X1,sK4(iPr_def_11)) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_60,c_45801]) ).
tcf(c_45821,plain,
! [X0: $i] :
( epsilon_transitive(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK1(sK4(iPr_def_11)))
| in(sK1(sK4(iPr_def_11)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( sK1(sK4(iPr_def_11)) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_64,c_45801]) ).
tcf(c_45822,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK2(sK4(iPr_def_11),X1,X2))
| in(sK2(sK4(iPr_def_11),X1,X2),X2)
| in(sK2(sK4(iPr_def_11),X1,X2),X1)
| in(sK2(sK4(iPr_def_11),X1,X2),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X1) = X2 )
| ( sK2(sK4(iPr_def_11),X1,X2) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_45801]) ).
tcf(c_45823,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK2(X1,X2,sK4(iPr_def_11)))
| in(sK2(X1,X2,sK4(iPr_def_11)),X2)
| in(sK2(X1,X2,sK4(iPr_def_11)),X1)
| in(sK2(X1,X2,sK4(iPr_def_11)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,X2) = sK4(iPr_def_11) )
| ( sK2(X1,X2,sK4(iPr_def_11)) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_45801]) ).
tcf(c_45824,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK2(X1,sK4(iPr_def_11),X2))
| in(sK2(X1,sK4(iPr_def_11),X2),X2)
| in(sK2(X1,sK4(iPr_def_11),X2),X1)
| in(sK2(X1,sK4(iPr_def_11),X2),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,sK4(iPr_def_11)) = X2 )
| ( sK2(X1,sK4(iPr_def_11),X2) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_45801]) ).
tcf(c_45827,plain,
! [X0: $i] :
( empty(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK5(sK4(iPr_def_11)))
| in(sK5(sK4(iPr_def_11)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( sK5(sK4(iPr_def_11)) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3768,c_45801]) ).
tcf(c_45828,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK0(X1,set_union2(sK4(iPr_def_11),X2)))
| in(sK0(X1,set_union2(sK4(iPr_def_11),X2)),X2)
| in(sK0(X1,set_union2(sK4(iPr_def_11),X2)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X2) = singleton(X1) )
| ( sK0(X1,set_union2(sK4(iPr_def_11),X2)) = X1 )
| ( sK0(X1,set_union2(sK4(iPr_def_11),X2)) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4023,c_45801]) ).
tcf(c_45829,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK0(X1,set_union2(X2,sK4(iPr_def_11))))
| in(sK0(X1,set_union2(X2,sK4(iPr_def_11))),X2)
| in(sK0(X1,set_union2(X2,sK4(iPr_def_11))),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X2,sK4(iPr_def_11)) = singleton(X1) )
| ( sK0(X1,set_union2(X2,sK4(iPr_def_11))) = X1 )
| ( sK0(X1,set_union2(X2,sK4(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4023,c_45801]) ).
tcf(c_45830,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| epsilon_transitive(set_union2(sK4(iPr_def_11),X1))
| in(X0,sK1(set_union2(sK4(iPr_def_11),X1)))
| in(sK1(set_union2(sK4(iPr_def_11),X1)),X1)
| in(sK1(set_union2(sK4(iPr_def_11),X1)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( sK1(set_union2(sK4(iPr_def_11),X1)) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4024,c_45801]) ).
tcf(c_45831,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| epsilon_transitive(set_union2(X1,sK4(iPr_def_11)))
| in(X0,sK1(set_union2(X1,sK4(iPr_def_11))))
| in(sK1(set_union2(X1,sK4(iPr_def_11))),X1)
| in(sK1(set_union2(X1,sK4(iPr_def_11))),X0)
| ( sK4(iPr_def_11) = X0 )
| ( sK1(set_union2(X1,sK4(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4024,c_45801]) ).
tcf(c_45832,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| epsilon_connected(set_union2(sK4(iPr_def_11),X1))
| in(X0,sK3(set_union2(sK4(iPr_def_11),X1)))
| in(sK3(set_union2(sK4(iPr_def_11),X1)),X1)
| in(sK3(set_union2(sK4(iPr_def_11),X1)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( sK3(set_union2(sK4(iPr_def_11),X1)) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4027,c_45801]) ).
tcf(c_45833,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| epsilon_connected(set_union2(X1,sK4(iPr_def_11)))
| in(X0,sK3(set_union2(X1,sK4(iPr_def_11))))
| in(sK3(set_union2(X1,sK4(iPr_def_11))),X1)
| in(sK3(set_union2(X1,sK4(iPr_def_11))),X0)
| ( sK4(iPr_def_11) = X0 )
| ( sK3(set_union2(X1,sK4(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4027,c_45801]) ).
tcf(c_45834,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| epsilon_connected(set_union2(sK4(iPr_def_11),X1))
| in(X0,sK4(set_union2(sK4(iPr_def_11),X1)))
| in(sK4(set_union2(sK4(iPr_def_11),X1)),X1)
| in(sK4(set_union2(sK4(iPr_def_11),X1)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( sK4(set_union2(sK4(iPr_def_11),X1)) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4028,c_45801]) ).
tcf(c_45835,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| epsilon_connected(set_union2(X1,sK4(iPr_def_11)))
| in(X0,sK4(set_union2(X1,sK4(iPr_def_11))))
| in(sK4(set_union2(X1,sK4(iPr_def_11))),X1)
| in(sK4(set_union2(X1,sK4(iPr_def_11))),X0)
| ( sK4(iPr_def_11) = X0 )
| ( sK4(set_union2(X1,sK4(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4028,c_45801]) ).
tcf(c_45836,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| empty(set_union2(sK4(iPr_def_11),X1))
| in(X0,sK5(set_union2(sK4(iPr_def_11),X1)))
| in(sK5(set_union2(sK4(iPr_def_11),X1)),X1)
| in(sK5(set_union2(sK4(iPr_def_11),X1)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( sK5(set_union2(sK4(iPr_def_11),X1)) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4029,c_45801]) ).
tcf(c_45837,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| empty(set_union2(X1,sK4(iPr_def_11)))
| in(X0,sK5(set_union2(X1,sK4(iPr_def_11))))
| in(sK5(set_union2(X1,sK4(iPr_def_11))),X1)
| in(sK5(set_union2(X1,sK4(iPr_def_11))),X0)
| ( sK4(iPr_def_11) = X0 )
| ( sK5(set_union2(X1,sK4(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4029,c_45801]) ).
tcf(c_45838,plain,
! [X0: $i] :
( empty(sK18)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(sK18))
| in(sK5(sK18),X0)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(sK18))
| ( sK5(sK18) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_45801]) ).
tcf(c_45839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X2)
| in(X2,sK2(sK4(iPr_def_11),X3,X1))
| in(X0,sK2(sK4(iPr_def_11),X3,X1))
| in(sK2(sK4(iPr_def_11),X3,X1),X3)
| in(sK2(sK4(iPr_def_11),X3,X1),X2)
| in(sK2(sK4(iPr_def_11),X3,X1),X0)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(sK4(iPr_def_11),X3) = X1 )
| ( sK2(sK4(iPr_def_11),X3,X1) = X2 )
| ( sK2(sK4(iPr_def_11),X3,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_45801]) ).
tcf(c_45840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X2)
| in(X2,sK2(X3,sK4(iPr_def_11),X1))
| in(X0,sK2(X3,sK4(iPr_def_11),X1))
| in(sK2(X3,sK4(iPr_def_11),X1),X3)
| in(sK2(X3,sK4(iPr_def_11),X1),X2)
| in(sK2(X3,sK4(iPr_def_11),X1),X0)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X3,sK4(iPr_def_11)) = X1 )
| ( sK2(X3,sK4(iPr_def_11),X1) = X2 )
| ( sK2(X3,sK4(iPr_def_11),X1) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_45801]) ).
tcf(c_45841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(X1,sK2(X2,X3,X0))
| in(sK2(X2,X3,X0),X3)
| in(sK2(X2,X3,X0),X2)
| in(sK2(X2,X3,X0),X1)
| in(sK4(iPr_def_11),sK2(X2,X3,X0))
| ( sK4(iPr_def_11) = X1 )
| ( set_union2(X2,X3) = X0 )
| ( sK2(X2,X3,X0) = X1 )
| ( sK2(X2,X3,X0) = sK4(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_4329,c_45801]) ).
tcf(c_45842,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,iPr_def_10)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_45801]) ).
tcf(c_45843,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ subset(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_23181,c_45801]) ).
tcf(c_45844,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X1)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_45801]) ).
tcf(c_45845,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_45801]) ).
tcf(c_45846,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7246,c_45801]) ).
tcf(c_45847,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_45801]) ).
tcf(c_45848,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_45801]) ).
tcf(c_45850,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X1)
| in(X0,sK3(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_45801]) ).
tcf(c_45851,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_45801]) ).
tcf(c_45853,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_45801]) ).
tcf(c_45860,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ( X0 = X1 )
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ subset(iPr_def_10,X2)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13646,c_45801]) ).
tcf(c_45861,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ( X0 = X1 )
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11188,c_45801]) ).
tcf(c_45862,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ( X0 = X1 )
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11185,c_45801]) ).
tcf(c_45863,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11211,c_45801]) ).
tcf(c_45864,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ( X0 = X1 )
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11035,c_45801]) ).
tcf(c_45865,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(X1,singleton(X0))
| in(singleton(X0),X1)
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ( singleton(X0) = X1 )
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_45801]) ).
tcf(c_45866,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| in(X2,set_union2(X0,X1))
| in(set_union2(X0,X1),X2)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = X2 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_11214,c_45801]) ).
tcf(c_45867,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(sK18))
| in(sK5(sK18),X0)
| in(sK4(iPr_def_11),X0)
| ( sK5(sK18) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_31298,c_45801]) ).
tcf(c_45868,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(sK18,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_36385,c_45801]) ).
tcf(c_46508,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| in(sK1(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK1(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK1(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_7260]) ).
tcf(c_46509,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),X1)
| ( sK1(iPr_def_11) = X2 )
| ( sK1(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X0)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ subset(sK1(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_8680,c_359]) ).
tcf(c_46510,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| element(X2,X0)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),X1)
| ( sK1(iPr_def_11) = X2 )
| ( sK1(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ subset(sK1(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_8680,c_358]) ).
tcf(c_46511,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,X0)
| in(X0,X2)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),X1)
| ( X0 = X2 )
| ( sK1(iPr_def_11) = X2 )
| ( sK1(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK1(iPr_def_11))
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_8680,c_77]) ).
tcf(c_46512,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| subset(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(sK1(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_65]) ).
tcf(c_46514,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK1(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_137]) ).
tcf(c_46515,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| element(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_127]) ).
tcf(c_46516,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),sK2(sK1(iPr_def_11),X0,X1))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(sK1(iPr_def_11),X0) = X1 )
| ( sK2(sK1(iPr_def_11),X0,X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK2(sK1(iPr_def_11),X0,X1),iPr_def_10)
| ~ in(sK2(sK1(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_8680,c_66]) ).
tcf(c_46517,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),sK2(X0,X1,sK1(iPr_def_11)))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ( sK2(X0,X1,sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK2(X0,X1,sK1(iPr_def_11)),iPr_def_10)
| ~ in(sK2(X0,X1,sK1(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_8680,c_67]) ).
tcf(c_46518,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK1(iPr_def_11),singleton(sK1(iPr_def_11)))
| ( sK1(iPr_def_11) = X0 )
| ( singleton(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(singleton(sK1(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_3522]) ).
tcf(c_46519,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK1(iPr_def_11),iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = iPr_def_11 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_11,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3523]) ).
tcf(c_46520,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),set_union2(X0,X1))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK1(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_3641]) ).
tcf(c_46521,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),set_union2(X0,X1))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK1(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_3615]) ).
tcf(c_46522,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),singleton(set_union2(sK1(iPr_def_11),X0)))
| ( sK1(iPr_def_11) = X1 )
| ( singleton(set_union2(sK1(iPr_def_11),X0)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(singleton(set_union2(sK1(iPr_def_11),X0)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_3618]) ).
tcf(c_46523,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),singleton(set_union2(X0,sK1(iPr_def_11))))
| ( sK1(iPr_def_11) = X1 )
| ( singleton(set_union2(X0,sK1(iPr_def_11))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(singleton(set_union2(X0,sK1(iPr_def_11))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_3644]) ).
tcf(c_46524,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),singleton(set_union2(set_union2(sK1(iPr_def_11),X0),X1)))
| ( sK1(iPr_def_11) = X2 )
| ( singleton(set_union2(set_union2(sK1(iPr_def_11),X0),X1)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(singleton(set_union2(set_union2(sK1(iPr_def_11),X0),X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_3944]) ).
tcf(c_46525,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),singleton(set_union2(set_union2(X0,sK1(iPr_def_11)),X1)))
| ( sK1(iPr_def_11) = X2 )
| ( singleton(set_union2(set_union2(X0,sK1(iPr_def_11)),X1)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(singleton(set_union2(set_union2(X0,sK1(iPr_def_11)),X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_3945]) ).
tcf(c_46526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),sK2(set_union2(sK1(iPr_def_11),X0),X1,X2))
| ( sK1(iPr_def_11) = X3 )
| ( set_union2(set_union2(sK1(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK1(iPr_def_11),X0),X1,X2) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(sK2(set_union2(sK1(iPr_def_11),X0),X1,X2),iPr_def_10)
| ~ in(sK2(set_union2(sK1(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_8680,c_4078]) ).
tcf(c_46527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),sK2(set_union2(X0,X1),X2,sK1(iPr_def_11)))
| ( sK1(iPr_def_11) = X3 )
| ( set_union2(set_union2(X0,X1),X2) = sK1(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK1(iPr_def_11)),iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X2,sK1(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_8680,c_4079]) ).
tcf(c_46528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),sK2(X0,X1,set_union2(sK1(iPr_def_11),X2)))
| ( sK1(iPr_def_11) = X3 )
| ( set_union2(sK1(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK1(iPr_def_11),X2)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(sK2(X0,X1,set_union2(sK1(iPr_def_11),X2)),iPr_def_10)
| ~ in(sK2(X0,X1,set_union2(sK1(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_8680,c_4095]) ).
tcf(c_46529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),sK2(X0,sK1(iPr_def_11),set_union2(X1,X2)))
| ( sK1(iPr_def_11) = X3 )
| ( set_union2(X0,sK1(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK1(iPr_def_11),set_union2(X1,X2)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(sK2(X0,sK1(iPr_def_11),set_union2(X1,X2)),iPr_def_10)
| ~ in(sK2(X0,sK1(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_8680,c_4096]) ).
tcf(c_46530,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),singleton(set_union2(X0,set_union2(sK1(iPr_def_11),X1))))
| ( sK1(iPr_def_11) = X2 )
| ( singleton(set_union2(X0,set_union2(sK1(iPr_def_11),X1))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(singleton(set_union2(X0,set_union2(sK1(iPr_def_11),X1))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_4131]) ).
tcf(c_46531,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK1(iPr_def_11)))))
| ( sK1(iPr_def_11) = X2 )
| ( singleton(set_union2(X0,set_union2(X1,sK1(iPr_def_11)))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK1(iPr_def_11)))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_4132]) ).
tcf(c_46532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK1(iPr_def_11),X0),X1),X2)))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(set_union2(sK1(iPr_def_11),X0),X1),X2)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(set_union2(set_union2(sK1(iPr_def_11),X0),X1),X2)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_5325]) ).
tcf(c_46533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK1(iPr_def_11)),X1),X2)))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(set_union2(X0,sK1(iPr_def_11)),X1),X2)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK1(iPr_def_11)),X1),X2)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_5326]) ).
tcf(c_46535,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK1(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| in(sK1(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK1(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK1(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_7260]) ).
tcf(c_46536,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),X1)
| ( sK1(iPr_def_11) = X2 )
| ( sK1(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X0)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ subset(sK1(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_8680,c_359]) ).
tcf(c_46537,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| element(X1,X0)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),X1)
| ( sK1(iPr_def_11) = X2 )
| ( sK1(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ subset(sK1(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_8680,c_358]) ).
tcf(c_46538,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,X0)
| in(X0,X1)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK1(iPr_def_11) = X2 )
| ( sK1(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK1(iPr_def_11))
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_8680,c_77]) ).
tcf(c_46539,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| subset(X0,sK1(iPr_def_11))
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(sK1(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_65]) ).
tcf(c_46541,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK1(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_137]) ).
tcf(c_46542,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| element(X0,sK1(iPr_def_11))
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_127]) ).
tcf(c_46543,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),sK2(sK1(iPr_def_11),X0,X1))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(sK1(iPr_def_11),X0) = X1 )
| ( sK2(sK1(iPr_def_11),X0,X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK2(sK1(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK1(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_8680,c_66]) ).
tcf(c_46544,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),sK2(X0,X1,sK1(iPr_def_11)))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ( sK2(X0,X1,sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK2(X0,X1,sK1(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK1(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_8680,c_67]) ).
tcf(c_46545,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK1(iPr_def_11),singleton(sK1(iPr_def_11)))
| ( sK1(iPr_def_11) = X0 )
| ( singleton(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(singleton(sK1(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3522]) ).
tcf(c_46547,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),set_union2(X0,X1))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK1(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3641]) ).
tcf(c_46548,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),set_union2(X0,X1))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK1(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3615]) ).
tcf(c_46549,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),singleton(set_union2(sK1(iPr_def_11),X0)))
| ( sK1(iPr_def_11) = X1 )
| ( singleton(set_union2(sK1(iPr_def_11),X0)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(singleton(set_union2(sK1(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3618]) ).
tcf(c_46550,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),singleton(set_union2(X0,sK1(iPr_def_11))))
| ( sK1(iPr_def_11) = X1 )
| ( singleton(set_union2(X0,sK1(iPr_def_11))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(singleton(set_union2(X0,sK1(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3644]) ).
tcf(c_46551,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),singleton(set_union2(set_union2(sK1(iPr_def_11),X0),X1)))
| ( sK1(iPr_def_11) = X2 )
| ( singleton(set_union2(set_union2(sK1(iPr_def_11),X0),X1)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(sK1(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3944]) ).
tcf(c_46552,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),singleton(set_union2(set_union2(X0,sK1(iPr_def_11)),X1)))
| ( sK1(iPr_def_11) = X2 )
| ( singleton(set_union2(set_union2(X0,sK1(iPr_def_11)),X1)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(X0,sK1(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3945]) ).
tcf(c_46553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),sK2(set_union2(sK1(iPr_def_11),X0),X1,X2))
| ( sK1(iPr_def_11) = X3 )
| ( set_union2(set_union2(sK1(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK1(iPr_def_11),X0),X1,X2) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(sK2(set_union2(sK1(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK1(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_8680,c_4078]) ).
tcf(c_46554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),sK2(set_union2(X0,X1),X2,sK1(iPr_def_11)))
| ( sK1(iPr_def_11) = X3 )
| ( set_union2(set_union2(X0,X1),X2) = sK1(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X2,sK1(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK1(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_8680,c_4079]) ).
tcf(c_46555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),sK2(X0,X1,set_union2(sK1(iPr_def_11),X2)))
| ( sK1(iPr_def_11) = X3 )
| ( set_union2(sK1(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK1(iPr_def_11),X2)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(sK2(X0,X1,set_union2(sK1(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK1(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_8680,c_4095]) ).
tcf(c_46556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),sK2(X0,sK1(iPr_def_11),set_union2(X1,X2)))
| ( sK1(iPr_def_11) = X3 )
| ( set_union2(X0,sK1(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK1(iPr_def_11),set_union2(X1,X2)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(sK2(X0,sK1(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK1(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_8680,c_4096]) ).
tcf(c_46557,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),singleton(set_union2(X0,set_union2(sK1(iPr_def_11),X1))))
| ( sK1(iPr_def_11) = X2 )
| ( singleton(set_union2(X0,set_union2(sK1(iPr_def_11),X1))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(sK1(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_4131]) ).
tcf(c_46558,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK1(iPr_def_11)))))
| ( sK1(iPr_def_11) = X2 )
| ( singleton(set_union2(X0,set_union2(X1,sK1(iPr_def_11)))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK1(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_4132]) ).
tcf(c_46559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK1(iPr_def_11),X0),X1),X2)))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(set_union2(sK1(iPr_def_11),X0),X1),X2)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(set_union2(sK1(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_5325]) ).
tcf(c_46560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK1(iPr_def_11)),X1),X2)))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(set_union2(X0,sK1(iPr_def_11)),X1),X2)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK1(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_5326]) ).
tcf(c_46562,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK1(iPr_def_11))
| in(sK1(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X1,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_7260]) ).
tcf(c_46563,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| ( sK1(iPr_def_11) = X2 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X1)
| ~ in(X2,sK18)
| ~ in(X0,iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_8680,c_359]) ).
tcf(c_46564,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),X1)
| in(X2,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| ( sK1(iPr_def_11) = X2 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(X0,iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_8680,c_358]) ).
tcf(c_46565,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X2 )
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X2,sK18)
| ~ in(X1,iPr_def_10)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_8680,c_77]) ).
tcf(c_46566,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| subset(sK1(iPr_def_11),X1)
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_65]) ).
tcf(c_46568,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X1)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_137]) ).
tcf(c_46569,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),X1)
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_127]) ).
tcf(c_46570,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(singleton(X0),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ( singleton(X0) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(singleton(X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_62]) ).
tcf(c_46571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),X2)
| in(set_union2(X0,X1),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X3 )
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_4213]) ).
tcf(c_46572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),X2)
| in(set_union2(X0,X1),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X3 )
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_4212]) ).
tcf(c_46573,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| in(set_union2(X0,X1),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_71]) ).
tcf(c_46574,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(empty_set,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = empty_set )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(empty_set,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_7097]) ).
tcf(c_46575,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| subset(sK1(iPr_def_11),iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_12813]) ).
tcf(c_46576,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,iPr_def_10)
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_8680,c_6841]) ).
tcf(c_46577,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_5047]) ).
tcf(c_46578,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(sK1(iPr_def_11),iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3640]) ).
tcf(c_46579,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| epsilon_transitive(sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK1(sK1(iPr_def_11)),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ( sK1(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK1(sK1(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_3523]) ).
tcf(c_46580,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| epsilon_connected(sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK3(sK1(iPr_def_11)),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ( sK3(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK3(sK1(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_3524]) ).
tcf(c_46581,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| epsilon_connected(sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK4(sK1(iPr_def_11)),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ( sK4(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK4(sK1(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_3525]) ).
tcf(c_46583,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(iPr_def_10,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = iPr_def_10 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_8680,c_6289]) ).
tcf(c_46584,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),iPr_def_11)
| in(iPr_def_10,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = iPr_def_10 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_4912]) ).
tcf(c_46585,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(iPr_def_10,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = iPr_def_10 )
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3592]) ).
tcf(c_46586,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(iPr_def_10,sK1(iPr_def_11))
| in(sK1(iPr_def_11),iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = iPr_def_10 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3614]) ).
tcf(c_46587,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(iPr_def_11,sK1(iPr_def_11))
| in(sK1(iPr_def_11),sK18)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = iPr_def_11 )
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_11,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_33457]) ).
tcf(c_46588,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(iPr_def_11,sK1(iPr_def_11))
| in(sK1(iPr_def_11),iPr_def_10)
| in(sK1(iPr_def_11),sK18)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = iPr_def_11 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_11,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_4035]) ).
tcf(c_46589,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| empty(sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK5(sK1(iPr_def_11)),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ( sK5(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK5(sK1(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_3900]) ).
tcf(c_46591,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ subset(iPr_def_11,sK1(iPr_def_11))
| ~ in(sK5(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_23189]) ).
tcf(c_46594,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK1(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK5(iPr_def_11),sK1(iPr_def_11))
| in(sK1(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_7260]) ).
tcf(c_46595,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| ( sK1(iPr_def_11) = X2 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X1)
| ~ in(X2,iPr_def_10)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_8680,c_359]) ).
tcf(c_46596,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),X1)
| in(X2,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| ( sK1(iPr_def_11) = X2 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_8680,c_358]) ).
tcf(c_46597,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = X2 )
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_8680,c_77]) ).
tcf(c_46598,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| subset(sK1(iPr_def_11),X0)
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_65]) ).
tcf(c_46600,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X0)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_137]) ).
tcf(c_46601,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),X0)
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_127]) ).
tcf(c_46602,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(singleton(X0),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ( singleton(X0) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_62]) ).
tcf(c_46603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),X2)
| in(set_union2(X0,X1),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X3 )
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_4213]) ).
tcf(c_46604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),X2)
| in(set_union2(X0,X1),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X3 )
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_4212]) ).
tcf(c_46605,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| in(set_union2(X0,X1),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_71]) ).
tcf(c_46606,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(empty_set,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = empty_set )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(empty_set,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_7097]) ).
tcf(c_46607,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| subset(sK1(iPr_def_11),iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_12813]) ).
tcf(c_46608,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,sK18)
| ~ in(X0,iPr_def_10)
| ~ in(iPr_def_11,sK1(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_8680,c_6841]) ).
tcf(c_46609,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_5047]) ).
tcf(c_46610,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(sK1(iPr_def_11),iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_3640]) ).
tcf(c_46611,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| epsilon_transitive(sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK1(sK1(iPr_def_11)),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ( sK1(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(sK1(sK1(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3523]) ).
tcf(c_46612,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| epsilon_connected(sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK3(sK1(iPr_def_11)),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ( sK3(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(sK3(sK1(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3524]) ).
tcf(c_46613,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| epsilon_connected(sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK4(sK1(iPr_def_11)),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ( sK4(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(sK4(sK1(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3525]) ).
tcf(c_46621,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| empty(sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK5(sK1(iPr_def_11)),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ( sK5(sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(sK5(sK1(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_3900]) ).
tcf(c_46622,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK1(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,iPr_def_10)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_7243]) ).
tcf(c_46623,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ subset(iPr_def_11,sK1(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_23189]) ).
tcf(c_46624,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_transitive(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK1(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,iPr_def_10)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_9906]) ).
tcf(c_46625,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK4(iPr_def_11),X1)
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK1(iPr_def_11))
| ( sK4(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,iPr_def_10)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_45801]) ).
tcf(c_46745,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(sK1(iPr_def_11),iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46578,c_3400]) ).
tcf(c_46755,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| element(sK1(iPr_def_11),iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46577,c_3400]) ).
tcf(c_46765,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| subset(sK1(iPr_def_11),iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46575,c_3400]) ).
tcf(c_46855,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK18,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| ( sK1(iPr_def_11) = sK18 )
| ( sK1(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK1(iPr_def_11)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46576,c_3400]) ).
tcf(c_48070,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,sK18)
| ~ in(X1,iPr_def_10)
| ~ epsilon_connected(iPr_def_10)
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X1 )
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),X1)
| in(X0,sK3(iPr_def_11))
| in(X1,sK3(iPr_def_11)) ),
inference(global_subsumption_just,[status(thm)],[c_9897,c_43364]) ).
tcf(c_48071,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(renaming,[status(thm)],[c_48070]) ).
tcf(c_48090,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_7260]) ).
tcf(c_48091,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X2 )
| ( sK3(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X0)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_48071,c_359]) ).
tcf(c_48092,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X0)
| in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X2 )
| ( sK3(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_48071,c_358]) ).
tcf(c_48093,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X0,X2)
| in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| ( X0 = X2 )
| ( sK3(iPr_def_11) = X2 )
| ( sK3(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_48071,c_77]) ).
tcf(c_48094,plain,
! [X0: $i,X1: $i] :
( subset(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_65]) ).
tcf(c_48096,plain,
! [X0: $i,X1: $i] :
( in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK3(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_137]) ).
tcf(c_48097,plain,
! [X0: $i,X1: $i] :
( element(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_127]) ).
tcf(c_48098,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),sK2(sK3(iPr_def_11),X0,X1))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(sK3(iPr_def_11),X0) = X1 )
| ( sK2(sK3(iPr_def_11),X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK2(sK3(iPr_def_11),X0,X1),iPr_def_10)
| ~ in(sK2(sK3(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_48071,c_66]) ).
tcf(c_48099,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),sK2(X0,X1,sK3(iPr_def_11)))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( sK2(X0,X1,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),iPr_def_10)
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_48071,c_67]) ).
tcf(c_48100,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_76]) ).
tcf(c_48101,plain,
! [X0: $i] :
( in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),singleton(sK3(iPr_def_11)))
| ( sK3(iPr_def_11) = X0 )
| ( singleton(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(singleton(sK3(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_3522]) ).
tcf(c_48102,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = iPr_def_11 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_11,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3524]) ).
tcf(c_48103,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(X0,X1))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK3(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_3641]) ).
tcf(c_48104,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(X0,X1))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK3(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_3615]) ).
tcf(c_48105,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( sK3(iPr_def_11) = X1 )
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_3618]) ).
tcf(c_48106,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( sK3(iPr_def_11) = X1 )
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_3644]) ).
tcf(c_48107,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)))
| ( sK3(iPr_def_11) = X2 )
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_3944]) ).
tcf(c_48108,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)))
| ( sK3(iPr_def_11) = X2 )
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_3945]) ).
tcf(c_48109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),sK2(set_union2(sK3(iPr_def_11),X0),X1,X2))
| ( sK3(iPr_def_11) = X3 )
| ( set_union2(set_union2(sK3(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK3(iPr_def_11),X0),X1,X2) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2),iPr_def_10)
| ~ in(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_48071,c_4078]) ).
tcf(c_48110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)))
| ( sK3(iPr_def_11) = X3 )
| ( set_union2(set_union2(X0,X1),X2) = sK3(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)),iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_48071,c_4079]) ).
tcf(c_48111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)))
| ( sK3(iPr_def_11) = X3 )
| ( set_union2(sK3(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)),iPr_def_10)
| ~ in(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_48071,c_4095]) ).
tcf(c_48112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)))
| ( sK3(iPr_def_11) = X3 )
| ( set_union2(X0,sK3(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)),iPr_def_10)
| ~ in(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_48071,c_4096]) ).
tcf(c_48113,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))))
| ( sK3(iPr_def_11) = X2 )
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_4131]) ).
tcf(c_48114,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))))
| ( sK3(iPr_def_11) = X2 )
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_4132]) ).
tcf(c_48115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_5325]) ).
tcf(c_48116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_5326]) ).
tcf(c_48117,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X2,X1)
| in(X1,X2)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( X1 = X2 )
| ( sK3(iPr_def_11) = X2 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_9906]) ).
tcf(c_48118,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = iPr_def_10 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_9899]) ).
tcf(c_48119,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = iPr_def_10 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK18)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_9637]) ).
tcf(c_48120,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_7260]) ).
tcf(c_48121,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X2 )
| ( sK3(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X0)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_48071,c_359]) ).
tcf(c_48122,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X1,X0)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X2 )
| ( sK3(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_48071,c_358]) ).
tcf(c_48123,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X0)
| in(X0,X1)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| ( X0 = X1 )
| ( sK3(iPr_def_11) = X2 )
| ( sK3(iPr_def_11) = X1 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_48071,c_77]) ).
tcf(c_48124,plain,
! [X0: $i,X1: $i] :
( subset(X0,sK3(iPr_def_11))
| in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_65]) ).
tcf(c_48126,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK3(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_137]) ).
tcf(c_48127,plain,
! [X0: $i,X1: $i] :
( element(X0,sK3(iPr_def_11))
| in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_127]) ).
tcf(c_48128,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),sK2(sK3(iPr_def_11),X0,X1))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(sK3(iPr_def_11),X0) = X1 )
| ( sK2(sK3(iPr_def_11),X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK2(sK3(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK3(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_48071,c_66]) ).
tcf(c_48129,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),sK2(X0,X1,sK3(iPr_def_11)))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( sK2(X0,X1,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_48071,c_67]) ).
tcf(c_48130,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_76]) ).
tcf(c_48131,plain,
! [X0: $i] :
( in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),singleton(sK3(iPr_def_11)))
| ( sK3(iPr_def_11) = X0 )
| ( singleton(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(singleton(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3522]) ).
tcf(c_48133,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(X0,X1))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK3(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3641]) ).
tcf(c_48134,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(X0,X1))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK3(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3615]) ).
tcf(c_48135,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( sK3(iPr_def_11) = X1 )
| ( singleton(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(singleton(set_union2(sK3(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3618]) ).
tcf(c_48136,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( sK3(iPr_def_11) = X1 )
| ( singleton(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(singleton(set_union2(X0,sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3644]) ).
tcf(c_48137,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)))
| ( sK3(iPr_def_11) = X2 )
| ( singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(sK3(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3944]) ).
tcf(c_48138,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)))
| ( sK3(iPr_def_11) = X2 )
| ( singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(X0,sK3(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3945]) ).
tcf(c_48139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),sK2(set_union2(sK3(iPr_def_11),X0),X1,X2))
| ( sK3(iPr_def_11) = X3 )
| ( set_union2(set_union2(sK3(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK3(iPr_def_11),X0),X1,X2) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK3(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_48071,c_4078]) ).
tcf(c_48140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)))
| ( sK3(iPr_def_11) = X3 )
| ( set_union2(set_union2(X0,X1),X2) = sK3(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK3(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_48071,c_4079]) ).
tcf(c_48141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)))
| ( sK3(iPr_def_11) = X3 )
| ( set_union2(sK3(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK3(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_48071,c_4095]) ).
tcf(c_48142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)))
| ( sK3(iPr_def_11) = X3 )
| ( set_union2(X0,sK3(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK3(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_48071,c_4096]) ).
tcf(c_48143,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))))
| ( sK3(iPr_def_11) = X2 )
| ( singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_4131]) ).
tcf(c_48144,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))))
| ( sK3(iPr_def_11) = X2 )
| ( singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_4132]) ).
tcf(c_48145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(set_union2(sK3(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_5325]) ).
tcf(c_48146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK3(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_5326]) ).
tcf(c_48147,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(X2,X0)
| in(X0,X2)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| ( X0 = X2 )
| ( sK3(iPr_def_11) = X2 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_9906]) ).
tcf(c_48150,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X1,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_7260]) ).
tcf(c_48151,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X1)
| ~ in(X2,sK18)
| ~ in(X0,iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_48071,c_359]) ).
tcf(c_48152,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(iPr_def_11),X1)
| in(X2,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(X0,iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_48071,c_358]) ).
tcf(c_48153,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X2 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X2,sK18)
| ~ in(X1,iPr_def_10)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_48071,c_77]) ).
tcf(c_48154,plain,
! [X0: $i,X1: $i] :
( subset(sK3(iPr_def_11),X1)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_65]) ).
tcf(c_48156,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X1)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_137]) ).
tcf(c_48157,plain,
! [X0: $i,X1: $i] :
( element(sK3(iPr_def_11),X1)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_127]) ).
tcf(c_48158,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(singleton(X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(singleton(X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_62]) ).
tcf(c_48159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),X2)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X3 )
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_4213]) ).
tcf(c_48160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),X2)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X3 )
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_4212]) ).
tcf(c_48161,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_71]) ).
tcf(c_48162,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_74]) ).
tcf(c_48163,plain,
! [X0: $i] :
( in(empty_set,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = empty_set )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(empty_set,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_7097]) ).
tcf(c_48164,plain,
! [X0: $i] :
( subset(sK3(iPr_def_11),iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_12813]) ).
tcf(c_48165,plain,
! [X0: $i] :
( in(sK18,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,iPr_def_10)
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_48071,c_6841]) ).
tcf(c_48166,plain,
! [X0: $i] :
( element(sK3(iPr_def_11),iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_5047]) ).
tcf(c_48167,plain,
! [X0: $i] :
( in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3640]) ).
tcf(c_48168,plain,
! [X0: $i] :
( epsilon_transitive(sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK1(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK1(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK1(sK3(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_3523]) ).
tcf(c_48169,plain,
! [X0: $i] :
( epsilon_connected(sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK3(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK3(sK3(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_3524]) ).
tcf(c_48170,plain,
! [X0: $i] :
( epsilon_connected(sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK4(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK4(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK4(sK3(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_3525]) ).
tcf(c_48171,plain,
! [X0: $i] :
( subset(sK3(iPr_def_11),iPr_def_11)
| in(iPr_def_10,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = iPr_def_10 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_11)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_9540]) ).
tcf(c_48172,plain,
! [X0: $i] :
( in(iPr_def_10,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = iPr_def_10 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_48071,c_6289]) ).
tcf(c_48173,plain,
! [X0: $i] :
( element(sK3(iPr_def_11),iPr_def_11)
| in(iPr_def_10,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = iPr_def_10 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_4912]) ).
tcf(c_48174,plain,
! [X0: $i] :
( in(iPr_def_10,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = iPr_def_10 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3592]) ).
tcf(c_48175,plain,
! [X0: $i] :
( in(iPr_def_10,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = iPr_def_10 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3614]) ).
tcf(c_48176,plain,
! [X0: $i] :
( in(iPr_def_11,sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK18)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = iPr_def_11 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_11,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_33457]) ).
tcf(c_48177,plain,
! [X0: $i] :
( in(iPr_def_11,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK18)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = iPr_def_11 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(iPr_def_11,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_4035]) ).
tcf(c_48178,plain,
! [X0: $i] :
( empty(sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK5(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK5(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK5(sK3(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_3900]) ).
tcf(c_48179,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_11771]) ).
tcf(c_48181,plain,
! [X0: $i] :
( in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ subset(iPr_def_11,sK3(iPr_def_11))
| ~ in(sK5(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_23189]) ).
tcf(c_48184,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_7260]) ).
tcf(c_48185,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X1)
| ~ in(X2,iPr_def_10)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_48071,c_359]) ).
tcf(c_48186,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(iPr_def_11),X1)
| in(X2,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_48071,c_358]) ).
tcf(c_48187,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X2 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X2,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_48071,c_77]) ).
tcf(c_48188,plain,
! [X0: $i,X1: $i] :
( subset(sK3(iPr_def_11),X0)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_65]) ).
tcf(c_48190,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(X0)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_137]) ).
tcf(c_48191,plain,
! [X0: $i,X1: $i] :
( element(sK3(iPr_def_11),X0)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_127]) ).
tcf(c_48192,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(singleton(X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_62]) ).
tcf(c_48193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),X2)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X3 )
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_4213]) ).
tcf(c_48194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),X2)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X3 )
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_4212]) ).
tcf(c_48195,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_71]) ).
tcf(c_48196,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_74]) ).
tcf(c_48197,plain,
! [X0: $i] :
( in(empty_set,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = empty_set )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(empty_set,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_7097]) ).
tcf(c_48198,plain,
! [X0: $i] :
( subset(sK3(iPr_def_11),iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_12813]) ).
tcf(c_48199,plain,
! [X0: $i] :
( in(sK18,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,sK18)
| ~ in(X0,iPr_def_10)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_48071,c_6841]) ).
tcf(c_48200,plain,
! [X0: $i] :
( element(sK3(iPr_def_11),iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_5047]) ).
tcf(c_48201,plain,
! [X0: $i] :
( in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_3640]) ).
tcf(c_48202,plain,
! [X0: $i] :
( epsilon_transitive(sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK1(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK1(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(sK1(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3523]) ).
tcf(c_48203,plain,
! [X0: $i] :
( epsilon_connected(sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK3(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(sK3(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3524]) ).
tcf(c_48204,plain,
! [X0: $i] :
( epsilon_connected(sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK4(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK4(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(sK4(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3525]) ).
tcf(c_48212,plain,
! [X0: $i] :
( empty(sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK5(sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK5(sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(sK5(sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_3900]) ).
tcf(c_48213,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_11771]) ).
tcf(c_48214,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,iPr_def_10)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_7243]) ).
tcf(c_48215,plain,
! [X0: $i] :
( in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ subset(iPr_def_11,sK3(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_23189]) ).
tcf(c_48217,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK4(iPr_def_11),X1)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK4(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,iPr_def_10)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_45801]) ).
tcf(c_48229,plain,
! [X0: $i] :
( in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ in(X0,sK18) ),
inference(equality_factoring,[status(thm)],[c_48071]) ).
tcf(c_48333,plain,
! [X0: $i] :
( in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48167,c_3400]) ).
tcf(c_48342,plain,
! [X0: $i] :
( element(sK3(iPr_def_11),iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48166,c_3400]) ).
tcf(c_48351,plain,
! [X0: $i] :
( subset(sK3(iPr_def_11),iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48164,c_3400]) ).
tcf(c_48441,plain,
! [X0: $i] :
( in(sK18,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48165,c_3400]) ).
tcf(c_48497,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48179,c_3400]) ).
tcf(c_49876,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ~ in(X1,sK18)
| ~ epsilon_connected(X1)
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X1 )
| in(sK3(iPr_def_11),X0)
| in(X0,sK3(iPr_def_11))
| in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_9924,c_43385]) ).
tcf(c_49877,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(renaming,[status(thm)],[c_49876]) ).
tcf(c_49896,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK0(X1,X0))
| in(sK0(X1,X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X1) = X0 )
| ( sK0(X1,X0) = X1 )
| ( sK0(X1,X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_60,c_49877]) ).
tcf(c_49897,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(singleton(X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(X0))
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_61,c_49877]) ).
tcf(c_49898,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK1(X0))
| in(sK1(X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK1(X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_64,c_49877]) ).
tcf(c_49899,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK3(iPr_def_11),sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_49877]) ).
tcf(c_49900,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| in(sK3(iPr_def_11),sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,X2) = X0 )
| ( sK2(X1,X2,X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_49877]) ).
tcf(c_49901,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| in(sK3(iPr_def_11),sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68,c_49877]) ).
tcf(c_49902,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_69,c_49877]) ).
tcf(c_49903,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_70,c_49877]) ).
tcf(c_49906,plain,
! [X0: $i] :
( empty(X0)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(X0))
| in(sK5(X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK5(X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_3768,c_49877]) ).
tcf(c_49907,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X0))
| in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(powerset(X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ( powerset(X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(powerset(X0))
| ~ subset(X1,X0)
| ~ in(powerset(X0),sK18) ),
inference(superposition,[status(thm)],[c_3769,c_49877]) ).
tcf(c_49908,plain,
( empty(powerset(empty_set))
| in(empty_set,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),empty_set)
| in(powerset(empty_set),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = empty_set )
| ( sK3(iPr_def_11) = powerset(empty_set) )
| ~ epsilon_connected(powerset(empty_set))
| ~ in(powerset(empty_set),sK18) ),
inference(superposition,[status(thm)],[c_32137,c_49877]) ).
tcf(c_49917,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK0(X1,set_union2(X0,X2)),X2)
| in(sK3(iPr_def_11),sK0(X1,set_union2(X0,X2)))
| in(sK0(X1,set_union2(X0,X2)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X2) = singleton(X1) )
| ( sK0(X1,set_union2(X0,X2)) = X1 )
| ( sK0(X1,set_union2(X0,X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4023,c_49877]) ).
tcf(c_49918,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK0(X1,set_union2(X2,X0)),X2)
| in(sK3(iPr_def_11),sK0(X1,set_union2(X2,X0)))
| in(sK0(X1,set_union2(X2,X0)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X2,X0) = singleton(X1) )
| ( sK0(X1,set_union2(X2,X0)) = X1 )
| ( sK0(X1,set_union2(X2,X0)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4023,c_49877]) ).
tcf(c_49919,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| epsilon_transitive(set_union2(X0,X1))
| in(sK1(set_union2(X0,X1)),X1)
| in(sK3(iPr_def_11),sK1(set_union2(X0,X1)))
| in(sK1(set_union2(X0,X1)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK1(set_union2(X0,X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4024,c_49877]) ).
tcf(c_49920,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| epsilon_transitive(set_union2(X1,X0))
| in(sK1(set_union2(X1,X0)),X1)
| in(sK3(iPr_def_11),sK1(set_union2(X1,X0)))
| in(sK1(set_union2(X1,X0)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK1(set_union2(X1,X0)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4024,c_49877]) ).
tcf(c_49921,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| epsilon_connected(set_union2(X0,X1))
| in(sK3(set_union2(X0,X1)),X1)
| in(sK3(iPr_def_11),sK3(set_union2(X0,X1)))
| in(sK3(set_union2(X0,X1)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(set_union2(X0,X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4027,c_49877]) ).
tcf(c_49922,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| epsilon_connected(set_union2(X1,X0))
| in(sK3(set_union2(X1,X0)),X1)
| in(sK3(iPr_def_11),sK3(set_union2(X1,X0)))
| in(sK3(set_union2(X1,X0)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(set_union2(X1,X0)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4027,c_49877]) ).
tcf(c_49923,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| epsilon_connected(set_union2(X0,X1))
| in(sK4(set_union2(X0,X1)),X1)
| in(sK3(iPr_def_11),sK4(set_union2(X0,X1)))
| in(sK4(set_union2(X0,X1)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK4(set_union2(X0,X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4028,c_49877]) ).
tcf(c_49924,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| epsilon_connected(set_union2(X1,X0))
| in(sK4(set_union2(X1,X0)),X1)
| in(sK3(iPr_def_11),sK4(set_union2(X1,X0)))
| in(sK4(set_union2(X1,X0)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK4(set_union2(X1,X0)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4028,c_49877]) ).
tcf(c_49925,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| empty(set_union2(X0,X1))
| in(sK5(set_union2(X0,X1)),X1)
| in(sK3(iPr_def_11),sK5(set_union2(X0,X1)))
| in(sK5(set_union2(X0,X1)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK5(set_union2(X0,X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4029,c_49877]) ).
tcf(c_49926,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| empty(set_union2(X1,X0))
| in(sK5(set_union2(X1,X0)),X1)
| in(sK3(iPr_def_11),sK5(set_union2(X1,X0)))
| in(sK5(set_union2(X1,X0)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK5(set_union2(X1,X0)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4029,c_49877]) ).
tcf(c_49927,plain,
! [X0: $i] :
( empty(sK18)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(sK18))
| in(X0,sK3(iPr_def_11))
| in(sK5(sK18),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(sK18))
| ( sK5(sK18) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ epsilon_connected(X0)
| ~ in(X0,iPr_def_11)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4222,c_49877]) ).
tcf(c_49928,plain,
! [X0: $i] :
( empty(sK18)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK5(sK18),X0)
| in(sK3(iPr_def_11),X0)
| in(sK5(sK18),sK3(iPr_def_11))
| ( sK5(sK18) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ epsilon_connected(sK5(sK18))
| ~ in(X0,iPr_def_11)
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_4222,c_49877]) ).
tcf(c_49929,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(X0,sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),X3)
| in(sK2(X2,X3,X1),X0)
| in(sK3(iPr_def_11),sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X2,X3) = X1 )
| ( sK2(X2,X3,X1) = X0 )
| ( sK2(X2,X3,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(X2)
| ~ epsilon_connected(X1)
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_49877]) ).
tcf(c_49930,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(X0,sK2(X3,X2,X1))
| in(sK2(X3,X2,X1),X3)
| in(sK2(X3,X2,X1),X0)
| in(sK3(iPr_def_11),sK2(X3,X2,X1))
| in(sK2(X3,X2,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X3,X2) = X1 )
| ( sK2(X3,X2,X1) = X0 )
| ( sK2(X3,X2,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(X2)
| ~ epsilon_connected(X1)
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_49877]) ).
tcf(c_49931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(X0,sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),X3)
| in(sK2(X2,X3,X1),X2)
| in(sK3(iPr_def_11),sK2(X2,X3,X1))
| in(sK2(X2,X3,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X2,X3) = X1 )
| ( sK2(X2,X3,X1) = X0 )
| ( sK2(X2,X3,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_49877]) ).
tcf(c_49932,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK2(X0,X1,X2),X3)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X3 )
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X3 )
| ( sK2(X0,X1,X2) = sK3(iPr_def_11) )
| ~ epsilon_connected(X2)
| ~ in(X3,X2)
| ~ epsilon_connected(sK2(X0,X1,X2))
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4329,c_49877]) ).
tcf(c_49942,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_6995,c_49877]) ).
tcf(c_49948,plain,
( in(sK18,sK3(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_7014,c_49877]) ).
tcf(c_49954,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_49877]) ).
tcf(c_49955,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ subset(iPr_def_11,X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_23181,c_49877]) ).
tcf(c_49956,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X1)
| in(X0,sK5(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13652,c_49877]) ).
tcf(c_49957,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7241,c_49877]) ).
tcf(c_49958,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7246,c_49877]) ).
tcf(c_49959,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7238,c_49877]) ).
tcf(c_49960,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7155,c_49877]) ).
tcf(c_49961,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_49877]) ).
tcf(c_49962,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X1)
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_49877]) ).
tcf(c_49963,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_49877]) ).
tcf(c_49964,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_49877]) ).
tcf(c_49965,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_49877]) ).
tcf(c_49966,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_49877]) ).
tcf(c_49968,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(X1,sK3(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X1,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_49877]) ).
tcf(c_49969,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X1)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X1 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_49877]) ).
tcf(c_49970,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(sK5(iPr_def_11),X0)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ( singleton(set_union2(sK5(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(sK5(iPr_def_11),X0)))
| ~ in(singleton(set_union2(sK5(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_7253,c_49877]) ).
tcf(c_49971,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(X0,sK5(iPr_def_11))),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,sK5(iPr_def_11))) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X0,sK5(iPr_def_11))))
| ~ in(singleton(set_union2(X0,sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7254,c_49877]) ).
tcf(c_49972,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)))
| ~ in(singleton(set_union2(set_union2(sK5(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7256,c_49877]) ).
tcf(c_49973,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)))
| ~ in(singleton(set_union2(set_union2(X0,sK5(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_7257,c_49877]) ).
tcf(c_49974,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))))
| ~ in(singleton(set_union2(X0,set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7258,c_49877]) ).
tcf(c_49975,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ epsilon_connected(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))))
| ~ in(singleton(set_union2(X0,set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7259,c_49877]) ).
tcf(c_49976,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),singleton(X0))
| in(singleton(X0),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( singleton(X0) = sK5(iPr_def_11) )
| ( singleton(X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_49877]) ).
tcf(c_49977,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),set_union2(X0,X1))
| in(set_union2(X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_7266,c_49877]) ).
tcf(c_49978,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK1(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK3(iPr_def_11),sK1(iPr_def_11))
| in(sK1(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_49877]) ).
tcf(c_49979,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK1(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| in(sK1(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK1(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK1(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_49877]) ).
tcf(c_49980,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(X1,sK1(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK1(iPr_def_11))
| in(sK1(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X1,iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_8680,c_49877]) ).
tcf(c_49981,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(X0,sK1(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),X0)
| in(sK1(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X1 )
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_connected(sK1(iPr_def_11))
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK1(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_49877]) ).
tcf(c_50004,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X1)
| in(X0,sK4(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_13646,c_49877]) ).
tcf(c_50005,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11188,c_49877]) ).
tcf(c_50007,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11185,c_49877]) ).
tcf(c_50009,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X1)
| in(X0,sK3(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_49877]) ).
tcf(c_50010,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_49877]) ).
tcf(c_50011,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_49877]) ).
tcf(c_50024,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK5(sK18),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(sK18))
| ( sK5(sK18) = sK5(iPr_def_11) )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( sK3(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18)
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_28367,c_49877]) ).
tcf(c_50028,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(sK18),sK3(iPr_def_11))
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(sK18))
| ( sK4(iPr_def_11) = sK5(sK18) )
| ( sK3(iPr_def_11) = sK5(sK18) )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(sK5(sK18),sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_31298,c_49877]) ).
tcf(c_50065,plain,
( in(sK18,sK3(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_49948,c_2427]) ).
tcf(c_50074,plain,
( empty(powerset(empty_set))
| in(empty_set,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(powerset(empty_set),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = empty_set )
| ( sK3(iPr_def_11) = powerset(empty_set) )
| ~ epsilon_connected(powerset(empty_set))
| ~ in(powerset(empty_set),sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_49908,c_7097]) ).
tcf(c_50083,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK3(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_49942,c_2427]) ).
tcf(c_51167,plain,
( ~ in(sK18,sK18)
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( sK3(iPr_def_11) = sK18 )
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_50065,c_43063,c_50065]) ).
tcf(c_51168,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(renaming,[status(thm)],[c_51167]) ).
tcf(c_51176,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51168,c_3592]) ).
tcf(c_51197,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK18,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_51176,c_359]) ).
tcf(c_51198,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_51176,c_358]) ).
tcf(c_51199,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(sK18,sK18)
| ~ in(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_51176,c_77]) ).
tcf(c_51200,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_51176,c_65]) ).
tcf(c_51202,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_51176,c_137]) ).
tcf(c_51203,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_51176,c_127]) ).
tcf(c_51204,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(sK18,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_51176,c_9906]) ).
tcf(c_51294,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4330,c_24092]) ).
tcf(c_51295,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4330,c_24090]) ).
tcf(c_51296,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4330,c_24084]) ).
tcf(c_51297,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK4(iPr_def_11))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK4(iPr_def_11) )
| ~ epsilon_transitive(X2)
| ~ empty(X2)
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4330,c_24160]) ).
tcf(c_51298,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK3(iPr_def_11))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK3(iPr_def_11) )
| ~ epsilon_transitive(X2)
| ~ empty(X2)
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4330,c_24149]) ).
tcf(c_51299,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK5(iPr_def_11))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X2)
| ~ empty(X2)
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4330,c_24137]) ).
tcf(c_51300,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK4(iPr_def_11))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK4(iPr_def_11) )
| ~ epsilon_transitive(X2)
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4330,c_13671]) ).
tcf(c_51301,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK3(iPr_def_11))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK3(iPr_def_11) )
| ~ epsilon_transitive(X2)
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4330,c_13665]) ).
tcf(c_51302,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK5(iPr_def_11))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X2)
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4330,c_13657]) ).
tcf(c_51303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X1)
| ( set_union2(X1,X2) = X3 )
| ~ epsilon_transitive(X3)
| ~ subset(X0,sK2(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_4330,c_128]) ).
tcf(c_51305,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_4330,c_3931]) ).
tcf(c_51307,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X2,sK5(powerset(X0))),X0)
| in(sK2(X1,X2,sK5(powerset(X0))),X2)
| in(sK2(X1,X2,sK5(powerset(X0))),X1)
| ( set_union2(X1,X2) = sK5(powerset(X0)) )
| ~ epsilon_transitive(sK5(powerset(X0))) ),
inference(superposition,[status(thm)],[c_4330,c_3864]) ).
tcf(c_51308,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,iPr_def_10),iPr_def_11)
| in(sK2(X0,X1,iPr_def_10),X1)
| in(sK2(X0,X1,iPr_def_10),X0)
| ( set_union2(X0,X1) = iPr_def_10 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4330,c_3868]) ).
tcf(c_51309,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK5(powerset(sK18))),iPr_def_11)
| in(sK2(X0,X1,sK5(powerset(sK18))),X1)
| in(sK2(X0,X1,sK5(powerset(sK18))),X0)
| ( set_union2(X0,X1) = sK5(powerset(sK18)) )
| ~ epsilon_transitive(sK5(powerset(sK18))) ),
inference(superposition,[status(thm)],[c_4330,c_4177]) ).
tcf(c_51310,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK5(powerset(iPr_def_10))),iPr_def_11)
| in(sK2(X0,X1,sK5(powerset(iPr_def_10))),X1)
| in(sK2(X0,X1,sK5(powerset(iPr_def_10))),X0)
| ( set_union2(X0,X1) = sK5(powerset(iPr_def_10)) )
| ~ epsilon_transitive(sK5(powerset(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_4330,c_4574]) ).
tcf(c_51311,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X2,sK5(powerset(sK5(powerset(X0))))),X0)
| in(sK2(X1,X2,sK5(powerset(sK5(powerset(X0))))),X2)
| in(sK2(X1,X2,sK5(powerset(sK5(powerset(X0))))),X1)
| ( sK5(powerset(sK5(powerset(X0)))) = set_union2(X1,X2) )
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_4330,c_5249]) ).
tcf(c_51312,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| subset(sK2(X0,X1,sK5(sK18)),iPr_def_10)
| in(sK2(X0,X1,sK5(sK18)),X1)
| in(sK2(X0,X1,sK5(sK18)),X0)
| ( set_union2(X0,X1) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_4330,c_7217]) ).
tcf(c_51313,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| subset(sK2(X0,X1,sK5(sK18)),iPr_def_11)
| in(sK2(X0,X1,sK5(sK18)),X1)
| in(sK2(X0,X1,sK5(sK18)),X0)
| ( set_union2(X0,X1) = sK5(sK18) )
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_4330,c_5354]) ).
tcf(c_51314,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| subset(sK2(X0,X1,sK5(powerset(sK5(sK18)))),iPr_def_11)
| in(sK2(X0,X1,sK5(powerset(sK5(sK18)))),X1)
| in(sK2(X0,X1,sK5(powerset(sK5(sK18)))),X0)
| ( sK5(powerset(sK5(sK18))) = set_union2(X0,X1) )
| ~ epsilon_transitive(sK5(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_4330,c_5478]) ).
tcf(c_51315,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| subset(sK2(X0,X1,sK5(powerset(sK5(powerset(sK5(sK18)))))),iPr_def_11)
| in(sK2(X0,X1,sK5(powerset(sK5(powerset(sK5(sK18)))))),X1)
| in(sK2(X0,X1,sK5(powerset(sK5(powerset(sK5(sK18)))))),X0)
| ( sK5(powerset(sK5(powerset(sK5(sK18))))) = set_union2(X0,X1) )
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK5(sK18)))))) ),
inference(superposition,[status(thm)],[c_4330,c_5491]) ).
tcf(c_51316,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| subset(sK2(X0,X1,sK1(powerset(sK5(sK18)))),iPr_def_11)
| in(sK2(X0,X1,sK1(powerset(sK5(sK18)))),X1)
| in(sK2(X0,X1,sK1(powerset(sK5(sK18)))),X0)
| ( sK1(powerset(sK5(sK18))) = set_union2(X0,X1) )
| ~ epsilon_transitive(sK1(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_4330,c_5502]) ).
tcf(c_51317,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK2(X0,X1,sK3(powerset(sK5(sK18)))),iPr_def_11)
| in(sK2(X0,X1,sK3(powerset(sK5(sK18)))),X1)
| in(sK2(X0,X1,sK3(powerset(sK5(sK18)))),X0)
| ( sK3(powerset(sK5(sK18))) = set_union2(X0,X1) )
| ~ epsilon_transitive(sK3(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_4330,c_5516]) ).
tcf(c_51318,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK2(X0,X1,sK4(powerset(sK5(sK18)))),iPr_def_11)
| in(sK2(X0,X1,sK4(powerset(sK5(sK18)))),X1)
| in(sK2(X0,X1,sK4(powerset(sK5(sK18)))),X0)
| ( sK4(powerset(sK5(sK18))) = set_union2(X0,X1) )
| ~ epsilon_transitive(sK4(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_4330,c_5528]) ).
tcf(c_51319,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK2(X0,X1,sK3(sK5(sK18))),iPr_def_11)
| in(sK2(X0,X1,sK3(sK5(sK18))),X1)
| in(sK2(X0,X1,sK3(sK5(sK18))),X0)
| ( set_union2(X0,X1) = sK3(sK5(sK18)) )
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK3(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_4330,c_5794]) ).
tcf(c_51320,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK2(X0,X1,sK4(sK5(sK18))),iPr_def_11)
| in(sK2(X0,X1,sK4(sK5(sK18))),X1)
| in(sK2(X0,X1,sK4(sK5(sK18))),X0)
| ( set_union2(X0,X1) = sK4(sK5(sK18)) )
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK4(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_4330,c_5809]) ).
tcf(c_51321,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| empty(sK5(sK18))
| subset(sK2(X0,X1,sK5(sK5(sK18))),iPr_def_11)
| in(sK2(X0,X1,sK5(sK5(sK18))),X1)
| in(sK2(X0,X1,sK5(sK5(sK18))),X0)
| ( set_union2(X0,X1) = sK5(sK5(sK18)) )
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK5(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_4330,c_5824]) ).
tcf(c_51322,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK5(iPr_def_11)),sK18)
| in(sK2(X0,X1,sK5(iPr_def_11)),X1)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4330,c_7199]) ).
tcf(c_51323,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK3(iPr_def_11)),sK18)
| in(sK2(X0,X1,sK3(iPr_def_11)),X1)
| in(sK2(X0,X1,sK3(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4330,c_9862]) ).
tcf(c_51324,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK4(iPr_def_11)),sK18)
| in(sK2(X0,X1,sK4(iPr_def_11)),X1)
| in(sK2(X0,X1,sK4(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4330,c_11154]) ).
tcf(c_51325,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X2,X0,X1),X1)
| in(sK2(X2,X0,X1),X2)
| in(sK3(iPr_def_11),sK2(X2,X0,X1))
| in(sK2(X2,X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X2,X0) = X1 )
| ( sK2(X2,X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4330,c_49877]) ).
tcf(c_51326,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X2,X0,X1),X1)
| in(sK2(X2,X0,X1),X2)
| in(sK5(iPr_def_11),sK2(X2,X0,X1))
| in(sK2(X2,X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X2,X0) = X1 )
| ( sK2(X2,X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4330,c_7260]) ).
tcf(c_51327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,X0,X2),X2)
| in(sK2(X3,X0,X2),X3)
| ( set_union2(X3,X0) = X2 )
| ~ epsilon_transitive(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4330,c_359]) ).
tcf(c_51328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X3,X0,X2),X1)
| subset(sK2(X3,X0,X2),X2)
| in(sK2(X3,X0,X2),X3)
| ( set_union2(X3,X0) = X2 )
| ~ epsilon_transitive(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4330,c_358]) ).
tcf(c_51329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,X1,X2),X2)
| in(X0,sK2(X3,X1,X2))
| in(sK2(X3,X1,X2),X3)
| in(sK2(X3,X1,X2),X0)
| ( set_union2(X3,X1) = X2 )
| ( sK2(X3,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4330,c_77]) ).
tcf(c_51330,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X1,X0),X1)
| subset(sK2(X2,X1,X0),X0)
| in(sK2(X2,X1,X0),X2)
| ( set_union2(X2,X1) = X0 )
| ~ epsilon_transitive(X1)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_65]) ).
tcf(c_51331,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ~ epsilon_transitive(X2)
| ~ in(X0,sK2(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_4330,c_49]) ).
tcf(c_51332,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X0,X1),X1)
| in(sK2(X2,X0,X1),X2)
| ( set_union2(X2,X0) = X1 )
| ~ epsilon_transitive(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4330,c_137]) ).
tcf(c_51333,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X2,X0),X2)
| subset(sK2(X1,X2,X0),X0)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_127]) ).
tcf(c_51334,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,singleton(X2),X0),X0)
| in(sK2(X1,singleton(X2),X0),X1)
| ( set_union2(X1,singleton(X2)) = X0 )
| ( sK2(X1,singleton(X2),X0) = X2 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_62]) ).
tcf(c_51335,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X0,X1),X1)
| in(sK2(X0,X0,X1),X0)
| ( set_union2(X0,X0) = X1 )
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X0,X1),X1) ),
inference(superposition,[status(thm)],[c_4330,c_66]) ).
tcf(c_51336,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,X1),X1)
| in(sK2(X0,X1,X1),X0)
| ( set_union2(X0,X1) = X1 )
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X1,X1),X1) ),
inference(superposition,[status(thm)],[c_4330,c_67]) ).
tcf(c_51337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(X4,set_union2(X0,X1),X3),X3)
| in(X2,sK2(X4,set_union2(X0,X1),X3))
| in(sK2(X4,set_union2(X0,X1),X3),X4)
| in(sK2(X4,set_union2(X0,X1),X3),X2)
| ( set_union2(X4,set_union2(X0,X1)) = X3 )
| ( sK2(X4,set_union2(X0,X1),X3) = X2 )
| ~ epsilon_transitive(X3)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4330,c_4213]) ).
tcf(c_51338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(X4,set_union2(X0,X1),X3),X3)
| in(X2,sK2(X4,set_union2(X0,X1),X3))
| in(sK2(X4,set_union2(X0,X1),X3),X4)
| in(sK2(X4,set_union2(X0,X1),X3),X2)
| ( set_union2(X4,set_union2(X0,X1)) = X3 )
| ( sK2(X4,set_union2(X0,X1),X3) = X2 )
| ~ epsilon_transitive(X3)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4330,c_4212]) ).
tcf(c_51339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X1,set_union2(X2,X3),X0),X0)
| in(sK2(X1,set_union2(X2,X3),X0),X3)
| in(sK2(X1,set_union2(X2,X3),X0),X2)
| in(sK2(X1,set_union2(X2,X3),X0),X1)
| ( set_union2(X1,set_union2(X2,X3)) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_71]) ).
tcf(c_51340,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,empty_set,X0),X0)
| in(sK2(X1,empty_set,X0),X1)
| ( set_union2(X1,empty_set) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_7097]) ).
tcf(c_51341,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK18,X0),iPr_def_11)
| subset(sK2(X1,sK18,X0),X0)
| in(sK2(X1,sK18,X0),X1)
| ( set_union2(X1,sK18) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_12813]) ).
tcf(c_51342,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,X1),X1)
| in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 )
| ~ epsilon_transitive(X1)
| ~ in(iPr_def_11,sK2(X0,sK18,X1)) ),
inference(superposition,[status(thm)],[c_4330,c_6841]) ).
tcf(c_51343,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK18,X0),iPr_def_11)
| subset(sK2(X1,sK18,X0),X0)
| in(sK2(X1,sK18,X0),X1)
| ( set_union2(X1,sK18) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_5047]) ).
tcf(c_51344,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK18,X0),iPr_def_11)
| subset(sK2(X1,sK18,X0),X0)
| in(sK2(X1,sK18,X0),X1)
| ( set_union2(X1,sK18) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_3640]) ).
tcf(c_51345,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,iPr_def_10,X0),iPr_def_11)
| subset(sK2(X1,iPr_def_10,X0),X0)
| in(sK2(X1,iPr_def_10,X0),X1)
| ( set_union2(X1,iPr_def_10) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_9540]) ).
tcf(c_51346,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_10,X1),X1)
| in(sK2(X0,iPr_def_10,X1),X0)
| ( set_union2(X0,iPr_def_10) = X1 )
| ~ epsilon_transitive(X1)
| ~ in(iPr_def_11,sK2(X0,iPr_def_10,X1)) ),
inference(superposition,[status(thm)],[c_4330,c_6289]) ).
tcf(c_51347,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,iPr_def_10,X0),iPr_def_11)
| subset(sK2(X1,iPr_def_10,X0),X0)
| in(sK2(X1,iPr_def_10,X0),X1)
| ( set_union2(X1,iPr_def_10) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_4912]) ).
tcf(c_51348,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,iPr_def_10,X0),X0)
| in(sK2(X1,iPr_def_10,X0),X1)
| ( set_union2(X1,iPr_def_10) = X0 )
| ( sK2(X1,iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_3592]) ).
tcf(c_51349,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,iPr_def_10,X0),iPr_def_11)
| subset(sK2(X1,iPr_def_10,X0),X0)
| in(sK2(X1,iPr_def_10,X0),X1)
| ( set_union2(X1,iPr_def_10) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_3614]) ).
tcf(c_51350,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,iPr_def_11,X0),sK18)
| subset(sK2(X1,iPr_def_11,X0),X0)
| in(sK2(X1,iPr_def_11,X0),X1)
| ( set_union2(X1,iPr_def_11) = X0 )
| ( sK2(X1,iPr_def_11,X0) = sK18 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_33457]) ).
tcf(c_51351,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,iPr_def_11,X0),iPr_def_10)
| in(sK2(X1,iPr_def_11,X0),sK18)
| subset(sK2(X1,iPr_def_11,X0),X0)
| in(sK2(X1,iPr_def_11,X0),X1)
| ( set_union2(X1,iPr_def_11) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_4035]) ).
tcf(c_51352,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),X0,X2),X2)
| in(sK2(set_union2(X0,X1),X0,X2),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X0) = X2 )
| ~ epsilon_transitive(X2)
| ~ in(sK2(set_union2(X0,X1),X0,X2),X2) ),
inference(superposition,[status(thm)],[c_4330,c_4078]) ).
tcf(c_51353,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),X2,X2),X2)
| in(sK2(set_union2(X0,X1),X2,X2),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = X2 )
| ~ epsilon_transitive(X2)
| ~ in(sK2(set_union2(X0,X1),X2,X2),X1) ),
inference(superposition,[status(thm)],[c_4330,c_4079]) ).
tcf(c_51354,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X1,X2)),X0)
| subset(sK2(X0,X1,set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X0,X1) = set_union2(X1,X2) )
| ~ epsilon_transitive(set_union2(X1,X2))
| ~ in(sK2(X0,X1,set_union2(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_4330,c_4095]) ).
tcf(c_51355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_union2(X2,X3)),X0)
| subset(sK2(X0,X1,set_union2(X2,X3)),set_union2(X2,X3))
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ~ epsilon_transitive(set_union2(X2,X3))
| ~ in(sK2(X0,X1,set_union2(X2,X3)),X3) ),
inference(superposition,[status(thm)],[c_4330,c_4096]) ).
tcf(c_51356,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(X2,sK5(iPr_def_11),X1),X1)
| in(X0,sK2(X2,sK5(iPr_def_11),X1))
| in(sK2(X2,sK5(iPr_def_11),X1),X2)
| in(sK2(X2,sK5(iPr_def_11),X1),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X2,sK5(iPr_def_11)) = X1 )
| ( sK2(X2,sK5(iPr_def_11),X1) = X0 )
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4330,c_7243]) ).
tcf(c_51357,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ~ epsilon_transitive(X1)
| ~ subset(iPr_def_11,sK2(X0,sK5(iPr_def_11),X1)) ),
inference(superposition,[status(thm)],[c_4330,c_23189]) ).
tcf(c_51358,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(X2,sK3(iPr_def_11),X1),X1)
| in(X0,sK2(X2,sK3(iPr_def_11),X1))
| in(sK2(X2,sK3(iPr_def_11),X1),X2)
| in(sK2(X2,sK3(iPr_def_11),X1),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X2,sK3(iPr_def_11)) = X1 )
| ( sK2(X2,sK3(iPr_def_11),X1) = X0 )
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4330,c_9906]) ).
tcf(c_51359,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(X2,sK4(iPr_def_11),X1),X1)
| in(X0,sK2(X2,sK4(iPr_def_11),X1))
| in(sK2(X2,sK4(iPr_def_11),X1),X2)
| in(sK2(X2,sK4(iPr_def_11),X1),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X2,sK4(iPr_def_11)) = X1 )
| ( sK2(X2,sK4(iPr_def_11),X1) = X0 )
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4330,c_45801]) ).
tcf(c_51360,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X0,X2,X1),X1)
| in(sK2(X0,X2,X1),X2)
| in(sK3(iPr_def_11),sK2(X0,X2,X1))
| in(sK2(X0,X2,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X2) = X1 )
| ( sK2(X0,X2,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4330,c_49877]) ).
tcf(c_51361,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X0,X2,X1),X1)
| in(sK2(X0,X2,X1),X2)
| in(sK5(iPr_def_11),sK2(X0,X2,X1))
| in(sK2(X0,X2,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X2) = X1 )
| ( sK2(X0,X2,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4330,c_7260]) ).
tcf(c_51362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X0,X3,X2),X2)
| in(sK2(X0,X3,X2),X3)
| ( set_union2(X0,X3) = X2 )
| ~ epsilon_transitive(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4330,c_359]) ).
tcf(c_51363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X3,X2),X1)
| subset(sK2(X0,X3,X2),X2)
| in(sK2(X0,X3,X2),X3)
| ( set_union2(X0,X3) = X2 )
| ~ epsilon_transitive(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4330,c_358]) ).
tcf(c_51364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X1,X3,X2),X2)
| in(X0,sK2(X1,X3,X2))
| in(sK2(X1,X3,X2),X3)
| in(sK2(X1,X3,X2),X0)
| ( set_union2(X1,X3) = X2 )
| ( sK2(X1,X3,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4330,c_77]) ).
tcf(c_51365,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X2,X0),X1)
| subset(sK2(X1,X2,X0),X0)
| in(sK2(X1,X2,X0),X2)
| ( set_union2(X1,X2) = X0 )
| ~ epsilon_transitive(X1)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_65]) ).
tcf(c_51366,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 )
| ~ epsilon_transitive(X2)
| ~ in(X0,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4330,c_49]) ).
tcf(c_51367,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X2,X1),X1)
| in(sK2(X0,X2,X1),X2)
| ( set_union2(X0,X2) = X1 )
| ~ epsilon_transitive(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4330,c_137]) ).
tcf(c_51368,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X2,X0),X1)
| subset(sK2(X1,X2,X0),X0)
| in(sK2(X1,X2,X0),X2)
| ( set_union2(X1,X2) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_127]) ).
tcf(c_51369,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(singleton(X1),X2,X0),X0)
| in(sK2(singleton(X1),X2,X0),X2)
| ( set_union2(singleton(X1),X2) = X0 )
| ( sK2(singleton(X1),X2,X0) = X1 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_62]) ).
tcf(c_51370,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 )
| ~ epsilon_transitive(X2)
| ~ in(sK2(X0,X1,X2),X2) ),
inference(superposition,[status(thm)],[c_4330,c_66]) ).
tcf(c_51372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(set_union2(X0,X1),X4,X3),X3)
| in(X2,sK2(set_union2(X0,X1),X4,X3))
| in(sK2(set_union2(X0,X1),X4,X3),X4)
| in(sK2(set_union2(X0,X1),X4,X3),X2)
| ( set_union2(set_union2(X0,X1),X4) = X3 )
| ( sK2(set_union2(X0,X1),X4,X3) = X2 )
| ~ epsilon_transitive(X3)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4330,c_4213]) ).
tcf(c_51373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(set_union2(X0,X1),X4,X3),X3)
| in(X2,sK2(set_union2(X0,X1),X4,X3))
| in(sK2(set_union2(X0,X1),X4,X3),X4)
| in(sK2(set_union2(X0,X1),X4,X3),X2)
| ( set_union2(set_union2(X0,X1),X4) = X3 )
| ( sK2(set_union2(X0,X1),X4,X3) = X2 )
| ~ epsilon_transitive(X3)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4330,c_4212]) ).
tcf(c_51374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X1,X2),X3,X0),X0)
| in(sK2(set_union2(X1,X2),X3,X0),X3)
| in(sK2(set_union2(X1,X2),X3,X0),X2)
| in(sK2(set_union2(X1,X2),X3,X0),X1)
| ( set_union2(set_union2(X1,X2),X3) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_71]) ).
tcf(c_51375,plain,
! [X0: $i,X1: $i] :
( subset(sK2(empty_set,X1,X0),X0)
| in(sK2(empty_set,X1,X0),X1)
| ( set_union2(empty_set,X1) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_7097]) ).
tcf(c_51376,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,X0),iPr_def_11)
| subset(sK2(sK18,X1,X0),X0)
| in(sK2(sK18,X1,X0),X1)
| ( set_union2(sK18,X1) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_12813]) ).
tcf(c_51377,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,X1),X1)
| in(sK2(sK18,X0,X1),X0)
| ( set_union2(sK18,X0) = X1 )
| ~ epsilon_transitive(X1)
| ~ in(iPr_def_11,sK2(sK18,X0,X1)) ),
inference(superposition,[status(thm)],[c_4330,c_6841]) ).
tcf(c_51378,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK18,X1,X0),iPr_def_11)
| subset(sK2(sK18,X1,X0),X0)
| in(sK2(sK18,X1,X0),X1)
| ( set_union2(sK18,X1) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_5047]) ).
tcf(c_51379,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK18,X1,X0),iPr_def_11)
| subset(sK2(sK18,X1,X0),X0)
| in(sK2(sK18,X1,X0),X1)
| ( set_union2(sK18,X1) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_3640]) ).
tcf(c_51380,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X1,X0),iPr_def_11)
| subset(sK2(iPr_def_10,X1,X0),X0)
| in(sK2(iPr_def_10,X1,X0),X1)
| ( set_union2(iPr_def_10,X1) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_9540]) ).
tcf(c_51381,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X0,X1),X1)
| in(sK2(iPr_def_10,X0,X1),X0)
| ( set_union2(iPr_def_10,X0) = X1 )
| ~ epsilon_transitive(X1)
| ~ in(iPr_def_11,sK2(iPr_def_10,X0,X1)) ),
inference(superposition,[status(thm)],[c_4330,c_6289]) ).
tcf(c_51382,plain,
! [X0: $i,X1: $i] :
( element(sK2(iPr_def_10,X1,X0),iPr_def_11)
| subset(sK2(iPr_def_10,X1,X0),X0)
| in(sK2(iPr_def_10,X1,X0),X1)
| ( set_union2(iPr_def_10,X1) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_4912]) ).
tcf(c_51383,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X1,X0),X0)
| in(sK2(iPr_def_10,X1,X0),X1)
| ( set_union2(iPr_def_10,X1) = X0 )
| ( sK2(iPr_def_10,X1,X0) = sK18 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_3592]) ).
tcf(c_51384,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_10,X1,X0),iPr_def_11)
| subset(sK2(iPr_def_10,X1,X0),X0)
| in(sK2(iPr_def_10,X1,X0),X1)
| ( set_union2(iPr_def_10,X1) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_3614]) ).
tcf(c_51385,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_11,X1,X0),sK18)
| subset(sK2(iPr_def_11,X1,X0),X0)
| in(sK2(iPr_def_11,X1,X0),X1)
| ( set_union2(iPr_def_11,X1) = X0 )
| ( sK2(iPr_def_11,X1,X0) = sK18 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_33457]) ).
tcf(c_51386,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_11,X1,X0),iPr_def_10)
| in(sK2(iPr_def_11,X1,X0),sK18)
| subset(sK2(iPr_def_11,X1,X0),X0)
| in(sK2(iPr_def_11,X1,X0),X1)
| ( set_union2(iPr_def_11,X1) = X0 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4330,c_4035]) ).
tcf(c_51387,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X2)
| subset(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = set_union2(X0,X1) )
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_4330,c_4079]) ).
tcf(c_51389,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_union2(X1,X2)),X0)
| subset(sK2(X0,X0,set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X0,X0) = set_union2(X1,X2) )
| ~ epsilon_transitive(set_union2(X1,X2))
| ~ in(sK2(X0,X0,set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4330,c_4096]) ).
tcf(c_51390,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK5(iPr_def_11),X2,X1),X1)
| in(X0,sK2(sK5(iPr_def_11),X2,X1))
| in(sK2(sK5(iPr_def_11),X2,X1),X2)
| in(sK2(sK5(iPr_def_11),X2,X1),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X2) = X1 )
| ( sK2(sK5(iPr_def_11),X2,X1) = X0 )
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4330,c_7243]) ).
tcf(c_51391,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK5(iPr_def_11),X0,X1),X1)
| in(sK2(sK5(iPr_def_11),X0,X1),X0)
| ( set_union2(sK5(iPr_def_11),X0) = X1 )
| ~ epsilon_transitive(X1)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,X1)) ),
inference(superposition,[status(thm)],[c_4330,c_23189]) ).
tcf(c_51392,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK3(iPr_def_11),X2,X1),X1)
| in(X0,sK2(sK3(iPr_def_11),X2,X1))
| in(sK2(sK3(iPr_def_11),X2,X1),X2)
| in(sK2(sK3(iPr_def_11),X2,X1),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X2) = X1 )
| ( sK2(sK3(iPr_def_11),X2,X1) = X0 )
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4330,c_9906]) ).
tcf(c_51393,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK4(iPr_def_11),X2,X1),X1)
| in(X0,sK2(sK4(iPr_def_11),X2,X1))
| in(sK2(sK4(iPr_def_11),X2,X1),X2)
| in(sK2(sK4(iPr_def_11),X2,X1),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X2) = X1 )
| ( sK2(sK4(iPr_def_11),X2,X1) = X0 )
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4330,c_45801]) ).
tcf(c_51394,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X1,X0),X0)
| in(sK2(X1,X1,X0),X1)
| ( set_union2(X1,X1) = X0 )
| ~ epsilon_transitive(X0) ),
inference(equality_factoring,[status(thm)],[c_4330]) ).
tcf(c_51534,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X0,X1),X1)
| in(sK2(X0,X0,X1),X0)
| ( X0 = X1 )
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X0,X1),X1) ),
inference(light_normalisation,[status(thm)],[c_51335,c_97]) ).
tcf(c_51593,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51305,c_2426]) ).
tcf(c_51719,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_union2(X1,X2)),X0)
| subset(sK2(X0,X0,set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X1,X2) = X0 )
| ~ epsilon_transitive(set_union2(X1,X2))
| ~ in(sK2(X0,X0,set_union2(X1,X2)),X2) ),
inference(light_normalisation,[status(thm)],[c_51389,c_97]) ).
tcf(c_52514,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(set_union2(set_union2(iPr_def_10,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_40308,c_359]) ).
tcf(c_52515,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,X2)
| ~ subset(set_union2(set_union2(iPr_def_10,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_40308,c_358]) ).
tcf(c_52516,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,X0)
| in(X0,sK18)
| ( X0 = sK18 )
| ~ epsilon_connected(set_union2(set_union2(iPr_def_10,X1),X2))
| ~ in(X0,set_union2(set_union2(iPr_def_10,X1),X2)) ),
inference(superposition,[status(thm)],[c_40308,c_77]) ).
tcf(c_52517,plain,
! [X0: $i,X1: $i] :
( subset(sK18,set_union2(set_union2(iPr_def_10,X0),X1))
| ~ epsilon_transitive(set_union2(set_union2(iPr_def_10,X0),X1)) ),
inference(superposition,[status(thm)],[c_40308,c_65]) ).
tcf(c_52518,plain,
! [X0: $i,X1: $i] : ~ in(set_union2(set_union2(iPr_def_10,X0),X1),sK18),
inference(superposition,[status(thm)],[c_40308,c_49]) ).
tcf(c_52521,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,X2)
| in(X2,sK18)
| ( X2 = sK18 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(set_union2(iPr_def_10,X0),X1)) ),
inference(superposition,[status(thm)],[c_40308,c_4213]) ).
tcf(c_52522,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,X2)
| in(X2,sK18)
| ( X2 = sK18 )
| ~ in(X2,set_union2(iPr_def_10,X0))
| ~ epsilon_connected(set_union2(set_union2(iPr_def_10,X0),X1)) ),
inference(superposition,[status(thm)],[c_40308,c_4212]) ).
tcf(c_52591,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,set_union2(X1,iPr_def_10)))
| in(sK18,set_union2(X0,set_union2(X1,iPr_def_10))) ),
inference(superposition,[status(thm)],[c_40315,c_131]) ).
tcf(c_52592,plain,
! [X0: $i,X1: $i] : in(sK18,set_union2(X0,set_union2(X1,iPr_def_10))),
inference(forward_subsumption_resolution,[status(thm)],[c_52591,c_37283]) ).
tcf(c_52604,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(set_union2(set_union2(X0,iPr_def_10),X1),X2) ),
inference(superposition,[status(thm)],[c_40333,c_359]) ).
tcf(c_52605,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,X2)
| ~ subset(set_union2(set_union2(X0,iPr_def_10),X1),X2) ),
inference(superposition,[status(thm)],[c_40333,c_358]) ).
tcf(c_52606,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,X0)
| in(X0,sK18)
| ( X0 = sK18 )
| ~ epsilon_connected(set_union2(set_union2(X1,iPr_def_10),X2))
| ~ in(X0,set_union2(set_union2(X1,iPr_def_10),X2)) ),
inference(superposition,[status(thm)],[c_40333,c_77]) ).
tcf(c_52607,plain,
! [X0: $i,X1: $i] :
( subset(sK18,set_union2(set_union2(X0,iPr_def_10),X1))
| ~ epsilon_transitive(set_union2(set_union2(X0,iPr_def_10),X1)) ),
inference(superposition,[status(thm)],[c_40333,c_65]) ).
tcf(c_52608,plain,
! [X0: $i,X1: $i] : ~ in(set_union2(set_union2(X0,iPr_def_10),X1),sK18),
inference(superposition,[status(thm)],[c_40333,c_49]) ).
tcf(c_52611,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,X2)
| in(X2,sK18)
| ( X2 = sK18 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(set_union2(X0,iPr_def_10),X1)) ),
inference(superposition,[status(thm)],[c_40333,c_4213]) ).
tcf(c_52612,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,X2)
| in(X2,sK18)
| ( X2 = sK18 )
| ~ in(X2,set_union2(X0,iPr_def_10))
| ~ epsilon_connected(set_union2(set_union2(X0,iPr_def_10),X1)) ),
inference(superposition,[status(thm)],[c_40333,c_4212]) ).
tcf(c_52728,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(set_union2(X0,set_union2(X1,iPr_def_10)),X2) ),
inference(superposition,[status(thm)],[c_52592,c_359]) ).
tcf(c_52729,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,X2)
| ~ subset(set_union2(X0,set_union2(X1,iPr_def_10)),X2) ),
inference(superposition,[status(thm)],[c_52592,c_358]) ).
tcf(c_52730,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,X0)
| in(X0,sK18)
| ( X0 = sK18 )
| ~ epsilon_connected(set_union2(X1,set_union2(X2,iPr_def_10)))
| ~ in(X0,set_union2(X1,set_union2(X2,iPr_def_10))) ),
inference(superposition,[status(thm)],[c_52592,c_77]) ).
tcf(c_52731,plain,
! [X0: $i,X1: $i] :
( subset(sK18,set_union2(X0,set_union2(X1,iPr_def_10)))
| ~ epsilon_transitive(set_union2(X0,set_union2(X1,iPr_def_10))) ),
inference(superposition,[status(thm)],[c_52592,c_65]) ).
tcf(c_52732,plain,
! [X0: $i,X1: $i] : ~ in(set_union2(X0,set_union2(X1,iPr_def_10)),sK18),
inference(superposition,[status(thm)],[c_52592,c_49]) ).
tcf(c_52735,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,X2)
| in(X2,sK18)
| ( X2 = sK18 )
| ~ in(X2,set_union2(X1,iPr_def_10))
| ~ epsilon_connected(set_union2(X0,set_union2(X1,iPr_def_10))) ),
inference(superposition,[status(thm)],[c_52592,c_4213]) ).
tcf(c_52736,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,X2)
| in(X2,sK18)
| ( X2 = sK18 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,set_union2(X1,iPr_def_10))) ),
inference(superposition,[status(thm)],[c_52592,c_4212]) ).
tcf(c_52787,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(set_union2(X0,set_union2(iPr_def_10,X1)),X2) ),
inference(superposition,[status(thm)],[c_40321,c_359]) ).
tcf(c_52788,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,X2)
| ~ subset(set_union2(X0,set_union2(iPr_def_10,X1)),X2) ),
inference(superposition,[status(thm)],[c_40321,c_358]) ).
tcf(c_52789,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,X0)
| in(X0,sK18)
| ( X0 = sK18 )
| ~ epsilon_connected(set_union2(X1,set_union2(iPr_def_10,X2)))
| ~ in(X0,set_union2(X1,set_union2(iPr_def_10,X2))) ),
inference(superposition,[status(thm)],[c_40321,c_77]) ).
tcf(c_52790,plain,
! [X0: $i,X1: $i] :
( subset(sK18,set_union2(X0,set_union2(iPr_def_10,X1)))
| ~ epsilon_transitive(set_union2(X0,set_union2(iPr_def_10,X1))) ),
inference(superposition,[status(thm)],[c_40321,c_65]) ).
tcf(c_52791,plain,
! [X0: $i,X1: $i] : ~ in(set_union2(X0,set_union2(iPr_def_10,X1)),sK18),
inference(superposition,[status(thm)],[c_40321,c_49]) ).
tcf(c_52794,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,X2)
| in(X2,sK18)
| ( X2 = sK18 )
| ~ in(X2,set_union2(iPr_def_10,X1))
| ~ epsilon_connected(set_union2(X0,set_union2(iPr_def_10,X1))) ),
inference(superposition,[status(thm)],[c_40321,c_4213]) ).
tcf(c_52795,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,X2)
| in(X2,sK18)
| ( X2 = sK18 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,set_union2(iPr_def_10,X1))) ),
inference(superposition,[status(thm)],[c_40321,c_4212]) ).
tcf(c_53086,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_51593,c_13671]) ).
tcf(c_53087,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_51593,c_13665]) ).
tcf(c_53088,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_51593,c_13657]) ).
tcf(c_53089,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,iPr_def_10)
| in(sK2(X1,X2,sK18),X2)
| in(sK2(X1,X2,sK18),X1)
| ( set_union2(X1,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(X1,X2,sK18)) ),
inference(superposition,[status(thm)],[c_51593,c_128]) ).
tcf(c_53091,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK2(X1,X0,sK18),X1)
| in(sK3(iPr_def_11),sK2(X1,X0,sK18))
| in(sK2(X1,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = sK18 )
| ( sK2(X1,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_51593,c_49877]) ).
tcf(c_53092,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK2(X1,X0,sK18),X1)
| in(sK5(iPr_def_11),sK2(X1,X0,sK18))
| in(sK2(X1,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = sK18 )
| ( sK2(X1,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_51593,c_7260]) ).
tcf(c_53093,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X0,sK18),iPr_def_10)
| in(sK2(X2,X0,sK18),X2)
| ( set_union2(X2,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_51593,c_359]) ).
tcf(c_53094,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X0,sK18),iPr_def_10)
| element(sK2(X2,X0,sK18),X1)
| in(sK2(X2,X0,sK18),X2)
| ( set_union2(X2,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_51593,c_358]) ).
tcf(c_53095,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X1,sK18),iPr_def_10)
| in(X0,sK2(X2,X1,sK18))
| in(sK2(X2,X1,sK18),X2)
| in(sK2(X2,X1,sK18),X0)
| ( set_union2(X2,X1) = sK18 )
| ( sK2(X2,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_51593,c_77]) ).
tcf(c_53096,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| subset(sK2(X1,X0,sK18),X0)
| in(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_51593,c_65]) ).
tcf(c_53097,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X1,X0,sK18)) ),
inference(superposition,[status(thm)],[c_51593,c_49]) ).
tcf(c_53098,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_51593,c_137]) ).
tcf(c_53099,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| element(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_127]) ).
tcf(c_53100,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,singleton(X1),sK18),iPr_def_10)
| in(sK2(X0,singleton(X1),sK18),X0)
| ( set_union2(X0,singleton(X1)) = sK18 )
| ( sK2(X0,singleton(X1),sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_62]) ).
tcf(c_53101,plain,
! [X0: $i] :
( subset(sK2(X0,X0,sK18),iPr_def_10)
| in(sK2(X0,X0,sK18),X0)
| ( set_union2(X0,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_51593,c_66]) ).
tcf(c_53102,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_51593,c_67]) ).
tcf(c_53103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(X3,set_union2(X0,X1),sK18))
| in(sK2(X3,set_union2(X0,X1),sK18),X3)
| in(sK2(X3,set_union2(X0,X1),sK18),X2)
| ( set_union2(X3,set_union2(X0,X1)) = sK18 )
| ( sK2(X3,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_51593,c_4213]) ).
tcf(c_53104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(X3,set_union2(X0,X1),sK18))
| in(sK2(X3,set_union2(X0,X1),sK18),X3)
| in(sK2(X3,set_union2(X0,X1),sK18),X2)
| ( set_union2(X3,set_union2(X0,X1)) = sK18 )
| ( sK2(X3,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_51593,c_4212]) ).
tcf(c_53105,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,set_union2(X1,X2),sK18),iPr_def_10)
| in(sK2(X0,set_union2(X1,X2),sK18),X2)
| in(sK2(X0,set_union2(X1,X2),sK18),X1)
| in(sK2(X0,set_union2(X1,X2),sK18),X0)
| ( set_union2(X0,set_union2(X1,X2)) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_71]) ).
tcf(c_53106,plain,
! [X0: $i] :
( subset(sK2(X0,empty_set,sK18),iPr_def_10)
| in(sK2(X0,empty_set,sK18),X0)
| ( set_union2(X0,empty_set) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_7097]) ).
tcf(c_53107,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_12813]) ).
tcf(c_53108,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(X0,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_51593,c_6841]) ).
tcf(c_53109,plain,
! [X0: $i] :
( element(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_5047]) ).
tcf(c_53110,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),iPr_def_11)
| in(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_3640]) ).
tcf(c_53111,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_9540]) ).
tcf(c_53112,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(X0,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_51593,c_6289]) ).
tcf(c_53113,plain,
! [X0: $i] :
( element(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_4912]) ).
tcf(c_53114,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_3592]) ).
tcf(c_53115,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| in(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_3614]) ).
tcf(c_53116,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),sK18)
| in(sK2(X0,iPr_def_11,sK18),X0)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ( sK2(X0,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_33457]) ).
tcf(c_53117,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),sK18)
| in(sK2(X0,iPr_def_11,sK18),X0)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_4035]) ).
tcf(c_53118,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),X0,sK18),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_51593,c_4078]) ).
tcf(c_53119,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),sK18,sK18),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),sK18,sK18),X1) ),
inference(superposition,[status(thm)],[c_51593,c_4079]) ).
tcf(c_53120,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(X1,sK5(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(X1,sK5(iPr_def_11),sK18))
| in(sK2(X1,sK5(iPr_def_11),sK18),X1)
| in(sK2(X1,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,sK5(iPr_def_11)) = sK18 )
| ( sK2(X1,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_51593,c_7243]) ).
tcf(c_53121,plain,
! [X0: $i] :
( subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(X0,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_51593,c_23189]) ).
tcf(c_53122,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(X1,sK3(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(X1,sK3(iPr_def_11),sK18))
| in(sK2(X1,sK3(iPr_def_11),sK18),X1)
| in(sK2(X1,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,sK3(iPr_def_11)) = sK18 )
| ( sK2(X1,sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_51593,c_9906]) ).
tcf(c_53123,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(X1,sK4(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(X1,sK4(iPr_def_11),sK18))
| in(sK2(X1,sK4(iPr_def_11),sK18),X1)
| in(sK2(X1,sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,sK4(iPr_def_11)) = sK18 )
| ( sK2(X1,sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_51593,c_45801]) ).
tcf(c_53124,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK3(iPr_def_11),sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_51593,c_49877]) ).
tcf(c_53125,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK5(iPr_def_11),sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_51593,c_7260]) ).
tcf(c_53126,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X2,sK18),iPr_def_10)
| in(sK2(X0,X2,sK18),X2)
| ( set_union2(X0,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_51593,c_359]) ).
tcf(c_53127,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X2,sK18),iPr_def_10)
| element(sK2(X0,X2,sK18),X1)
| in(sK2(X0,X2,sK18),X2)
| ( set_union2(X0,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_51593,c_358]) ).
tcf(c_53128,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X2,sK18),iPr_def_10)
| in(X0,sK2(X1,X2,sK18))
| in(sK2(X1,X2,sK18),X2)
| in(sK2(X1,X2,sK18),X0)
| ( set_union2(X1,X2) = sK18 )
| ( sK2(X1,X2,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_51593,c_77]) ).
tcf(c_53129,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| subset(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_51593,c_65]) ).
tcf(c_53130,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_51593,c_49]) ).
tcf(c_53131,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_51593,c_137]) ).
tcf(c_53132,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| element(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_127]) ).
tcf(c_53133,plain,
! [X0: $i,X1: $i] :
( subset(sK2(singleton(X0),X1,sK18),iPr_def_10)
| in(sK2(singleton(X0),X1,sK18),X1)
| ( set_union2(singleton(X0),X1) = sK18 )
| ( sK2(singleton(X0),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_62]) ).
tcf(c_53134,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_51593,c_66]) ).
tcf(c_53136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X0,X1),X3,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),X3,sK18))
| in(sK2(set_union2(X0,X1),X3,sK18),X3)
| in(sK2(set_union2(X0,X1),X3,sK18),X2)
| ( set_union2(set_union2(X0,X1),X3) = sK18 )
| ( sK2(set_union2(X0,X1),X3,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_51593,c_4213]) ).
tcf(c_53137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X0,X1),X3,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),X3,sK18))
| in(sK2(set_union2(X0,X1),X3,sK18),X3)
| in(sK2(set_union2(X0,X1),X3,sK18),X2)
| ( set_union2(set_union2(X0,X1),X3) = sK18 )
| ( sK2(set_union2(X0,X1),X3,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_51593,c_4212]) ).
tcf(c_53138,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),X2,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),X2,sK18),X2)
| in(sK2(set_union2(X0,X1),X2,sK18),X1)
| in(sK2(set_union2(X0,X1),X2,sK18),X0)
| ( set_union2(set_union2(X0,X1),X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_71]) ).
tcf(c_53139,plain,
! [X0: $i] :
( subset(sK2(empty_set,X0,sK18),iPr_def_10)
| in(sK2(empty_set,X0,sK18),X0)
| ( set_union2(empty_set,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_7097]) ).
tcf(c_53140,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_11)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_12813]) ).
tcf(c_53141,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(sK18,X0,sK18)) ),
inference(superposition,[status(thm)],[c_51593,c_6841]) ).
tcf(c_53142,plain,
! [X0: $i] :
( element(sK2(sK18,X0,sK18),iPr_def_11)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_5047]) ).
tcf(c_53143,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),iPr_def_11)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_3640]) ).
tcf(c_53144,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_9540]) ).
tcf(c_53145,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(iPr_def_10,X0,sK18)) ),
inference(superposition,[status(thm)],[c_51593,c_6289]) ).
tcf(c_53146,plain,
! [X0: $i] :
( element(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_4912]) ).
tcf(c_53147,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_3592]) ).
tcf(c_53148,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| in(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_3614]) ).
tcf(c_53149,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),sK18)
| in(sK2(iPr_def_11,X0,sK18),X0)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ( sK2(iPr_def_11,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_33457]) ).
tcf(c_53150,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),sK18)
| in(sK2(iPr_def_11,X0,sK18),X0)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_4035]) ).
tcf(c_53151,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK5(iPr_def_11),X1,sK18),iPr_def_10)
| in(X0,sK2(sK5(iPr_def_11),X1,sK18))
| in(sK2(sK5(iPr_def_11),X1,sK18),X1)
| in(sK2(sK5(iPr_def_11),X1,sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X1) = sK18 )
| ( sK2(sK5(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_51593,c_7243]) ).
tcf(c_53152,plain,
! [X0: $i] :
( subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,sK18)) ),
inference(superposition,[status(thm)],[c_51593,c_23189]) ).
tcf(c_53153,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK3(iPr_def_11),X1,sK18),iPr_def_10)
| in(X0,sK2(sK3(iPr_def_11),X1,sK18))
| in(sK2(sK3(iPr_def_11),X1,sK18),X1)
| in(sK2(sK3(iPr_def_11),X1,sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X1) = sK18 )
| ( sK2(sK3(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_51593,c_9906]) ).
tcf(c_53154,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK4(iPr_def_11),X1,sK18),iPr_def_10)
| in(X0,sK2(sK4(iPr_def_11),X1,sK18))
| in(sK2(sK4(iPr_def_11),X1,sK18),X1)
| in(sK2(sK4(iPr_def_11),X1,sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X1) = sK18 )
| ( sK2(sK4(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_51593,c_45801]) ).
tcf(c_53155,plain,
! [X0: $i] :
( subset(sK2(X0,X0,sK18),iPr_def_10)
| in(sK2(X0,X0,sK18),X0)
| ( set_union2(X0,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(equality_factoring,[status(thm)],[c_51593]) ).
tcf(c_53157,plain,
! [X0: $i] :
( subset(sK2(X0,X0,sK18),iPr_def_10)
| in(sK2(X0,X0,sK18),X0)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_53155,c_97]) ).
tcf(c_53162,plain,
! [X0: $i] :
( subset(sK2(empty_set,X0,sK18),iPr_def_10)
| in(sK2(empty_set,X0,sK18),X0)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_53139,c_3423]) ).
tcf(c_53167,plain,
! [X0: $i] :
( subset(sK2(X0,empty_set,sK18),iPr_def_10)
| in(sK2(X0,empty_set,sK18),X0)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_53106,c_126]) ).
tcf(c_53954,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53098,c_13671]) ).
tcf(c_53955,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53098,c_13665]) ).
tcf(c_53956,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53098,c_13657]) ).
tcf(c_53957,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,iPr_def_10)
| in(sK2(X1,X2,sK18),X1)
| ( set_union2(X1,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X2)
| ~ subset(X0,sK2(X1,X2,sK18)) ),
inference(superposition,[status(thm)],[c_53098,c_128]) ).
tcf(c_53958,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_11)
| in(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_3868]) ).
tcf(c_53959,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ empty(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53098,c_49877]) ).
tcf(c_53960,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ empty(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53098,c_7260]) ).
tcf(c_53961,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X2,sK18),iPr_def_10)
| ( set_union2(X0,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53098,c_359]) ).
tcf(c_53962,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X2,sK18),iPr_def_10)
| element(sK2(X0,X2,sK18),X1)
| ( set_union2(X0,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53098,c_358]) ).
tcf(c_53963,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X2,sK18),iPr_def_10)
| in(X0,sK2(X1,X2,sK18))
| in(sK2(X1,X2,sK18),X0)
| ( set_union2(X1,X2) = sK18 )
| ( sK2(X1,X2,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53098,c_77]) ).
tcf(c_53964,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| subset(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_65]) ).
tcf(c_53965,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ in(X0,sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_53098,c_49]) ).
tcf(c_53966,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_137]) ).
tcf(c_53967,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| element(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_127]) ).
tcf(c_53968,plain,
! [X0: $i,X1: $i] :
( subset(sK2(singleton(X1),X0,sK18),iPr_def_10)
| ( set_union2(singleton(X1),X0) = sK18 )
| ( sK2(singleton(X1),X0,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_62]) ).
tcf(c_53969,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53098,c_66]) ).
tcf(c_53970,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(sK2(sK18,X0,sK18),X0) ),
inference(superposition,[status(thm)],[c_53098,c_67]) ).
tcf(c_53971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X0,X1),X3,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),X3,sK18))
| in(sK2(set_union2(X0,X1),X3,sK18),X2)
| ( set_union2(set_union2(X0,X1),X3) = sK18 )
| ( sK2(set_union2(X0,X1),X3,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X3)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53098,c_4213]) ).
tcf(c_53972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X0,X1),X3,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),X3,sK18))
| in(sK2(set_union2(X0,X1),X3,sK18),X2)
| ( set_union2(set_union2(X0,X1),X3) = sK18 )
| ( sK2(set_union2(X0,X1),X3,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X3)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53098,c_4212]) ).
tcf(c_53973,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X1,X2),X0,sK18),iPr_def_10)
| in(sK2(set_union2(X1,X2),X0,sK18),X2)
| in(sK2(set_union2(X1,X2),X0,sK18),X1)
| ( set_union2(set_union2(X1,X2),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_71]) ).
tcf(c_53974,plain,
! [X0: $i] :
( subset(sK2(empty_set,X0,sK18),iPr_def_10)
| ( set_union2(empty_set,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_7097]) ).
tcf(c_53975,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_11)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_12813]) ).
tcf(c_53976,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(iPr_def_11,sK2(sK18,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53098,c_6841]) ).
tcf(c_53977,plain,
! [X0: $i] :
( element(sK2(sK18,X0,sK18),iPr_def_11)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_5047]) ).
tcf(c_53978,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),iPr_def_11)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_3640]) ).
tcf(c_53979,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_9540]) ).
tcf(c_53980,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(iPr_def_11,sK2(iPr_def_10,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53098,c_6289]) ).
tcf(c_53981,plain,
! [X0: $i] :
( element(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_4912]) ).
tcf(c_53982,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_3592]) ).
tcf(c_53983,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_3614]) ).
tcf(c_53984,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),sK18)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ( sK2(iPr_def_11,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_33457]) ).
tcf(c_53985,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),sK18)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_4035]) ).
tcf(c_53986,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK5(iPr_def_11),X1,sK18),iPr_def_10)
| in(X0,sK2(sK5(iPr_def_11),X1,sK18))
| in(sK2(sK5(iPr_def_11),X1,sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X1) = sK18 )
| ( sK2(sK5(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53098,c_7243]) ).
tcf(c_53987,plain,
! [X0: $i] :
( subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,sK18)) ),
inference(superposition,[status(thm)],[c_53098,c_23189]) ).
tcf(c_53988,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK3(iPr_def_11),X1,sK18),iPr_def_10)
| in(X0,sK2(sK3(iPr_def_11),X1,sK18))
| in(sK2(sK3(iPr_def_11),X1,sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X1) = sK18 )
| ( sK2(sK3(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53098,c_9906]) ).
tcf(c_53989,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK4(iPr_def_11),X1,sK18),iPr_def_10)
| in(X0,sK2(sK4(iPr_def_11),X1,sK18))
| in(sK2(sK4(iPr_def_11),X1,sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X1) = sK18 )
| ( sK2(sK4(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53098,c_45801]) ).
tcf(c_53990,plain,
! [X0: $i] :
( subset(sK2(empty_set,X0,sK18),iPr_def_10)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(light_normalisation,[status(thm)],[c_53974,c_3423]) ).
tcf(c_54482,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53131,c_13671]) ).
tcf(c_54483,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53131,c_13665]) ).
tcf(c_54484,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53131,c_13657]) ).
tcf(c_54485,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,iPr_def_10)
| in(sK2(X1,X2,sK18),X2)
| ( set_union2(X1,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,sK2(X1,X2,sK18)) ),
inference(superposition,[status(thm)],[c_53131,c_128]) ).
tcf(c_54486,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_11)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_3868]) ).
tcf(c_54487,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(X1,X0,sK18))
| in(sK2(X1,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = sK18 )
| ( sK2(X1,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ empty(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53131,c_49877]) ).
tcf(c_54488,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(X1,X0,sK18))
| in(sK2(X1,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = sK18 )
| ( sK2(X1,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ empty(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53131,c_7260]) ).
tcf(c_54489,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X0,sK18),iPr_def_10)
| ( set_union2(X2,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53131,c_359]) ).
tcf(c_54490,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X0,sK18),iPr_def_10)
| element(sK2(X2,X0,sK18),X1)
| ( set_union2(X2,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53131,c_358]) ).
tcf(c_54491,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X1,sK18),iPr_def_10)
| in(X0,sK2(X2,X1,sK18))
| in(sK2(X2,X1,sK18),X0)
| ( set_union2(X2,X1) = sK18 )
| ( sK2(X2,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53131,c_77]) ).
tcf(c_54492,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| subset(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_65]) ).
tcf(c_54493,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ in(X0,sK2(X1,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53131,c_49]) ).
tcf(c_54494,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_137]) ).
tcf(c_54495,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| element(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_127]) ).
tcf(c_54496,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,singleton(X1),sK18),iPr_def_10)
| ( set_union2(X0,singleton(X1)) = sK18 )
| ( sK2(X0,singleton(X1),sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_62]) ).
tcf(c_54497,plain,
! [X0: $i] :
( subset(sK2(X0,X0,sK18),iPr_def_10)
| ( set_union2(X0,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(sK2(X0,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53131,c_66]) ).
tcf(c_54498,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53131,c_67]) ).
tcf(c_54499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(X3,set_union2(X0,X1),sK18))
| in(sK2(X3,set_union2(X0,X1),sK18),X2)
| ( set_union2(X3,set_union2(X0,X1)) = sK18 )
| ( sK2(X3,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X3)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53131,c_4213]) ).
tcf(c_54500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(X3,set_union2(X0,X1),sK18))
| in(sK2(X3,set_union2(X0,X1),sK18),X2)
| ( set_union2(X3,set_union2(X0,X1)) = sK18 )
| ( sK2(X3,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X3)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53131,c_4212]) ).
tcf(c_54501,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,set_union2(X1,X2),sK18),iPr_def_10)
| in(sK2(X0,set_union2(X1,X2),sK18),X2)
| in(sK2(X0,set_union2(X1,X2),sK18),X1)
| ( set_union2(X0,set_union2(X1,X2)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_71]) ).
tcf(c_54502,plain,
! [X0: $i] :
( subset(sK2(X0,empty_set,sK18),iPr_def_10)
| ( set_union2(X0,empty_set) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_7097]) ).
tcf(c_54503,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_12813]) ).
tcf(c_54504,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(iPr_def_11,sK2(X0,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_53131,c_6841]) ).
tcf(c_54505,plain,
! [X0: $i] :
( element(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_5047]) ).
tcf(c_54506,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),iPr_def_11)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_3640]) ).
tcf(c_54507,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_9540]) ).
tcf(c_54508,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(iPr_def_11,sK2(X0,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53131,c_6289]) ).
tcf(c_54509,plain,
! [X0: $i] :
( element(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_4912]) ).
tcf(c_54510,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_3592]) ).
tcf(c_54511,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_3614]) ).
tcf(c_54512,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),sK18)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ( sK2(X0,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_33457]) ).
tcf(c_54513,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),sK18)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53131,c_4035]) ).
tcf(c_54514,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| ( set_union2(set_union2(X0,X1),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(set_union2(X0,X1))
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53131,c_4078]) ).
tcf(c_54515,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_10)
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(set_union2(X0,X1))
| ~ in(sK2(set_union2(X0,X1),sK18,sK18),X1) ),
inference(superposition,[status(thm)],[c_53131,c_4079]) ).
tcf(c_54516,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(X1,sK5(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(X1,sK5(iPr_def_11),sK18))
| in(sK2(X1,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,sK5(iPr_def_11)) = sK18 )
| ( sK2(X1,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53131,c_7243]) ).
tcf(c_54517,plain,
! [X0: $i] :
( subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ subset(iPr_def_11,sK2(X0,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53131,c_23189]) ).
tcf(c_54518,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(X1,sK3(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(X1,sK3(iPr_def_11),sK18))
| in(sK2(X1,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,sK3(iPr_def_11)) = sK18 )
| ( sK2(X1,sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53131,c_9906]) ).
tcf(c_54519,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(X1,sK4(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(X1,sK4(iPr_def_11),sK18))
| in(sK2(X1,sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,sK4(iPr_def_11)) = sK18 )
| ( sK2(X1,sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53131,c_45801]) ).
tcf(c_54520,plain,
! [X0: $i] :
( subset(sK2(X0,empty_set,sK18),iPr_def_10)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(light_normalisation,[status(thm)],[c_54502,c_126]) ).
tcf(c_54585,plain,
! [X0: $i] :
( subset(sK2(X0,X0,sK18),iPr_def_10)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(sK2(X0,X0,sK18),sK18) ),
inference(light_normalisation,[status(thm)],[c_54497,c_97]) ).
tcf(c_55060,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,powerset(X1),sK18),iPr_def_10)
| subset(sK2(X0,powerset(X1),sK18),X1)
| in(sK2(X0,powerset(X1),sK18),X0)
| ( set_union2(X0,powerset(X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_133]) ).
tcf(c_55061,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X0,X1,sK18),iPr_def_10)
| element(sK2(X0,X1,sK18),X1)
| in(sK3(iPr_def_11),sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53099,c_49877]) ).
tcf(c_55062,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X0,X1,sK18),iPr_def_10)
| element(sK2(X0,X1,sK18),X1)
| in(sK5(iPr_def_11),sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53099,c_7260]) ).
tcf(c_55063,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X2,sK18),iPr_def_10)
| element(sK2(X0,X2,sK18),X2)
| ( set_union2(X0,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53099,c_359]) ).
tcf(c_55064,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X2,sK18),iPr_def_10)
| element(sK2(X0,X2,sK18),X2)
| element(sK2(X0,X2,sK18),X1)
| ( set_union2(X0,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53099,c_358]) ).
tcf(c_55065,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X2,sK18),iPr_def_10)
| element(sK2(X1,X2,sK18),X2)
| in(X0,sK2(X1,X2,sK18))
| in(sK2(X1,X2,sK18),X0)
| ( set_union2(X1,X2) = sK18 )
| ( sK2(X1,X2,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53099,c_77]) ).
tcf(c_55066,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| element(sK2(X0,X1,sK18),X1)
| subset(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53099,c_65]) ).
tcf(c_55067,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| element(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_53099,c_49]) ).
tcf(c_55069,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| element(sK2(X0,X1,sK18),X1)
| element(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_127]) ).
tcf(c_55070,plain,
! [X0: $i,X1: $i] :
( subset(sK2(singleton(X0),X1,sK18),iPr_def_10)
| element(sK2(singleton(X0),X1,sK18),X1)
| ( set_union2(singleton(X0),X1) = sK18 )
| ( sK2(singleton(X0),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_62]) ).
tcf(c_55071,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| element(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53099,c_66]) ).
tcf(c_55072,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| element(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,X0,sK18),X0) ),
inference(superposition,[status(thm)],[c_53099,c_67]) ).
tcf(c_55073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X0,X1),X3,sK18),iPr_def_10)
| element(sK2(set_union2(X0,X1),X3,sK18),X3)
| in(X2,sK2(set_union2(X0,X1),X3,sK18))
| in(sK2(set_union2(X0,X1),X3,sK18),X2)
| ( set_union2(set_union2(X0,X1),X3) = sK18 )
| ( sK2(set_union2(X0,X1),X3,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53099,c_4213]) ).
tcf(c_55074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X0,X1),X3,sK18),iPr_def_10)
| element(sK2(set_union2(X0,X1),X3,sK18),X3)
| in(X2,sK2(set_union2(X0,X1),X3,sK18))
| in(sK2(set_union2(X0,X1),X3,sK18),X2)
| ( set_union2(set_union2(X0,X1),X3) = sK18 )
| ( sK2(set_union2(X0,X1),X3,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53099,c_4212]) ).
tcf(c_55075,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),X2,sK18),iPr_def_10)
| element(sK2(set_union2(X0,X1),X2,sK18),X2)
| in(sK2(set_union2(X0,X1),X2,sK18),X1)
| in(sK2(set_union2(X0,X1),X2,sK18),X0)
| ( set_union2(set_union2(X0,X1),X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_71]) ).
tcf(c_55076,plain,
! [X0: $i] :
( subset(sK2(empty_set,X0,sK18),iPr_def_10)
| element(sK2(empty_set,X0,sK18),X0)
| ( set_union2(empty_set,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_7097]) ).
tcf(c_55077,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_11)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| element(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_12813]) ).
tcf(c_55078,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| element(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(sK18,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53099,c_6841]) ).
tcf(c_55079,plain,
! [X0: $i] :
( element(sK2(sK18,X0,sK18),iPr_def_11)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| element(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_5047]) ).
tcf(c_55080,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),iPr_def_11)
| element(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_3640]) ).
tcf(c_55081,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| element(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_9540]) ).
tcf(c_55082,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| element(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(iPr_def_10,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53099,c_6289]) ).
tcf(c_55083,plain,
! [X0: $i] :
( element(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| element(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_4912]) ).
tcf(c_55084,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| element(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_3592]) ).
tcf(c_55085,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| element(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_3614]) ).
tcf(c_55086,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),sK18)
| element(sK2(iPr_def_11,X0,sK18),X0)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ( sK2(iPr_def_11,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_33457]) ).
tcf(c_55087,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),sK18)
| element(sK2(iPr_def_11,X0,sK18),X0)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_4035]) ).
tcf(c_55088,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK5(iPr_def_11),X1,sK18),iPr_def_10)
| element(sK2(sK5(iPr_def_11),X1,sK18),X1)
| in(X0,sK2(sK5(iPr_def_11),X1,sK18))
| in(sK2(sK5(iPr_def_11),X1,sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X1) = sK18 )
| ( sK2(sK5(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53099,c_7243]) ).
tcf(c_55089,plain,
! [X0: $i] :
( subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| element(sK2(sK5(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,sK18)) ),
inference(superposition,[status(thm)],[c_53099,c_23189]) ).
tcf(c_55090,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK3(iPr_def_11),X1,sK18),iPr_def_10)
| element(sK2(sK3(iPr_def_11),X1,sK18),X1)
| in(X0,sK2(sK3(iPr_def_11),X1,sK18))
| in(sK2(sK3(iPr_def_11),X1,sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X1) = sK18 )
| ( sK2(sK3(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53099,c_9906]) ).
tcf(c_55091,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK4(iPr_def_11),X1,sK18),iPr_def_10)
| element(sK2(sK4(iPr_def_11),X1,sK18),X1)
| in(X0,sK2(sK4(iPr_def_11),X1,sK18))
| in(sK2(sK4(iPr_def_11),X1,sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X1) = sK18 )
| ( sK2(sK4(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53099,c_45801]) ).
tcf(c_55092,plain,
! [X0: $i] :
( subset(sK2(empty_set,X0,sK18),iPr_def_10)
| element(sK2(empty_set,X0,sK18),X0)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_55076,c_3423]) ).
tcf(c_55425,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_11)
| in(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53107,c_3868]) ).
tcf(c_55445,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK18,sK18),X0)
| in(sK2(X0,sK18,sK18),sK3(iPr_def_11))
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_55425,c_13665]) ).
tcf(c_55446,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK18,sK18),X0)
| in(sK2(X0,sK18,sK18),sK5(iPr_def_11))
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_55425,c_13657]) ).
tcf(c_55447,plain,
! [X0: $i,X1: $i] :
( subset(X0,iPr_def_11)
| in(sK2(X1,sK18,sK18),X1)
| ( set_union2(X1,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(X1,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_55425,c_128]) ).
tcf(c_55448,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X0,sK18,sK18),iPr_def_11)
| in(sK3(iPr_def_11),sK2(X0,sK18,sK18))
| in(sK2(X0,sK18,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_55425,c_49877]) ).
tcf(c_55449,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X0,sK18,sK18),iPr_def_11)
| in(sK5(iPr_def_11),sK2(X0,sK18,sK18))
| in(sK2(X0,sK18,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_55425,c_7260]) ).
tcf(c_55450,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_11)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_55425,c_359]) ).
tcf(c_55451,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_11)
| element(sK2(X0,sK18,sK18),X1)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_55425,c_358]) ).
tcf(c_55452,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK18,sK18),iPr_def_11)
| in(X0,sK2(X1,sK18,sK18))
| in(sK2(X1,sK18,sK18),X0)
| ( set_union2(X1,sK18) = sK18 )
| ( sK2(X1,sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_55425,c_77]) ).
tcf(c_55453,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_55425,c_65]) ).
tcf(c_55454,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_11)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X0,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_55425,c_49]) ).
tcf(c_55455,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_11)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55425,c_137]) ).
tcf(c_55456,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_11)
| element(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55425,c_127]) ).
tcf(c_55457,plain,
! [X0: $i] :
( subset(sK2(singleton(X0),sK18,sK18),iPr_def_11)
| ( set_union2(singleton(X0),sK18) = sK18 )
| ( sK2(singleton(X0),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55425,c_62]) ).
tcf(c_55458,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_11)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_55425,c_66]) ).
tcf(c_55459,plain,
( subset(sK2(sK18,sK18,sK18),iPr_def_11)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_55425,c_67]) ).
tcf(c_55460,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_11)
| in(X2,sK2(set_union2(X0,X1),sK18,sK18))
| in(sK2(set_union2(X0,X1),sK18,sK18),X2)
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ( sK2(set_union2(X0,X1),sK18,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_55425,c_4213]) ).
tcf(c_55461,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_11)
| in(X2,sK2(set_union2(X0,X1),sK18,sK18))
| in(sK2(set_union2(X0,X1),sK18,sK18),X2)
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ( sK2(set_union2(X0,X1),sK18,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_55425,c_4212]) ).
tcf(c_55462,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_11)
| in(sK2(set_union2(X0,X1),sK18,sK18),X1)
| in(sK2(set_union2(X0,X1),sK18,sK18),X0)
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55425,c_71]) ).
tcf(c_55463,plain,
( subset(sK2(empty_set,sK18,sK18),iPr_def_11)
| ( set_union2(empty_set,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55425,c_7097]) ).
tcf(c_55464,plain,
( subset(sK2(sK18,sK18,sK18),iPr_def_11)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55425,c_12813]) ).
tcf(c_55465,plain,
( subset(sK2(sK18,sK18,sK18),iPr_def_11)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(sK18,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_55425,c_6841]) ).
tcf(c_55466,plain,
( element(sK2(sK18,sK18,sK18),iPr_def_11)
| subset(sK2(sK18,sK18,sK18),iPr_def_11)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55425,c_5047]) ).
tcf(c_55467,plain,
( subset(sK2(sK18,sK18,sK18),iPr_def_11)
| in(sK2(sK18,sK18,sK18),iPr_def_11)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55425,c_3640]) ).
tcf(c_55468,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55425,c_9540]) ).
tcf(c_55469,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(iPr_def_10,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_55425,c_6289]) ).
tcf(c_55470,plain,
( element(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55425,c_4912]) ).
tcf(c_55471,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ( sK2(iPr_def_10,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55425,c_3592]) ).
tcf(c_55472,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| in(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55425,c_3614]) ).
tcf(c_55473,plain,
( subset(sK2(iPr_def_11,sK18,sK18),iPr_def_11)
| in(sK2(iPr_def_11,sK18,sK18),sK18)
| ( set_union2(iPr_def_11,sK18) = sK18 )
| ( sK2(iPr_def_11,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55425,c_33457]) ).
tcf(c_55474,plain,
( subset(sK2(iPr_def_11,sK18,sK18),iPr_def_11)
| in(sK2(iPr_def_11,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_11,sK18,sK18),sK18)
| ( set_union2(iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_55425,c_4035]) ).
tcf(c_55475,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK5(iPr_def_11),sK18,sK18),iPr_def_11)
| in(X0,sK2(sK5(iPr_def_11),sK18,sK18))
| in(sK2(sK5(iPr_def_11),sK18,sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),sK18) = sK18 )
| ( sK2(sK5(iPr_def_11),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_55425,c_7243]) ).
tcf(c_55476,plain,
( subset(sK2(sK5(iPr_def_11),sK18,sK18),iPr_def_11)
| ( set_union2(sK5(iPr_def_11),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),sK18,sK18)) ),
inference(superposition,[status(thm)],[c_55425,c_23189]) ).
tcf(c_55477,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK3(iPr_def_11),sK18,sK18),iPr_def_11)
| in(X0,sK2(sK3(iPr_def_11),sK18,sK18))
| in(sK2(sK3(iPr_def_11),sK18,sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),sK18) = sK18 )
| ( sK2(sK3(iPr_def_11),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_55425,c_9906]) ).
tcf(c_55478,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK4(iPr_def_11),sK18,sK18),iPr_def_11)
| in(X0,sK2(sK4(iPr_def_11),sK18,sK18))
| in(sK2(sK4(iPr_def_11),sK18,sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),sK18) = sK18 )
| ( sK2(sK4(iPr_def_11),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_55425,c_45801]) ).
tcf(c_55479,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( sK18 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_55468,c_3424]) ).
tcf(c_55488,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| in(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( sK18 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_55472,c_3424]) ).
tcf(c_55493,plain,
( element(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( sK18 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_55470,c_3424]) ).
tcf(c_55502,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( sK18 = iPr_def_11 )
| ( sK2(iPr_def_10,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_55471,c_3424]) ).
tcf(c_55507,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( sK18 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(iPr_def_10,sK18,sK18)) ),
inference(light_normalisation,[status(thm)],[c_55469,c_3424]) ).
tcf(c_55728,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| element(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(X0,sK18,sK18))
| in(sK2(X0,sK18,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53109,c_49877]) ).
tcf(c_55729,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| element(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(X0,sK18,sK18))
| in(sK2(X0,sK18,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53109,c_7260]) ).
tcf(c_55730,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53109,c_359]) ).
tcf(c_55731,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| element(sK2(X0,sK18,sK18),X1)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53109,c_358]) ).
tcf(c_55732,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK18,sK18),iPr_def_11)
| subset(sK2(X1,sK18,sK18),iPr_def_10)
| in(X0,sK2(X1,sK18,sK18))
| in(sK2(X1,sK18,sK18),X0)
| ( set_union2(X1,sK18) = sK18 )
| ( sK2(X1,sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53109,c_77]) ).
tcf(c_55733,plain,
! [X0: $i] :
( element(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| subset(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53109,c_65]) ).
tcf(c_55734,plain,
! [X0: $i] :
( element(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X0,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_53109,c_49]) ).
tcf(c_55736,plain,
! [X0: $i] :
( element(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| element(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53109,c_127]) ).
tcf(c_55737,plain,
! [X0: $i] :
( element(sK2(singleton(X0),sK18,sK18),iPr_def_11)
| subset(sK2(singleton(X0),sK18,sK18),iPr_def_10)
| ( set_union2(singleton(X0),sK18) = sK18 )
| ( sK2(singleton(X0),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53109,c_62]) ).
tcf(c_55738,plain,
! [X0: $i] :
( element(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53109,c_66]) ).
tcf(c_55739,plain,
( element(sK2(sK18,sK18,sK18),iPr_def_11)
| subset(sK2(sK18,sK18,sK18),iPr_def_10)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53109,c_67]) ).
tcf(c_55740,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_11)
| subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),sK18,sK18))
| in(sK2(set_union2(X0,X1),sK18,sK18),X2)
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ( sK2(set_union2(X0,X1),sK18,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53109,c_4213]) ).
tcf(c_55741,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_11)
| subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),sK18,sK18))
| in(sK2(set_union2(X0,X1),sK18,sK18),X2)
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ( sK2(set_union2(X0,X1),sK18,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53109,c_4212]) ).
tcf(c_55742,plain,
! [X0: $i,X1: $i] :
( element(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_11)
| subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),sK18,sK18),X1)
| in(sK2(set_union2(X0,X1),sK18,sK18),X0)
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53109,c_71]) ).
tcf(c_55743,plain,
( element(sK2(empty_set,sK18,sK18),iPr_def_11)
| subset(sK2(empty_set,sK18,sK18),iPr_def_10)
| ( set_union2(empty_set,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53109,c_7097]) ).
tcf(c_55744,plain,
( element(sK2(sK18,sK18,sK18),iPr_def_11)
| subset(sK2(sK18,sK18,sK18),iPr_def_11)
| subset(sK2(sK18,sK18,sK18),iPr_def_10)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53109,c_12813]) ).
tcf(c_55745,plain,
( element(sK2(sK18,sK18,sK18),iPr_def_11)
| subset(sK2(sK18,sK18,sK18),iPr_def_10)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(sK18,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_53109,c_6841]) ).
tcf(c_55746,plain,
( element(sK2(sK18,sK18,sK18),iPr_def_11)
| subset(sK2(sK18,sK18,sK18),iPr_def_10)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53109,c_5047]) ).
tcf(c_55747,plain,
( element(sK2(sK18,sK18,sK18),iPr_def_11)
| subset(sK2(sK18,sK18,sK18),iPr_def_10)
| in(sK2(sK18,sK18,sK18),iPr_def_11)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53109,c_3640]) ).
tcf(c_55748,plain,
( element(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53109,c_9540]) ).
tcf(c_55749,plain,
( element(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(iPr_def_10,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_53109,c_6289]) ).
tcf(c_55750,plain,
( element(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53109,c_4912]) ).
tcf(c_55751,plain,
( element(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ( sK2(iPr_def_10,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53109,c_3592]) ).
tcf(c_55752,plain,
( element(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53109,c_3614]) ).
tcf(c_55753,plain,
( element(sK2(iPr_def_11,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_11,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_11,sK18,sK18),sK18)
| ( set_union2(iPr_def_11,sK18) = sK18 )
| ( sK2(iPr_def_11,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53109,c_33457]) ).
tcf(c_55754,plain,
( element(sK2(iPr_def_11,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_11,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_11,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_11,sK18,sK18),sK18)
| ( set_union2(iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53109,c_4035]) ).
tcf(c_55755,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| element(sK2(sK5(iPr_def_11),sK18,sK18),iPr_def_11)
| subset(sK2(sK5(iPr_def_11),sK18,sK18),iPr_def_10)
| in(X0,sK2(sK5(iPr_def_11),sK18,sK18))
| in(sK2(sK5(iPr_def_11),sK18,sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),sK18) = sK18 )
| ( sK2(sK5(iPr_def_11),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53109,c_7243]) ).
tcf(c_55756,plain,
( element(sK2(sK5(iPr_def_11),sK18,sK18),iPr_def_11)
| subset(sK2(sK5(iPr_def_11),sK18,sK18),iPr_def_10)
| ( set_union2(sK5(iPr_def_11),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),sK18,sK18)) ),
inference(superposition,[status(thm)],[c_53109,c_23189]) ).
tcf(c_55757,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| element(sK2(sK3(iPr_def_11),sK18,sK18),iPr_def_11)
| subset(sK2(sK3(iPr_def_11),sK18,sK18),iPr_def_10)
| in(X0,sK2(sK3(iPr_def_11),sK18,sK18))
| in(sK2(sK3(iPr_def_11),sK18,sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),sK18) = sK18 )
| ( sK2(sK3(iPr_def_11),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53109,c_9906]) ).
tcf(c_55758,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| element(sK2(sK4(iPr_def_11),sK18,sK18),iPr_def_11)
| subset(sK2(sK4(iPr_def_11),sK18,sK18),iPr_def_10)
| in(X0,sK2(sK4(iPr_def_11),sK18,sK18))
| in(sK2(sK4(iPr_def_11),sK18,sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),sK18) = sK18 )
| ( sK2(sK4(iPr_def_11),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53109,c_45801]) ).
tcf(c_55759,plain,
( element(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( sK18 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_55750,c_3424]) ).
tcf(c_55764,plain,
( element(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( sK18 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_55752,c_3424]) ).
tcf(c_55775,plain,
( element(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( sK18 = iPr_def_11 )
| ( sK2(iPr_def_10,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_55751,c_3424]) ).
tcf(c_55798,plain,
( element(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( sK18 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_55748,c_3424]) ).
tcf(c_55989,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK18,sK18),iPr_def_11)
| in(sK2(X0,sK18,sK18),X0)
| in(sK2(X0,sK18,sK18),sK4(iPr_def_11))
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53110,c_13671]) ).
tcf(c_55990,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK18,sK18),iPr_def_11)
| in(sK2(X0,sK18,sK18),X0)
| in(sK2(X0,sK18,sK18),sK3(iPr_def_11))
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53110,c_13665]) ).
tcf(c_55991,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK18,sK18),iPr_def_11)
| in(sK2(X0,sK18,sK18),X0)
| in(sK2(X0,sK18,sK18),sK5(iPr_def_11))
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53110,c_13657]) ).
tcf(c_55992,plain,
! [X0: $i,X1: $i] :
( subset(X0,iPr_def_10)
| in(sK2(X1,sK18,sK18),iPr_def_11)
| in(sK2(X1,sK18,sK18),X1)
| ( set_union2(X1,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(X1,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_53110,c_128]) ).
tcf(c_55993,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_11)
| in(sK2(X0,sK18,sK18),iPr_def_11)
| in(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53110,c_3868]) ).
tcf(c_55994,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),iPr_def_11)
| in(sK3(iPr_def_11),sK2(X0,sK18,sK18))
| in(sK2(X0,sK18,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53110,c_49877]) ).
tcf(c_55995,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),iPr_def_11)
| in(sK5(iPr_def_11),sK2(X0,sK18,sK18))
| in(sK2(X0,sK18,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53110,c_7260]) ).
tcf(c_55996,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),iPr_def_11)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53110,c_359]) ).
tcf(c_55997,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),iPr_def_11)
| element(sK2(X0,sK18,sK18),X1)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53110,c_358]) ).
tcf(c_55998,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK18,sK18),iPr_def_10)
| in(sK2(X1,sK18,sK18),iPr_def_11)
| in(X0,sK2(X1,sK18,sK18))
| in(sK2(X1,sK18,sK18),X0)
| ( set_union2(X1,sK18) = sK18 )
| ( sK2(X1,sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53110,c_77]) ).
tcf(c_55999,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53110,c_65]) ).
tcf(c_56000,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),iPr_def_11)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X0,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_53110,c_49]) ).
tcf(c_56002,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),iPr_def_11)
| element(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53110,c_127]) ).
tcf(c_56003,plain,
! [X0: $i] :
( subset(sK2(singleton(X0),sK18,sK18),iPr_def_10)
| in(sK2(singleton(X0),sK18,sK18),iPr_def_11)
| ( set_union2(singleton(X0),sK18) = sK18 )
| ( sK2(singleton(X0),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53110,c_62]) ).
tcf(c_56004,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),iPr_def_11)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53110,c_66]) ).
tcf(c_56005,plain,
( subset(sK2(sK18,sK18,sK18),iPr_def_10)
| in(sK2(sK18,sK18,sK18),iPr_def_11)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53110,c_67]) ).
tcf(c_56006,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_11)
| in(X2,sK2(set_union2(X0,X1),sK18,sK18))
| in(sK2(set_union2(X0,X1),sK18,sK18),X2)
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ( sK2(set_union2(X0,X1),sK18,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53110,c_4213]) ).
tcf(c_56007,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_11)
| in(X2,sK2(set_union2(X0,X1),sK18,sK18))
| in(sK2(set_union2(X0,X1),sK18,sK18),X2)
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ( sK2(set_union2(X0,X1),sK18,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53110,c_4212]) ).
tcf(c_56008,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_11)
| in(sK2(set_union2(X0,X1),sK18,sK18),X1)
| in(sK2(set_union2(X0,X1),sK18,sK18),X0)
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53110,c_71]) ).
tcf(c_56009,plain,
( subset(sK2(empty_set,sK18,sK18),iPr_def_10)
| in(sK2(empty_set,sK18,sK18),iPr_def_11)
| ( set_union2(empty_set,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53110,c_7097]) ).
tcf(c_56010,plain,
( subset(sK2(sK18,sK18,sK18),iPr_def_11)
| subset(sK2(sK18,sK18,sK18),iPr_def_10)
| in(sK2(sK18,sK18,sK18),iPr_def_11)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53110,c_12813]) ).
tcf(c_56011,plain,
( subset(sK2(sK18,sK18,sK18),iPr_def_10)
| in(sK2(sK18,sK18,sK18),iPr_def_11)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(sK18,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_53110,c_6841]) ).
tcf(c_56013,plain,
( subset(sK2(sK18,sK18,sK18),iPr_def_10)
| in(sK2(sK18,sK18,sK18),iPr_def_11)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53110,c_3640]) ).
tcf(c_56014,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53110,c_9540]) ).
tcf(c_56015,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(iPr_def_10,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_53110,c_6289]) ).
tcf(c_56017,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ( sK2(iPr_def_10,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53110,c_3592]) ).
tcf(c_56018,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53110,c_3614]) ).
tcf(c_56019,plain,
( subset(sK2(iPr_def_11,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_11,sK18,sK18),iPr_def_11)
| in(sK2(iPr_def_11,sK18,sK18),sK18)
| ( set_union2(iPr_def_11,sK18) = sK18 )
| ( sK2(iPr_def_11,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53110,c_33457]) ).
tcf(c_56020,plain,
( subset(sK2(iPr_def_11,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_11,sK18,sK18),iPr_def_11)
| in(sK2(iPr_def_11,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_11,sK18,sK18),sK18)
| ( set_union2(iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53110,c_4035]) ).
tcf(c_56021,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK5(iPr_def_11),sK18,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),sK18,sK18),iPr_def_11)
| in(X0,sK2(sK5(iPr_def_11),sK18,sK18))
| in(sK2(sK5(iPr_def_11),sK18,sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),sK18) = sK18 )
| ( sK2(sK5(iPr_def_11),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53110,c_7243]) ).
tcf(c_56022,plain,
( subset(sK2(sK5(iPr_def_11),sK18,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),sK18,sK18),iPr_def_11)
| ( set_union2(sK5(iPr_def_11),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),sK18,sK18)) ),
inference(superposition,[status(thm)],[c_53110,c_23189]) ).
tcf(c_56023,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK3(iPr_def_11),sK18,sK18),iPr_def_10)
| in(sK2(sK3(iPr_def_11),sK18,sK18),iPr_def_11)
| in(X0,sK2(sK3(iPr_def_11),sK18,sK18))
| in(sK2(sK3(iPr_def_11),sK18,sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),sK18) = sK18 )
| ( sK2(sK3(iPr_def_11),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53110,c_9906]) ).
tcf(c_56024,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK4(iPr_def_11),sK18,sK18),iPr_def_10)
| in(sK2(sK4(iPr_def_11),sK18,sK18),iPr_def_11)
| in(X0,sK2(sK4(iPr_def_11),sK18,sK18))
| in(sK2(sK4(iPr_def_11),sK18,sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),sK18) = sK18 )
| ( sK2(sK4(iPr_def_11),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53110,c_45801]) ).
tcf(c_56025,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( sK18 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_56018,c_3424]) ).
tcf(c_56040,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( sK18 = iPr_def_11 )
| ( sK2(iPr_def_10,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_56017,c_3424]) ).
tcf(c_56063,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( sK18 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_56014,c_3424]) ).
tcf(c_56401,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK2(X0,X1,sK5(sK18)),X1)
| in(sK2(X0,X1,sK5(sK18)),X0)
| in(sK2(X0,X1,sK5(sK18)),sK5(sK18))
| ( set_union2(X0,X1) = sK5(sK18) )
| ( sK2(X0,X1,sK5(sK18)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK2(X0,X1,sK5(sK18)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_4331]) ).
tcf(c_56402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X4),X3)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X0,X1,sK2(X2,X3,X4)),X1)
| in(sK2(X0,X1,sK2(X2,X3,X4)),X0)
| in(sK2(X0,X1,sK2(X2,X3,X4)),sK2(X2,X3,X4))
| ( set_union2(X2,X3) = X4 )
| ( sK2(X2,X3,X4) = set_union2(X0,X1) )
| ( sK2(X0,X1,sK2(X2,X3,X4)) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X4)
| ~ in(sK2(X0,X1,sK2(X2,X3,X4)),X4) ),
inference(superposition,[status(thm)],[c_4329,c_4331]) ).
tcf(c_56403,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| in(sK2(X1,X2,X0),X0)
| ( set_union2(X1,X2) = X0 )
| ( sK2(X1,X2,X0) = X0 )
| ~ epsilon_connected(X0)
| ~ in(X0,X0) ),
inference(superposition,[status(thm)],[c_4329,c_4331]) ).
tcf(c_56404,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK2(X0,X1,sK5(iPr_def_11)),X1)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| in(sK2(X0,X1,sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_4331]) ).
tcf(c_56406,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK2(X0,X1,sK5(iPr_def_11)),X1)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| in(sK2(X0,X1,sK5(iPr_def_11)),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_4331]) ).
tcf(c_56407,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK5(iPr_def_11)),X1)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| in(sK2(X0,X1,sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_4331]) ).
tcf(c_56408,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK5(iPr_def_11)),X1)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ empty(sK5(iPr_def_11))
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7246,c_4331]) ).
tcf(c_56409,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK5(iPr_def_11)),X1)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| in(sK2(X0,X1,sK5(iPr_def_11)),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_4331]) ).
tcf(c_56410,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK5(iPr_def_11)),X1)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| in(sK2(X0,X1,sK5(iPr_def_11)),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_4331]) ).
tcf(c_56411,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK2(X0,X1,sK5(iPr_def_11)),X1)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| in(sK2(X0,X1,sK5(iPr_def_11)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK2(X0,X1,sK5(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_4331]) ).
tcf(c_56412,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK2(X0,X1,sK1(iPr_def_11)),X1)
| in(sK2(X0,X1,sK1(iPr_def_11)),X0)
| in(sK2(X0,X1,sK1(iPr_def_11)),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ( sK2(X0,X1,sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK2(X0,X1,sK1(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_4331]) ).
tcf(c_56413,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK2(X0,X1,sK1(iPr_def_11)),X1)
| in(sK2(X0,X1,sK1(iPr_def_11)),X0)
| in(sK2(X0,X1,sK1(iPr_def_11)),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK1(iPr_def_11) )
| ( sK2(X0,X1,sK1(iPr_def_11)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK2(X0,X1,sK1(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_4331]) ).
tcf(c_56414,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK2(X0,X1,sK3(iPr_def_11)),X1)
| in(sK2(X0,X1,sK3(iPr_def_11)),X0)
| in(sK2(X0,X1,sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( sK2(X0,X1,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_4331]) ).
tcf(c_56415,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK2(X0,X1,sK3(iPr_def_11)),X1)
| in(sK2(X0,X1,sK3(iPr_def_11)),X0)
| in(sK2(X0,X1,sK3(iPr_def_11)),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( sK2(X0,X1,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_4331]) ).
tcf(c_56416,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK2(X0,X1,sK3(iPr_def_11)),X1)
| in(sK2(X0,X1,sK3(iPr_def_11)),X0)
| in(sK2(X0,X1,sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( sK2(X0,X1,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_4331]) ).
tcf(c_56417,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK3(iPr_def_11)),X1)
| in(sK2(X0,X1,sK3(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( sK2(X0,X1,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_4331]) ).
tcf(c_56418,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK3(iPr_def_11)),X1)
| in(sK2(X0,X1,sK3(iPr_def_11)),X0)
| in(sK2(X0,X1,sK3(iPr_def_11)),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( sK2(X0,X1,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_4331]) ).
tcf(c_56419,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK3(iPr_def_11)),X1)
| in(sK2(X0,X1,sK3(iPr_def_11)),X0)
| in(sK2(X0,X1,sK3(iPr_def_11)),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( sK2(X0,X1,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_4331]) ).
tcf(c_56420,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK2(X0,X1,sK3(iPr_def_11)),X1)
| in(sK2(X0,X1,sK3(iPr_def_11)),X0)
| in(sK2(X0,X1,sK3(iPr_def_11)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( sK2(X0,X1,sK3(iPr_def_11)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK2(X0,X1,sK3(iPr_def_11)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_4331]) ).
tcf(c_56421,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK2(X0,X1,sK4(iPr_def_11)),X1)
| in(sK2(X0,X1,sK4(iPr_def_11)),X0)
| in(sK2(X0,X1,sK4(iPr_def_11)),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ( sK2(X0,X1,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_4331]) ).
tcf(c_56422,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK2(X0,X1,sK4(iPr_def_11)),X1)
| in(sK2(X0,X1,sK4(iPr_def_11)),X0)
| in(sK2(X0,X1,sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ( sK2(X0,X1,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_4331]) ).
tcf(c_56423,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK4(iPr_def_11)),X1)
| in(sK2(X0,X1,sK4(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ( sK2(X0,X1,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ empty(sK4(iPr_def_11))
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11193,c_4331]) ).
tcf(c_56424,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK4(iPr_def_11)),X1)
| in(sK2(X0,X1,sK4(iPr_def_11)),X0)
| in(sK2(X0,X1,sK4(iPr_def_11)),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ( sK2(X0,X1,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_4331]) ).
tcf(c_56425,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK4(iPr_def_11)),X1)
| in(sK2(X0,X1,sK4(iPr_def_11)),X0)
| in(sK2(X0,X1,sK4(iPr_def_11)),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ( sK2(X0,X1,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_4331]) ).
tcf(c_56800,plain,
( epsilon_transitive(powerset(sK5(powerset(sK5(powerset(sK18))))))
| subset(sK1(powerset(sK5(powerset(sK5(powerset(sK18)))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3566,c_5379]) ).
tcf(c_56801,plain,
( epsilon_connected(powerset(sK5(powerset(sK5(powerset(sK18))))))
| subset(sK3(powerset(sK5(powerset(sK5(powerset(sK18)))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3567,c_5379]) ).
tcf(c_56802,plain,
( epsilon_connected(powerset(sK5(powerset(sK5(powerset(sK18))))))
| subset(sK4(powerset(sK5(powerset(sK5(powerset(sK18)))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3568,c_5379]) ).
tcf(c_56803,plain,
( epsilon_connected(sK5(powerset(sK5(powerset(sK18)))))
| subset(sK3(sK5(powerset(sK5(powerset(sK18))))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK18))))) ),
inference(superposition,[status(thm)],[c_3807,c_5379]) ).
tcf(c_56804,plain,
( epsilon_connected(sK5(powerset(sK5(powerset(sK18)))))
| subset(sK4(sK5(powerset(sK5(powerset(sK18))))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK18))))) ),
inference(superposition,[status(thm)],[c_3808,c_5379]) ).
tcf(c_56805,plain,
( empty(sK5(powerset(sK5(powerset(sK18)))))
| subset(sK5(sK5(powerset(sK5(powerset(sK18))))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK18))))) ),
inference(superposition,[status(thm)],[c_3899,c_5379]) ).
tcf(c_56806,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK5(powerset(sK5(powerset(sK18))))),iPr_def_11)
| in(sK2(X0,X1,sK5(powerset(sK5(powerset(sK18))))),X1)
| in(sK2(X0,X1,sK5(powerset(sK5(powerset(sK18))))),X0)
| ( sK5(powerset(sK5(powerset(sK18)))) = set_union2(X0,X1) )
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK18))))) ),
inference(superposition,[status(thm)],[c_4330,c_5379]) ).
tcf(c_56810,plain,
subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK18)))))))))),iPr_def_11),
inference(superposition,[status(thm)],[c_5252,c_5379]) ).
tcf(c_56858,plain,
( epsilon_transitive(powerset(sK5(powerset(sK5(powerset(iPr_def_10))))))
| subset(sK1(powerset(sK5(powerset(sK5(powerset(iPr_def_10)))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3566,c_5407]) ).
tcf(c_56859,plain,
( epsilon_connected(powerset(sK5(powerset(sK5(powerset(iPr_def_10))))))
| subset(sK3(powerset(sK5(powerset(sK5(powerset(iPr_def_10)))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3567,c_5407]) ).
tcf(c_56860,plain,
( epsilon_connected(powerset(sK5(powerset(sK5(powerset(iPr_def_10))))))
| subset(sK4(powerset(sK5(powerset(sK5(powerset(iPr_def_10)))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3568,c_5407]) ).
tcf(c_56861,plain,
( epsilon_connected(sK5(powerset(sK5(powerset(iPr_def_10)))))
| subset(sK3(sK5(powerset(sK5(powerset(iPr_def_10))))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(iPr_def_10))))) ),
inference(superposition,[status(thm)],[c_3807,c_5407]) ).
tcf(c_56862,plain,
( epsilon_connected(sK5(powerset(sK5(powerset(iPr_def_10)))))
| subset(sK4(sK5(powerset(sK5(powerset(iPr_def_10))))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(iPr_def_10))))) ),
inference(superposition,[status(thm)],[c_3808,c_5407]) ).
tcf(c_56863,plain,
( empty(sK5(powerset(sK5(powerset(iPr_def_10)))))
| subset(sK5(sK5(powerset(sK5(powerset(iPr_def_10))))),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(iPr_def_10))))) ),
inference(superposition,[status(thm)],[c_3899,c_5407]) ).
tcf(c_56864,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK5(powerset(sK5(powerset(iPr_def_10))))),iPr_def_11)
| in(sK2(X0,X1,sK5(powerset(sK5(powerset(iPr_def_10))))),X1)
| in(sK2(X0,X1,sK5(powerset(sK5(powerset(iPr_def_10))))),X0)
| ( sK5(powerset(sK5(powerset(iPr_def_10)))) = set_union2(X0,X1) )
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(iPr_def_10))))) ),
inference(superposition,[status(thm)],[c_4330,c_5407]) ).
tcf(c_56868,plain,
subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(powerset(iPr_def_10)))))))))),iPr_def_11),
inference(superposition,[status(thm)],[c_5252,c_5407]) ).
tcf(c_56947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(set_union2(X0,set_union2(set_union2(X1,X2),X3)),X4)),X1),
inference(superposition,[status(thm)],[c_69,c_5547]) ).
tcf(c_56948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(set_union2(X0,set_union2(set_union2(X1,X2),X3)),X4)),X2),
inference(superposition,[status(thm)],[c_70,c_5547]) ).
tcf(c_56949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(powerset(X1))
| ~ subset(singleton(set_union2(set_union2(X0,set_union2(powerset(X1),X2)),X3)),X1) ),
inference(superposition,[status(thm)],[c_3769,c_5547]) ).
tcf(c_56950,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK18)
| in(sK5(sK18),singleton(set_union2(set_union2(X0,set_union2(sK5(sK18),X1)),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(sK5(sK18),X1)),X2)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK5(sK18),X1)),X2)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_5547]) ).
tcf(c_56951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),singleton(set_union2(set_union2(X0,set_union2(sK2(X1,X2,X3),X4)),X5)))
| ( set_union2(X1,X2) = X3 )
| ( singleton(set_union2(set_union2(X0,set_union2(sK2(X1,X2,X3),X4)),X5)) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X3)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK2(X1,X2,X3),X4)),X5)),X3) ),
inference(superposition,[status(thm)],[c_4329,c_5547]) ).
tcf(c_56952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_5547]) ).
tcf(c_56953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_5547]) ).
tcf(c_56954,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_5547]) ).
tcf(c_56955,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_5547]) ).
tcf(c_56956,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)) = sK5(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)))
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_5547]) ).
tcf(c_56957,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_5547]) ).
tcf(c_56958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_5547]) ).
tcf(c_56959,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK5(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_5547]) ).
tcf(c_56960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK1(iPr_def_11),X1)),X2)))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(X0,set_union2(sK1(iPr_def_11),X1)),X2)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK1(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_5547]) ).
tcf(c_56961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK1(iPr_def_11),X1)),X2)))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(X0,set_union2(sK1(iPr_def_11),X1)),X2)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK1(iPr_def_11),X1)),X2)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_5547]) ).
tcf(c_56962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_5547]) ).
tcf(c_56963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_5547]) ).
tcf(c_56964,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_5547]) ).
tcf(c_56965,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_5547]) ).
tcf(c_56966,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)) = sK3(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)))
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_5547]) ).
tcf(c_56967,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_5547]) ).
tcf(c_56968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_5547]) ).
tcf(c_56969,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2) = sK3(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK3(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_5547]) ).
tcf(c_56970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X3)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_5547]) ).
tcf(c_56971,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_5547]) ).
tcf(c_56972,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_5547]) ).
tcf(c_56973,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)) = sK4(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)))
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_5547]) ).
tcf(c_56974,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_5547]) ).
tcf(c_56975,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2) = sK4(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_5547]) ).
tcf(c_57391,plain,
! [X0: $i] :
( ~ epsilon_transitive(singleton(set_union2(X0,iPr_def_10)))
| ~ empty(singleton(set_union2(X0,iPr_def_10))) ),
inference(superposition,[status(thm)],[c_3803,c_26770]) ).
tcf(c_57392,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(set_union2(X1,X2))
| ~ subset(set_union2(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_3863,c_26770]) ).
tcf(c_57393,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ epsilon_transitive(set_union2(X2,X1))
| ~ empty(set_union2(X2,X1))
| ~ in(set_union2(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_3806,c_26770]) ).
tcf(c_57394,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ epsilon_transitive(set_union2(X1,X2))
| ~ empty(set_union2(X1,X2))
| ~ in(set_union2(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_3805,c_26770]) ).
tcf(c_57395,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(set_union2(X2,X1))
| ~ subset(set_union2(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_3865,c_26770]) ).
tcf(c_57422,plain,
! [X0: $i] :
( element(sK18,singleton(set_union2(X0,iPr_def_10)))
| ~ epsilon_transitive(singleton(set_union2(X0,iPr_def_10))) ),
inference(superposition,[status(thm)],[c_3803,c_26771]) ).
tcf(c_57423,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X1,X2))
| ~ subset(set_union2(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_3863,c_26771]) ).
tcf(c_57424,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X2,X1))
| ~ epsilon_transitive(set_union2(X2,X1))
| ~ in(set_union2(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_3806,c_26771]) ).
tcf(c_57425,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X1,X2))
| ~ epsilon_transitive(set_union2(X1,X2))
| ~ in(set_union2(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_3805,c_26771]) ).
tcf(c_57426,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK18,set_union2(X2,X1))
| ~ subset(set_union2(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_3865,c_26771]) ).
tcf(c_57463,plain,
epsilon_transitive(sK5(powerset(sK5(powerset(empty_set))))),
inference(global_subsumption_just,[status(thm)],[c_26845,c_95,c_27004]) ).
tcf(c_57477,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| element(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(X0,iPr_def_10,sK18))
| in(sK2(X0,iPr_def_10,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53113,c_49877]) ).
tcf(c_57478,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| element(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(X0,iPr_def_10,sK18))
| in(sK2(X0,iPr_def_10,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53113,c_7260]) ).
tcf(c_57479,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53113,c_359]) ).
tcf(c_57480,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| element(sK2(X0,iPr_def_10,sK18),X1)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53113,c_358]) ).
tcf(c_57481,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X1,iPr_def_10,sK18),iPr_def_10)
| in(X0,sK2(X1,iPr_def_10,sK18))
| in(sK2(X1,iPr_def_10,sK18),X0)
| ( set_union2(X1,iPr_def_10) = sK18 )
| ( sK2(X1,iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53113,c_77]) ).
tcf(c_57482,plain,
! [X0: $i] :
( element(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| subset(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53113,c_65]) ).
tcf(c_57483,plain,
! [X0: $i] :
( element(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X0,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53113,c_49]) ).
tcf(c_57485,plain,
! [X0: $i] :
( element(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| element(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53113,c_127]) ).
tcf(c_57486,plain,
! [X0: $i] :
( element(sK2(singleton(X0),iPr_def_10,sK18),iPr_def_11)
| subset(sK2(singleton(X0),iPr_def_10,sK18),iPr_def_10)
| ( set_union2(singleton(X0),iPr_def_10) = sK18 )
| ( sK2(singleton(X0),iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53113,c_62]) ).
tcf(c_57487,plain,
! [X0: $i] :
( element(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,iPr_def_10,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53113,c_66]) ).
tcf(c_57489,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_11)
| subset(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),iPr_def_10,sK18))
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),X2)
| ( set_union2(set_union2(X0,X1),iPr_def_10) = sK18 )
| ( sK2(set_union2(X0,X1),iPr_def_10,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53113,c_4213]) ).
tcf(c_57490,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_11)
| subset(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),iPr_def_10,sK18))
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),X2)
| ( set_union2(set_union2(X0,X1),iPr_def_10) = sK18 )
| ( sK2(set_union2(X0,X1),iPr_def_10,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53113,c_4212]) ).
tcf(c_57491,plain,
! [X0: $i,X1: $i] :
( element(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_11)
| subset(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),X1)
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),X0)
| ( set_union2(set_union2(X0,X1),iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53113,c_71]) ).
tcf(c_57492,plain,
( element(sK2(empty_set,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(empty_set,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(empty_set,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53113,c_7097]) ).
tcf(c_57493,plain,
( element(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53113,c_12813]) ).
tcf(c_57495,plain,
( element(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53113,c_5047]) ).
tcf(c_57496,plain,
( element(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53113,c_3640]) ).
tcf(c_57497,plain,
( element(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53113,c_9540]) ).
tcf(c_57499,plain,
( element(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53113,c_4912]) ).
tcf(c_57500,plain,
( element(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,iPr_def_10) = sK18 )
| ( sK2(iPr_def_10,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53113,c_3592]) ).
tcf(c_57501,plain,
( element(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53113,c_3614]) ).
tcf(c_57502,plain,
( element(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_11,iPr_def_10,sK18),sK18)
| ( set_union2(iPr_def_11,iPr_def_10) = sK18 )
| ( sK2(iPr_def_11,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53113,c_33457]) ).
tcf(c_57503,plain,
( element(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_11,iPr_def_10,sK18),sK18)
| ( set_union2(iPr_def_11,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53113,c_4035]) ).
tcf(c_57504,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| element(sK2(sK5(iPr_def_11),iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK5(iPr_def_11),iPr_def_10,sK18),iPr_def_10)
| in(X0,sK2(sK5(iPr_def_11),iPr_def_10,sK18))
| in(sK2(sK5(iPr_def_11),iPr_def_10,sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),iPr_def_10) = sK18 )
| ( sK2(sK5(iPr_def_11),iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53113,c_7243]) ).
tcf(c_57505,plain,
( element(sK2(sK5(iPr_def_11),iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK5(iPr_def_11),iPr_def_10,sK18),iPr_def_10)
| ( set_union2(sK5(iPr_def_11),iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53113,c_23189]) ).
tcf(c_57506,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| element(sK2(sK3(iPr_def_11),iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK3(iPr_def_11),iPr_def_10,sK18),iPr_def_10)
| in(X0,sK2(sK3(iPr_def_11),iPr_def_10,sK18))
| in(sK2(sK3(iPr_def_11),iPr_def_10,sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),iPr_def_10) = sK18 )
| ( sK2(sK3(iPr_def_11),iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53113,c_9906]) ).
tcf(c_57507,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| element(sK2(sK4(iPr_def_11),iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK4(iPr_def_11),iPr_def_10,sK18),iPr_def_10)
| in(X0,sK2(sK4(iPr_def_11),iPr_def_10,sK18))
| in(sK2(sK4(iPr_def_11),iPr_def_10,sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),iPr_def_10) = sK18 )
| ( sK2(sK4(iPr_def_11),iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53113,c_45801]) ).
tcf(c_57832,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| in(sK2(X0,iPr_def_10,sK18),X0)
| in(sK2(X0,iPr_def_10,sK18),sK4(iPr_def_11))
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,iPr_def_10,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53115,c_13671]) ).
tcf(c_57833,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| in(sK2(X0,iPr_def_10,sK18),X0)
| in(sK2(X0,iPr_def_10,sK18),sK3(iPr_def_11))
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,iPr_def_10,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53115,c_13665]) ).
tcf(c_57834,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| in(sK2(X0,iPr_def_10,sK18),X0)
| in(sK2(X0,iPr_def_10,sK18),sK5(iPr_def_11))
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,iPr_def_10,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53115,c_13657]) ).
tcf(c_57835,plain,
! [X0: $i,X1: $i] :
( subset(X0,iPr_def_10)
| in(sK2(X1,iPr_def_10,sK18),iPr_def_11)
| in(sK2(X1,iPr_def_10,sK18),X1)
| ( set_union2(X1,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(X1,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53115,c_128]) ).
tcf(c_57836,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| in(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53115,c_3868]) ).
tcf(c_57837,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| in(sK3(iPr_def_11),sK2(X0,iPr_def_10,sK18))
| in(sK2(X0,iPr_def_10,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53115,c_49877]) ).
tcf(c_57838,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| in(sK5(iPr_def_11),sK2(X0,iPr_def_10,sK18))
| in(sK2(X0,iPr_def_10,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53115,c_7260]) ).
tcf(c_57839,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53115,c_359]) ).
tcf(c_57840,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| element(sK2(X0,iPr_def_10,sK18),X1)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53115,c_358]) ).
tcf(c_57841,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X1,iPr_def_10,sK18),iPr_def_11)
| in(X0,sK2(X1,iPr_def_10,sK18))
| in(sK2(X1,iPr_def_10,sK18),X0)
| ( set_union2(X1,iPr_def_10) = sK18 )
| ( sK2(X1,iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53115,c_77]) ).
tcf(c_57842,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53115,c_65]) ).
tcf(c_57843,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X0,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53115,c_49]) ).
tcf(c_57845,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| element(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53115,c_127]) ).
tcf(c_57846,plain,
! [X0: $i] :
( subset(sK2(singleton(X0),iPr_def_10,sK18),iPr_def_10)
| in(sK2(singleton(X0),iPr_def_10,sK18),iPr_def_11)
| ( set_union2(singleton(X0),iPr_def_10) = sK18 )
| ( sK2(singleton(X0),iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53115,c_62]) ).
tcf(c_57847,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,iPr_def_10,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53115,c_66]) ).
tcf(c_57849,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_11)
| in(X2,sK2(set_union2(X0,X1),iPr_def_10,sK18))
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),X2)
| ( set_union2(set_union2(X0,X1),iPr_def_10) = sK18 )
| ( sK2(set_union2(X0,X1),iPr_def_10,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53115,c_4213]) ).
tcf(c_57850,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_11)
| in(X2,sK2(set_union2(X0,X1),iPr_def_10,sK18))
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),X2)
| ( set_union2(set_union2(X0,X1),iPr_def_10) = sK18 )
| ( sK2(set_union2(X0,X1),iPr_def_10,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53115,c_4212]) ).
tcf(c_57851,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_11)
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),X1)
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),X0)
| ( set_union2(set_union2(X0,X1),iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53115,c_71]) ).
tcf(c_57852,plain,
( subset(sK2(empty_set,iPr_def_10,sK18),iPr_def_10)
| in(sK2(empty_set,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(empty_set,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53115,c_7097]) ).
tcf(c_57856,plain,
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53115,c_3640]) ).
tcf(c_57857,plain,
( subset(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53115,c_9540]) ).
tcf(c_57860,plain,
( subset(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,iPr_def_10) = sK18 )
| ( sK2(iPr_def_10,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53115,c_3592]) ).
tcf(c_57861,plain,
( subset(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53115,c_3614]) ).
tcf(c_57862,plain,
( subset(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_11)
| in(sK2(iPr_def_11,iPr_def_10,sK18),sK18)
| ( set_union2(iPr_def_11,iPr_def_10) = sK18 )
| ( sK2(iPr_def_11,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53115,c_33457]) ).
tcf(c_57863,plain,
( subset(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_11)
| in(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_11,iPr_def_10,sK18),sK18)
| ( set_union2(iPr_def_11,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53115,c_4035]) ).
tcf(c_57864,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK5(iPr_def_11),iPr_def_10,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),iPr_def_10,sK18),iPr_def_11)
| in(X0,sK2(sK5(iPr_def_11),iPr_def_10,sK18))
| in(sK2(sK5(iPr_def_11),iPr_def_10,sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),iPr_def_10) = sK18 )
| ( sK2(sK5(iPr_def_11),iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53115,c_7243]) ).
tcf(c_57865,plain,
( subset(sK2(sK5(iPr_def_11),iPr_def_10,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),iPr_def_10,sK18),iPr_def_11)
| ( set_union2(sK5(iPr_def_11),iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53115,c_23189]) ).
tcf(c_57866,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK3(iPr_def_11),iPr_def_10,sK18),iPr_def_10)
| in(sK2(sK3(iPr_def_11),iPr_def_10,sK18),iPr_def_11)
| in(X0,sK2(sK3(iPr_def_11),iPr_def_10,sK18))
| in(sK2(sK3(iPr_def_11),iPr_def_10,sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),iPr_def_10) = sK18 )
| ( sK2(sK3(iPr_def_11),iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53115,c_9906]) ).
tcf(c_57867,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK4(iPr_def_11),iPr_def_10,sK18),iPr_def_10)
| in(sK2(sK4(iPr_def_11),iPr_def_10,sK18),iPr_def_11)
| in(X0,sK2(sK4(iPr_def_11),iPr_def_10,sK18))
| in(sK2(sK4(iPr_def_11),iPr_def_10,sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),iPr_def_10) = sK18 )
| ( sK2(sK4(iPr_def_11),iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53115,c_45801]) ).
tcf(c_58201,plain,
! [X0: $i,X1: $i] :
( subset(sK2(powerset(X0),X1,sK18),iPr_def_10)
| subset(sK2(powerset(X0),X1,sK18),X0)
| in(sK2(powerset(X0),X1,sK18),X1)
| ( set_union2(powerset(X0),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53132,c_133]) ).
tcf(c_58202,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X1,X0,sK18),iPr_def_10)
| element(sK2(X1,X0,sK18),X1)
| in(sK3(iPr_def_11),sK2(X1,X0,sK18))
| in(sK2(X1,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = sK18 )
| ( sK2(X1,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53132,c_49877]) ).
tcf(c_58203,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X1,X0,sK18),iPr_def_10)
| element(sK2(X1,X0,sK18),X1)
| in(sK5(iPr_def_11),sK2(X1,X0,sK18))
| in(sK2(X1,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = sK18 )
| ( sK2(X1,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53132,c_7260]) ).
tcf(c_58204,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X0,sK18),iPr_def_10)
| element(sK2(X2,X0,sK18),X2)
| ( set_union2(X2,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53132,c_359]) ).
tcf(c_58205,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X0,sK18),iPr_def_10)
| element(sK2(X2,X0,sK18),X2)
| element(sK2(X2,X0,sK18),X1)
| ( set_union2(X2,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53132,c_358]) ).
tcf(c_58206,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X1,sK18),iPr_def_10)
| element(sK2(X2,X1,sK18),X2)
| in(X0,sK2(X2,X1,sK18))
| in(sK2(X2,X1,sK18),X0)
| ( set_union2(X2,X1) = sK18 )
| ( sK2(X2,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53132,c_77]) ).
tcf(c_58207,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| element(sK2(X1,X0,sK18),X1)
| subset(sK2(X1,X0,sK18),X0)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53132,c_65]) ).
tcf(c_58208,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| element(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X1,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53132,c_49]) ).
tcf(c_58211,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,singleton(X1),sK18),iPr_def_10)
| element(sK2(X0,singleton(X1),sK18),X0)
| ( set_union2(X0,singleton(X1)) = sK18 )
| ( sK2(X0,singleton(X1),sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53132,c_62]) ).
tcf(c_58212,plain,
! [X0: $i] :
( subset(sK2(X0,X0,sK18),iPr_def_10)
| element(sK2(X0,X0,sK18),X0)
| ( set_union2(X0,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53132,c_66]) ).
tcf(c_58213,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| element(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53132,c_67]) ).
tcf(c_58214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,set_union2(X0,X1),sK18),iPr_def_10)
| element(sK2(X3,set_union2(X0,X1),sK18),X3)
| in(X2,sK2(X3,set_union2(X0,X1),sK18))
| in(sK2(X3,set_union2(X0,X1),sK18),X2)
| ( set_union2(X3,set_union2(X0,X1)) = sK18 )
| ( sK2(X3,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53132,c_4213]) ).
tcf(c_58215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,set_union2(X0,X1),sK18),iPr_def_10)
| element(sK2(X3,set_union2(X0,X1),sK18),X3)
| in(X2,sK2(X3,set_union2(X0,X1),sK18))
| in(sK2(X3,set_union2(X0,X1),sK18),X2)
| ( set_union2(X3,set_union2(X0,X1)) = sK18 )
| ( sK2(X3,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53132,c_4212]) ).
tcf(c_58216,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,set_union2(X1,X2),sK18),iPr_def_10)
| element(sK2(X0,set_union2(X1,X2),sK18),X0)
| in(sK2(X0,set_union2(X1,X2),sK18),X2)
| in(sK2(X0,set_union2(X1,X2),sK18),X1)
| ( set_union2(X0,set_union2(X1,X2)) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53132,c_71]) ).
tcf(c_58217,plain,
! [X0: $i] :
( subset(sK2(X0,empty_set,sK18),iPr_def_10)
| element(sK2(X0,empty_set,sK18),X0)
| ( set_union2(X0,empty_set) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53132,c_7097]) ).
tcf(c_58218,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_11)
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| element(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53132,c_12813]) ).
tcf(c_58219,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| element(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(X0,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_53132,c_6841]) ).
tcf(c_58222,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| element(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53132,c_9540]) ).
tcf(c_58223,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| element(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(X0,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53132,c_6289]) ).
tcf(c_58225,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| element(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53132,c_3592]) ).
tcf(c_58227,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),sK18)
| element(sK2(X0,iPr_def_11,sK18),X0)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ( sK2(X0,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53132,c_33457]) ).
tcf(c_58228,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),sK18)
| element(sK2(X0,iPr_def_11,sK18),X0)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53132,c_4035]) ).
tcf(c_58229,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| element(sK2(set_union2(X0,X1),X0,sK18),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53132,c_4078]) ).
tcf(c_58230,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_10)
| element(sK2(set_union2(X0,X1),sK18,sK18),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),sK18,sK18),X1) ),
inference(superposition,[status(thm)],[c_53132,c_4079]) ).
tcf(c_58231,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(X1,sK5(iPr_def_11),sK18),iPr_def_10)
| element(sK2(X1,sK5(iPr_def_11),sK18),X1)
| in(X0,sK2(X1,sK5(iPr_def_11),sK18))
| in(sK2(X1,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,sK5(iPr_def_11)) = sK18 )
| ( sK2(X1,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53132,c_7243]) ).
tcf(c_58232,plain,
! [X0: $i] :
( subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| element(sK2(X0,sK5(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(X0,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53132,c_23189]) ).
tcf(c_58233,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(X1,sK3(iPr_def_11),sK18),iPr_def_10)
| element(sK2(X1,sK3(iPr_def_11),sK18),X1)
| in(X0,sK2(X1,sK3(iPr_def_11),sK18))
| in(sK2(X1,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,sK3(iPr_def_11)) = sK18 )
| ( sK2(X1,sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53132,c_9906]) ).
tcf(c_58234,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(X1,sK4(iPr_def_11),sK18),iPr_def_10)
| element(sK2(X1,sK4(iPr_def_11),sK18),X1)
| in(X0,sK2(X1,sK4(iPr_def_11),sK18))
| in(sK2(X1,sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,sK4(iPr_def_11)) = sK18 )
| ( sK2(X1,sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53132,c_45801]) ).
tcf(c_58235,plain,
! [X0: $i] :
( subset(sK2(X0,empty_set,sK18),iPr_def_10)
| element(sK2(X0,empty_set,sK18),X0)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_58217,c_126]) ).
tcf(c_58265,plain,
! [X0: $i] :
( subset(sK2(X0,X0,sK18),iPr_def_10)
| element(sK2(X0,X0,sK18),X0)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,X0,sK18),sK18) ),
inference(light_normalisation,[status(thm)],[c_58212,c_97]) ).
tcf(c_58667,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_11)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53140,c_3868]) ).
tcf(c_58687,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK3(iPr_def_11))
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_58667,c_13665]) ).
tcf(c_58688,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK5(iPr_def_11))
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_58667,c_13657]) ).
tcf(c_58689,plain,
! [X0: $i,X1: $i] :
( subset(X0,iPr_def_11)
| in(sK2(sK18,X1,sK18),X1)
| ( set_union2(sK18,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(sK18,X1,sK18)) ),
inference(superposition,[status(thm)],[c_58667,c_128]) ).
tcf(c_58690,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(sK18,X0,sK18),iPr_def_11)
| in(sK3(iPr_def_11),sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_58667,c_49877]) ).
tcf(c_58691,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(sK18,X0,sK18),iPr_def_11)
| in(sK5(iPr_def_11),sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_58667,c_7260]) ).
tcf(c_58692,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_11)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_58667,c_359]) ).
tcf(c_58693,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_11)
| element(sK2(sK18,X0,sK18),X1)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_58667,c_358]) ).
tcf(c_58694,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_11)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X0)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_58667,c_77]) ).
tcf(c_58695,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_11)
| subset(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_58667,c_65]) ).
tcf(c_58696,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_11)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(sK18,X0,sK18)) ),
inference(superposition,[status(thm)],[c_58667,c_49]) ).
tcf(c_58697,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_11)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_58667,c_137]) ).
tcf(c_58698,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_11)
| element(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_58667,c_127]) ).
tcf(c_58699,plain,
! [X0: $i] :
( subset(sK2(sK18,singleton(X0),sK18),iPr_def_11)
| ( set_union2(sK18,singleton(X0)) = sK18 )
| ( sK2(sK18,singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_58667,c_62]) ).
tcf(c_58702,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_11)
| in(X2,sK2(sK18,set_union2(X0,X1),sK18))
| in(sK2(sK18,set_union2(X0,X1),sK18),X2)
| ( set_union2(sK18,set_union2(X0,X1)) = sK18 )
| ( sK2(sK18,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_58667,c_4213]) ).
tcf(c_58703,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_11)
| in(X2,sK2(sK18,set_union2(X0,X1),sK18))
| in(sK2(sK18,set_union2(X0,X1),sK18),X2)
| ( set_union2(sK18,set_union2(X0,X1)) = sK18 )
| ( sK2(sK18,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_58667,c_4212]) ).
tcf(c_58704,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_11)
| in(sK2(sK18,set_union2(X0,X1),sK18),X1)
| in(sK2(sK18,set_union2(X0,X1),sK18),X0)
| ( set_union2(sK18,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_58667,c_71]) ).
tcf(c_58705,plain,
( subset(sK2(sK18,empty_set,sK18),iPr_def_11)
| ( set_union2(sK18,empty_set) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_58667,c_7097]) ).
tcf(c_58710,plain,
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_58667,c_9540]) ).
tcf(c_58711,plain,
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(sK18,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_58667,c_6289]) ).
tcf(c_58712,plain,
( element(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_58667,c_4912]) ).
tcf(c_58713,plain,
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ( sK2(sK18,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_58667,c_3592]) ).
tcf(c_58714,plain,
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| in(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_58667,c_3614]) ).
tcf(c_58715,plain,
( subset(sK2(sK18,iPr_def_11,sK18),iPr_def_11)
| in(sK2(sK18,iPr_def_11,sK18),sK18)
| ( set_union2(sK18,iPr_def_11) = sK18 )
| ( sK2(sK18,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_58667,c_33457]) ).
tcf(c_58716,plain,
( subset(sK2(sK18,iPr_def_11,sK18),iPr_def_11)
| in(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_11,sK18),sK18)
| ( set_union2(sK18,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_58667,c_4035]) ).
tcf(c_58717,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK18,sK5(iPr_def_11),sK18),iPr_def_11)
| in(X0,sK2(sK18,sK5(iPr_def_11),sK18))
| in(sK2(sK18,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK18,sK5(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_58667,c_7243]) ).
tcf(c_58718,plain,
( subset(sK2(sK18,sK5(iPr_def_11),sK18),iPr_def_11)
| ( set_union2(sK18,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK18,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_58667,c_23189]) ).
tcf(c_58719,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK18,sK3(iPr_def_11),sK18),iPr_def_11)
| in(X0,sK2(sK18,sK3(iPr_def_11),sK18))
| in(sK2(sK18,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK18,sK3(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_58667,c_9906]) ).
tcf(c_58720,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK18,sK4(iPr_def_11),sK18),iPr_def_11)
| in(X0,sK2(sK18,sK4(iPr_def_11),sK18))
| in(sK2(sK18,sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK18,sK4(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_58667,c_45801]) ).
tcf(c_59049,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| element(sK2(sK18,X0,sK18),iPr_def_11)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53142,c_49877]) ).
tcf(c_59050,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| element(sK2(sK18,X0,sK18),iPr_def_11)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53142,c_7260]) ).
tcf(c_59051,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK18,X0,sK18),iPr_def_11)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53142,c_359]) ).
tcf(c_59052,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK18,X0,sK18),iPr_def_11)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| element(sK2(sK18,X0,sK18),X1)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53142,c_358]) ).
tcf(c_59053,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK18,X1,sK18),iPr_def_11)
| subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X0)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53142,c_77]) ).
tcf(c_59054,plain,
! [X0: $i] :
( element(sK2(sK18,X0,sK18),iPr_def_11)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| subset(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53142,c_65]) ).
tcf(c_59055,plain,
! [X0: $i] :
( element(sK2(sK18,X0,sK18),iPr_def_11)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(sK18,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53142,c_49]) ).
tcf(c_59058,plain,
! [X0: $i] :
( element(sK2(sK18,singleton(X0),sK18),iPr_def_11)
| subset(sK2(sK18,singleton(X0),sK18),iPr_def_10)
| ( set_union2(sK18,singleton(X0)) = sK18 )
| ( sK2(sK18,singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53142,c_62]) ).
tcf(c_59061,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_11)
| subset(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(sK18,set_union2(X0,X1),sK18))
| in(sK2(sK18,set_union2(X0,X1),sK18),X2)
| ( set_union2(sK18,set_union2(X0,X1)) = sK18 )
| ( sK2(sK18,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53142,c_4213]) ).
tcf(c_59062,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_11)
| subset(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(sK18,set_union2(X0,X1),sK18))
| in(sK2(sK18,set_union2(X0,X1),sK18),X2)
| ( set_union2(sK18,set_union2(X0,X1)) = sK18 )
| ( sK2(sK18,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53142,c_4212]) ).
tcf(c_59063,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_11)
| subset(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_10)
| in(sK2(sK18,set_union2(X0,X1),sK18),X1)
| in(sK2(sK18,set_union2(X0,X1),sK18),X0)
| ( set_union2(sK18,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53142,c_71]) ).
tcf(c_59064,plain,
( element(sK2(sK18,empty_set,sK18),iPr_def_11)
| subset(sK2(sK18,empty_set,sK18),iPr_def_10)
| ( set_union2(sK18,empty_set) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53142,c_7097]) ).
tcf(c_59069,plain,
( element(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53142,c_9540]) ).
tcf(c_59072,plain,
( element(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ( sK2(sK18,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53142,c_3592]) ).
tcf(c_59074,plain,
( element(sK2(sK18,iPr_def_11,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_11,sK18),sK18)
| ( set_union2(sK18,iPr_def_11) = sK18 )
| ( sK2(sK18,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53142,c_33457]) ).
tcf(c_59075,plain,
( element(sK2(sK18,iPr_def_11,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_11,sK18),sK18)
| ( set_union2(sK18,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53142,c_4035]) ).
tcf(c_59076,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| element(sK2(sK18,sK5(iPr_def_11),sK18),iPr_def_11)
| subset(sK2(sK18,sK5(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(sK18,sK5(iPr_def_11),sK18))
| in(sK2(sK18,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK18,sK5(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53142,c_7243]) ).
tcf(c_59077,plain,
( element(sK2(sK18,sK5(iPr_def_11),sK18),iPr_def_11)
| subset(sK2(sK18,sK5(iPr_def_11),sK18),iPr_def_10)
| ( set_union2(sK18,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK18,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53142,c_23189]) ).
tcf(c_59078,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| element(sK2(sK18,sK3(iPr_def_11),sK18),iPr_def_11)
| subset(sK2(sK18,sK3(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(sK18,sK3(iPr_def_11),sK18))
| in(sK2(sK18,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK18,sK3(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53142,c_9906]) ).
tcf(c_59079,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| element(sK2(sK18,sK4(iPr_def_11),sK18),iPr_def_11)
| subset(sK2(sK18,sK4(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(sK18,sK4(iPr_def_11),sK18))
| in(sK2(sK18,sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK18,sK4(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53142,c_45801]) ).
tcf(c_59278,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(sK18,X0,sK18),iPr_def_11)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK4(iPr_def_11))
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53143,c_13671]) ).
tcf(c_59279,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(sK18,X0,sK18),iPr_def_11)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK3(iPr_def_11))
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53143,c_13665]) ).
tcf(c_59280,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(sK18,X0,sK18),iPr_def_11)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK5(iPr_def_11))
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53143,c_13657]) ).
tcf(c_59281,plain,
! [X0: $i,X1: $i] :
( subset(X0,iPr_def_10)
| in(sK2(sK18,X1,sK18),iPr_def_11)
| in(sK2(sK18,X1,sK18),X1)
| ( set_union2(sK18,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(sK18,X1,sK18)) ),
inference(superposition,[status(thm)],[c_53143,c_128]) ).
tcf(c_59282,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_11)
| in(sK2(sK18,X0,sK18),iPr_def_11)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53143,c_3868]) ).
tcf(c_59283,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),iPr_def_11)
| in(sK3(iPr_def_11),sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53143,c_49877]) ).
tcf(c_59284,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),iPr_def_11)
| in(sK5(iPr_def_11),sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53143,c_7260]) ).
tcf(c_59285,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),iPr_def_11)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53143,c_359]) ).
tcf(c_59286,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),iPr_def_11)
| element(sK2(sK18,X0,sK18),X1)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53143,c_358]) ).
tcf(c_59287,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(sK2(sK18,X1,sK18),iPr_def_11)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X0)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53143,c_77]) ).
tcf(c_59288,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),iPr_def_11)
| subset(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53143,c_65]) ).
tcf(c_59289,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),iPr_def_11)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(sK18,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53143,c_49]) ).
tcf(c_59292,plain,
! [X0: $i] :
( subset(sK2(sK18,singleton(X0),sK18),iPr_def_10)
| in(sK2(sK18,singleton(X0),sK18),iPr_def_11)
| ( set_union2(sK18,singleton(X0)) = sK18 )
| ( sK2(sK18,singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53143,c_62]) ).
tcf(c_59295,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_10)
| in(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_11)
| in(X2,sK2(sK18,set_union2(X0,X1),sK18))
| in(sK2(sK18,set_union2(X0,X1),sK18),X2)
| ( set_union2(sK18,set_union2(X0,X1)) = sK18 )
| ( sK2(sK18,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53143,c_4213]) ).
tcf(c_59296,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_10)
| in(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_11)
| in(X2,sK2(sK18,set_union2(X0,X1),sK18))
| in(sK2(sK18,set_union2(X0,X1),sK18),X2)
| ( set_union2(sK18,set_union2(X0,X1)) = sK18 )
| ( sK2(sK18,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53143,c_4212]) ).
tcf(c_59297,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_10)
| in(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_11)
| in(sK2(sK18,set_union2(X0,X1),sK18),X1)
| in(sK2(sK18,set_union2(X0,X1),sK18),X0)
| ( set_union2(sK18,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53143,c_71]) ).
tcf(c_59298,plain,
( subset(sK2(sK18,empty_set,sK18),iPr_def_10)
| in(sK2(sK18,empty_set,sK18),iPr_def_11)
| ( set_union2(sK18,empty_set) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53143,c_7097]) ).
tcf(c_59303,plain,
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53143,c_9540]) ).
tcf(c_59306,plain,
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ( sK2(sK18,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53143,c_3592]) ).
tcf(c_59308,plain,
( subset(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_11,sK18),iPr_def_11)
| in(sK2(sK18,iPr_def_11,sK18),sK18)
| ( set_union2(sK18,iPr_def_11) = sK18 )
| ( sK2(sK18,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53143,c_33457]) ).
tcf(c_59309,plain,
( subset(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_11,sK18),iPr_def_11)
| in(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_11,sK18),sK18)
| ( set_union2(sK18,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53143,c_4035]) ).
tcf(c_59310,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK18,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(sK18,sK5(iPr_def_11),sK18),iPr_def_11)
| in(X0,sK2(sK18,sK5(iPr_def_11),sK18))
| in(sK2(sK18,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK18,sK5(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53143,c_7243]) ).
tcf(c_59311,plain,
( subset(sK2(sK18,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(sK18,sK5(iPr_def_11),sK18),iPr_def_11)
| ( set_union2(sK18,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK18,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53143,c_23189]) ).
tcf(c_59312,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK18,sK3(iPr_def_11),sK18),iPr_def_10)
| in(sK2(sK18,sK3(iPr_def_11),sK18),iPr_def_11)
| in(X0,sK2(sK18,sK3(iPr_def_11),sK18))
| in(sK2(sK18,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK18,sK3(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53143,c_9906]) ).
tcf(c_59313,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK18,sK4(iPr_def_11),sK18),iPr_def_10)
| in(sK2(sK18,sK4(iPr_def_11),sK18),iPr_def_11)
| in(X0,sK2(sK18,sK4(iPr_def_11),sK18))
| in(sK2(sK18,sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK18,sK4(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53143,c_45801]) ).
tcf(c_59567,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| element(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(iPr_def_10,X0,sK18))
| in(sK2(iPr_def_10,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53146,c_49877]) ).
tcf(c_59568,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| element(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(iPr_def_10,X0,sK18))
| in(sK2(iPr_def_10,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53146,c_7260]) ).
tcf(c_59569,plain,
! [X0: $i,X1: $i] :
( element(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53146,c_359]) ).
tcf(c_59570,plain,
! [X0: $i,X1: $i] :
( element(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| element(sK2(iPr_def_10,X0,sK18),X1)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53146,c_358]) ).
tcf(c_59571,plain,
! [X0: $i,X1: $i] :
( element(sK2(iPr_def_10,X1,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X1,sK18),iPr_def_10)
| in(X0,sK2(iPr_def_10,X1,sK18))
| in(sK2(iPr_def_10,X1,sK18),X0)
| ( set_union2(iPr_def_10,X1) = sK18 )
| ( sK2(iPr_def_10,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53146,c_77]) ).
tcf(c_59572,plain,
! [X0: $i] :
( element(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| subset(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53146,c_65]) ).
tcf(c_59573,plain,
! [X0: $i] :
( element(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(iPr_def_10,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53146,c_49]) ).
tcf(c_59576,plain,
! [X0: $i] :
( element(sK2(iPr_def_10,singleton(X0),sK18),iPr_def_11)
| subset(sK2(iPr_def_10,singleton(X0),sK18),iPr_def_10)
| ( set_union2(iPr_def_10,singleton(X0)) = sK18 )
| ( sK2(iPr_def_10,singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53146,c_62]) ).
tcf(c_59578,plain,
( element(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(iPr_def_10,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53146,c_67]) ).
tcf(c_59579,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_11)
| subset(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(iPr_def_10,set_union2(X0,X1),sK18))
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),X2)
| ( set_union2(iPr_def_10,set_union2(X0,X1)) = sK18 )
| ( sK2(iPr_def_10,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53146,c_4213]) ).
tcf(c_59580,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_11)
| subset(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(iPr_def_10,set_union2(X0,X1),sK18))
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),X2)
| ( set_union2(iPr_def_10,set_union2(X0,X1)) = sK18 )
| ( sK2(iPr_def_10,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53146,c_4212]) ).
tcf(c_59581,plain,
! [X0: $i,X1: $i] :
( element(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_11)
| subset(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_10)
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),X1)
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),X0)
| ( set_union2(iPr_def_10,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53146,c_71]) ).
tcf(c_59582,plain,
( element(sK2(iPr_def_10,empty_set,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,empty_set,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,empty_set) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53146,c_7097]) ).
tcf(c_59583,plain,
( element(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53146,c_12813]) ).
tcf(c_59592,plain,
( element(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_10)
| in(sK2(iPr_def_10,iPr_def_11,sK18),sK18)
| ( set_union2(iPr_def_10,iPr_def_11) = sK18 )
| ( sK2(iPr_def_10,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53146,c_33457]) ).
tcf(c_59593,plain,
( element(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_10)
| in(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_10)
| in(sK2(iPr_def_10,iPr_def_11,sK18),sK18)
| ( set_union2(iPr_def_10,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53146,c_4035]) ).
tcf(c_59594,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| element(sK2(iPr_def_10,sK5(iPr_def_11),sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK5(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(iPr_def_10,sK5(iPr_def_11),sK18))
| in(sK2(iPr_def_10,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,sK5(iPr_def_11)) = sK18 )
| ( sK2(iPr_def_10,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53146,c_7243]) ).
tcf(c_59595,plain,
( element(sK2(iPr_def_10,sK5(iPr_def_11),sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK5(iPr_def_11),sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(iPr_def_10,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53146,c_23189]) ).
tcf(c_59596,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| element(sK2(iPr_def_10,sK3(iPr_def_11),sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK3(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(iPr_def_10,sK3(iPr_def_11),sK18))
| in(sK2(iPr_def_10,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,sK3(iPr_def_11)) = sK18 )
| ( sK2(iPr_def_10,sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53146,c_9906]) ).
tcf(c_59597,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| element(sK2(iPr_def_10,sK4(iPr_def_11),sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK4(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(iPr_def_10,sK4(iPr_def_11),sK18))
| in(sK2(iPr_def_10,sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,sK4(iPr_def_11)) = sK18 )
| ( sK2(iPr_def_10,sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53146,c_45801]) ).
tcf(c_59602,plain,
( element(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( sK18 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_59583,c_3424]) ).
tcf(c_60161,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| in(sK2(iPr_def_10,X0,sK18),X0)
| in(sK2(iPr_def_10,X0,sK18),sK4(iPr_def_11))
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(iPr_def_10,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53148,c_13671]) ).
tcf(c_60162,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| in(sK2(iPr_def_10,X0,sK18),X0)
| in(sK2(iPr_def_10,X0,sK18),sK3(iPr_def_11))
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(iPr_def_10,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53148,c_13665]) ).
tcf(c_60163,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| in(sK2(iPr_def_10,X0,sK18),X0)
| in(sK2(iPr_def_10,X0,sK18),sK5(iPr_def_11))
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(iPr_def_10,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53148,c_13657]) ).
tcf(c_60164,plain,
! [X0: $i,X1: $i] :
( subset(X0,iPr_def_10)
| in(sK2(iPr_def_10,X1,sK18),iPr_def_11)
| in(sK2(iPr_def_10,X1,sK18),X1)
| ( set_union2(iPr_def_10,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(iPr_def_10,X1,sK18)) ),
inference(superposition,[status(thm)],[c_53148,c_128]) ).
tcf(c_60165,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| in(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53148,c_3868]) ).
tcf(c_60166,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| in(sK3(iPr_def_11),sK2(iPr_def_10,X0,sK18))
| in(sK2(iPr_def_10,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53148,c_49877]) ).
tcf(c_60167,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| in(sK5(iPr_def_11),sK2(iPr_def_10,X0,sK18))
| in(sK2(iPr_def_10,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53148,c_7260]) ).
tcf(c_60168,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53148,c_359]) ).
tcf(c_60169,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| element(sK2(iPr_def_10,X0,sK18),X1)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53148,c_358]) ).
tcf(c_60170,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X1,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X1,sK18),iPr_def_11)
| in(X0,sK2(iPr_def_10,X1,sK18))
| in(sK2(iPr_def_10,X1,sK18),X0)
| ( set_union2(iPr_def_10,X1) = sK18 )
| ( sK2(iPr_def_10,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53148,c_77]) ).
tcf(c_60171,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53148,c_65]) ).
tcf(c_60172,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(iPr_def_10,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53148,c_49]) ).
tcf(c_60175,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,singleton(X0),sK18),iPr_def_10)
| in(sK2(iPr_def_10,singleton(X0),sK18),iPr_def_11)
| ( set_union2(iPr_def_10,singleton(X0)) = sK18 )
| ( sK2(iPr_def_10,singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53148,c_62]) ).
tcf(c_60177,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(iPr_def_10,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53148,c_67]) ).
tcf(c_60178,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_10)
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_11)
| in(X2,sK2(iPr_def_10,set_union2(X0,X1),sK18))
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),X2)
| ( set_union2(iPr_def_10,set_union2(X0,X1)) = sK18 )
| ( sK2(iPr_def_10,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53148,c_4213]) ).
tcf(c_60179,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_10)
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_11)
| in(X2,sK2(iPr_def_10,set_union2(X0,X1),sK18))
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),X2)
| ( set_union2(iPr_def_10,set_union2(X0,X1)) = sK18 )
| ( sK2(iPr_def_10,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53148,c_4212]) ).
tcf(c_60180,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_10)
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_11)
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),X1)
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),X0)
| ( set_union2(iPr_def_10,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53148,c_71]) ).
tcf(c_60181,plain,
( subset(sK2(iPr_def_10,empty_set,sK18),iPr_def_10)
| in(sK2(iPr_def_10,empty_set,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,empty_set) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53148,c_7097]) ).
tcf(c_60182,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53148,c_12813]) ).
tcf(c_60191,plain,
( subset(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_10)
| in(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_11)
| in(sK2(iPr_def_10,iPr_def_11,sK18),sK18)
| ( set_union2(iPr_def_10,iPr_def_11) = sK18 )
| ( sK2(iPr_def_10,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53148,c_33457]) ).
tcf(c_60192,plain,
( subset(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_10)
| in(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_11)
| in(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_10)
| in(sK2(iPr_def_10,iPr_def_11,sK18),sK18)
| ( set_union2(iPr_def_10,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53148,c_4035]) ).
tcf(c_60193,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(iPr_def_10,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK5(iPr_def_11),sK18),iPr_def_11)
| in(X0,sK2(iPr_def_10,sK5(iPr_def_11),sK18))
| in(sK2(iPr_def_10,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,sK5(iPr_def_11)) = sK18 )
| ( sK2(iPr_def_10,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53148,c_7243]) ).
tcf(c_60194,plain,
( subset(sK2(iPr_def_10,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK5(iPr_def_11),sK18),iPr_def_11)
| ( set_union2(iPr_def_10,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(iPr_def_10,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53148,c_23189]) ).
tcf(c_60195,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(iPr_def_10,sK3(iPr_def_11),sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK3(iPr_def_11),sK18),iPr_def_11)
| in(X0,sK2(iPr_def_10,sK3(iPr_def_11),sK18))
| in(sK2(iPr_def_10,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,sK3(iPr_def_11)) = sK18 )
| ( sK2(iPr_def_10,sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53148,c_9906]) ).
tcf(c_60196,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(iPr_def_10,sK4(iPr_def_11),sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK4(iPr_def_11),sK18),iPr_def_11)
| in(X0,sK2(iPr_def_10,sK4(iPr_def_11),sK18))
| in(sK2(iPr_def_10,sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,sK4(iPr_def_11)) = sK18 )
| ( sK2(iPr_def_10,sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53148,c_45801]) ).
tcf(c_60445,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X2,X0,X1),X2)
| in(sK3(iPr_def_11),sK2(X2,X0,X1))
| in(sK2(X2,X0,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X2,X0) = X1 )
| ( sK2(X2,X0,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ empty(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4332,c_49877]) ).
tcf(c_60446,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X2,X0,X1),X2)
| in(sK5(iPr_def_11),sK2(X2,X0,X1))
| in(sK2(X2,X0,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X2,X0) = X1 )
| ( sK2(X2,X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ empty(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4332,c_7260]) ).
tcf(c_60447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,X0,X2),X3)
| ( set_union2(X3,X0) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4332,c_359]) ).
tcf(c_60448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X3,X0,X2),X1)
| in(sK2(X3,X0,X2),X3)
| ( set_union2(X3,X0) = X2 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4332,c_358]) ).
tcf(c_60449,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X3,X1,X2))
| in(sK2(X3,X1,X2),X3)
| in(sK2(X3,X1,X2),X0)
| ( set_union2(X3,X1) = X2 )
| ( sK2(X3,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4332,c_77]) ).
tcf(c_60450,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X1,X0),X1)
| in(sK2(X2,X1,X0),X2)
| ( set_union2(X2,X1) = X0 )
| ~ epsilon_transitive(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_65]) ).
tcf(c_60451,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ~ empty(X2)
| ~ in(X0,sK2(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_4332,c_49]) ).
tcf(c_60452,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X1,X0),X2)
| ( set_union2(X2,X1) = X0 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_137]) ).
tcf(c_60453,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_127]) ).
tcf(c_60454,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,singleton(X2),X0),X1)
| ( set_union2(X1,singleton(X2)) = X0 )
| ( sK2(X1,singleton(X2),X0) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_62]) ).
tcf(c_60455,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X0,X1),X0)
| ( set_union2(X0,X0) = X1 )
| ~ empty(X1)
| ~ in(sK2(X0,X0,X1),X1) ),
inference(superposition,[status(thm)],[c_4332,c_66]) ).
tcf(c_60456,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,X1),X0)
| ( set_union2(X0,X1) = X1 )
| ~ empty(X1)
| ~ in(sK2(X0,X1,X1),X1) ),
inference(superposition,[status(thm)],[c_4332,c_67]) ).
tcf(c_60457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(X4,set_union2(X0,X1),X3))
| in(sK2(X4,set_union2(X0,X1),X3),X4)
| in(sK2(X4,set_union2(X0,X1),X3),X2)
| ( set_union2(X4,set_union2(X0,X1)) = X3 )
| ( sK2(X4,set_union2(X0,X1),X3) = X2 )
| ~ empty(X3)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4332,c_4213]) ).
tcf(c_60458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(X4,set_union2(X0,X1),X3))
| in(sK2(X4,set_union2(X0,X1),X3),X4)
| in(sK2(X4,set_union2(X0,X1),X3),X2)
| ( set_union2(X4,set_union2(X0,X1)) = X3 )
| ( sK2(X4,set_union2(X0,X1),X3) = X2 )
| ~ empty(X3)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4332,c_4212]) ).
tcf(c_60459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_union2(X2,X3),X0),X3)
| in(sK2(X1,set_union2(X2,X3),X0),X2)
| in(sK2(X1,set_union2(X2,X3),X0),X1)
| ( set_union2(X1,set_union2(X2,X3)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_71]) ).
tcf(c_60460,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,empty_set,X0),X1)
| ( set_union2(X1,empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_7097]) ).
tcf(c_60461,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK18,X0),iPr_def_11)
| in(sK2(X1,sK18,X0),X1)
| ( set_union2(X1,sK18) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_12813]) ).
tcf(c_60462,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 )
| ~ empty(X1)
| ~ in(iPr_def_11,sK2(X0,sK18,X1)) ),
inference(superposition,[status(thm)],[c_4332,c_6841]) ).
tcf(c_60463,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,sK18,X0),iPr_def_11)
| in(sK2(X1,sK18,X0),X1)
| ( set_union2(X1,sK18) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_5047]) ).
tcf(c_60464,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK18,X0),iPr_def_11)
| in(sK2(X1,sK18,X0),X1)
| ( set_union2(X1,sK18) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_3640]) ).
tcf(c_60465,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,iPr_def_10,X0),iPr_def_11)
| in(sK2(X1,iPr_def_10,X0),X1)
| ( set_union2(X1,iPr_def_10) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_9540]) ).
tcf(c_60466,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_10,X1),X0)
| ( set_union2(X0,iPr_def_10) = X1 )
| ~ empty(X1)
| ~ in(iPr_def_11,sK2(X0,iPr_def_10,X1)) ),
inference(superposition,[status(thm)],[c_4332,c_6289]) ).
tcf(c_60467,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,iPr_def_10,X0),iPr_def_11)
| in(sK2(X1,iPr_def_10,X0),X1)
| ( set_union2(X1,iPr_def_10) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_4912]) ).
tcf(c_60468,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,iPr_def_10,X0),X1)
| ( set_union2(X1,iPr_def_10) = X0 )
| ( sK2(X1,iPr_def_10,X0) = sK18 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_3592]) ).
tcf(c_60469,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,iPr_def_10,X0),iPr_def_11)
| in(sK2(X1,iPr_def_10,X0),X1)
| ( set_union2(X1,iPr_def_10) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_3614]) ).
tcf(c_60470,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,iPr_def_11,X0),sK18)
| in(sK2(X1,iPr_def_11,X0),X1)
| ( set_union2(X1,iPr_def_11) = X0 )
| ( sK2(X1,iPr_def_11,X0) = sK18 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_33457]) ).
tcf(c_60471,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,iPr_def_11,X0),iPr_def_10)
| in(sK2(X1,iPr_def_11,X0),sK18)
| in(sK2(X1,iPr_def_11,X0),X1)
| ( set_union2(X1,iPr_def_11) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_4035]) ).
tcf(c_60472,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_union2(X0,X1),X0,X2),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X0) = X2 )
| ~ empty(X2)
| ~ in(sK2(set_union2(X0,X1),X0,X2),X2) ),
inference(superposition,[status(thm)],[c_4332,c_4078]) ).
tcf(c_60473,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_union2(X0,X1),X2,X2),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = X2 )
| ~ empty(X2)
| ~ in(sK2(set_union2(X0,X1),X2,X2),X1) ),
inference(superposition,[status(thm)],[c_4332,c_4079]) ).
tcf(c_60474,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X1,X2)),X0)
| ( set_union2(X0,X1) = set_union2(X1,X2) )
| ~ empty(set_union2(X1,X2))
| ~ in(sK2(X0,X1,set_union2(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_4332,c_4095]) ).
tcf(c_60475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_union2(X2,X3)),X0)
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ~ empty(set_union2(X2,X3))
| ~ in(sK2(X0,X1,set_union2(X2,X3)),X3) ),
inference(superposition,[status(thm)],[c_4332,c_4096]) ).
tcf(c_60476,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK2(X2,sK5(iPr_def_11),X1))
| in(sK2(X2,sK5(iPr_def_11),X1),X2)
| in(sK2(X2,sK5(iPr_def_11),X1),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X2,sK5(iPr_def_11)) = X1 )
| ( sK2(X2,sK5(iPr_def_11),X1) = X0 )
| ~ empty(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4332,c_7243]) ).
tcf(c_60477,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK5(iPr_def_11),X1),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ~ empty(X1)
| ~ subset(iPr_def_11,sK2(X0,sK5(iPr_def_11),X1)) ),
inference(superposition,[status(thm)],[c_4332,c_23189]) ).
tcf(c_60478,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK2(X2,sK3(iPr_def_11),X1))
| in(sK2(X2,sK3(iPr_def_11),X1),X2)
| in(sK2(X2,sK3(iPr_def_11),X1),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X2,sK3(iPr_def_11)) = X1 )
| ( sK2(X2,sK3(iPr_def_11),X1) = X0 )
| ~ empty(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4332,c_9906]) ).
tcf(c_60479,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK2(X2,sK4(iPr_def_11),X1))
| in(sK2(X2,sK4(iPr_def_11),X1),X2)
| in(sK2(X2,sK4(iPr_def_11),X1),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X2,sK4(iPr_def_11)) = X1 )
| ( sK2(X2,sK4(iPr_def_11),X1) = X0 )
| ~ empty(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4332,c_45801]) ).
tcf(c_60480,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X0,X2,X1),X2)
| in(sK3(iPr_def_11),sK2(X0,X2,X1))
| in(sK2(X0,X2,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X2) = X1 )
| ( sK2(X0,X2,X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ empty(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4332,c_49877]) ).
tcf(c_60481,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X0,X2,X1),X2)
| in(sK5(iPr_def_11),sK2(X0,X2,X1))
| in(sK2(X0,X2,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X2) = X1 )
| ( sK2(X0,X2,X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ empty(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4332,c_7260]) ).
tcf(c_60482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X3,X2),X3)
| ( set_union2(X0,X3) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4332,c_359]) ).
tcf(c_60483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X3,X2),X1)
| in(sK2(X0,X3,X2),X3)
| ( set_union2(X0,X3) = X2 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4332,c_358]) ).
tcf(c_60484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X1,X3,X2))
| in(sK2(X1,X3,X2),X3)
| in(sK2(X1,X3,X2),X0)
| ( set_union2(X1,X3) = X2 )
| ( sK2(X1,X3,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4332,c_77]) ).
tcf(c_60485,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X2,X0),X1)
| in(sK2(X1,X2,X0),X2)
| ( set_union2(X1,X2) = X0 )
| ~ epsilon_transitive(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_65]) ).
tcf(c_60486,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 )
| ~ empty(X2)
| ~ in(X0,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4332,c_49]) ).
tcf(c_60487,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| ( set_union2(X1,X2) = X0 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_137]) ).
tcf(c_60488,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X2,X0),X1)
| in(sK2(X1,X2,X0),X2)
| ( set_union2(X1,X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_127]) ).
tcf(c_60489,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(singleton(X1),X2,X0),X2)
| ( set_union2(singleton(X1),X2) = X0 )
| ( sK2(singleton(X1),X2,X0) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_62]) ).
tcf(c_60490,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 )
| ~ empty(X2)
| ~ in(sK2(X0,X1,X2),X2) ),
inference(superposition,[status(thm)],[c_4332,c_66]) ).
tcf(c_60492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(set_union2(X0,X1),X4,X3))
| in(sK2(set_union2(X0,X1),X4,X3),X4)
| in(sK2(set_union2(X0,X1),X4,X3),X2)
| ( set_union2(set_union2(X0,X1),X4) = X3 )
| ( sK2(set_union2(X0,X1),X4,X3) = X2 )
| ~ empty(X3)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4332,c_4213]) ).
tcf(c_60493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(set_union2(X0,X1),X4,X3))
| in(sK2(set_union2(X0,X1),X4,X3),X4)
| in(sK2(set_union2(X0,X1),X4,X3),X2)
| ( set_union2(set_union2(X0,X1),X4) = X3 )
| ( sK2(set_union2(X0,X1),X4,X3) = X2 )
| ~ empty(X3)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4332,c_4212]) ).
tcf(c_60494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_union2(X1,X2),X3,X0),X3)
| in(sK2(set_union2(X1,X2),X3,X0),X2)
| in(sK2(set_union2(X1,X2),X3,X0),X1)
| ( set_union2(set_union2(X1,X2),X3) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_71]) ).
tcf(c_60495,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,X0),X1)
| ( set_union2(empty_set,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_7097]) ).
tcf(c_60496,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,X0),iPr_def_11)
| in(sK2(sK18,X1,X0),X1)
| ( set_union2(sK18,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_12813]) ).
tcf(c_60497,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK18,X0,X1),X0)
| ( set_union2(sK18,X0) = X1 )
| ~ empty(X1)
| ~ in(iPr_def_11,sK2(sK18,X0,X1)) ),
inference(superposition,[status(thm)],[c_4332,c_6841]) ).
tcf(c_60498,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK18,X1,X0),iPr_def_11)
| in(sK2(sK18,X1,X0),X1)
| ( set_union2(sK18,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_5047]) ).
tcf(c_60499,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK18,X1,X0),iPr_def_11)
| in(sK2(sK18,X1,X0),X1)
| ( set_union2(sK18,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_3640]) ).
tcf(c_60500,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X1,X0),iPr_def_11)
| in(sK2(iPr_def_10,X1,X0),X1)
| ( set_union2(iPr_def_10,X1) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_9540]) ).
tcf(c_60501,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_10,X0,X1),X0)
| ( set_union2(iPr_def_10,X0) = X1 )
| ~ empty(X1)
| ~ in(iPr_def_11,sK2(iPr_def_10,X0,X1)) ),
inference(superposition,[status(thm)],[c_4332,c_6289]) ).
tcf(c_60502,plain,
! [X0: $i,X1: $i] :
( element(sK2(iPr_def_10,X1,X0),iPr_def_11)
| in(sK2(iPr_def_10,X1,X0),X1)
| ( set_union2(iPr_def_10,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_4912]) ).
tcf(c_60503,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_10,X1,X0),X1)
| ( set_union2(iPr_def_10,X1) = X0 )
| ( sK2(iPr_def_10,X1,X0) = sK18 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_3592]) ).
tcf(c_60504,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_10,X1,X0),iPr_def_11)
| in(sK2(iPr_def_10,X1,X0),X1)
| ( set_union2(iPr_def_10,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_3614]) ).
tcf(c_60505,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_11,X1,X0),sK18)
| in(sK2(iPr_def_11,X1,X0),X1)
| ( set_union2(iPr_def_11,X1) = X0 )
| ( sK2(iPr_def_11,X1,X0) = sK18 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_33457]) ).
tcf(c_60506,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_11,X1,X0),iPr_def_10)
| in(sK2(iPr_def_11,X1,X0),sK18)
| in(sK2(iPr_def_11,X1,X0),X1)
| ( set_union2(iPr_def_11,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4332,c_4035]) ).
tcf(c_60507,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X2)
| ( set_union2(set_union2(X0,X1),X2) = set_union2(X0,X1) )
| ~ empty(set_union2(X0,X1))
| ~ in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_4332,c_4079]) ).
tcf(c_60509,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_union2(X1,X2)),X0)
| ( set_union2(X0,X0) = set_union2(X1,X2) )
| ~ empty(set_union2(X1,X2))
| ~ in(sK2(X0,X0,set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4332,c_4096]) ).
tcf(c_60510,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK2(sK5(iPr_def_11),X2,X1))
| in(sK2(sK5(iPr_def_11),X2,X1),X2)
| in(sK2(sK5(iPr_def_11),X2,X1),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X2) = X1 )
| ( sK2(sK5(iPr_def_11),X2,X1) = X0 )
| ~ empty(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4332,c_7243]) ).
tcf(c_60511,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK5(iPr_def_11),X0,X1),X0)
| ( set_union2(sK5(iPr_def_11),X0) = X1 )
| ~ empty(X1)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,X1)) ),
inference(superposition,[status(thm)],[c_4332,c_23189]) ).
tcf(c_60512,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK2(sK3(iPr_def_11),X2,X1))
| in(sK2(sK3(iPr_def_11),X2,X1),X2)
| in(sK2(sK3(iPr_def_11),X2,X1),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X2) = X1 )
| ( sK2(sK3(iPr_def_11),X2,X1) = X0 )
| ~ empty(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4332,c_9906]) ).
tcf(c_60513,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK2(sK4(iPr_def_11),X2,X1))
| in(sK2(sK4(iPr_def_11),X2,X1),X2)
| in(sK2(sK4(iPr_def_11),X2,X1),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X2) = X1 )
| ( sK2(sK4(iPr_def_11),X2,X1) = X0 )
| ~ empty(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4332,c_45801]) ).
tcf(c_60514,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X1,X0),X1)
| ( set_union2(X1,X1) = X0 )
| ~ empty(X0) ),
inference(equality_factoring,[status(thm)],[c_4332]) ).
tcf(c_60622,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X0,X1),X0)
| ( X0 = X1 )
| ~ empty(X1)
| ~ in(sK2(X0,X0,X1),X1) ),
inference(light_normalisation,[status(thm)],[c_60455,c_97]) ).
tcf(c_60702,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_union2(X1,X2)),X0)
| ( set_union2(X1,X2) = X0 )
| ~ empty(set_union2(X1,X2))
| ~ in(sK2(X0,X0,set_union2(X1,X2)),X2) ),
inference(light_normalisation,[status(thm)],[c_60509,c_97]) ).
tcf(c_61090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,set_union2(X2,X3))),X4)),X2),
inference(superposition,[status(thm)],[c_69,c_5548]) ).
tcf(c_61091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,set_union2(X2,X3))),X4)),X3),
inference(superposition,[status(thm)],[c_70,c_5548]) ).
tcf(c_61092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(powerset(X2))
| ~ subset(singleton(set_union2(set_union2(X0,set_union2(X1,powerset(X2))),X3)),X2) ),
inference(superposition,[status(thm)],[c_3769,c_5548]) ).
tcf(c_61093,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK18)
| in(sK5(sK18),singleton(set_union2(set_union2(X0,set_union2(X1,sK5(sK18))),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK5(sK18))),X2)) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK5(sK18))),X2)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_5548]) ).
tcf(c_61094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,X3,X4),X3)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X2,X3,X4),singleton(set_union2(set_union2(X0,set_union2(X1,sK2(X2,X3,X4))),X5)))
| ( set_union2(X2,X3) = X4 )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK2(X2,X3,X4))),X5)) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X4)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK2(X2,X3,X4))),X5)),X4) ),
inference(superposition,[status(thm)],[c_4329,c_5548]) ).
tcf(c_61095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_5548]) ).
tcf(c_61096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_5548]) ).
tcf(c_61097,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_5548]) ).
tcf(c_61098,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_5548]) ).
tcf(c_61099,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)) = sK5(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)))
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_5548]) ).
tcf(c_61100,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_5548]) ).
tcf(c_61101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_5548]) ).
tcf(c_61102,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2) = sK5(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK5(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_5548]) ).
tcf(c_61103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK1(iPr_def_11))),X2)))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK1(iPr_def_11))),X2)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK1(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_5548]) ).
tcf(c_61104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK1(iPr_def_11))),X2)))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK1(iPr_def_11))),X2)) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK1(iPr_def_11))),X2)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_5548]) ).
tcf(c_61105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_5548]) ).
tcf(c_61106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_5548]) ).
tcf(c_61107,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_5548]) ).
tcf(c_61108,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_5548]) ).
tcf(c_61109,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)) = sK3(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)))
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_5548]) ).
tcf(c_61110,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_5548]) ).
tcf(c_61111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_5548]) ).
tcf(c_61112,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2) = sK3(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK3(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_5548]) ).
tcf(c_61113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X3)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_5548]) ).
tcf(c_61114,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_5548]) ).
tcf(c_61115,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_5548]) ).
tcf(c_61116,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)) = sK4(iPr_def_11) )
| ~ empty(singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)))
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_5548]) ).
tcf(c_61117,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_5548]) ).
tcf(c_61118,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2) = sK4(iPr_def_11) )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_5548]) ).
tcf(c_61356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(X0,set_union2(set_union2(set_union2(X1,X2),X3),X4))),X1),
inference(superposition,[status(thm)],[c_69,c_5584]) ).
tcf(c_61357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(X0,set_union2(set_union2(set_union2(X1,X2),X3),X4))),X2),
inference(superposition,[status(thm)],[c_70,c_5584]) ).
tcf(c_61358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(powerset(X1))
| ~ subset(singleton(set_union2(X0,set_union2(set_union2(powerset(X1),X2),X3))),X1) ),
inference(superposition,[status(thm)],[c_3769,c_5584]) ).
tcf(c_61359,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK18)
| in(sK5(sK18),singleton(set_union2(X0,set_union2(set_union2(sK5(sK18),X1),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(sK5(sK18),X1),X2))) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK5(sK18),X1),X2))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_5584]) ).
tcf(c_61360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),singleton(set_union2(X0,set_union2(set_union2(sK2(X1,X2,X3),X4),X5))))
| ( set_union2(X1,X2) = X3 )
| ( singleton(set_union2(X0,set_union2(set_union2(sK2(X1,X2,X3),X4),X5))) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X3)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK2(X1,X2,X3),X4),X5))),X3) ),
inference(superposition,[status(thm)],[c_4329,c_5584]) ).
tcf(c_61361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_5584]) ).
tcf(c_61362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_5584]) ).
tcf(c_61363,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_5584]) ).
tcf(c_61364,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_5584]) ).
tcf(c_61365,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))) = sK5(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))))
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_5584]) ).
tcf(c_61366,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_5584]) ).
tcf(c_61367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_5584]) ).
tcf(c_61368,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2)) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK5(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_5584]) ).
tcf(c_61369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK1(iPr_def_11),X1),X2))))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(set_union2(sK1(iPr_def_11),X1),X2))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK1(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_5584]) ).
tcf(c_61370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK1(iPr_def_11),X1),X2))))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(set_union2(sK1(iPr_def_11),X1),X2))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK1(iPr_def_11),X1),X2))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_5584]) ).
tcf(c_61371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_5584]) ).
tcf(c_61372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_5584]) ).
tcf(c_61373,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_5584]) ).
tcf(c_61374,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_5584]) ).
tcf(c_61375,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))) = sK3(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))))
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_5584]) ).
tcf(c_61376,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_5584]) ).
tcf(c_61377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_5584]) ).
tcf(c_61378,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2)) = sK3(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK3(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_5584]) ).
tcf(c_61379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X3)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_5584]) ).
tcf(c_61380,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_5584]) ).
tcf(c_61381,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_5584]) ).
tcf(c_61382,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))) = sK4(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))))
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_5584]) ).
tcf(c_61383,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_5584]) ).
tcf(c_61384,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2)) = sK4(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_5584]) ).
tcf(c_61397,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(singleton(set_union2(X0,set_union2(X1,X2))),empty_set),
inference(superposition,[status(thm)],[c_3423,c_5584]) ).
tcf(c_61733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,set_union2(X2,X3)),X4))),X2),
inference(superposition,[status(thm)],[c_69,c_5585]) ).
tcf(c_61734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,set_union2(X2,X3)),X4))),X3),
inference(superposition,[status(thm)],[c_70,c_5585]) ).
tcf(c_61735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(powerset(X2))
| ~ subset(singleton(set_union2(X0,set_union2(set_union2(X1,powerset(X2)),X3))),X2) ),
inference(superposition,[status(thm)],[c_3769,c_5585]) ).
tcf(c_61736,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK18)
| in(sK5(sK18),singleton(set_union2(X0,set_union2(set_union2(X1,sK5(sK18)),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK5(sK18)),X2))) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK5(sK18)),X2))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_5585]) ).
tcf(c_61737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,X3,X4),X3)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X2,X3,X4),singleton(set_union2(X0,set_union2(set_union2(X1,sK2(X2,X3,X4)),X5))))
| ( set_union2(X2,X3) = X4 )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK2(X2,X3,X4)),X5))) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X4)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK2(X2,X3,X4)),X5))),X4) ),
inference(superposition,[status(thm)],[c_4329,c_5585]) ).
tcf(c_61738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_5585]) ).
tcf(c_61739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_5585]) ).
tcf(c_61740,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_5585]) ).
tcf(c_61741,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_5585]) ).
tcf(c_61742,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))) = sK5(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))))
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_5585]) ).
tcf(c_61743,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_5585]) ).
tcf(c_61744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_5585]) ).
tcf(c_61745,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2)) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK5(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_5585]) ).
tcf(c_61746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK1(iPr_def_11)),X2))))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK1(iPr_def_11)),X2))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK1(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_5585]) ).
tcf(c_61747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK1(iPr_def_11)),X2))))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK1(iPr_def_11)),X2))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK1(iPr_def_11)),X2))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_5585]) ).
tcf(c_61748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_5585]) ).
tcf(c_61749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_5585]) ).
tcf(c_61750,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_5585]) ).
tcf(c_61751,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_5585]) ).
tcf(c_61752,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))) = sK3(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))))
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_5585]) ).
tcf(c_61753,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_5585]) ).
tcf(c_61754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_5585]) ).
tcf(c_61755,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2)) = sK3(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK3(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_5585]) ).
tcf(c_61756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X3)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_5585]) ).
tcf(c_61757,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_5585]) ).
tcf(c_61758,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_5585]) ).
tcf(c_61759,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))) = sK4(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))))
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_5585]) ).
tcf(c_61760,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_5585]) ).
tcf(c_61761,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2)) = sK4(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_5585]) ).
tcf(c_61955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(set_union2(X2,X3),X4)))),X2),
inference(superposition,[status(thm)],[c_69,c_5597]) ).
tcf(c_61956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(set_union2(X2,X3),X4)))),X3),
inference(superposition,[status(thm)],[c_70,c_5597]) ).
tcf(c_61957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(powerset(X2))
| ~ subset(singleton(set_union2(X0,set_union2(X1,set_union2(powerset(X2),X3)))),X2) ),
inference(superposition,[status(thm)],[c_3769,c_5597]) ).
tcf(c_61958,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK18)
| in(sK5(sK18),singleton(set_union2(X0,set_union2(X1,set_union2(sK5(sK18),X2)))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK5(sK18),X2)))) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK5(sK18),X2)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_5597]) ).
tcf(c_61959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,X3,X4),X3)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X2,X3,X4),singleton(set_union2(X0,set_union2(X1,set_union2(sK2(X2,X3,X4),X5)))))
| ( set_union2(X2,X3) = X4 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK2(X2,X3,X4),X5)))) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X4)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK2(X2,X3,X4),X5)))),X4) ),
inference(superposition,[status(thm)],[c_4329,c_5597]) ).
tcf(c_61960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_5597]) ).
tcf(c_61961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_5597]) ).
tcf(c_61962,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_5597]) ).
tcf(c_61963,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_5597]) ).
tcf(c_61964,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))) = sK5(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))))
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_5597]) ).
tcf(c_61965,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_5597]) ).
tcf(c_61966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_5597]) ).
tcf(c_61967,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2))) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK5(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_5597]) ).
tcf(c_61968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK1(iPr_def_11),X2)))))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK1(iPr_def_11),X2)))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK1(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_5597]) ).
tcf(c_61969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK1(iPr_def_11),X2)))))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK1(iPr_def_11),X2)))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK1(iPr_def_11),X2)))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_5597]) ).
tcf(c_61970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_5597]) ).
tcf(c_61971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_5597]) ).
tcf(c_61972,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_5597]) ).
tcf(c_61973,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_5597]) ).
tcf(c_61974,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))) = sK3(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))))
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_5597]) ).
tcf(c_61975,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_5597]) ).
tcf(c_61976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_5597]) ).
tcf(c_61977,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2))) = sK3(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK3(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_5597]) ).
tcf(c_61978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X3)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_5597]) ).
tcf(c_61979,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_5597]) ).
tcf(c_61980,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_5597]) ).
tcf(c_61981,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))) = sK4(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))))
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_5597]) ).
tcf(c_61982,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_5597]) ).
tcf(c_61983,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2))) = sK4(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_5597]) ).
tcf(c_62235,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ subset(iPr_def_10,empty_set) ),
inference(superposition,[status(thm)],[c_3423,c_27084]) ).
tcf(c_62239,plain,
~ subset(iPr_def_10,empty_set),
inference(global_subsumption_just,[status(thm)],[c_62235,c_95,c_24592]) ).
tcf(c_62269,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X0,sK18),iPr_def_10)
| in(sK2(X2,X0,sK18),X2)
| ( set_union2(X2,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_138,c_53093]) ).
tcf(c_62270,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK5(powerset(X0)),sK18),iPr_def_10)
| in(sK2(X1,sK5(powerset(X0)),sK18),X1)
| ( set_union2(X1,sK5(powerset(X0))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3564,c_53093]) ).
tcf(c_62271,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X1,sK18),iPr_def_10)
| in(sK2(X2,X1,sK18),X2)
| ( set_union2(X2,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3397,c_53093]) ).
tcf(c_62272,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,empty_set,sK18),iPr_def_10)
| in(sK2(X1,empty_set,sK18),X1)
| ( set_union2(X1,empty_set) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3420,c_53093]) ).
tcf(c_62275,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(powerset(X0))
| subset(sK2(X1,sK1(powerset(X0)),sK18),iPr_def_10)
| in(sK2(X1,sK1(powerset(X0)),sK18),X1)
| ( set_union2(X1,sK1(powerset(X0))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3566,c_53093]) ).
tcf(c_62276,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(X0))
| subset(sK2(X1,sK3(powerset(X0)),sK18),iPr_def_10)
| in(sK2(X1,sK3(powerset(X0)),sK18),X1)
| ( set_union2(X1,sK3(powerset(X0))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3567,c_53093]) ).
tcf(c_62277,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(X0))
| subset(sK2(X1,sK4(powerset(X0)),sK18),iPr_def_10)
| in(sK2(X1,sK4(powerset(X0)),sK18),X1)
| ( set_union2(X1,sK4(powerset(X0))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3568,c_53093]) ).
tcf(c_62279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,X2,sK18),iPr_def_10)
| in(sK2(X3,X2,sK18),X3)
| ( set_union2(X3,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X2,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_53093]) ).
tcf(c_62280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,X2,sK18),iPr_def_10)
| in(sK2(X3,X2,sK18),X3)
| ( set_union2(X3,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_53093]) ).
tcf(c_62281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,X2,sK18),iPr_def_10)
| in(sK2(X3,X2,sK18),X3)
| ( set_union2(X3,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_53093]) ).
tcf(c_62282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,X2,sK18),iPr_def_10)
| in(sK2(X3,X2,sK18),X3)
| ( set_union2(X3,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X2,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_53093]) ).
tcf(c_62283,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| subset(sK2(X1,sK3(X0),sK18),iPr_def_10)
| in(sK2(X1,sK3(X0),sK18),X1)
| ( set_union2(X1,sK3(X0)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3807,c_53093]) ).
tcf(c_62284,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| subset(sK2(X1,sK4(X0),sK18),iPr_def_10)
| in(sK2(X1,sK4(X0),sK18),X1)
| ( set_union2(X1,sK4(X0)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3808,c_53093]) ).
tcf(c_62295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X3)
| in(sK2(X2,X3,X0),X2)
| subset(sK2(X1,sK2(X2,X3,X0),sK18),iPr_def_10)
| in(sK2(X1,sK2(X2,X3,X0),sK18),X1)
| ( set_union2(X2,X3) = X0 )
| ( set_union2(X1,sK2(X2,X3,X0)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4330,c_53093]) ).
tcf(c_62298,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(empty_set))
| subset(sK2(X1,sK3(powerset(empty_set)),sK18),iPr_def_10)
| in(sK2(X1,sK3(powerset(empty_set)),sK18),X1)
| ( set_union2(X1,sK3(powerset(empty_set))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4620,c_53093]) ).
tcf(c_62301,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(empty_set))
| subset(sK2(X1,sK4(powerset(empty_set)),sK18),iPr_def_10)
| in(sK2(X1,sK4(powerset(empty_set)),sK18),X1)
| ( set_union2(X1,sK4(powerset(empty_set))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4637,c_53093]) ).
tcf(c_62304,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK5(powerset(sK5(powerset(X0)))),sK18),iPr_def_10)
| in(sK2(X1,sK5(powerset(sK5(powerset(X0)))),sK18),X1)
| ( set_union2(X1,sK5(powerset(sK5(powerset(X0))))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5196,c_53093]) ).
tcf(c_62306,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),sK18),iPr_def_10)
| in(sK2(X1,sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),sK18),X1)
| ( set_union2(X1,sK5(powerset(sK5(powerset(sK5(powerset(X0))))))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5252,c_53093]) ).
tcf(c_62324,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_7152,c_53093]) ).
tcf(c_62326,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK2(X1,X0,sK18),X1)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_53093]) ).
tcf(c_62331,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X1,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X1,sK5(iPr_def_11),sK18),X1)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7261,c_53093]) ).
tcf(c_62332,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK5(powerset(sK5(iPr_def_11))),sK18),iPr_def_10)
| in(sK2(X0,sK5(powerset(sK5(iPr_def_11))),sK18),X0)
| ( set_union2(X0,sK5(powerset(sK5(iPr_def_11)))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_7587,c_53093]) ).
tcf(c_62333,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK3(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK3(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK3(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_9591,c_53093]) ).
tcf(c_62335,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK2(X1,X0,sK18),X1)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9907,c_53093]) ).
tcf(c_62338,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X1,sK3(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X1,sK3(iPr_def_11),sK18),X1)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,sK3(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9925,c_53093]) ).
tcf(c_62339,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK4(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_11031,c_53093]) ).
tcf(c_62341,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK2(X1,X0,sK18),X1)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11191,c_53093]) ).
tcf(c_62344,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| subset(sK2(X1,sK4(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X1,sK4(iPr_def_11),sK18),X1)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,sK4(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11209,c_53093]) ).
tcf(c_62353,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ empty(singleton(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_15774,c_53093]) ).
tcf(c_62625,plain,
! [X0: $i] :
( empty(sK18)
| subset(sK2(X0,sK5(sK18),sK18),iPr_def_10)
| in(sK2(X0,sK5(sK18),sK18),X0)
| in(sK2(X0,sK5(sK18),sK18),sK5(sK18))
| ( set_union2(X0,sK5(sK18)) = sK18 )
| ( sK2(X0,sK5(sK18),sK18) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK5(sK18),sK18),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_53097]) ).
tcf(c_62626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X1)
| subset(sK2(X0,sK2(X1,X2,X3),sK18),iPr_def_10)
| in(sK2(X0,sK2(X1,X2,X3),sK18),X0)
| in(sK2(X0,sK2(X1,X2,X3),sK18),sK2(X1,X2,X3))
| ( set_union2(X1,X2) = X3 )
| ( set_union2(X0,sK2(X1,X2,X3)) = sK18 )
| ( sK2(X0,sK2(X1,X2,X3),sK18) = sK2(X1,X2,X3) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X3)
| ~ in(sK2(X0,sK2(X1,X2,X3),sK18),X3) ),
inference(superposition,[status(thm)],[c_4329,c_53097]) ).
tcf(c_62627,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK2(X1,X0,sK18),X1)
| in(sK2(X1,X0,sK18),X0)
| ( set_union2(X1,X0) = sK18 )
| ( sK2(X1,X0,sK18) = X0 )
| ~ epsilon_connected(sK18)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4329,c_53097]) ).
tcf(c_62628,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| in(sK2(X0,sK5(iPr_def_11),sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ( sK2(X0,sK5(iPr_def_11),sK18) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(sK2(X0,sK5(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_53097]) ).
tcf(c_62630,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| in(sK2(X0,sK5(iPr_def_11),sK18),sK5(iPr_def_11))
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ( sK2(X0,sK5(iPr_def_11),sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_10,X1)
| ~ in(sK2(X0,sK5(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_53097]) ).
tcf(c_62631,plain,
! [X0: $i] :
( subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| in(sK2(X0,sK5(iPr_def_11),sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ( sK2(X0,sK5(iPr_def_11),sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK5(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_53097]) ).
tcf(c_62632,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ( sK2(X0,sK5(iPr_def_11),sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK5(iPr_def_11))
| ~ in(sK2(X0,sK5(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_7246,c_53097]) ).
tcf(c_62633,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| in(sK2(X0,sK5(iPr_def_11),sK18),sK5(iPr_def_11))
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ( sK2(X0,sK5(iPr_def_11),sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK5(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_53097]) ).
tcf(c_62634,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| in(sK2(X0,sK5(iPr_def_11),sK18),sK5(iPr_def_11))
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ( sK2(X0,sK5(iPr_def_11),sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK5(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_53097]) ).
tcf(c_62635,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| in(sK2(X0,sK5(iPr_def_11),sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ( sK2(X0,sK5(iPr_def_11),sK18) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_53097]) ).
tcf(c_62636,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| subset(sK2(X0,sK1(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK1(iPr_def_11),sK18),X0)
| in(sK2(X0,sK1(iPr_def_11),sK18),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X1 )
| ( set_union2(X0,sK1(iPr_def_11)) = sK18 )
| ( sK2(X0,sK1(iPr_def_11),sK18) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(sK2(X0,sK1(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_53097]) ).
tcf(c_62637,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| subset(sK2(X0,sK1(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK1(iPr_def_11),sK18),X0)
| in(sK2(X0,sK1(iPr_def_11),sK18),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X1 )
| ( set_union2(X0,sK1(iPr_def_11)) = sK18 )
| ( sK2(X0,sK1(iPr_def_11),sK18) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(sK2(X0,sK1(iPr_def_11),sK18),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_53097]) ).
tcf(c_62638,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| subset(sK2(X0,sK3(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK3(iPr_def_11),sK18),X0)
| in(sK2(X0,sK3(iPr_def_11),sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ( set_union2(X0,sK3(iPr_def_11)) = sK18 )
| ( sK2(X0,sK3(iPr_def_11),sK18) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(sK2(X0,sK3(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_53097]) ).
tcf(c_62639,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X1)
| subset(sK2(X0,sK3(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK3(iPr_def_11),sK18),X0)
| in(sK2(X0,sK3(iPr_def_11),sK18),sK3(iPr_def_11))
| ( set_union2(X0,sK3(iPr_def_11)) = sK18 )
| ( sK2(X0,sK3(iPr_def_11),sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_10,X1)
| ~ in(sK2(X0,sK3(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_53097]) ).
tcf(c_62640,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK2(X0,sK3(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK3(iPr_def_11),sK18),X0)
| in(sK2(X0,sK3(iPr_def_11),sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(X0,sK3(iPr_def_11)) = sK18 )
| ( sK2(X0,sK3(iPr_def_11),sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK3(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_53097]) ).
tcf(c_62641,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK3(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK3(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK3(iPr_def_11)) = sK18 )
| ( sK2(X0,sK3(iPr_def_11),sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK3(iPr_def_11))
| ~ in(sK2(X0,sK3(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_53097]) ).
tcf(c_62642,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK3(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK3(iPr_def_11),sK18),X0)
| in(sK2(X0,sK3(iPr_def_11),sK18),sK3(iPr_def_11))
| ( set_union2(X0,sK3(iPr_def_11)) = sK18 )
| ( sK2(X0,sK3(iPr_def_11),sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK3(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_53097]) ).
tcf(c_62643,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK3(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK3(iPr_def_11),sK18),X0)
| in(sK2(X0,sK3(iPr_def_11),sK18),sK3(iPr_def_11))
| ( set_union2(X0,sK3(iPr_def_11)) = sK18 )
| ( sK2(X0,sK3(iPr_def_11),sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK3(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_53097]) ).
tcf(c_62644,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| subset(sK2(X0,sK3(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK3(iPr_def_11),sK18),X0)
| in(sK2(X0,sK3(iPr_def_11),sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ( set_union2(X0,sK3(iPr_def_11)) = sK18 )
| ( sK2(X0,sK3(iPr_def_11),sK18) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(sK2(X0,sK3(iPr_def_11),sK18),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_53097]) ).
tcf(c_62645,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X1)
| subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK4(iPr_def_11),sK18),X0)
| in(sK2(X0,sK4(iPr_def_11),sK18),sK4(iPr_def_11))
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ( sK2(X0,sK4(iPr_def_11),sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_10,X1)
| ~ in(sK2(X0,sK4(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_53097]) ).
tcf(c_62646,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK4(iPr_def_11),sK18),X0)
| in(sK2(X0,sK4(iPr_def_11),sK18),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ( sK2(X0,sK4(iPr_def_11),sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK4(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_53097]) ).
tcf(c_62647,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK4(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ( sK2(X0,sK4(iPr_def_11),sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK4(iPr_def_11))
| ~ in(sK2(X0,sK4(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_11193,c_53097]) ).
tcf(c_62648,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK4(iPr_def_11),sK18),X0)
| in(sK2(X0,sK4(iPr_def_11),sK18),sK4(iPr_def_11))
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ( sK2(X0,sK4(iPr_def_11),sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK4(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_53097]) ).
tcf(c_62649,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK4(iPr_def_11),sK18),X0)
| in(sK2(X0,sK4(iPr_def_11),sK18),sK4(iPr_def_11))
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ( sK2(X0,sK4(iPr_def_11),sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK4(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_53097]) ).
tcf(c_62650,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK2(X1,X0,sK18),X1)
| in(sK2(X1,X0,sK18),X0)
| ( set_union2(X1,X0) = sK18 )
| ( sK2(X1,X0,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_62627,c_2427]) ).
tcf(c_63091,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53102,c_51593]) ).
tcf(c_63111,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK18,sK18),X0)
| in(sK2(X0,sK18,sK18),sK4(iPr_def_11))
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_63091,c_13671]) ).
tcf(c_63112,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK18,sK18),X0)
| in(sK2(X0,sK18,sK18),sK3(iPr_def_11))
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_63091,c_13665]) ).
tcf(c_63113,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK18,sK18),X0)
| in(sK2(X0,sK18,sK18),sK5(iPr_def_11))
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_63091,c_13657]) ).
tcf(c_63114,plain,
! [X0: $i,X1: $i] :
( subset(X0,iPr_def_10)
| in(sK2(X1,sK18,sK18),X1)
| ( set_union2(X1,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(X1,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_63091,c_128]) ).
tcf(c_63116,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(X0,sK18,sK18))
| in(sK2(X0,sK18,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_63091,c_49877]) ).
tcf(c_63117,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(X0,sK18,sK18))
| in(sK2(X0,sK18,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,sK18) = sK18 )
| ( sK2(X0,sK18,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_63091,c_7260]) ).
tcf(c_63118,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_63091,c_359]) ).
tcf(c_63119,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| element(sK2(X0,sK18,sK18),X1)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_63091,c_358]) ).
tcf(c_63120,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK18,sK18),iPr_def_10)
| in(X0,sK2(X1,sK18,sK18))
| in(sK2(X1,sK18,sK18),X0)
| ( set_union2(X1,sK18) = sK18 )
| ( sK2(X1,sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_63091,c_77]) ).
tcf(c_63121,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| subset(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_63091,c_65]) ).
tcf(c_63122,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X0,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_63091,c_49]) ).
tcf(c_63123,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_63091,c_137]) ).
tcf(c_63124,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| element(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_63091,c_127]) ).
tcf(c_63125,plain,
! [X0: $i] :
( subset(sK2(singleton(X0),sK18,sK18),iPr_def_10)
| ( set_union2(singleton(X0),sK18) = sK18 )
| ( sK2(singleton(X0),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_63091,c_62]) ).
tcf(c_63126,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_63091,c_66]) ).
tcf(c_63127,plain,
( subset(sK2(sK18,sK18,sK18),iPr_def_10)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_63091,c_67]) ).
tcf(c_63128,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),sK18,sK18))
| in(sK2(set_union2(X0,X1),sK18,sK18),X2)
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ( sK2(set_union2(X0,X1),sK18,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_63091,c_4213]) ).
tcf(c_63129,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),sK18,sK18))
| in(sK2(set_union2(X0,X1),sK18,sK18),X2)
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ( sK2(set_union2(X0,X1),sK18,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_63091,c_4212]) ).
tcf(c_63130,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),sK18,sK18),X1)
| in(sK2(set_union2(X0,X1),sK18,sK18),X0)
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_63091,c_71]) ).
tcf(c_63131,plain,
( subset(sK2(empty_set,sK18,sK18),iPr_def_10)
| ( set_union2(empty_set,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_63091,c_7097]) ).
tcf(c_63132,plain,
( subset(sK2(sK18,sK18,sK18),iPr_def_11)
| subset(sK2(sK18,sK18,sK18),iPr_def_10)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_63091,c_12813]) ).
tcf(c_63133,plain,
( subset(sK2(sK18,sK18,sK18),iPr_def_10)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(sK18,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_63091,c_6841]) ).
tcf(c_63136,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_63091,c_9540]) ).
tcf(c_63137,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(iPr_def_10,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_63091,c_6289]) ).
tcf(c_63139,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ( sK2(iPr_def_10,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_63091,c_3592]) ).
tcf(c_63141,plain,
( subset(sK2(iPr_def_11,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_11,sK18,sK18),sK18)
| ( set_union2(iPr_def_11,sK18) = sK18 )
| ( sK2(iPr_def_11,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_63091,c_33457]) ).
tcf(c_63142,plain,
( subset(sK2(iPr_def_11,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_11,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_11,sK18,sK18),sK18)
| ( set_union2(iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_63091,c_4035]) ).
tcf(c_63143,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK5(iPr_def_11),sK18,sK18),iPr_def_10)
| in(X0,sK2(sK5(iPr_def_11),sK18,sK18))
| in(sK2(sK5(iPr_def_11),sK18,sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),sK18) = sK18 )
| ( sK2(sK5(iPr_def_11),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_63091,c_7243]) ).
tcf(c_63144,plain,
( subset(sK2(sK5(iPr_def_11),sK18,sK18),iPr_def_10)
| ( set_union2(sK5(iPr_def_11),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),sK18,sK18)) ),
inference(superposition,[status(thm)],[c_63091,c_23189]) ).
tcf(c_63145,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK3(iPr_def_11),sK18,sK18),iPr_def_10)
| in(X0,sK2(sK3(iPr_def_11),sK18,sK18))
| in(sK2(sK3(iPr_def_11),sK18,sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),sK18) = sK18 )
| ( sK2(sK3(iPr_def_11),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_63091,c_9906]) ).
tcf(c_63146,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK4(iPr_def_11),sK18,sK18),iPr_def_10)
| in(X0,sK2(sK4(iPr_def_11),sK18,sK18))
| in(sK2(sK4(iPr_def_11),sK18,sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),sK18) = sK18 )
| ( sK2(sK4(iPr_def_11),sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_63091,c_45801]) ).
tcf(c_63155,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( sK18 = iPr_def_11 )
| ( sK2(iPr_def_10,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_63139,c_3424]) ).
tcf(c_63160,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( sK18 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(iPr_def_10,sK18,sK18)) ),
inference(light_normalisation,[status(thm)],[c_63137,c_3424]) ).
tcf(c_63178,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( sK18 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_63136,c_3424]) ).
tcf(c_63441,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),X0)
| in(sK2(X0,iPr_def_10,sK18),sK4(iPr_def_11))
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,iPr_def_10,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53114,c_13671]) ).
tcf(c_63442,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),X0)
| in(sK2(X0,iPr_def_10,sK18),sK3(iPr_def_11))
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,iPr_def_10,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53114,c_13665]) ).
tcf(c_63443,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),X0)
| in(sK2(X0,iPr_def_10,sK18),sK5(iPr_def_11))
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,iPr_def_10,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53114,c_13657]) ).
tcf(c_63444,plain,
! [X0: $i,X1: $i] :
( subset(X0,iPr_def_10)
| in(sK2(X1,iPr_def_10,sK18),X1)
| ( set_union2(X1,iPr_def_10) = sK18 )
| ( sK2(X1,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(X1,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53114,c_128]) ).
tcf(c_63445,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| in(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53114,c_3868]) ).
tcf(c_63446,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(X0,iPr_def_10,sK18))
| in(sK2(X0,iPr_def_10,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53114,c_49877]) ).
tcf(c_63447,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(X0,iPr_def_10,sK18))
| in(sK2(X0,iPr_def_10,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53114,c_7260]) ).
tcf(c_63448,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53114,c_359]) ).
tcf(c_63449,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| element(sK2(X0,iPr_def_10,sK18),X1)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53114,c_358]) ).
tcf(c_63450,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,iPr_def_10,sK18),iPr_def_10)
| in(X0,sK2(X1,iPr_def_10,sK18))
| in(sK2(X1,iPr_def_10,sK18),X0)
| ( set_union2(X1,iPr_def_10) = sK18 )
| ( sK2(X1,iPr_def_10,sK18) = sK18 )
| ( sK2(X1,iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53114,c_77]) ).
tcf(c_63451,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| subset(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53114,c_65]) ).
tcf(c_63452,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X0,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53114,c_49]) ).
tcf(c_63455,plain,
! [X0: $i] :
( subset(sK2(singleton(X0),iPr_def_10,sK18),iPr_def_10)
| ( set_union2(singleton(X0),iPr_def_10) = sK18 )
| ( sK2(singleton(X0),iPr_def_10,sK18) = sK18 )
| ( sK2(singleton(X0),iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53114,c_62]) ).
tcf(c_63456,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,iPr_def_10,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53114,c_66]) ).
tcf(c_63457,plain,
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ( sK2(sK18,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,iPr_def_10,sK18),iPr_def_10) ),
inference(superposition,[status(thm)],[c_53114,c_67]) ).
tcf(c_63458,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),iPr_def_10,sK18))
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),X2)
| ( set_union2(set_union2(X0,X1),iPr_def_10) = sK18 )
| ( sK2(set_union2(X0,X1),iPr_def_10,sK18) = sK18 )
| ( sK2(set_union2(X0,X1),iPr_def_10,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53114,c_4213]) ).
tcf(c_63459,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),iPr_def_10,sK18))
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),X2)
| ( set_union2(set_union2(X0,X1),iPr_def_10) = sK18 )
| ( sK2(set_union2(X0,X1),iPr_def_10,sK18) = sK18 )
| ( sK2(set_union2(X0,X1),iPr_def_10,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53114,c_4212]) ).
tcf(c_63460,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),iPr_def_10,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),X1)
| in(sK2(set_union2(X0,X1),iPr_def_10,sK18),X0)
| ( set_union2(set_union2(X0,X1),iPr_def_10) = sK18 )
| ( sK2(set_union2(X0,X1),iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53114,c_71]) ).
tcf(c_63461,plain,
( subset(sK2(empty_set,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(empty_set,iPr_def_10) = sK18 )
| ( sK2(empty_set,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53114,c_7097]) ).
tcf(c_63462,plain,
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ( sK2(sK18,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53114,c_12813]) ).
tcf(c_63463,plain,
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ( sK2(sK18,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(sK18,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53114,c_6841]) ).
tcf(c_63466,plain,
( subset(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,iPr_def_10) = sK18 )
| ( sK2(iPr_def_10,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53114,c_9540]) ).
tcf(c_63469,plain,
( subset(sK2(iPr_def_10,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,iPr_def_10) = sK18 )
| ( sK2(iPr_def_10,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53114,c_3592]) ).
tcf(c_63471,plain,
( subset(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_11,iPr_def_10,sK18),sK18)
| ( set_union2(iPr_def_11,iPr_def_10) = sK18 )
| ( sK2(iPr_def_11,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53114,c_33457]) ).
tcf(c_63472,plain,
( subset(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_11,iPr_def_10,sK18),sK18)
| ( set_union2(iPr_def_11,iPr_def_10) = sK18 )
| ( sK2(iPr_def_11,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53114,c_4035]) ).
tcf(c_63473,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK5(iPr_def_11),iPr_def_10,sK18),iPr_def_10)
| in(X0,sK2(sK5(iPr_def_11),iPr_def_10,sK18))
| in(sK2(sK5(iPr_def_11),iPr_def_10,sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),iPr_def_10) = sK18 )
| ( sK2(sK5(iPr_def_11),iPr_def_10,sK18) = sK18 )
| ( sK2(sK5(iPr_def_11),iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53114,c_7243]) ).
tcf(c_63474,plain,
( subset(sK2(sK5(iPr_def_11),iPr_def_10,sK18),iPr_def_10)
| ( set_union2(sK5(iPr_def_11),iPr_def_10) = sK18 )
| ( sK2(sK5(iPr_def_11),iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53114,c_23189]) ).
tcf(c_63475,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK3(iPr_def_11),iPr_def_10,sK18),iPr_def_10)
| in(X0,sK2(sK3(iPr_def_11),iPr_def_10,sK18))
| in(sK2(sK3(iPr_def_11),iPr_def_10,sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),iPr_def_10) = sK18 )
| ( sK2(sK3(iPr_def_11),iPr_def_10,sK18) = sK18 )
| ( sK2(sK3(iPr_def_11),iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53114,c_9906]) ).
tcf(c_63476,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK4(iPr_def_11),iPr_def_10,sK18),iPr_def_10)
| in(X0,sK2(sK4(iPr_def_11),iPr_def_10,sK18))
| in(sK2(sK4(iPr_def_11),iPr_def_10,sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),iPr_def_10) = sK18 )
| ( sK2(sK4(iPr_def_11),iPr_def_10,sK18) = sK18 )
| ( sK2(sK4(iPr_def_11),iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53114,c_45801]) ).
tcf(c_63515,plain,
( subset(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(iPr_def_11,iPr_def_10) = sK18 )
| ( sK2(iPr_def_11,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(backward_subsumption_resolution,[status(thm)],[c_63471,c_63456]) ).
tcf(c_63725,plain,
! [X0: $i] :
( element(X0,iPr_def_11)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_40994,c_41256]) ).
tcf(c_63759,plain,
( element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_41868,c_63725]) ).
tcf(c_63902,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X2,sK18),iPr_def_10)
| in(sK2(X0,X2,sK18),X2)
| ( set_union2(X0,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_138,c_53126]) ).
tcf(c_63903,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK5(powerset(X0)),X1,sK18),iPr_def_10)
| in(sK2(sK5(powerset(X0)),X1,sK18),X1)
| ( set_union2(sK5(powerset(X0)),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3564,c_53126]) ).
tcf(c_63904,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X2,sK18),iPr_def_10)
| in(sK2(X1,X2,sK18),X2)
| ( set_union2(X1,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3397,c_53126]) ).
tcf(c_63905,plain,
! [X0: $i,X1: $i] :
( subset(sK2(empty_set,X1,sK18),iPr_def_10)
| in(sK2(empty_set,X1,sK18),X1)
| ( set_union2(empty_set,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3420,c_53126]) ).
tcf(c_63908,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(powerset(X0))
| subset(sK2(sK1(powerset(X0)),X1,sK18),iPr_def_10)
| in(sK2(sK1(powerset(X0)),X1,sK18),X1)
| ( set_union2(sK1(powerset(X0)),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3566,c_53126]) ).
tcf(c_63909,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(X0))
| subset(sK2(sK3(powerset(X0)),X1,sK18),iPr_def_10)
| in(sK2(sK3(powerset(X0)),X1,sK18),X1)
| ( set_union2(sK3(powerset(X0)),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3567,c_53126]) ).
tcf(c_63910,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(X0))
| subset(sK2(sK4(powerset(X0)),X1,sK18),iPr_def_10)
| in(sK2(sK4(powerset(X0)),X1,sK18),X1)
| ( set_union2(sK4(powerset(X0)),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3568,c_53126]) ).
tcf(c_63912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X3,sK18),iPr_def_10)
| in(sK2(X2,X3,sK18),X3)
| ( set_union2(X2,X3) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X2,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3863,c_53126]) ).
tcf(c_63913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X3,sK18),iPr_def_10)
| in(sK2(X2,X3,sK18),X3)
| ( set_union2(X2,X3) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3806,c_53126]) ).
tcf(c_63914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X3,sK18),iPr_def_10)
| in(sK2(X2,X3,sK18),X3)
| ( set_union2(X2,X3) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3805,c_53126]) ).
tcf(c_63915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X3,sK18),iPr_def_10)
| in(sK2(X2,X3,sK18),X3)
| ( set_union2(X2,X3) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X2,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_3865,c_53126]) ).
tcf(c_63916,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| subset(sK2(sK3(X0),X1,sK18),iPr_def_10)
| in(sK2(sK3(X0),X1,sK18),X1)
| ( set_union2(sK3(X0),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3807,c_53126]) ).
tcf(c_63917,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| subset(sK2(sK4(X0),X1,sK18),iPr_def_10)
| in(sK2(sK4(X0),X1,sK18),X1)
| ( set_union2(sK4(X0),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3808,c_53126]) ).
tcf(c_63928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| subset(sK2(sK2(X1,X2,X0),X3,sK18),iPr_def_10)
| in(sK2(sK2(X1,X2,X0),X3,sK18),X3)
| ( set_union2(X1,X2) = X0 )
| ( set_union2(sK2(X1,X2,X0),X3) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4330,c_53126]) ).
tcf(c_63931,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(empty_set))
| subset(sK2(sK3(powerset(empty_set)),X1,sK18),iPr_def_10)
| in(sK2(sK3(powerset(empty_set)),X1,sK18),X1)
| ( set_union2(sK3(powerset(empty_set)),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4620,c_53126]) ).
tcf(c_63934,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(empty_set))
| subset(sK2(sK4(powerset(empty_set)),X1,sK18),iPr_def_10)
| in(sK2(sK4(powerset(empty_set)),X1,sK18),X1)
| ( set_union2(sK4(powerset(empty_set)),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4637,c_53126]) ).
tcf(c_63937,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK5(powerset(sK5(powerset(X0)))),X1,sK18),iPr_def_10)
| in(sK2(sK5(powerset(sK5(powerset(X0)))),X1,sK18),X1)
| ( set_union2(sK5(powerset(sK5(powerset(X0)))),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5196,c_53126]) ).
tcf(c_63939,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),X1,sK18),iPr_def_10)
| in(sK2(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),X1,sK18),X1)
| ( set_union2(sK5(powerset(sK5(powerset(sK5(powerset(X0)))))),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5252,c_53126]) ).
tcf(c_63957,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_7152,c_53126]) ).
tcf(c_63959,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ empty(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_53126]) ).
tcf(c_63964,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(sK5(iPr_def_11),X1,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),X1,sK18),X1)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7261,c_53126]) ).
tcf(c_63965,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(sK5(powerset(sK5(iPr_def_11))),X0,sK18),iPr_def_10)
| in(sK2(sK5(powerset(sK5(iPr_def_11))),X0,sK18),X0)
| ( set_union2(sK5(powerset(sK5(iPr_def_11))),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_7587,c_53126]) ).
tcf(c_63966,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(sK3(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK3(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK3(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_9591,c_53126]) ).
tcf(c_63968,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ empty(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9907,c_53126]) ).
tcf(c_63971,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(sK3(iPr_def_11),X1,sK18),iPr_def_10)
| in(sK2(sK3(iPr_def_11),X1,sK18),X1)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_9925,c_53126]) ).
tcf(c_63972,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK4(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_11031,c_53126]) ).
tcf(c_63974,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11191,c_53126]) ).
tcf(c_63977,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| subset(sK2(sK4(iPr_def_11),X1,sK18),iPr_def_10)
| in(sK2(sK4(iPr_def_11),X1,sK18),X1)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_11209,c_53126]) ).
tcf(c_63986,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(singleton(iPr_def_10))
| ~ empty(singleton(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_15774,c_53126]) ).
tcf(c_64249,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,powerset(X2)),X2)
| in(sK2(X0,X1,powerset(X2)),X1)
| in(sK2(X0,X1,powerset(X2)),X0)
| ( set_union2(X0,X1) = powerset(X2) ) ),
inference(superposition,[status(thm)],[c_4333,c_133]) ).
tcf(c_64250,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| element(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| in(sK3(iPr_def_11),sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4333,c_49877]) ).
tcf(c_64251,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| element(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| in(sK5(iPr_def_11),sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4333,c_7260]) ).
tcf(c_64252,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X0,X3),X3)
| in(sK2(X2,X0,X3),X2)
| ( set_union2(X2,X0) = X3 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4333,c_359]) ).
tcf(c_64253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X0,X3),X3)
| element(sK2(X2,X0,X3),X1)
| in(sK2(X2,X0,X3),X2)
| ( set_union2(X2,X0) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4333,c_358]) ).
tcf(c_64254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X1,X3),X3)
| in(X0,sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),X2)
| in(sK2(X2,X1,X3),X0)
| ( set_union2(X2,X1) = X3 )
| ( sK2(X2,X1,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4333,c_77]) ).
tcf(c_64255,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X0,X2),X2)
| subset(sK2(X1,X0,X2),X0)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4333,c_65]) ).
tcf(c_64256,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ~ in(X0,sK2(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_4333,c_49]) ).
tcf(c_64257,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4333,c_137]) ).
tcf(c_64258,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| element(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_4333,c_127]) ).
tcf(c_64259,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,singleton(X1),X2),X2)
| in(sK2(X0,singleton(X1),X2),X0)
| ( set_union2(X0,singleton(X1)) = X2 )
| ( sK2(X0,singleton(X1),X2) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_62]) ).
tcf(c_64260,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X0,X1),X1)
| in(sK2(X0,X0,X1),X0)
| ( set_union2(X0,X0) = X1 )
| ~ in(sK2(X0,X0,X1),X1) ),
inference(superposition,[status(thm)],[c_4333,c_66]) ).
tcf(c_64261,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,X1),X1)
| in(sK2(X0,X1,X1),X0)
| ( set_union2(X0,X1) = X1 )
| ~ in(sK2(X0,X1,X1),X1) ),
inference(superposition,[status(thm)],[c_4333,c_67]) ).
tcf(c_64262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,set_union2(X0,X1),X4),X4)
| in(X2,sK2(X3,set_union2(X0,X1),X4))
| in(sK2(X3,set_union2(X0,X1),X4),X3)
| in(sK2(X3,set_union2(X0,X1),X4),X2)
| ( set_union2(X3,set_union2(X0,X1)) = X4 )
| ( sK2(X3,set_union2(X0,X1),X4) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4333,c_4213]) ).
tcf(c_64263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,set_union2(X0,X1),X4),X4)
| in(X2,sK2(X3,set_union2(X0,X1),X4))
| in(sK2(X3,set_union2(X0,X1),X4),X3)
| in(sK2(X3,set_union2(X0,X1),X4),X2)
| ( set_union2(X3,set_union2(X0,X1)) = X4 )
| ( sK2(X3,set_union2(X0,X1),X4) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4333,c_4212]) ).
tcf(c_64264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,set_union2(X1,X2),X3),X3)
| in(sK2(X0,set_union2(X1,X2),X3),X2)
| in(sK2(X0,set_union2(X1,X2),X3),X1)
| in(sK2(X0,set_union2(X1,X2),X3),X0)
| ( set_union2(X0,set_union2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_4333,c_71]) ).
tcf(c_64265,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,empty_set,X1),X1)
| in(sK2(X0,empty_set,X1),X0)
| ( set_union2(X0,empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_7097]) ).
tcf(c_64266,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,X1),iPr_def_11)
| element(sK2(X0,sK18,X1),X1)
| in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_12813]) ).
tcf(c_64267,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK18,X1),X1)
| in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 )
| ~ in(iPr_def_11,sK2(X0,sK18,X1)) ),
inference(superposition,[status(thm)],[c_4333,c_6841]) ).
tcf(c_64268,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK18,X1),iPr_def_11)
| element(sK2(X0,sK18,X1),X1)
| in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_5047]) ).
tcf(c_64269,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK18,X1),iPr_def_11)
| element(sK2(X0,sK18,X1),X1)
| in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_3640]) ).
tcf(c_64270,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_10,X1),iPr_def_11)
| element(sK2(X0,iPr_def_10,X1),X1)
| in(sK2(X0,iPr_def_10,X1),X0)
| ( set_union2(X0,iPr_def_10) = X1 )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4333,c_9540]) ).
tcf(c_64271,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,iPr_def_10,X1),X1)
| in(sK2(X0,iPr_def_10,X1),X0)
| ( set_union2(X0,iPr_def_10) = X1 )
| ~ in(iPr_def_11,sK2(X0,iPr_def_10,X1)) ),
inference(superposition,[status(thm)],[c_4333,c_6289]) ).
tcf(c_64272,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,iPr_def_10,X1),iPr_def_11)
| element(sK2(X0,iPr_def_10,X1),X1)
| in(sK2(X0,iPr_def_10,X1),X0)
| ( set_union2(X0,iPr_def_10) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_4912]) ).
tcf(c_64273,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,iPr_def_10,X1),X1)
| in(sK2(X0,iPr_def_10,X1),X0)
| ( set_union2(X0,iPr_def_10) = X1 )
| ( sK2(X0,iPr_def_10,X1) = sK18 ) ),
inference(superposition,[status(thm)],[c_4333,c_3592]) ).
tcf(c_64274,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_10,X1),iPr_def_11)
| element(sK2(X0,iPr_def_10,X1),X1)
| in(sK2(X0,iPr_def_10,X1),X0)
| ( set_union2(X0,iPr_def_10) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_3614]) ).
tcf(c_64275,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_11,X1),sK18)
| element(sK2(X0,iPr_def_11,X1),X1)
| in(sK2(X0,iPr_def_11,X1),X0)
| ( set_union2(X0,iPr_def_11) = X1 )
| ( sK2(X0,iPr_def_11,X1) = sK18 ) ),
inference(superposition,[status(thm)],[c_4333,c_33457]) ).
tcf(c_64276,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_11,X1),iPr_def_10)
| in(sK2(X0,iPr_def_11,X1),sK18)
| element(sK2(X0,iPr_def_11,X1),X1)
| in(sK2(X0,iPr_def_11,X1),X0)
| ( set_union2(X0,iPr_def_11) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_4035]) ).
tcf(c_64277,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_union2(X0,X1),X0,X2),X2)
| in(sK2(set_union2(X0,X1),X0,X2),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X0) = X2 )
| ~ in(sK2(set_union2(X0,X1),X0,X2),X2) ),
inference(superposition,[status(thm)],[c_4333,c_4078]) ).
tcf(c_64278,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_union2(X0,X1),X2,X2),X2)
| in(sK2(set_union2(X0,X1),X2,X2),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = X2 )
| ~ in(sK2(set_union2(X0,X1),X2,X2),X1) ),
inference(superposition,[status(thm)],[c_4333,c_4079]) ).
tcf(c_64279,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X1,X2)),X0)
| element(sK2(X0,X1,set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X0,X1) = set_union2(X1,X2) )
| ~ in(sK2(X0,X1,set_union2(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_4333,c_4095]) ).
tcf(c_64280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_union2(X2,X3)),X0)
| element(sK2(X0,X1,set_union2(X2,X3)),set_union2(X2,X3))
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ~ in(sK2(X0,X1,set_union2(X2,X3)),X3) ),
inference(superposition,[status(thm)],[c_4333,c_4096]) ).
tcf(c_64281,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| element(sK2(X1,sK5(iPr_def_11),X2),X2)
| in(X0,sK2(X1,sK5(iPr_def_11),X2))
| in(sK2(X1,sK5(iPr_def_11),X2),X1)
| in(sK2(X1,sK5(iPr_def_11),X2),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,sK5(iPr_def_11)) = X2 )
| ( sK2(X1,sK5(iPr_def_11),X2) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4333,c_7243]) ).
tcf(c_64282,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ~ subset(iPr_def_11,sK2(X0,sK5(iPr_def_11),X1)) ),
inference(superposition,[status(thm)],[c_4333,c_23189]) ).
tcf(c_64283,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| element(sK2(X1,sK3(iPr_def_11),X2),X2)
| in(X0,sK2(X1,sK3(iPr_def_11),X2))
| in(sK2(X1,sK3(iPr_def_11),X2),X1)
| in(sK2(X1,sK3(iPr_def_11),X2),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,sK3(iPr_def_11)) = X2 )
| ( sK2(X1,sK3(iPr_def_11),X2) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4333,c_9906]) ).
tcf(c_64284,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| element(sK2(X1,sK4(iPr_def_11),X2),X2)
| in(X0,sK2(X1,sK4(iPr_def_11),X2))
| in(sK2(X1,sK4(iPr_def_11),X2),X1)
| in(sK2(X1,sK4(iPr_def_11),X2),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,sK4(iPr_def_11)) = X2 )
| ( sK2(X1,sK4(iPr_def_11),X2) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4333,c_45801]) ).
tcf(c_64285,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| element(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK3(iPr_def_11),sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4333,c_49877]) ).
tcf(c_64286,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| element(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| in(sK5(iPr_def_11),sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4333,c_7260]) ).
tcf(c_64287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X2,X3),X3)
| in(sK2(X0,X2,X3),X2)
| ( set_union2(X0,X2) = X3 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4333,c_359]) ).
tcf(c_64288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X2,X3),X3)
| element(sK2(X0,X2,X3),X1)
| in(sK2(X0,X2,X3),X2)
| ( set_union2(X0,X2) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4333,c_358]) ).
tcf(c_64289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X1,X2,X3),X3)
| in(X0,sK2(X1,X2,X3))
| in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X0)
| ( set_union2(X1,X2) = X3 )
| ( sK2(X1,X2,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4333,c_77]) ).
tcf(c_64290,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| subset(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4333,c_65]) ).
tcf(c_64291,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 )
| ~ in(X0,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4333,c_49]) ).
tcf(c_64292,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4333,c_137]) ).
tcf(c_64293,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| element(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_4333,c_127]) ).
tcf(c_64294,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(singleton(X0),X1,X2),X2)
| in(sK2(singleton(X0),X1,X2),X1)
| ( set_union2(singleton(X0),X1) = X2 )
| ( sK2(singleton(X0),X1,X2) = X0 ) ),
inference(superposition,[status(thm)],[c_4333,c_62]) ).
tcf(c_64295,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_union2(X0,X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2) ),
inference(superposition,[status(thm)],[c_4333,c_66]) ).
tcf(c_64297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_union2(X0,X1),X3,X4),X4)
| in(X2,sK2(set_union2(X0,X1),X3,X4))
| in(sK2(set_union2(X0,X1),X3,X4),X3)
| in(sK2(set_union2(X0,X1),X3,X4),X2)
| ( set_union2(set_union2(X0,X1),X3) = X4 )
| ( sK2(set_union2(X0,X1),X3,X4) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4333,c_4213]) ).
tcf(c_64298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_union2(X0,X1),X3,X4),X4)
| in(X2,sK2(set_union2(X0,X1),X3,X4))
| in(sK2(set_union2(X0,X1),X3,X4),X3)
| in(sK2(set_union2(X0,X1),X3,X4),X2)
| ( set_union2(set_union2(X0,X1),X3) = X4 )
| ( sK2(set_union2(X0,X1),X3,X4) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4333,c_4212]) ).
tcf(c_64299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_union2(X0,X1),X2,X3),X3)
| in(sK2(set_union2(X0,X1),X2,X3),X2)
| in(sK2(set_union2(X0,X1),X2,X3),X1)
| in(sK2(set_union2(X0,X1),X2,X3),X0)
| ( set_union2(set_union2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_4333,c_71]) ).
tcf(c_64300,plain,
! [X0: $i,X1: $i] :
( element(sK2(empty_set,X0,X1),X1)
| in(sK2(empty_set,X0,X1),X0)
| ( set_union2(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_7097]) ).
tcf(c_64301,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,X1),iPr_def_11)
| element(sK2(sK18,X0,X1),X1)
| in(sK2(sK18,X0,X1),X0)
| ( set_union2(sK18,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_12813]) ).
tcf(c_64302,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK18,X0,X1),X1)
| in(sK2(sK18,X0,X1),X0)
| ( set_union2(sK18,X0) = X1 )
| ~ in(iPr_def_11,sK2(sK18,X0,X1)) ),
inference(superposition,[status(thm)],[c_4333,c_6841]) ).
tcf(c_64303,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK18,X0,X1),iPr_def_11)
| element(sK2(sK18,X0,X1),X1)
| in(sK2(sK18,X0,X1),X0)
| ( set_union2(sK18,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_5047]) ).
tcf(c_64304,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK18,X0,X1),iPr_def_11)
| element(sK2(sK18,X0,X1),X1)
| in(sK2(sK18,X0,X1),X0)
| ( set_union2(sK18,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_3640]) ).
tcf(c_64305,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X0,X1),iPr_def_11)
| element(sK2(iPr_def_10,X0,X1),X1)
| in(sK2(iPr_def_10,X0,X1),X0)
| ( set_union2(iPr_def_10,X0) = X1 )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4333,c_9540]) ).
tcf(c_64306,plain,
! [X0: $i,X1: $i] :
( element(sK2(iPr_def_10,X0,X1),X1)
| in(sK2(iPr_def_10,X0,X1),X0)
| ( set_union2(iPr_def_10,X0) = X1 )
| ~ in(iPr_def_11,sK2(iPr_def_10,X0,X1)) ),
inference(superposition,[status(thm)],[c_4333,c_6289]) ).
tcf(c_64307,plain,
! [X0: $i,X1: $i] :
( element(sK2(iPr_def_10,X0,X1),iPr_def_11)
| element(sK2(iPr_def_10,X0,X1),X1)
| in(sK2(iPr_def_10,X0,X1),X0)
| ( set_union2(iPr_def_10,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_4912]) ).
tcf(c_64308,plain,
! [X0: $i,X1: $i] :
( element(sK2(iPr_def_10,X0,X1),X1)
| in(sK2(iPr_def_10,X0,X1),X0)
| ( set_union2(iPr_def_10,X0) = X1 )
| ( sK2(iPr_def_10,X0,X1) = sK18 ) ),
inference(superposition,[status(thm)],[c_4333,c_3592]) ).
tcf(c_64309,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_10,X0,X1),iPr_def_11)
| element(sK2(iPr_def_10,X0,X1),X1)
| in(sK2(iPr_def_10,X0,X1),X0)
| ( set_union2(iPr_def_10,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_3614]) ).
tcf(c_64310,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_11,X0,X1),sK18)
| element(sK2(iPr_def_11,X0,X1),X1)
| in(sK2(iPr_def_11,X0,X1),X0)
| ( set_union2(iPr_def_11,X0) = X1 )
| ( sK2(iPr_def_11,X0,X1) = sK18 ) ),
inference(superposition,[status(thm)],[c_4333,c_33457]) ).
tcf(c_64311,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_11,X0,X1),iPr_def_10)
| in(sK2(iPr_def_11,X0,X1),sK18)
| element(sK2(iPr_def_11,X0,X1),X1)
| in(sK2(iPr_def_11,X0,X1),X0)
| ( set_union2(iPr_def_11,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_4333,c_4035]) ).
tcf(c_64312,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X2)
| element(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = set_union2(X0,X1) )
| ~ in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_4333,c_4079]) ).
tcf(c_64314,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_union2(X1,X2)),X0)
| element(sK2(X0,X0,set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X0,X0) = set_union2(X1,X2) )
| ~ in(sK2(X0,X0,set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4333,c_4096]) ).
tcf(c_64315,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| element(sK2(sK5(iPr_def_11),X1,X2),X2)
| in(X0,sK2(sK5(iPr_def_11),X1,X2))
| in(sK2(sK5(iPr_def_11),X1,X2),X1)
| in(sK2(sK5(iPr_def_11),X1,X2),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X1) = X2 )
| ( sK2(sK5(iPr_def_11),X1,X2) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4333,c_7243]) ).
tcf(c_64316,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK5(iPr_def_11),X0,X1),X1)
| in(sK2(sK5(iPr_def_11),X0,X1),X0)
| ( set_union2(sK5(iPr_def_11),X0) = X1 )
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,X1)) ),
inference(superposition,[status(thm)],[c_4333,c_23189]) ).
tcf(c_64317,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| element(sK2(sK3(iPr_def_11),X1,X2),X2)
| in(X0,sK2(sK3(iPr_def_11),X1,X2))
| in(sK2(sK3(iPr_def_11),X1,X2),X1)
| in(sK2(sK3(iPr_def_11),X1,X2),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X1) = X2 )
| ( sK2(sK3(iPr_def_11),X1,X2) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4333,c_9906]) ).
tcf(c_64318,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| element(sK2(sK4(iPr_def_11),X1,X2),X2)
| in(X0,sK2(sK4(iPr_def_11),X1,X2))
| in(sK2(sK4(iPr_def_11),X1,X2),X1)
| in(sK2(sK4(iPr_def_11),X1,X2),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X1) = X2 )
| ( sK2(sK4(iPr_def_11),X1,X2) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4333,c_45801]) ).
tcf(c_64319,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X0,X1),X1)
| in(sK2(X0,X0,X1),X0)
| ( set_union2(X0,X0) = X1 ) ),
inference(equality_factoring,[status(thm)],[c_4333]) ).
tcf(c_64321,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X0,X1),X1)
| in(sK2(X0,X0,X1),X0)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_64319,c_97]) ).
tcf(c_64325,plain,
! [X0: $i,X1: $i] :
( element(sK2(empty_set,X0,X1),X1)
| in(sK2(empty_set,X0,X1),X0)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_64300,c_3423]) ).
tcf(c_64329,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,empty_set,X1),X1)
| in(sK2(X0,empty_set,X1),X0)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_64265,c_126]) ).
tcf(c_64510,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_union2(X1,X2)),X0)
| element(sK2(X0,X0,set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X1,X2) = X0 )
| ~ in(sK2(X0,X0,set_union2(X1,X2)),X2) ),
inference(light_normalisation,[status(thm)],[c_64314,c_97]) ).
tcf(c_64814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,set_union2(X3,X4))))),X3),
inference(superposition,[status(thm)],[c_69,c_5598]) ).
tcf(c_64815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,set_union2(X3,X4))))),X4),
inference(superposition,[status(thm)],[c_70,c_5598]) ).
tcf(c_64816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(powerset(X3))
| ~ subset(singleton(set_union2(X0,set_union2(X1,set_union2(X2,powerset(X3))))),X3) ),
inference(superposition,[status(thm)],[c_3769,c_5598]) ).
tcf(c_64817,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK18)
| in(sK5(sK18),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(sK18))))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(sK18))))) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(sK18))))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_5598]) ).
tcf(c_64818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,X4,X5),X4)
| in(sK2(X3,X4,X5),X3)
| in(sK2(X3,X4,X5),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK2(X3,X4,X5))))))
| ( set_union2(X3,X4) = X5 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK2(X3,X4,X5))))) = sK2(X3,X4,X5) )
| ~ epsilon_connected(X5)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK2(X3,X4,X5))))),X5) ),
inference(superposition,[status(thm)],[c_4329,c_5598]) ).
tcf(c_64819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_5598]) ).
tcf(c_64820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_5598]) ).
tcf(c_64821,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))))
| ( sK5(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_5598]) ).
tcf(c_64822,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_5598]) ).
tcf(c_64823,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))) = sK5(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))))
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_5598]) ).
tcf(c_64824,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_5598]) ).
tcf(c_64825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK5(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))))
| ( sK5(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_5598]) ).
tcf(c_64826,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))) = sK5(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK5(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_7265,c_5598]) ).
tcf(c_64827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK1(iPr_def_11))))))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK1(iPr_def_11))))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK1(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_5598]) ).
tcf(c_64828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(iPr_def_11)
| in(X3,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X3)
| in(sK1(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK1(iPr_def_11))))))
| ( sK1(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK1(iPr_def_11))))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK1(iPr_def_11))))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_5598]) ).
tcf(c_64829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_5598]) ).
tcf(c_64830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_5598]) ).
tcf(c_64831,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))))
| ( sK3(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_5598]) ).
tcf(c_64832,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_5598]) ).
tcf(c_64833,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))) = sK3(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))))
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_5598]) ).
tcf(c_64834,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_5598]) ).
tcf(c_64835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK3(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))))
| ( sK3(iPr_def_11) = X3 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_5598]) ).
tcf(c_64836,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))) = sK3(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK3(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_9929,c_5598]) ).
tcf(c_64837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X3)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X3)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_5598]) ).
tcf(c_64838,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))))
| ( sK4(iPr_def_11) = sK18 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_5598]) ).
tcf(c_64839,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_5598]) ).
tcf(c_64840,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))) = sK4(iPr_def_11) )
| ~ empty(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))))
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_5598]) ).
tcf(c_64841,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_5598]) ).
tcf(c_64842,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_11213,c_5598]) ).
tcf(c_65237,plain,
( subset(sK5(powerset(sK5(iPr_def_11))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3564,c_7570]) ).
tcf(c_65239,plain,
( epsilon_transitive(powerset(sK5(iPr_def_11)))
| subset(sK1(powerset(sK5(iPr_def_11))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3566,c_7570]) ).
tcf(c_65240,plain,
( epsilon_connected(powerset(sK5(iPr_def_11)))
| subset(sK3(powerset(sK5(iPr_def_11))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3567,c_7570]) ).
tcf(c_65241,plain,
( epsilon_connected(powerset(sK5(iPr_def_11)))
| subset(sK4(powerset(sK5(iPr_def_11))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3568,c_7570]) ).
tcf(c_65242,plain,
( epsilon_connected(sK5(iPr_def_11))
| subset(sK3(sK5(iPr_def_11)),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3807,c_7570]) ).
tcf(c_65243,plain,
( epsilon_connected(sK5(iPr_def_11))
| subset(sK4(sK5(iPr_def_11)),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3808,c_7570]) ).
tcf(c_65244,plain,
( empty(sK5(iPr_def_11))
| subset(sK5(sK5(iPr_def_11)),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3899,c_7570]) ).
tcf(c_65245,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK5(iPr_def_11)),iPr_def_10)
| in(sK2(X0,X1,sK5(iPr_def_11)),X1)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4330,c_7570]) ).
tcf(c_65248,plain,
( subset(sK5(powerset(sK5(powerset(sK5(iPr_def_11))))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5196,c_7570]) ).
tcf(c_65249,plain,
( subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(iPr_def_11))))))),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5252,c_7570]) ).
tcf(c_65250,plain,
! [X0: $i] :
( subset(X0,iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_7570]) ).
tcf(c_65252,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_7570]) ).
tcf(c_65253,plain,
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_7570]) ).
tcf(c_65335,plain,
( subset(sK5(powerset(sK5(iPr_def_11))),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3564,c_7902]) ).
tcf(c_65336,plain,
( subset(empty_set,iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3420,c_7902]) ).
tcf(c_65337,plain,
( epsilon_transitive(powerset(sK5(iPr_def_11)))
| subset(sK1(powerset(sK5(iPr_def_11))),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3566,c_7902]) ).
tcf(c_65338,plain,
( epsilon_connected(powerset(sK5(iPr_def_11)))
| subset(sK3(powerset(sK5(iPr_def_11))),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3567,c_7902]) ).
tcf(c_65339,plain,
( epsilon_connected(powerset(sK5(iPr_def_11)))
| subset(sK4(powerset(sK5(iPr_def_11))),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3568,c_7902]) ).
tcf(c_65340,plain,
( epsilon_connected(sK5(iPr_def_11))
| subset(sK3(sK5(iPr_def_11)),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3807,c_7902]) ).
tcf(c_65341,plain,
( epsilon_connected(sK5(iPr_def_11))
| subset(sK4(sK5(iPr_def_11)),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3808,c_7902]) ).
tcf(c_65342,plain,
( empty(sK5(iPr_def_11))
| subset(sK5(sK5(iPr_def_11)),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3899,c_7902]) ).
tcf(c_65343,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK5(iPr_def_11)),iPr_def_11)
| in(sK2(X0,X1,sK5(iPr_def_11)),X1)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4330,c_7902]) ).
tcf(c_65344,plain,
( epsilon_connected(powerset(empty_set))
| subset(sK3(powerset(empty_set)),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4620,c_7902]) ).
tcf(c_65345,plain,
( epsilon_connected(powerset(empty_set))
| subset(sK4(powerset(empty_set)),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4637,c_7902]) ).
tcf(c_65346,plain,
( subset(sK5(powerset(sK5(powerset(sK5(iPr_def_11))))),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5196,c_7902]) ).
tcf(c_65347,plain,
( subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(iPr_def_11))))))),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5252,c_7902]) ).
tcf(c_65348,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_7902]) ).
tcf(c_65425,plain,
( subset(sK5(powerset(sK5(iPr_def_11))),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3564,c_8544]) ).
tcf(c_65426,plain,
( subset(empty_set,iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3420,c_8544]) ).
tcf(c_65427,plain,
( epsilon_transitive(powerset(sK5(iPr_def_11)))
| subset(sK1(powerset(sK5(iPr_def_11))),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3566,c_8544]) ).
tcf(c_65428,plain,
( epsilon_connected(powerset(sK5(iPr_def_11)))
| subset(sK3(powerset(sK5(iPr_def_11))),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3567,c_8544]) ).
tcf(c_65429,plain,
( epsilon_connected(powerset(sK5(iPr_def_11)))
| subset(sK4(powerset(sK5(iPr_def_11))),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3568,c_8544]) ).
tcf(c_65430,plain,
( epsilon_connected(sK5(iPr_def_11))
| subset(sK3(sK5(iPr_def_11)),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3807,c_8544]) ).
tcf(c_65431,plain,
( epsilon_connected(sK5(iPr_def_11))
| subset(sK4(sK5(iPr_def_11)),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3808,c_8544]) ).
tcf(c_65432,plain,
( empty(sK5(iPr_def_11))
| subset(sK5(sK5(iPr_def_11)),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3899,c_8544]) ).
tcf(c_65433,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK5(iPr_def_11)),iPr_def_11)
| in(sK2(X0,X1,sK5(iPr_def_11)),X1)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4330,c_8544]) ).
tcf(c_65434,plain,
( epsilon_connected(powerset(empty_set))
| subset(sK3(powerset(empty_set)),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4620,c_8544]) ).
tcf(c_65435,plain,
( epsilon_connected(powerset(empty_set))
| subset(sK4(powerset(empty_set)),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4637,c_8544]) ).
tcf(c_65436,plain,
( subset(sK5(powerset(sK5(powerset(sK5(iPr_def_11))))),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_5196,c_8544]) ).
tcf(c_65437,plain,
( subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(iPr_def_11))))))),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_5252,c_8544]) ).
tcf(c_65438,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_8544]) ).
tcf(c_65507,plain,
epsilon_connected(sK5(powerset(sK5(powerset(empty_set))))),
inference(global_subsumption_just,[status(thm)],[c_27689,c_95,c_27848]) ).
tcf(c_65514,plain,
! [X0: $i,X1: $i] :
( empty(powerset(set_union2(X0,X1)))
| ~ subset(singleton(powerset(set_union2(X0,X1))),X0) ),
inference(superposition,[status(thm)],[c_3863,c_29295]) ).
tcf(c_65515,plain,
! [X0: $i,X1: $i] :
( empty(powerset(set_union2(X0,X1)))
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ in(singleton(powerset(set_union2(X0,X1))),X1) ),
inference(superposition,[status(thm)],[c_3806,c_29295]) ).
tcf(c_65516,plain,
! [X0: $i,X1: $i] :
( empty(powerset(set_union2(X0,X1)))
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ in(singleton(powerset(set_union2(X0,X1))),X0) ),
inference(superposition,[status(thm)],[c_3805,c_29295]) ).
tcf(c_65517,plain,
! [X0: $i,X1: $i] :
( empty(powerset(set_union2(X0,X1)))
| ~ subset(singleton(powerset(set_union2(X0,X1))),X1) ),
inference(superposition,[status(thm)],[c_3865,c_29295]) ).
tcf(c_65518,plain,
( empty(powerset(sK5(iPr_def_11)))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(powerset(sK5(iPr_def_11))))
| ( singleton(powerset(sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(singleton(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7244,c_29295]) ).
tcf(c_65519,plain,
( epsilon_connected(iPr_def_11)
| empty(powerset(sK3(iPr_def_11)))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(powerset(sK3(iPr_def_11))))
| ( singleton(powerset(sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(singleton(powerset(sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9907,c_29295]) ).
tcf(c_65520,plain,
( epsilon_connected(iPr_def_11)
| empty(powerset(sK4(iPr_def_11)))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(powerset(sK4(iPr_def_11))))
| ( singleton(powerset(sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(singleton(powerset(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11191,c_29295]) ).
tcf(c_65558,plain,
! [X0: $i,X1: $i] :
( ( sK5(powerset(sK5(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_31902,c_139]) ).
tcf(c_65559,plain,
! [X0: $i] :
( ( sK5(powerset(sK5(powerset(sK5(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_31902,c_32111]) ).
tcf(c_65569,plain,
empty(sK5(powerset(sK5(powerset(empty_set))))),
inference(global_subsumption_just,[status(thm)],[c_31903,c_95,c_32061]) ).
tcf(c_65582,plain,
! [X0: $i] :
( empty(sK18)
| subset(sK2(sK5(sK18),X0,sK18),iPr_def_10)
| in(sK2(sK5(sK18),X0,sK18),X0)
| in(sK2(sK5(sK18),X0,sK18),sK5(sK18))
| ( set_union2(sK5(sK18),X0) = sK18 )
| ( sK2(sK5(sK18),X0,sK18) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK5(sK18),X0,sK18),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_53130]) ).
tcf(c_65583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| subset(sK2(sK2(X0,X1,X2),X3,sK18),iPr_def_10)
| in(sK2(sK2(X0,X1,X2),X3,sK18),X3)
| in(sK2(sK2(X0,X1,X2),X3,sK18),sK2(X0,X1,X2))
| ( set_union2(X0,X1) = X2 )
| ( set_union2(sK2(X0,X1,X2),X3) = sK18 )
| ( sK2(sK2(X0,X1,X2),X3,sK18) = sK2(X0,X1,X2) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X2)
| ~ in(sK2(sK2(X0,X1,X2),X3,sK18),X2) ),
inference(superposition,[status(thm)],[c_4329,c_53130]) ).
tcf(c_65584,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = X0 )
| ~ epsilon_connected(sK18)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4329,c_53130]) ).
tcf(c_65585,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| in(sK2(sK5(iPr_def_11),X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ( sK2(sK5(iPr_def_11),X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(sK2(sK5(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_53130]) ).
tcf(c_65587,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| in(sK2(sK5(iPr_def_11),X0,sK18),sK5(iPr_def_11))
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ( sK2(sK5(iPr_def_11),X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_10,X1)
| ~ in(sK2(sK5(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_53130]) ).
tcf(c_65588,plain,
! [X0: $i] :
( subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| in(sK2(sK5(iPr_def_11),X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ( sK2(sK5(iPr_def_11),X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK5(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_53130]) ).
tcf(c_65589,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ( sK2(sK5(iPr_def_11),X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK5(iPr_def_11))
| ~ in(sK2(sK5(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_7246,c_53130]) ).
tcf(c_65590,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| in(sK2(sK5(iPr_def_11),X0,sK18),sK5(iPr_def_11))
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ( sK2(sK5(iPr_def_11),X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK5(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_53130]) ).
tcf(c_65591,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| in(sK2(sK5(iPr_def_11),X0,sK18),sK5(iPr_def_11))
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ( sK2(sK5(iPr_def_11),X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK5(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_53130]) ).
tcf(c_65592,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| in(sK2(sK5(iPr_def_11),X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ( sK2(sK5(iPr_def_11),X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_53130]) ).
tcf(c_65593,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| subset(sK2(sK1(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK1(iPr_def_11),X0,sK18),X0)
| in(sK2(sK1(iPr_def_11),X0,sK18),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X1 )
| ( set_union2(sK1(iPr_def_11),X0) = sK18 )
| ( sK2(sK1(iPr_def_11),X0,sK18) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(sK2(sK1(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_53130]) ).
tcf(c_65594,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| subset(sK2(sK1(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK1(iPr_def_11),X0,sK18),X0)
| in(sK2(sK1(iPr_def_11),X0,sK18),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X1 )
| ( set_union2(sK1(iPr_def_11),X0) = sK18 )
| ( sK2(sK1(iPr_def_11),X0,sK18) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(sK2(sK1(iPr_def_11),X0,sK18),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_53130]) ).
tcf(c_65595,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| subset(sK2(sK3(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK3(iPr_def_11),X0,sK18),X0)
| in(sK2(sK3(iPr_def_11),X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ( set_union2(sK3(iPr_def_11),X0) = sK18 )
| ( sK2(sK3(iPr_def_11),X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(sK2(sK3(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_53130]) ).
tcf(c_65596,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X1)
| subset(sK2(sK3(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK3(iPr_def_11),X0,sK18),X0)
| in(sK2(sK3(iPr_def_11),X0,sK18),sK3(iPr_def_11))
| ( set_union2(sK3(iPr_def_11),X0) = sK18 )
| ( sK2(sK3(iPr_def_11),X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_10,X1)
| ~ in(sK2(sK3(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_53130]) ).
tcf(c_65597,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK2(sK3(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK3(iPr_def_11),X0,sK18),X0)
| in(sK2(sK3(iPr_def_11),X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(sK3(iPr_def_11),X0) = sK18 )
| ( sK2(sK3(iPr_def_11),X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK3(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_53130]) ).
tcf(c_65598,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(sK3(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK3(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK3(iPr_def_11),X0) = sK18 )
| ( sK2(sK3(iPr_def_11),X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK3(iPr_def_11))
| ~ in(sK2(sK3(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_53130]) ).
tcf(c_65599,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(sK3(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK3(iPr_def_11),X0,sK18),X0)
| in(sK2(sK3(iPr_def_11),X0,sK18),sK3(iPr_def_11))
| ( set_union2(sK3(iPr_def_11),X0) = sK18 )
| ( sK2(sK3(iPr_def_11),X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK3(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_53130]) ).
tcf(c_65600,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(sK3(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK3(iPr_def_11),X0,sK18),X0)
| in(sK2(sK3(iPr_def_11),X0,sK18),sK3(iPr_def_11))
| ( set_union2(sK3(iPr_def_11),X0) = sK18 )
| ( sK2(sK3(iPr_def_11),X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK3(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_53130]) ).
tcf(c_65601,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| subset(sK2(sK3(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK3(iPr_def_11),X0,sK18),X0)
| in(sK2(sK3(iPr_def_11),X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ( set_union2(sK3(iPr_def_11),X0) = sK18 )
| ( sK2(sK3(iPr_def_11),X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(sK2(sK3(iPr_def_11),X0,sK18),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_53130]) ).
tcf(c_65602,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X1)
| subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK4(iPr_def_11),X0,sK18),X0)
| in(sK2(sK4(iPr_def_11),X0,sK18),sK4(iPr_def_11))
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ( sK2(sK4(iPr_def_11),X0,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_10,X1)
| ~ in(sK2(sK4(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_53130]) ).
tcf(c_65603,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK4(iPr_def_11),X0,sK18),X0)
| in(sK2(sK4(iPr_def_11),X0,sK18),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ( sK2(sK4(iPr_def_11),X0,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK4(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_53130]) ).
tcf(c_65604,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK4(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ( sK2(sK4(iPr_def_11),X0,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK4(iPr_def_11))
| ~ in(sK2(sK4(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_11193,c_53130]) ).
tcf(c_65605,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK4(iPr_def_11),X0,sK18),X0)
| in(sK2(sK4(iPr_def_11),X0,sK18),sK4(iPr_def_11))
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ( sK2(sK4(iPr_def_11),X0,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK4(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_53130]) ).
tcf(c_65606,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK4(iPr_def_11),X0,sK18),X0)
| in(sK2(sK4(iPr_def_11),X0,sK18),sK4(iPr_def_11))
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ( sK2(sK4(iPr_def_11),X0,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK4(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_53130]) ).
tcf(c_65607,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_65584,c_2427]) ).
tcf(c_66160,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| ~ in(sK2(X0,X1,sK18),sK18)
| ~ epsilon_transitive(iPr_def_10)
| ( set_union2(X0,X1) = sK18 ) ),
inference(global_subsumption_just,[status(thm)],[c_53134,c_12903,c_53134]) ).
tcf(c_66161,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(renaming,[status(thm)],[c_66160]) ).
tcf(c_66172,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),sK18)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_68,c_66161]) ).
tcf(c_66175,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| in(sK2(X0,sK18,sK18),sK18)
| in(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_68,c_66161]) ).
tcf(c_66176,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),X0)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_connected(sK18)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4329,c_66161]) ).
tcf(c_66177,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK18,sK18),iPr_def_10)
| in(X0,sK2(X1,sK18,sK18))
| in(sK2(X1,sK18,sK18),X1)
| in(sK2(X1,sK18,sK18),X0)
| ( set_union2(X1,sK18) = sK18 )
| ( sK2(X1,sK18,sK18) = X0 )
| ~ epsilon_connected(sK18)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4329,c_66161]) ).
tcf(c_66178,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK18,sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK18 )
| ~ epsilon_connected(sK18)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_4329,c_66161]) ).
tcf(c_66180,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| subset(sK2(sK18,X0,sK18),sK18)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_4330,c_66161]) ).
tcf(c_66182,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| subset(sK2(X0,sK18,sK18),sK18)
| in(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_4330,c_66161]) ).
tcf(c_66183,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| element(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53099,c_66161]) ).
tcf(c_66184,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_51593,c_66161]) ).
tcf(c_66188,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53098,c_66161]) ).
tcf(c_66189,plain,
( subset(sK2(sK18,sK18,sK18),iPr_def_10)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_63091,c_66161]) ).
tcf(c_66191,plain,
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ( sK2(sK18,iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53114,c_66161]) ).
tcf(c_66225,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK18),iPr_def_10)
| subset(sK2(X0,sK18,sK18),sK18)
| in(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_66182,c_2426]) ).
tcf(c_66231,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| subset(sK2(sK18,X0,sK18),sK18)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_66180,c_2426]) ).
tcf(c_66237,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK18,sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_66178,c_2427]) ).
tcf(c_66246,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK18,sK18),iPr_def_10)
| in(X0,sK2(X1,sK18,sK18))
| in(sK2(X1,sK18,sK18),X1)
| in(sK2(X1,sK18,sK18),X0)
| ( set_union2(X1,sK18) = sK18 )
| ( sK2(X1,sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_66177,c_2427]) ).
tcf(c_66255,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),X0)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_66176,c_2427]) ).
tcf(c_66299,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X1,sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),X1)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK4(iPr_def_11))
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = X1 )
| ( sK2(sK18,X0,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(sK2(sK18,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_13671]) ).
tcf(c_66300,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),X1)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK3(iPr_def_11))
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = X1 )
| ( sK2(sK18,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(sK2(sK18,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_13665]) ).
tcf(c_66301,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),X1)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK5(iPr_def_11))
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = X1 )
| ( sK2(sK18,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(sK2(sK18,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_13657]) ).
tcf(c_66302,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,iPr_def_10)
| in(X2,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X2)
| in(sK2(sK18,X1,sK18),X1)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,sK18)
| ~ subset(X0,sK2(sK18,X1,sK18)) ),
inference(superposition,[status(thm)],[c_66255,c_128]) ).
tcf(c_66303,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_11)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),X0)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_3868]) ).
tcf(c_66304,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X1)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = X1 )
| ( sK2(sK18,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,sK18)
| ~ epsilon_connected(sK2(sK18,X0,sK18))
| ~ in(sK2(sK18,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_49877]) ).
tcf(c_66305,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X1)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = X1 )
| ( sK2(sK18,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,sK18)
| ~ epsilon_connected(sK2(sK18,X0,sK18))
| ~ in(sK2(sK18,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_7260]) ).
tcf(c_66306,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X2)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ in(X2,sK18)
| ~ subset(sK2(sK18,X0,sK18),X1) ),
inference(superposition,[status(thm)],[c_66255,c_359]) ).
tcf(c_66307,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X2)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,sK18)
| ~ subset(sK2(sK18,X0,sK18),X1) ),
inference(superposition,[status(thm)],[c_66255,c_358]) ).
tcf(c_66308,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X0,X2)
| subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(sK2(sK18,X1,sK18),X2)
| in(sK2(sK18,X1,sK18),X1)
| ( X0 = X2 )
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,sK18)
| ~ epsilon_connected(sK2(sK18,X1,sK18))
| ~ in(X0,sK2(sK18,X1,sK18)) ),
inference(superposition,[status(thm)],[c_66255,c_77]) ).
tcf(c_66309,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| subset(X1,sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),X1)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,sK18)
| ~ epsilon_transitive(sK2(sK18,X0,sK18)) ),
inference(superposition,[status(thm)],[c_66255,c_65]) ).
tcf(c_66311,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X1)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,sK18)
| ~ empty(sK2(sK18,X0,sK18)) ),
inference(superposition,[status(thm)],[c_66255,c_137]) ).
tcf(c_66312,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| element(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),X0)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_127]) ).
tcf(c_66313,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK2(sK2(sK18,X0,sK18),X1,X2))
| ( set_union2(sK18,X0) = sK18 )
| ( set_union2(sK2(sK18,X0,sK18),X1) = X2 )
| ( sK2(sK2(sK18,X0,sK18),X1,X2) = sK2(sK18,X0,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK2(sK18,X0,sK18),X1,X2),sK18)
| ~ in(sK2(sK2(sK18,X0,sK18),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_66255,c_66]) ).
tcf(c_66314,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X2,sK18),iPr_def_10)
| in(sK2(sK18,X2,sK18),X2)
| in(sK2(sK18,X2,sK18),sK2(X0,X1,sK2(sK18,X2,sK18)))
| ( set_union2(sK18,X2) = sK18 )
| ( sK2(sK18,X2,sK18) = set_union2(X0,X1) )
| ( sK2(X0,X1,sK2(sK18,X2,sK18)) = sK2(sK18,X2,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,X1,sK2(sK18,X2,sK18)),sK18)
| ~ in(sK2(X0,X1,sK2(sK18,X2,sK18)),X1) ),
inference(superposition,[status(thm)],[c_66255,c_67]) ).
tcf(c_66315,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),singleton(sK2(sK18,X0,sK18)))
| ( set_union2(sK18,X0) = sK18 )
| ( singleton(sK2(sK18,X0,sK18)) = sK2(sK18,X0,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(sK2(sK18,X0,sK18)),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_3522]) ).
tcf(c_66316,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),set_union2(X2,X1))
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = set_union2(X2,X1) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(set_union2(X2,X1),sK18)
| ~ in(sK2(sK18,X0,sK18),X1) ),
inference(superposition,[status(thm)],[c_66255,c_3641]) ).
tcf(c_66317,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),set_union2(X1,X2))
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = set_union2(X1,X2) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(set_union2(X1,X2),sK18)
| ~ in(sK2(sK18,X0,sK18),X1) ),
inference(superposition,[status(thm)],[c_66255,c_3615]) ).
tcf(c_66318,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),singleton(set_union2(sK2(sK18,X0,sK18),X1)))
| ( set_union2(sK18,X0) = sK18 )
| ( singleton(set_union2(sK2(sK18,X0,sK18),X1)) = sK2(sK18,X0,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(set_union2(sK2(sK18,X0,sK18),X1)),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_3618]) ).
tcf(c_66319,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),singleton(set_union2(X0,sK2(sK18,X1,sK18))))
| ( set_union2(sK18,X1) = sK18 )
| ( singleton(set_union2(X0,sK2(sK18,X1,sK18))) = sK2(sK18,X1,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(set_union2(X0,sK2(sK18,X1,sK18))),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_3644]) ).
tcf(c_66320,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),singleton(set_union2(set_union2(sK2(sK18,X0,sK18),X1),X2)))
| ( set_union2(sK18,X0) = sK18 )
| ( singleton(set_union2(set_union2(sK2(sK18,X0,sK18),X1),X2)) = sK2(sK18,X0,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(set_union2(set_union2(sK2(sK18,X0,sK18),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_3944]) ).
tcf(c_66321,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),singleton(set_union2(set_union2(X0,sK2(sK18,X1,sK18)),X2)))
| ( set_union2(sK18,X1) = sK18 )
| ( singleton(set_union2(set_union2(X0,sK2(sK18,X1,sK18)),X2)) = sK2(sK18,X1,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(set_union2(set_union2(X0,sK2(sK18,X1,sK18)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_3945]) ).
tcf(c_66322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK2(set_union2(sK2(sK18,X0,sK18),X1),X2,X3))
| ( set_union2(sK18,X0) = sK18 )
| ( set_union2(set_union2(sK2(sK18,X0,sK18),X1),X2) = X3 )
| ( sK2(set_union2(sK2(sK18,X0,sK18),X1),X2,X3) = sK2(sK18,X0,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(sK2(sK18,X0,sK18),X1),X2,X3),sK18)
| ~ in(sK2(set_union2(sK2(sK18,X0,sK18),X1),X2,X3),X3) ),
inference(superposition,[status(thm)],[c_66255,c_4078]) ).
tcf(c_66323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,X3,sK18),iPr_def_10)
| in(sK2(sK18,X3,sK18),X3)
| in(sK2(sK18,X3,sK18),sK2(set_union2(X0,X1),X2,sK2(sK18,X3,sK18)))
| ( set_union2(sK18,X3) = sK18 )
| ( set_union2(set_union2(X0,X1),X2) = sK2(sK18,X3,sK18) )
| ( sK2(set_union2(X0,X1),X2,sK2(sK18,X3,sK18)) = sK2(sK18,X3,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X2,sK2(sK18,X3,sK18)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK2(sK18,X3,sK18)),X1) ),
inference(superposition,[status(thm)],[c_66255,c_4079]) ).
tcf(c_66324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,X2,sK18),iPr_def_10)
| in(sK2(sK18,X2,sK18),X2)
| in(sK2(sK18,X2,sK18),sK2(X0,X1,set_union2(sK2(sK18,X2,sK18),X3)))
| ( set_union2(sK18,X2) = sK18 )
| ( set_union2(sK2(sK18,X2,sK18),X3) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK2(sK18,X2,sK18),X3)) = sK2(sK18,X2,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,X1,set_union2(sK2(sK18,X2,sK18),X3)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK2(sK18,X2,sK18),X3)),X1) ),
inference(superposition,[status(thm)],[c_66255,c_4095]) ).
tcf(c_66325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),sK2(X0,sK2(sK18,X1,sK18),set_union2(X2,X3)))
| ( set_union2(sK18,X1) = sK18 )
| ( set_union2(X0,sK2(sK18,X1,sK18)) = set_union2(X2,X3) )
| ( sK2(X0,sK2(sK18,X1,sK18),set_union2(X2,X3)) = sK2(sK18,X1,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK2(sK18,X1,sK18),set_union2(X2,X3)),sK18)
| ~ in(sK2(X0,sK2(sK18,X1,sK18),set_union2(X2,X3)),X3) ),
inference(superposition,[status(thm)],[c_66255,c_4096]) ).
tcf(c_66326,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),singleton(set_union2(X0,set_union2(sK2(sK18,X1,sK18),X2))))
| ( set_union2(sK18,X1) = sK18 )
| ( singleton(set_union2(X0,set_union2(sK2(sK18,X1,sK18),X2))) = sK2(sK18,X1,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(sK2(sK18,X1,sK18),X2))),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_4131]) ).
tcf(c_66327,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X2,sK18),iPr_def_10)
| in(sK2(sK18,X2,sK18),X2)
| in(sK2(sK18,X2,sK18),singleton(set_union2(X0,set_union2(X1,sK2(sK18,X2,sK18)))))
| ( set_union2(sK18,X2) = sK18 )
| ( singleton(set_union2(X0,set_union2(X1,sK2(sK18,X2,sK18)))) = sK2(sK18,X2,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK2(sK18,X2,sK18)))),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_4132]) ).
tcf(c_66329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),singleton(set_union2(set_union2(set_union2(sK2(sK18,X0,sK18),X1),X2),X3)))
| ( set_union2(sK18,X0) = sK18 )
| ( singleton(set_union2(set_union2(set_union2(sK2(sK18,X0,sK18),X1),X2),X3)) = sK2(sK18,X0,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(set_union2(set_union2(set_union2(sK2(sK18,X0,sK18),X1),X2),X3)),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_5325]) ).
tcf(c_66330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),singleton(set_union2(set_union2(set_union2(X0,sK2(sK18,X1,sK18)),X2),X3)))
| ( set_union2(sK18,X1) = sK18 )
| ( singleton(set_union2(set_union2(set_union2(X0,sK2(sK18,X1,sK18)),X2),X3)) = sK2(sK18,X1,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK2(sK18,X1,sK18)),X2),X3)),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_5326]) ).
tcf(c_66331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),singleton(set_union2(set_union2(X0,set_union2(sK2(sK18,X1,sK18),X2)),X3)))
| ( set_union2(sK18,X1) = sK18 )
| ( singleton(set_union2(set_union2(X0,set_union2(sK2(sK18,X1,sK18),X2)),X3)) = sK2(sK18,X1,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK2(sK18,X1,sK18),X2)),X3)),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_5547]) ).
tcf(c_66332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,X2,sK18),iPr_def_10)
| in(sK2(sK18,X2,sK18),X2)
| in(sK2(sK18,X2,sK18),singleton(set_union2(set_union2(X0,set_union2(X1,sK2(sK18,X2,sK18))),X3)))
| ( set_union2(sK18,X2) = sK18 )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK2(sK18,X2,sK18))),X3)) = sK2(sK18,X2,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK2(sK18,X2,sK18))),X3)),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_5548]) ).
tcf(c_66333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),singleton(set_union2(X0,set_union2(set_union2(sK2(sK18,X1,sK18),X2),X3))))
| ( set_union2(sK18,X1) = sK18 )
| ( singleton(set_union2(X0,set_union2(set_union2(sK2(sK18,X1,sK18),X2),X3))) = sK2(sK18,X1,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK2(sK18,X1,sK18),X2),X3))),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_5584]) ).
tcf(c_66334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,X2,sK18),iPr_def_10)
| in(sK2(sK18,X2,sK18),X2)
| in(sK2(sK18,X2,sK18),singleton(set_union2(X0,set_union2(set_union2(X1,sK2(sK18,X2,sK18)),X3))))
| ( set_union2(sK18,X2) = sK18 )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK2(sK18,X2,sK18)),X3))) = sK2(sK18,X2,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK2(sK18,X2,sK18)),X3))),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_5585]) ).
tcf(c_66335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,X2,sK18),iPr_def_10)
| in(sK2(sK18,X2,sK18),X2)
| in(sK2(sK18,X2,sK18),singleton(set_union2(X0,set_union2(X1,set_union2(sK2(sK18,X2,sK18),X3)))))
| ( set_union2(sK18,X2) = sK18 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK2(sK18,X2,sK18),X3)))) = sK2(sK18,X2,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK2(sK18,X2,sK18),X3)))),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_5597]) ).
tcf(c_66336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,X3,sK18),iPr_def_10)
| in(sK2(sK18,X3,sK18),X3)
| in(sK2(sK18,X3,sK18),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK2(sK18,X3,sK18))))))
| ( set_union2(sK18,X3) = sK18 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK2(sK18,X3,sK18))))) = sK2(sK18,X3,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK2(sK18,X3,sK18))))),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_5598]) ).
tcf(c_66337,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),sK18)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_53097]) ).
tcf(c_66339,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),sK18)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_53130]) ).
tcf(c_66340,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X0)
| in(sK3(iPr_def_11),sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ( sK2(sK18,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_49877]) ).
tcf(c_66341,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X0)
| in(sK5(iPr_def_11),sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ( sK2(sK18,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_7260]) ).
tcf(c_66342,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(X2,sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),X2)
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ in(X2,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_66255,c_359]) ).
tcf(c_66343,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| element(sK2(sK18,X0,sK18),X1)
| in(X2,sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),X2)
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_66255,c_358]) ).
tcf(c_66344,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(X2,sK2(sK18,X1,sK18))
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X2)
| in(sK2(sK18,X1,sK18),X0)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X2 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_66255,c_77]) ).
tcf(c_66345,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| subset(sK2(sK18,X1,sK18),X1)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X0)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_65]) ).
tcf(c_66346,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(X1,sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),X1)
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(X0,sK2(sK18,X0,sK18)) ),
inference(superposition,[status(thm)],[c_66255,c_49]) ).
tcf(c_66347,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X0)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_137]) ).
tcf(c_66348,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| element(sK2(sK18,X1,sK18),X1)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X0)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_127]) ).
tcf(c_66349,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,singleton(X1),sK18),iPr_def_10)
| in(X0,sK2(sK18,singleton(X1),sK18))
| in(sK2(sK18,singleton(X1),sK18),X0)
| ( set_union2(sK18,singleton(X1)) = sK18 )
| ( sK2(sK18,singleton(X1),sK18) = X1 )
| ( sK2(sK18,singleton(X1),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_62]) ).
tcf(c_66350,plain,
! [X0: $i] :
( subset(sK2(sK18,sK18,sK18),iPr_def_10)
| in(X0,sK2(sK18,sK18,sK18))
| in(sK2(sK18,sK18,sK18),X0)
| ( set_union2(sK18,sK18) = sK18 )
| ( sK2(sK18,sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(sK2(sK18,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_66]) ).
tcf(c_66352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_10)
| in(X3,sK2(sK18,set_union2(X0,X1),sK18))
| in(X2,sK2(sK18,set_union2(X0,X1),sK18))
| in(sK2(sK18,set_union2(X0,X1),sK18),X3)
| in(sK2(sK18,set_union2(X0,X1),sK18),X2)
| ( set_union2(sK18,set_union2(X0,X1)) = sK18 )
| ( sK2(sK18,set_union2(X0,X1),sK18) = X3 )
| ( sK2(sK18,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_66255,c_4213]) ).
tcf(c_66353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_10)
| in(X3,sK2(sK18,set_union2(X0,X1),sK18))
| in(X2,sK2(sK18,set_union2(X0,X1),sK18))
| in(sK2(sK18,set_union2(X0,X1),sK18),X3)
| in(sK2(sK18,set_union2(X0,X1),sK18),X2)
| ( set_union2(sK18,set_union2(X0,X1)) = sK18 )
| ( sK2(sK18,set_union2(X0,X1),sK18) = X3 )
| ( sK2(sK18,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X3,sK18)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_66255,c_4212]) ).
tcf(c_66354,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,set_union2(X1,X2),sK18),iPr_def_10)
| in(X0,sK2(sK18,set_union2(X1,X2),sK18))
| in(sK2(sK18,set_union2(X1,X2),sK18),X2)
| in(sK2(sK18,set_union2(X1,X2),sK18),X1)
| in(sK2(sK18,set_union2(X1,X2),sK18),X0)
| ( set_union2(sK18,set_union2(X1,X2)) = sK18 )
| ( sK2(sK18,set_union2(X1,X2),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_71]) ).
tcf(c_66355,plain,
! [X0: $i] :
( subset(sK2(sK18,empty_set,sK18),iPr_def_10)
| in(X0,sK2(sK18,empty_set,sK18))
| in(sK2(sK18,empty_set,sK18),X0)
| ( set_union2(sK18,empty_set) = sK18 )
| ( sK2(sK18,empty_set,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_7097]) ).
tcf(c_66356,plain,
! [X0: $i] :
( subset(sK2(sK18,sK18,sK18),iPr_def_11)
| subset(sK2(sK18,sK18,sK18),iPr_def_10)
| in(X0,sK2(sK18,sK18,sK18))
| in(sK2(sK18,sK18,sK18),X0)
| ( set_union2(sK18,sK18) = sK18 )
| ( sK2(sK18,sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_12813]) ).
tcf(c_66357,plain,
! [X0: $i] :
( subset(sK2(sK18,sK18,sK18),iPr_def_10)
| in(X0,sK2(sK18,sK18,sK18))
| in(sK2(sK18,sK18,sK18),X0)
| ( set_union2(sK18,sK18) = sK18 )
| ( sK2(sK18,sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK2(sK18,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_66255,c_6841]) ).
tcf(c_66358,plain,
! [X0: $i] :
( element(sK2(sK18,sK18,sK18),iPr_def_11)
| subset(sK2(sK18,sK18,sK18),iPr_def_10)
| in(X0,sK2(sK18,sK18,sK18))
| in(sK2(sK18,sK18,sK18),X0)
| ( set_union2(sK18,sK18) = sK18 )
| ( sK2(sK18,sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_5047]) ).
tcf(c_66359,plain,
! [X0: $i] :
( subset(sK2(sK18,sK18,sK18),iPr_def_10)
| in(sK2(sK18,sK18,sK18),iPr_def_11)
| in(X0,sK2(sK18,sK18,sK18))
| in(sK2(sK18,sK18,sK18),X0)
| ( set_union2(sK18,sK18) = sK18 )
| ( sK2(sK18,sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_3640]) ).
tcf(c_66360,plain,
! [X0: $i] :
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| in(X0,sK2(sK18,iPr_def_10,sK18))
| in(sK2(sK18,iPr_def_10,sK18),X0)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ( sK2(sK18,iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_9540]) ).
tcf(c_66361,plain,
! [X0: $i] :
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| in(X0,sK2(sK18,iPr_def_10,sK18))
| in(sK2(sK18,iPr_def_10,sK18),X0)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ( sK2(sK18,iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18)
| ~ in(iPr_def_11,sK2(sK18,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_66255,c_6289]) ).
tcf(c_66362,plain,
! [X0: $i] :
( element(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| in(X0,sK2(sK18,iPr_def_10,sK18))
| in(sK2(sK18,iPr_def_10,sK18),X0)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ( sK2(sK18,iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_4912]) ).
tcf(c_66363,plain,
! [X0: $i] :
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| in(X0,sK2(sK18,iPr_def_10,sK18))
| in(sK2(sK18,iPr_def_10,sK18),X0)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ( sK2(sK18,iPr_def_10,sK18) = sK18 )
| ( sK2(sK18,iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_3592]) ).
tcf(c_66364,plain,
! [X0: $i] :
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| in(X0,sK2(sK18,iPr_def_10,sK18))
| in(sK2(sK18,iPr_def_10,sK18),X0)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ( sK2(sK18,iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_3614]) ).
tcf(c_66365,plain,
! [X0: $i] :
( subset(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_11,sK18),sK18)
| in(X0,sK2(sK18,iPr_def_11,sK18))
| in(sK2(sK18,iPr_def_11,sK18),X0)
| ( set_union2(sK18,iPr_def_11) = sK18 )
| ( sK2(sK18,iPr_def_11,sK18) = sK18 )
| ( sK2(sK18,iPr_def_11,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_33457]) ).
tcf(c_66366,plain,
! [X0: $i] :
( subset(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_11,sK18),sK18)
| in(X0,sK2(sK18,iPr_def_11,sK18))
| in(sK2(sK18,iPr_def_11,sK18),X0)
| ( set_union2(sK18,iPr_def_11) = sK18 )
| ( sK2(sK18,iPr_def_11,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_4035]) ).
tcf(c_66367,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| subset(sK2(sK18,sK5(iPr_def_11),sK18),iPr_def_10)
| in(X1,sK2(sK18,sK5(iPr_def_11),sK18))
| in(X0,sK2(sK18,sK5(iPr_def_11),sK18))
| in(sK2(sK18,sK5(iPr_def_11),sK18),X1)
| in(sK2(sK18,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X1 )
| ( set_union2(sK18,sK5(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK5(iPr_def_11),sK18) = X1 )
| ( sK2(sK18,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_7243]) ).
tcf(c_66368,plain,
! [X0: $i] :
( subset(sK2(sK18,sK5(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(sK18,sK5(iPr_def_11),sK18))
| in(sK2(sK18,sK5(iPr_def_11),sK18),X0)
| ( set_union2(sK18,sK5(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18)
| ~ subset(iPr_def_11,sK2(sK18,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_66255,c_23189]) ).
tcf(c_66369,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| subset(sK2(sK18,sK3(iPr_def_11),sK18),iPr_def_10)
| in(X1,sK2(sK18,sK3(iPr_def_11),sK18))
| in(X0,sK2(sK18,sK3(iPr_def_11),sK18))
| in(sK2(sK18,sK3(iPr_def_11),sK18),X1)
| in(sK2(sK18,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X1 )
| ( set_union2(sK18,sK3(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK3(iPr_def_11),sK18) = X1 )
| ( sK2(sK18,sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_9906]) ).
tcf(c_66370,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| subset(sK2(sK18,sK4(iPr_def_11),sK18),iPr_def_10)
| in(X1,sK2(sK18,sK4(iPr_def_11),sK18))
| in(X0,sK2(sK18,sK4(iPr_def_11),sK18))
| in(sK2(sK18,sK4(iPr_def_11),sK18),X1)
| in(sK2(sK18,sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X1 )
| ( set_union2(sK18,sK4(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK4(iPr_def_11),sK18) = X1 )
| ( sK2(sK18,sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_45801]) ).
tcf(c_66371,plain,
! [X0: $i] :
( subset(sK2(sK18,sK18,sK18),iPr_def_10)
| in(X0,sK2(sK18,sK18,sK18))
| in(sK2(sK18,sK18,sK18),X0)
| ( set_union2(sK18,sK18) = sK18 )
| ( sK2(sK18,sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_66161]) ).
tcf(c_66372,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X1)
| in(sK3(iPr_def_11),sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ( sK2(sK18,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_49877]) ).
tcf(c_66373,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X1)
| in(sK5(iPr_def_11),sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ( sK2(sK18,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_7260]) ).
tcf(c_66374,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X2,sK18),iPr_def_10)
| in(X0,sK2(sK18,X2,sK18))
| in(sK2(sK18,X2,sK18),X2)
| ( set_union2(sK18,X2) = sK18 )
| ( sK2(sK18,X2,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_66255,c_359]) ).
tcf(c_66375,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X2,sK18),iPr_def_10)
| element(sK2(sK18,X2,sK18),X1)
| in(X0,sK2(sK18,X2,sK18))
| in(sK2(sK18,X2,sK18),X2)
| ( set_union2(sK18,X2) = sK18 )
| ( sK2(sK18,X2,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_66255,c_358]) ).
tcf(c_66376,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X2,sK18),iPr_def_10)
| in(X1,sK2(sK18,X2,sK18))
| in(X0,sK2(sK18,X2,sK18))
| in(sK2(sK18,X2,sK18),X2)
| in(sK2(sK18,X2,sK18),X0)
| ( set_union2(sK18,X2) = sK18 )
| ( sK2(sK18,X2,sK18) = X1 )
| ( sK2(sK18,X2,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_66255,c_77]) ).
tcf(c_66377,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| subset(sK2(sK18,X1,sK18),X0)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X1)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_65]) ).
tcf(c_66379,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X1)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_137]) ).
tcf(c_66380,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| element(sK2(sK18,X1,sK18),X0)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X1)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_127]) ).
tcf(c_66381,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(sK2(sK18,X1,sK18),X1)
| in(singleton(X0),sK2(sK18,X1,sK18))
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ( sK2(sK18,X1,sK18) = singleton(X0) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_62]) ).
tcf(c_66384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,X3,sK18),iPr_def_10)
| in(X2,sK2(sK18,X3,sK18))
| in(sK2(sK18,X3,sK18),X3)
| in(sK2(sK18,X3,sK18),X2)
| in(set_union2(X0,X1),sK2(sK18,X3,sK18))
| ( set_union2(sK18,X3) = sK18 )
| ( sK2(sK18,X3,sK18) = X2 )
| ( sK2(sK18,X3,sK18) = set_union2(X0,X1) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_4213]) ).
tcf(c_66385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(sK18,X3,sK18),iPr_def_10)
| in(X2,sK2(sK18,X3,sK18))
| in(sK2(sK18,X3,sK18),X3)
| in(sK2(sK18,X3,sK18),X2)
| in(set_union2(X0,X1),sK2(sK18,X3,sK18))
| ( set_union2(sK18,X3) = sK18 )
| ( sK2(sK18,X3,sK18) = X2 )
| ( sK2(sK18,X3,sK18) = set_union2(X0,X1) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_4212]) ).
tcf(c_66386,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X2,sK18),iPr_def_10)
| in(sK2(sK18,X2,sK18),X2)
| in(sK2(sK18,X2,sK18),X1)
| in(sK2(sK18,X2,sK18),X0)
| in(set_union2(X0,X1),sK2(sK18,X2,sK18))
| ( set_union2(sK18,X2) = sK18 )
| ( sK2(sK18,X2,sK18) = set_union2(X0,X1) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_71]) ).
tcf(c_66387,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(empty_set,sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = empty_set )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_7097]) ).
tcf(c_66391,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK18,sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),iPr_def_11)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_3640]) ).
tcf(c_66392,plain,
! [X0: $i] :
( epsilon_transitive(sK2(sK18,X0,sK18))
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK1(sK2(sK18,X0,sK18)),sK2(sK18,X0,sK18))
| ( set_union2(sK18,X0) = sK18 )
| ( sK1(sK2(sK18,X0,sK18)) = sK2(sK18,X0,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK1(sK2(sK18,X0,sK18)),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_3523]) ).
tcf(c_66393,plain,
! [X0: $i] :
( epsilon_connected(sK2(sK18,X0,sK18))
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK3(sK2(sK18,X0,sK18)),sK2(sK18,X0,sK18))
| ( set_union2(sK18,X0) = sK18 )
| ( sK3(sK2(sK18,X0,sK18)) = sK2(sK18,X0,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK3(sK2(sK18,X0,sK18)),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_3524]) ).
tcf(c_66394,plain,
! [X0: $i] :
( epsilon_connected(sK2(sK18,X0,sK18))
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK4(sK2(sK18,X0,sK18)),sK2(sK18,X0,sK18))
| ( set_union2(sK18,X0) = sK18 )
| ( sK4(sK2(sK18,X0,sK18)) = sK2(sK18,X0,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK4(sK2(sK18,X0,sK18)),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_3525]) ).
tcf(c_66402,plain,
! [X0: $i] :
( empty(sK2(sK18,X0,sK18))
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK5(sK2(sK18,X0,sK18)),sK2(sK18,X0,sK18))
| ( set_union2(sK18,X0) = sK18 )
| ( sK5(sK2(sK18,X0,sK18)) = sK2(sK18,X0,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(sK2(sK18,X0,sK18)),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_3900]) ).
tcf(c_66403,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X2,sK18),iPr_def_10)
| in(sK2(sK18,X2,sK18),X2)
| in(sK2(X0,X1,sK2(sK18,X2,sK18)),X1)
| in(sK2(X0,X1,sK2(sK18,X2,sK18)),X0)
| in(sK2(X0,X1,sK2(sK18,X2,sK18)),sK2(sK18,X2,sK18))
| ( set_union2(sK18,X2) = sK18 )
| ( sK2(sK18,X2,sK18) = set_union2(X0,X1) )
| ( sK2(X0,X1,sK2(sK18,X2,sK18)) = sK2(sK18,X2,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,X1,sK2(sK18,X2,sK18)),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_4331]) ).
tcf(c_66404,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),X0)
| in(sK5(iPr_def_11),sK2(sK18,X1,sK18))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ( sK2(sK18,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_7243]) ).
tcf(c_66405,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK5(iPr_def_11),sK2(sK18,X0,sK18))
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(iPr_def_11),sK18)
| ~ subset(iPr_def_11,sK2(sK18,X0,sK18)) ),
inference(superposition,[status(thm)],[c_66255,c_23189]) ).
tcf(c_66406,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),X0)
| in(sK3(iPr_def_11),sK2(sK18,X1,sK18))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ( sK2(sK18,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_9906]) ).
tcf(c_66407,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),X0)
| in(sK4(iPr_def_11),sK2(sK18,X1,sK18))
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ( sK2(sK18,X1,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_45801]) ).
tcf(c_66408,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK18,sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_66255,c_66161]) ).
tcf(c_66409,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(sK2(sK18,X1,sK18),X1)
| subset(sK2(X0,sK2(sK18,X1,sK18),sK18),iPr_def_10)
| in(sK2(X0,sK2(sK18,X1,sK18),sK18),X0)
| in(sK2(X0,sK2(sK18,X1,sK18),sK18),sK2(sK18,X1,sK18))
| ( set_union2(sK18,X1) = sK18 )
| ( set_union2(X0,sK2(sK18,X1,sK18)) = sK18 )
| ( sK2(X0,sK2(sK18,X1,sK18),sK18) = sK2(sK18,X1,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK2(sK18,X1,sK18),sK18),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_53097]) ).
tcf(c_66410,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| subset(sK2(sK2(sK18,X0,sK18),X1,sK18),iPr_def_10)
| in(sK2(sK2(sK18,X0,sK18),X1,sK18),X1)
| in(sK2(sK2(sK18,X0,sK18),X1,sK18),sK2(sK18,X0,sK18))
| ( set_union2(sK18,X0) = sK18 )
| ( set_union2(sK2(sK18,X0,sK18),X1) = sK18 )
| ( sK2(sK2(sK18,X0,sK18),X1,sK18) = sK2(sK18,X0,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK2(sK18,X0,sK18),X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_53130]) ).
tcf(c_66414,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(X0,sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(equality_factoring,[status(thm)],[c_66255]) ).
tcf(c_67496,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_10),X1)
| in(sK2(X0,X1,singleton(sK18)),X0)
| ( set_union2(X0,X1) = singleton(sK18) )
| ( sK2(X0,X1,singleton(sK18)) = sK18 ) ),
inference(superposition,[status(thm)],[c_2420,c_4334]) ).
tcf(c_67497,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_10),X0)
| in(sK2(X0,X1,singleton(sK18)),X1)
| ( set_union2(X0,X1) = singleton(sK18) )
| ( sK2(X0,X1,singleton(sK18)) = sK18 ) ),
inference(superposition,[status(thm)],[c_2420,c_4334]) ).
tcf(c_67498,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X1,X0,singleton(X2)),X1)
| in(sK3(iPr_def_11),sK2(X1,X0,singleton(X2)))
| in(sK2(X1,X0,singleton(X2)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = singleton(X2) )
| ( sK2(X1,X0,singleton(X2)) = X2 )
| ( sK2(X1,X0,singleton(X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4334,c_49877]) ).
tcf(c_67499,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X1,X0,singleton(X2)),X1)
| in(sK5(iPr_def_11),sK2(X1,X0,singleton(X2)))
| in(sK2(X1,X0,singleton(X2)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = singleton(X2) )
| ( sK2(X1,X0,singleton(X2)) = X2 )
| ( sK2(X1,X0,singleton(X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4334,c_7260]) ).
tcf(c_67500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X0,singleton(X3)),X2)
| ( set_union2(X2,X0) = singleton(X3) )
| ( sK2(X2,X0,singleton(X3)) = X3 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4334,c_359]) ).
tcf(c_67501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X0,singleton(X3)),X1)
| in(sK2(X2,X0,singleton(X3)),X2)
| ( set_union2(X2,X0) = singleton(X3) )
| ( sK2(X2,X0,singleton(X3)) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4334,c_358]) ).
tcf(c_67502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X2,X1,singleton(X3)))
| in(sK2(X2,X1,singleton(X3)),X2)
| in(sK2(X2,X1,singleton(X3)),X0)
| ( set_union2(X2,X1) = singleton(X3) )
| ( sK2(X2,X1,singleton(X3)) = X3 )
| ( sK2(X2,X1,singleton(X3)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4334,c_77]) ).
tcf(c_67503,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X0,singleton(X2)),X0)
| in(sK2(X1,X0,singleton(X2)),X1)
| ( set_union2(X1,X0) = singleton(X2) )
| ( sK2(X1,X0,singleton(X2)) = X2 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4334,c_65]) ).
tcf(c_67504,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,singleton(X2)),X1)
| ( set_union2(X1,X0) = singleton(X2) )
| ( sK2(X1,X0,singleton(X2)) = X2 )
| ~ in(X0,sK2(X1,X0,singleton(X2))) ),
inference(superposition,[status(thm)],[c_4334,c_49]) ).
tcf(c_67505,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,singleton(X2)),X1)
| ( set_union2(X1,X0) = singleton(X2) )
| ( sK2(X1,X0,singleton(X2)) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4334,c_137]) ).
tcf(c_67506,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,singleton(X2)),X1)
| in(sK2(X0,X1,singleton(X2)),X0)
| ( set_union2(X0,X1) = singleton(X2) )
| ( sK2(X0,X1,singleton(X2)) = X2 ) ),
inference(superposition,[status(thm)],[c_4334,c_127]) ).
tcf(c_67507,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,singleton(X1),singleton(X2)),X0)
| ( set_union2(X0,singleton(X1)) = singleton(X2) )
| ( sK2(X0,singleton(X1),singleton(X2)) = X2 )
| ( sK2(X0,singleton(X1),singleton(X2)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_62]) ).
tcf(c_67508,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X0,singleton(X1)),X0)
| ( set_union2(X0,X0) = singleton(X1) )
| ( sK2(X0,X0,singleton(X1)) = X1 )
| ~ in(sK2(X0,X0,singleton(X1)),singleton(X1)) ),
inference(superposition,[status(thm)],[c_4334,c_66]) ).
tcf(c_67509,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,singleton(X1),singleton(X1)),X0)
| ( set_union2(X0,singleton(X1)) = singleton(X1) )
| ( sK2(X0,singleton(X1),singleton(X1)) = X1 )
| ~ in(sK2(X0,singleton(X1),singleton(X1)),singleton(X1)) ),
inference(superposition,[status(thm)],[c_4334,c_67]) ).
tcf(c_67510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(X3,set_union2(X0,X1),singleton(X4)))
| in(sK2(X3,set_union2(X0,X1),singleton(X4)),X3)
| in(sK2(X3,set_union2(X0,X1),singleton(X4)),X2)
| ( set_union2(X3,set_union2(X0,X1)) = singleton(X4) )
| ( sK2(X3,set_union2(X0,X1),singleton(X4)) = X4 )
| ( sK2(X3,set_union2(X0,X1),singleton(X4)) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4334,c_4213]) ).
tcf(c_67511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(X3,set_union2(X0,X1),singleton(X4)))
| in(sK2(X3,set_union2(X0,X1),singleton(X4)),X3)
| in(sK2(X3,set_union2(X0,X1),singleton(X4)),X2)
| ( set_union2(X3,set_union2(X0,X1)) = singleton(X4) )
| ( sK2(X3,set_union2(X0,X1),singleton(X4)) = X4 )
| ( sK2(X3,set_union2(X0,X1),singleton(X4)) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4334,c_4212]) ).
tcf(c_67512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_union2(X1,X2),singleton(X3)),X2)
| in(sK2(X0,set_union2(X1,X2),singleton(X3)),X1)
| in(sK2(X0,set_union2(X1,X2),singleton(X3)),X0)
| ( set_union2(X0,set_union2(X1,X2)) = singleton(X3) )
| ( sK2(X0,set_union2(X1,X2),singleton(X3)) = X3 ) ),
inference(superposition,[status(thm)],[c_4334,c_71]) ).
tcf(c_67513,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,empty_set,singleton(X1)),X0)
| ( set_union2(X0,empty_set) = singleton(X1) )
| ( sK2(X0,empty_set,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_7097]) ).
tcf(c_67514,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,singleton(X1)),iPr_def_11)
| in(sK2(X0,sK18,singleton(X1)),X0)
| ( set_union2(X0,sK18) = singleton(X1) )
| ( sK2(X0,sK18,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_12813]) ).
tcf(c_67515,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK18,singleton(X1)),X0)
| ( set_union2(X0,sK18) = singleton(X1) )
| ( sK2(X0,sK18,singleton(X1)) = X1 )
| ~ in(iPr_def_11,sK2(X0,sK18,singleton(X1))) ),
inference(superposition,[status(thm)],[c_4334,c_6841]) ).
tcf(c_67516,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK18,singleton(X1)),iPr_def_11)
| in(sK2(X0,sK18,singleton(X1)),X0)
| ( set_union2(X0,sK18) = singleton(X1) )
| ( sK2(X0,sK18,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_5047]) ).
tcf(c_67517,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK18,singleton(X1)),iPr_def_11)
| in(sK2(X0,sK18,singleton(X1)),X0)
| ( set_union2(X0,sK18) = singleton(X1) )
| ( sK2(X0,sK18,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_3640]) ).
tcf(c_67518,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_10,singleton(X1)),iPr_def_11)
| in(sK2(X0,iPr_def_10,singleton(X1)),X0)
| ( set_union2(X0,iPr_def_10) = singleton(X1) )
| ( sK2(X0,iPr_def_10,singleton(X1)) = X1 )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4334,c_9540]) ).
tcf(c_67519,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_10,singleton(X1)),X0)
| ( set_union2(X0,iPr_def_10) = singleton(X1) )
| ( sK2(X0,iPr_def_10,singleton(X1)) = X1 )
| ~ in(iPr_def_11,sK2(X0,iPr_def_10,singleton(X1))) ),
inference(superposition,[status(thm)],[c_4334,c_6289]) ).
tcf(c_67520,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,iPr_def_10,singleton(X1)),iPr_def_11)
| in(sK2(X0,iPr_def_10,singleton(X1)),X0)
| ( set_union2(X0,iPr_def_10) = singleton(X1) )
| ( sK2(X0,iPr_def_10,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_4912]) ).
tcf(c_67521,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_10,singleton(X1)),X0)
| ( set_union2(X0,iPr_def_10) = singleton(X1) )
| ( sK2(X0,iPr_def_10,singleton(X1)) = sK18 )
| ( sK2(X0,iPr_def_10,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_3592]) ).
tcf(c_67522,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_10,singleton(X1)),iPr_def_11)
| in(sK2(X0,iPr_def_10,singleton(X1)),X0)
| ( set_union2(X0,iPr_def_10) = singleton(X1) )
| ( sK2(X0,iPr_def_10,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_3614]) ).
tcf(c_67523,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_11,singleton(X1)),sK18)
| in(sK2(X0,iPr_def_11,singleton(X1)),X0)
| ( set_union2(X0,iPr_def_11) = singleton(X1) )
| ( sK2(X0,iPr_def_11,singleton(X1)) = sK18 )
| ( sK2(X0,iPr_def_11,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_33457]) ).
tcf(c_67524,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,iPr_def_11,singleton(X1)),iPr_def_10)
| in(sK2(X0,iPr_def_11,singleton(X1)),sK18)
| in(sK2(X0,iPr_def_11,singleton(X1)),X0)
| ( set_union2(X0,iPr_def_11) = singleton(X1) )
| ( sK2(X0,iPr_def_11,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_4035]) ).
tcf(c_67525,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_union2(X0,X1),X0,singleton(X2)),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X0) = singleton(X2) )
| ( sK2(set_union2(X0,X1),X0,singleton(X2)) = X2 )
| ~ in(sK2(set_union2(X0,X1),X0,singleton(X2)),singleton(X2)) ),
inference(superposition,[status(thm)],[c_4334,c_4078]) ).
tcf(c_67526,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_union2(X0,X1),singleton(X2),singleton(X2)),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),singleton(X2)) = singleton(X2) )
| ( sK2(set_union2(X0,X1),singleton(X2),singleton(X2)) = X2 )
| ~ in(sK2(set_union2(X0,X1),singleton(X2),singleton(X2)),X1) ),
inference(superposition,[status(thm)],[c_4334,c_4079]) ).
tcf(c_67527,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK2(X1,sK5(iPr_def_11),singleton(X2)))
| in(sK2(X1,sK5(iPr_def_11),singleton(X2)),X1)
| in(sK2(X1,sK5(iPr_def_11),singleton(X2)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,sK5(iPr_def_11)) = singleton(X2) )
| ( sK2(X1,sK5(iPr_def_11),singleton(X2)) = X2 )
| ( sK2(X1,sK5(iPr_def_11),singleton(X2)) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4334,c_7243]) ).
tcf(c_67528,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK5(iPr_def_11),singleton(X1)),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = singleton(X1) )
| ( sK2(X0,sK5(iPr_def_11),singleton(X1)) = X1 )
| ~ subset(iPr_def_11,sK2(X0,sK5(iPr_def_11),singleton(X1))) ),
inference(superposition,[status(thm)],[c_4334,c_23189]) ).
tcf(c_67529,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK2(X1,sK3(iPr_def_11),singleton(X2)))
| in(sK2(X1,sK3(iPr_def_11),singleton(X2)),X1)
| in(sK2(X1,sK3(iPr_def_11),singleton(X2)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,sK3(iPr_def_11)) = singleton(X2) )
| ( sK2(X1,sK3(iPr_def_11),singleton(X2)) = X2 )
| ( sK2(X1,sK3(iPr_def_11),singleton(X2)) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4334,c_9906]) ).
tcf(c_67530,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK2(X1,sK4(iPr_def_11),singleton(X2)))
| in(sK2(X1,sK4(iPr_def_11),singleton(X2)),X1)
| in(sK2(X1,sK4(iPr_def_11),singleton(X2)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,sK4(iPr_def_11)) = singleton(X2) )
| ( sK2(X1,sK4(iPr_def_11),singleton(X2)) = X2 )
| ( sK2(X1,sK4(iPr_def_11),singleton(X2)) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4334,c_45801]) ).
tcf(c_67531,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X0,X1,singleton(X2)),X1)
| in(sK3(iPr_def_11),sK2(X0,X1,singleton(X2)))
| in(sK2(X0,X1,singleton(X2)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = singleton(X2) )
| ( sK2(X0,X1,singleton(X2)) = X2 )
| ( sK2(X0,X1,singleton(X2)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4334,c_49877]) ).
tcf(c_67532,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X0,X1,singleton(X2)),X1)
| in(sK5(iPr_def_11),sK2(X0,X1,singleton(X2)))
| in(sK2(X0,X1,singleton(X2)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = singleton(X2) )
| ( sK2(X0,X1,singleton(X2)) = X2 )
| ( sK2(X0,X1,singleton(X2)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4334,c_7260]) ).
tcf(c_67533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X2,singleton(X3)),X2)
| ( set_union2(X0,X2) = singleton(X3) )
| ( sK2(X0,X2,singleton(X3)) = X3 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4334,c_359]) ).
tcf(c_67534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X2,singleton(X3)),X1)
| in(sK2(X0,X2,singleton(X3)),X2)
| ( set_union2(X0,X2) = singleton(X3) )
| ( sK2(X0,X2,singleton(X3)) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4334,c_358]) ).
tcf(c_67535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X1,X2,singleton(X3)))
| in(sK2(X1,X2,singleton(X3)),X2)
| in(sK2(X1,X2,singleton(X3)),X0)
| ( set_union2(X1,X2) = singleton(X3) )
| ( sK2(X1,X2,singleton(X3)) = X3 )
| ( sK2(X1,X2,singleton(X3)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4334,c_77]) ).
tcf(c_67536,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,singleton(X2)),X0)
| in(sK2(X0,X1,singleton(X2)),X1)
| ( set_union2(X0,X1) = singleton(X2) )
| ( sK2(X0,X1,singleton(X2)) = X2 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4334,c_65]) ).
tcf(c_67537,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,singleton(X2)),X1)
| ( set_union2(X0,X1) = singleton(X2) )
| ( sK2(X0,X1,singleton(X2)) = X2 )
| ~ in(X0,sK2(X0,X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_4334,c_49]) ).
tcf(c_67538,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,singleton(X2)),X1)
| ( set_union2(X0,X1) = singleton(X2) )
| ( sK2(X0,X1,singleton(X2)) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4334,c_137]) ).
tcf(c_67539,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,singleton(X2)),X0)
| in(sK2(X0,X1,singleton(X2)),X1)
| ( set_union2(X0,X1) = singleton(X2) )
| ( sK2(X0,X1,singleton(X2)) = X2 ) ),
inference(superposition,[status(thm)],[c_4334,c_127]) ).
tcf(c_67540,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(singleton(X0),X1,singleton(X2)),X1)
| ( set_union2(singleton(X0),X1) = singleton(X2) )
| ( sK2(singleton(X0),X1,singleton(X2)) = X2 )
| ( sK2(singleton(X0),X1,singleton(X2)) = X0 ) ),
inference(superposition,[status(thm)],[c_4334,c_62]) ).
tcf(c_67541,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,singleton(X2)),X1)
| ( set_union2(X0,X1) = singleton(X2) )
| ( sK2(X0,X1,singleton(X2)) = X2 )
| ~ in(sK2(X0,X1,singleton(X2)),singleton(X2)) ),
inference(superposition,[status(thm)],[c_4334,c_66]) ).
tcf(c_67543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(set_union2(X0,X1),X3,singleton(X4)))
| in(sK2(set_union2(X0,X1),X3,singleton(X4)),X3)
| in(sK2(set_union2(X0,X1),X3,singleton(X4)),X2)
| ( set_union2(set_union2(X0,X1),X3) = singleton(X4) )
| ( sK2(set_union2(X0,X1),X3,singleton(X4)) = X4 )
| ( sK2(set_union2(X0,X1),X3,singleton(X4)) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4334,c_4213]) ).
tcf(c_67544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(set_union2(X0,X1),X3,singleton(X4)))
| in(sK2(set_union2(X0,X1),X3,singleton(X4)),X3)
| in(sK2(set_union2(X0,X1),X3,singleton(X4)),X2)
| ( set_union2(set_union2(X0,X1),X3) = singleton(X4) )
| ( sK2(set_union2(X0,X1),X3,singleton(X4)) = X4 )
| ( sK2(set_union2(X0,X1),X3,singleton(X4)) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4334,c_4212]) ).
tcf(c_67545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_union2(X0,X1),X2,singleton(X3)),X2)
| in(sK2(set_union2(X0,X1),X2,singleton(X3)),X1)
| in(sK2(set_union2(X0,X1),X2,singleton(X3)),X0)
| ( set_union2(set_union2(X0,X1),X2) = singleton(X3) )
| ( sK2(set_union2(X0,X1),X2,singleton(X3)) = X3 ) ),
inference(superposition,[status(thm)],[c_4334,c_71]) ).
tcf(c_67546,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X0,singleton(X1)),X0)
| ( set_union2(empty_set,X0) = singleton(X1) )
| ( sK2(empty_set,X0,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_7097]) ).
tcf(c_67547,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,singleton(X1)),iPr_def_11)
| in(sK2(sK18,X0,singleton(X1)),X0)
| ( set_union2(sK18,X0) = singleton(X1) )
| ( sK2(sK18,X0,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_12813]) ).
tcf(c_67548,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK18,X0,singleton(X1)),X0)
| ( set_union2(sK18,X0) = singleton(X1) )
| ( sK2(sK18,X0,singleton(X1)) = X1 )
| ~ in(iPr_def_11,sK2(sK18,X0,singleton(X1))) ),
inference(superposition,[status(thm)],[c_4334,c_6841]) ).
tcf(c_67549,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK18,X0,singleton(X1)),iPr_def_11)
| in(sK2(sK18,X0,singleton(X1)),X0)
| ( set_union2(sK18,X0) = singleton(X1) )
| ( sK2(sK18,X0,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_5047]) ).
tcf(c_67550,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK18,X0,singleton(X1)),iPr_def_11)
| in(sK2(sK18,X0,singleton(X1)),X0)
| ( set_union2(sK18,X0) = singleton(X1) )
| ( sK2(sK18,X0,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_3640]) ).
tcf(c_67551,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X0,singleton(X1)),iPr_def_11)
| in(sK2(iPr_def_10,X0,singleton(X1)),X0)
| ( set_union2(iPr_def_10,X0) = singleton(X1) )
| ( sK2(iPr_def_10,X0,singleton(X1)) = X1 )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4334,c_9540]) ).
tcf(c_67552,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_10,X0,singleton(X1)),X0)
| ( set_union2(iPr_def_10,X0) = singleton(X1) )
| ( sK2(iPr_def_10,X0,singleton(X1)) = X1 )
| ~ in(iPr_def_11,sK2(iPr_def_10,X0,singleton(X1))) ),
inference(superposition,[status(thm)],[c_4334,c_6289]) ).
tcf(c_67553,plain,
! [X0: $i,X1: $i] :
( element(sK2(iPr_def_10,X0,singleton(X1)),iPr_def_11)
| in(sK2(iPr_def_10,X0,singleton(X1)),X0)
| ( set_union2(iPr_def_10,X0) = singleton(X1) )
| ( sK2(iPr_def_10,X0,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_4912]) ).
tcf(c_67554,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_10,X0,singleton(X1)),X0)
| ( set_union2(iPr_def_10,X0) = singleton(X1) )
| ( sK2(iPr_def_10,X0,singleton(X1)) = sK18 )
| ( sK2(iPr_def_10,X0,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_3592]) ).
tcf(c_67555,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_10,X0,singleton(X1)),iPr_def_11)
| in(sK2(iPr_def_10,X0,singleton(X1)),X0)
| ( set_union2(iPr_def_10,X0) = singleton(X1) )
| ( sK2(iPr_def_10,X0,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_3614]) ).
tcf(c_67556,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_11,X0,singleton(X1)),sK18)
| in(sK2(iPr_def_11,X0,singleton(X1)),X0)
| ( set_union2(iPr_def_11,X0) = singleton(X1) )
| ( sK2(iPr_def_11,X0,singleton(X1)) = sK18 )
| ( sK2(iPr_def_11,X0,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_33457]) ).
tcf(c_67557,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_11,X0,singleton(X1)),iPr_def_10)
| in(sK2(iPr_def_11,X0,singleton(X1)),sK18)
| in(sK2(iPr_def_11,X0,singleton(X1)),X0)
| ( set_union2(iPr_def_11,X0) = singleton(X1) )
| ( sK2(iPr_def_11,X0,singleton(X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_4334,c_4035]) ).
tcf(c_67558,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK2(sK5(iPr_def_11),X1,singleton(X2)))
| in(sK2(sK5(iPr_def_11),X1,singleton(X2)),X1)
| in(sK2(sK5(iPr_def_11),X1,singleton(X2)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X1) = singleton(X2) )
| ( sK2(sK5(iPr_def_11),X1,singleton(X2)) = X2 )
| ( sK2(sK5(iPr_def_11),X1,singleton(X2)) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4334,c_7243]) ).
tcf(c_67559,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK5(iPr_def_11),X0,singleton(X1)),X0)
| ( set_union2(sK5(iPr_def_11),X0) = singleton(X1) )
| ( sK2(sK5(iPr_def_11),X0,singleton(X1)) = X1 )
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,singleton(X1))) ),
inference(superposition,[status(thm)],[c_4334,c_23189]) ).
tcf(c_67560,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK2(sK3(iPr_def_11),X1,singleton(X2)))
| in(sK2(sK3(iPr_def_11),X1,singleton(X2)),X1)
| in(sK2(sK3(iPr_def_11),X1,singleton(X2)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X1) = singleton(X2) )
| ( sK2(sK3(iPr_def_11),X1,singleton(X2)) = X2 )
| ( sK2(sK3(iPr_def_11),X1,singleton(X2)) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4334,c_9906]) ).
tcf(c_67561,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK2(sK4(iPr_def_11),X1,singleton(X2)))
| in(sK2(sK4(iPr_def_11),X1,singleton(X2)),X1)
| in(sK2(sK4(iPr_def_11),X1,singleton(X2)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X1) = singleton(X2) )
| ( sK2(sK4(iPr_def_11),X1,singleton(X2)) = X2 )
| ( sK2(sK4(iPr_def_11),X1,singleton(X2)) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4334,c_45801]) ).
tcf(c_67562,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X0,singleton(X1)),X0)
| ( set_union2(X0,X0) = singleton(X1) )
| ( sK2(X0,X0,singleton(X1)) = X1 ) ),
inference(equality_factoring,[status(thm)],[c_4334]) ).
tcf(c_67564,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X0,singleton(X1)),X0)
| ( singleton(X1) = X0 )
| ( sK2(X0,X0,singleton(X1)) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_67562,c_97]) ).
tcf(c_67568,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X0,singleton(X1)),X0)
| ( singleton(X1) = X0 )
| ( sK2(empty_set,X0,singleton(X1)) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_67546,c_3423]) ).
tcf(c_67572,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,empty_set,singleton(X1)),X0)
| ( singleton(X1) = X0 )
| ( sK2(X0,empty_set,singleton(X1)) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_67513,c_126]) ).
tcf(c_68373,plain,
( ~ in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_9567,c_43063]) ).
tcf(c_68374,plain,
( in(sK3(iPr_def_11),iPr_def_10)
| ~ in(sK18,sK3(iPr_def_11)) ),
inference(renaming,[status(thm)],[c_68373]) ).
tcf(c_68379,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK18)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_68374]) ).
tcf(c_68382,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK18)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9901,c_68374]) ).
tcf(c_68383,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ empty(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_9927,c_68374]) ).
tcf(c_68385,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK18)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_68374]) ).
tcf(c_68397,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK18)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_68385,c_3400]) ).
tcf(c_68415,plain,
( ~ in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_11003,c_43125]) ).
tcf(c_68416,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| ~ in(sK18,sK4(iPr_def_11)) ),
inference(renaming,[status(thm)],[c_68415]) ).
tcf(c_68423,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK18)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11185,c_68416]) ).
tcf(c_68424,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ empty(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_11211,c_68416]) ).
tcf(c_68437,plain,
! [X0: $i,X1: $i] : in(X0,set_union2(singleton(X0),X1)),
inference(global_subsumption_just,[status(thm)],[c_14278,c_61,c_4062]) ).
tcf(c_68440,plain,
! [X0: $i,X1: $i] : in(X0,set_union2(X1,singleton(X0))),
inference(superposition,[status(thm)],[c_58,c_68437]) ).
tcf(c_68445,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(set_union2(singleton(X0),X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(singleton(X0),X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(set_union2(singleton(X0),X1))
| ~ in(set_union2(singleton(X0),X1),sK18) ),
inference(superposition,[status(thm)],[c_68437,c_49877]) ).
tcf(c_68446,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(set_union2(singleton(X0),X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(singleton(X0),X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(set_union2(singleton(X0),X1))
| ~ in(set_union2(singleton(X0),X1),sK18) ),
inference(superposition,[status(thm)],[c_68437,c_7260]) ).
tcf(c_68447,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(set_union2(singleton(X0),X1),X2) ),
inference(superposition,[status(thm)],[c_68437,c_359]) ).
tcf(c_68448,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(set_union2(singleton(X0),X1),X2) ),
inference(superposition,[status(thm)],[c_68437,c_358]) ).
tcf(c_68449,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ epsilon_connected(set_union2(singleton(X1),X2))
| ~ in(X0,set_union2(singleton(X1),X2)) ),
inference(superposition,[status(thm)],[c_68437,c_77]) ).
tcf(c_68450,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_union2(singleton(X0),X1))
| ~ epsilon_transitive(set_union2(singleton(X0),X1)) ),
inference(superposition,[status(thm)],[c_68437,c_65]) ).
tcf(c_68451,plain,
! [X0: $i,X1: $i] : ~ in(set_union2(singleton(X0),X1),X0),
inference(superposition,[status(thm)],[c_68437,c_49]) ).
tcf(c_68454,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X0,X2)
| ( X0 = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(singleton(X0),X1)) ),
inference(superposition,[status(thm)],[c_68437,c_4213]) ).
tcf(c_68455,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X0,X2)
| ( X0 = X2 )
| ~ in(X2,singleton(X0))
| ~ epsilon_connected(set_union2(singleton(X0),X1)) ),
inference(superposition,[status(thm)],[c_68437,c_4212]) ).
tcf(c_68457,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(singleton(set_union2(X0,X1)),X2),X1),
inference(superposition,[status(thm)],[c_68437,c_3641]) ).
tcf(c_68458,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(singleton(set_union2(X0,X1)),X2),X0),
inference(superposition,[status(thm)],[c_68437,c_3615]) ).
tcf(c_68555,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(set_union2(X0,singleton(X1)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X1 )
| ( set_union2(X0,singleton(X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(set_union2(X0,singleton(X1)))
| ~ in(set_union2(X0,singleton(X1)),sK18) ),
inference(superposition,[status(thm)],[c_68440,c_49877]) ).
tcf(c_68556,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(set_union2(X0,singleton(X1)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X1 )
| ( set_union2(X0,singleton(X1)) = sK5(iPr_def_11) )
| ~ epsilon_connected(set_union2(X0,singleton(X1)))
| ~ in(set_union2(X0,singleton(X1)),sK18) ),
inference(superposition,[status(thm)],[c_68440,c_7260]) ).
tcf(c_68557,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(set_union2(X0,singleton(X1)),X2) ),
inference(superposition,[status(thm)],[c_68440,c_359]) ).
tcf(c_68558,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X1,X2)
| ~ subset(set_union2(X0,singleton(X1)),X2) ),
inference(superposition,[status(thm)],[c_68440,c_358]) ).
tcf(c_68559,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X0,X2)
| ( X0 = X2 )
| ~ epsilon_connected(set_union2(X1,singleton(X2)))
| ~ in(X0,set_union2(X1,singleton(X2))) ),
inference(superposition,[status(thm)],[c_68440,c_77]) ).
tcf(c_68560,plain,
! [X0: $i,X1: $i] :
( subset(X1,set_union2(X0,singleton(X1)))
| ~ epsilon_transitive(set_union2(X0,singleton(X1))) ),
inference(superposition,[status(thm)],[c_68440,c_65]) ).
tcf(c_68561,plain,
! [X0: $i,X1: $i] : ~ in(set_union2(X0,singleton(X1)),X1),
inference(superposition,[status(thm)],[c_68440,c_49]) ).
tcf(c_68564,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| in(X1,X2)
| ( X1 = X2 )
| ~ in(X2,singleton(X1))
| ~ epsilon_connected(set_union2(X0,singleton(X1))) ),
inference(superposition,[status(thm)],[c_68440,c_4213]) ).
tcf(c_68565,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| in(X1,X2)
| ( X1 = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,singleton(X1))) ),
inference(superposition,[status(thm)],[c_68440,c_4212]) ).
tcf(c_68567,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(X0,singleton(set_union2(X1,X2))),X2),
inference(superposition,[status(thm)],[c_68440,c_3641]) ).
tcf(c_68568,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(X0,singleton(set_union2(X1,X2))),X1),
inference(superposition,[status(thm)],[c_68440,c_3615]) ).
tcf(c_68737,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X0))
| ~ subset(set_union2(singleton(powerset(X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_3769,c_68451]) ).
tcf(c_68738,plain,
! [X0: $i] :
( empty(sK18)
| in(sK5(sK18),set_union2(singleton(sK5(sK18)),X0))
| ( set_union2(singleton(sK5(sK18)),X0) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(set_union2(singleton(sK5(sK18)),X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_68451]) ).
tcf(c_68739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),set_union2(singleton(sK2(X0,X1,X2)),X3))
| ( set_union2(X0,X1) = X2 )
| ( set_union2(singleton(sK2(X0,X1,X2)),X3) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X2)
| ~ in(set_union2(singleton(sK2(X0,X1,X2)),X3),X2) ),
inference(superposition,[status(thm)],[c_4329,c_68451]) ).
tcf(c_68740,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),set_union2(singleton(sK5(iPr_def_11)),X0))
| ( sK5(iPr_def_11) = X1 )
| ( set_union2(singleton(sK5(iPr_def_11)),X0) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(set_union2(singleton(sK5(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_68451]) ).
tcf(c_68741,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),set_union2(singleton(sK5(iPr_def_11)),X0))
| ( set_union2(singleton(sK5(iPr_def_11)),X0) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(set_union2(singleton(sK5(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_68451]) ).
tcf(c_68742,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),set_union2(singleton(sK5(iPr_def_11)),X0))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(singleton(sK5(iPr_def_11)),X0) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(sK5(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_68451]) ).
tcf(c_68743,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(singleton(sK5(iPr_def_11)),X0))
| ( set_union2(singleton(sK5(iPr_def_11)),X0) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(sK5(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_68451]) ).
tcf(c_68744,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(sK5(iPr_def_11)),X0) = sK5(iPr_def_11) )
| ~ empty(set_union2(singleton(sK5(iPr_def_11)),X0))
| ~ in(set_union2(singleton(sK5(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_68451]) ).
tcf(c_68745,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(singleton(sK5(iPr_def_11)),X0))
| ( set_union2(singleton(sK5(iPr_def_11)),X0) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(sK5(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_68451]) ).
tcf(c_68746,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),set_union2(singleton(sK5(iPr_def_11)),X0))
| ( sK5(iPr_def_11) = X1 )
| ( set_union2(singleton(sK5(iPr_def_11)),X0) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(set_union2(singleton(sK5(iPr_def_11)),X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_68451]) ).
tcf(c_68747,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(sK5(iPr_def_11),singleton(sK5(iPr_def_11)))
| ( set_union2(singleton(sK5(iPr_def_11)),X0) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(sK5(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_7266,c_68451]) ).
tcf(c_68748,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),set_union2(singleton(sK1(iPr_def_11)),X0))
| ( sK1(iPr_def_11) = X1 )
| ( set_union2(singleton(sK1(iPr_def_11)),X0) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(set_union2(singleton(sK1(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_68451]) ).
tcf(c_68749,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),set_union2(singleton(sK1(iPr_def_11)),X0))
| ( sK1(iPr_def_11) = X1 )
| ( set_union2(singleton(sK1(iPr_def_11)),X0) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(set_union2(singleton(sK1(iPr_def_11)),X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_68451]) ).
tcf(c_68750,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),set_union2(singleton(sK3(iPr_def_11)),X0))
| ( sK3(iPr_def_11) = X1 )
| ( set_union2(singleton(sK3(iPr_def_11)),X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(set_union2(singleton(sK3(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_68451]) ).
tcf(c_68751,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),set_union2(singleton(sK3(iPr_def_11)),X0))
| ( set_union2(singleton(sK3(iPr_def_11)),X0) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(set_union2(singleton(sK3(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_68451]) ).
tcf(c_68752,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),set_union2(singleton(sK3(iPr_def_11)),X0))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(singleton(sK3(iPr_def_11)),X0) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(sK3(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_68451]) ).
tcf(c_68753,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(singleton(sK3(iPr_def_11)),X0))
| ( set_union2(singleton(sK3(iPr_def_11)),X0) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(sK3(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_68451]) ).
tcf(c_68754,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(sK3(iPr_def_11)),X0) = sK3(iPr_def_11) )
| ~ empty(set_union2(singleton(sK3(iPr_def_11)),X0))
| ~ in(set_union2(singleton(sK3(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_68451]) ).
tcf(c_68755,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(singleton(sK3(iPr_def_11)),X0))
| ( set_union2(singleton(sK3(iPr_def_11)),X0) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(sK3(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_68451]) ).
tcf(c_68756,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),set_union2(singleton(sK3(iPr_def_11)),X0))
| ( sK3(iPr_def_11) = X1 )
| ( set_union2(singleton(sK3(iPr_def_11)),X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(set_union2(singleton(sK3(iPr_def_11)),X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_68451]) ).
tcf(c_68757,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),singleton(sK3(iPr_def_11)))
| ( set_union2(singleton(sK3(iPr_def_11)),X0) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(sK3(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_9930,c_68451]) ).
tcf(c_68758,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),set_union2(singleton(sK4(iPr_def_11)),X0))
| ( set_union2(singleton(sK4(iPr_def_11)),X0) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(set_union2(singleton(sK4(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_68451]) ).
tcf(c_68759,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),set_union2(singleton(sK4(iPr_def_11)),X0))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(singleton(sK4(iPr_def_11)),X0) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(sK4(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_68451]) ).
tcf(c_68760,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(sK4(iPr_def_11)),X0))
| ( set_union2(singleton(sK4(iPr_def_11)),X0) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(sK4(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_68451]) ).
tcf(c_68761,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(sK4(iPr_def_11)),X0) = sK4(iPr_def_11) )
| ~ empty(set_union2(singleton(sK4(iPr_def_11)),X0))
| ~ in(set_union2(singleton(sK4(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_68451]) ).
tcf(c_68762,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(sK4(iPr_def_11)),X0))
| ( set_union2(singleton(sK4(iPr_def_11)),X0) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(sK4(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_68451]) ).
tcf(c_68763,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),singleton(sK4(iPr_def_11)))
| ( set_union2(singleton(sK4(iPr_def_11)),X0) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(sK4(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_11214,c_68451]) ).
tcf(c_68764,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),set_union2(singleton(sK2(sK18,X0,sK18)),X1))
| ( set_union2(sK18,X0) = sK18 )
| ( set_union2(singleton(sK2(sK18,X0,sK18)),X1) = sK2(sK18,X0,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(set_union2(singleton(sK2(sK18,X0,sK18)),X1),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_68451]) ).
tcf(c_68775,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ subset(set_union2(X0,singleton(powerset(X1))),X1) ),
inference(superposition,[status(thm)],[c_3769,c_68561]) ).
tcf(c_68776,plain,
! [X0: $i] :
( empty(sK18)
| in(sK5(sK18),set_union2(X0,singleton(sK5(sK18))))
| ( set_union2(X0,singleton(sK5(sK18))) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(set_union2(X0,singleton(sK5(sK18))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_68561]) ).
tcf(c_68777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),set_union2(X0,singleton(sK2(X1,X2,X3))))
| ( set_union2(X1,X2) = X3 )
| ( set_union2(X0,singleton(sK2(X1,X2,X3))) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X3)
| ~ in(set_union2(X0,singleton(sK2(X1,X2,X3))),X3) ),
inference(superposition,[status(thm)],[c_4329,c_68561]) ).
tcf(c_68778,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),set_union2(X0,singleton(sK5(iPr_def_11))))
| ( sK5(iPr_def_11) = X1 )
| ( set_union2(X0,singleton(sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(set_union2(X0,singleton(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_68561]) ).
tcf(c_68779,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),set_union2(X0,singleton(sK5(iPr_def_11))))
| ( set_union2(X0,singleton(sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(set_union2(X0,singleton(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_68561]) ).
tcf(c_68780,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),set_union2(X0,singleton(sK5(iPr_def_11))))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,singleton(sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_68561]) ).
tcf(c_68781,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,singleton(sK5(iPr_def_11))))
| ( set_union2(X0,singleton(sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_68561]) ).
tcf(c_68782,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ empty(set_union2(X0,singleton(sK5(iPr_def_11))))
| ~ in(set_union2(X0,singleton(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_68561]) ).
tcf(c_68783,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,singleton(sK5(iPr_def_11))))
| ( set_union2(X0,singleton(sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_68561]) ).
tcf(c_68784,plain,
! [X0: $i,X1: $i] :
( in(X1,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),set_union2(X0,singleton(sK5(iPr_def_11))))
| ( sK5(iPr_def_11) = X1 )
| ( set_union2(X0,singleton(sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(set_union2(X0,singleton(sK5(iPr_def_11))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_68561]) ).
tcf(c_68785,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(sK5(iPr_def_11),singleton(sK5(iPr_def_11)))
| ( set_union2(X0,singleton(sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7266,c_68561]) ).
tcf(c_68786,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),set_union2(X0,singleton(sK1(iPr_def_11))))
| ( sK1(iPr_def_11) = X1 )
| ( set_union2(X0,singleton(sK1(iPr_def_11))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(set_union2(X0,singleton(sK1(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_68561]) ).
tcf(c_68787,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(iPr_def_11)
| in(X1,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X1)
| in(sK1(iPr_def_11),set_union2(X0,singleton(sK1(iPr_def_11))))
| ( sK1(iPr_def_11) = X1 )
| ( set_union2(X0,singleton(sK1(iPr_def_11))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(set_union2(X0,singleton(sK1(iPr_def_11))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_68561]) ).
tcf(c_68788,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),set_union2(X0,singleton(sK3(iPr_def_11))))
| ( sK3(iPr_def_11) = X1 )
| ( set_union2(X0,singleton(sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(set_union2(X0,singleton(sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_68561]) ).
tcf(c_68789,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),set_union2(X0,singleton(sK3(iPr_def_11))))
| ( set_union2(X0,singleton(sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(set_union2(X0,singleton(sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_68561]) ).
tcf(c_68790,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),set_union2(X0,singleton(sK3(iPr_def_11))))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(X0,singleton(sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_68561]) ).
tcf(c_68791,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,singleton(sK3(iPr_def_11))))
| ( set_union2(X0,singleton(sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_68561]) ).
tcf(c_68792,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ empty(set_union2(X0,singleton(sK3(iPr_def_11))))
| ~ in(set_union2(X0,singleton(sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_68561]) ).
tcf(c_68793,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,singleton(sK3(iPr_def_11))))
| ( set_union2(X0,singleton(sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_68561]) ).
tcf(c_68794,plain,
! [X0: $i,X1: $i] :
( in(X1,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),set_union2(X0,singleton(sK3(iPr_def_11))))
| ( sK3(iPr_def_11) = X1 )
| ( set_union2(X0,singleton(sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,sK18)
| ~ in(set_union2(X0,singleton(sK3(iPr_def_11))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_68561]) ).
tcf(c_68795,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),singleton(sK3(iPr_def_11)))
| ( set_union2(X0,singleton(sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9930,c_68561]) ).
tcf(c_68796,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),set_union2(X0,singleton(sK4(iPr_def_11))))
| ( set_union2(X0,singleton(sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X1)
| ~ in(set_union2(X0,singleton(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_68561]) ).
tcf(c_68797,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),set_union2(X0,singleton(sK4(iPr_def_11))))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(X0,singleton(sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_68561]) ).
tcf(c_68798,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,singleton(sK4(iPr_def_11))))
| ( set_union2(X0,singleton(sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_68561]) ).
tcf(c_68799,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ empty(set_union2(X0,singleton(sK4(iPr_def_11))))
| ~ in(set_union2(X0,singleton(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_68561]) ).
tcf(c_68800,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,singleton(sK4(iPr_def_11))))
| ( set_union2(X0,singleton(sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_68561]) ).
tcf(c_68801,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),singleton(sK4(iPr_def_11)))
| ( set_union2(X0,singleton(sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11214,c_68561]) ).
tcf(c_68802,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(sK2(sK18,X1,sK18),X1)
| in(sK2(sK18,X1,sK18),set_union2(X0,singleton(sK2(sK18,X1,sK18))))
| ( set_union2(sK18,X1) = sK18 )
| ( set_union2(X0,singleton(sK2(sK18,X1,sK18))) = sK2(sK18,X1,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(set_union2(X0,singleton(sK2(sK18,X1,sK18))),sK18) ),
inference(superposition,[status(thm)],[c_66255,c_68561]) ).
tcf(c_68815,plain,
( in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_33496,c_49877]) ).
tcf(c_68817,plain,
! [X0: $i] :
( ( sK5(iPr_def_11) = sK18 )
| ~ empty(X0)
| ~ subset(sK18,X0) ),
inference(superposition,[status(thm)],[c_33496,c_359]) ).
tcf(c_68818,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ~ subset(sK18,X0) ),
inference(superposition,[status(thm)],[c_33496,c_358]) ).
tcf(c_68819,plain,
! [X0: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_33496,c_77]) ).
tcf(c_68820,plain,
( subset(sK5(iPr_def_11),sK18)
| ( sK5(iPr_def_11) = sK18 )
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_33496,c_65]) ).
tcf(c_68821,plain,
( ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_33496,c_49]) ).
tcf(c_68823,plain,
( element(sK5(iPr_def_11),sK18)
| ( sK5(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_33496,c_127]) ).
tcf(c_68824,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| ( sK5(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_33496,c_12813]) ).
tcf(c_68826,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| ( sK5(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_33496,c_5047]) ).
tcf(c_68834,plain,
( subset(sK5(iPr_def_11),sK18)
| ( sK5(iPr_def_11) = sK18 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_68820,c_2426]) ).
tcf(c_68844,plain,
( in(sK18,sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_68815,c_2427]) ).
tcf(c_68859,plain,
! [X0: $i] :
( subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_68834,c_53126]) ).
tcf(c_68860,plain,
! [X0: $i] :
( subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_68834,c_53093]) ).
tcf(c_68864,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_68834,c_24160]) ).
tcf(c_68865,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_68834,c_24149]) ).
tcf(c_68870,plain,
! [X0: $i] :
( subset(X0,sK18)
| ( sK5(iPr_def_11) = sK18 )
| ~ subset(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_68834,c_128]) ).
tcf(c_68871,plain,
( subset(sK5(iPr_def_11),iPr_def_10)
| ( sK5(iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_68834,c_3931]) ).
tcf(c_68873,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ empty(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68834,c_24142]) ).
tcf(c_68874,plain,
! [X0: $i] :
( element(X0,sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68834,c_13661]) ).
tcf(c_68923,plain,
( ~ in(sK18,sK18)
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( sK3(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = sK18 )
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_68844,c_43063,c_68844]) ).
tcf(c_68924,plain,
( in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(renaming,[status(thm)],[c_68923]) ).
tcf(c_68932,plain,
( in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_68924,c_3592]) ).
tcf(c_68953,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK18,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_68932,c_359]) ).
tcf(c_68954,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_68932,c_358]) ).
tcf(c_68955,plain,
! [X0: $i] :
( in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(sK18,sK18)
| ~ in(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_68932,c_77]) ).
tcf(c_68956,plain,
( subset(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_68932,c_65]) ).
tcf(c_68958,plain,
( in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_68932,c_137]) ).
tcf(c_68959,plain,
( element(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_68932,c_127]) ).
tcf(c_68960,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(sK18,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68932,c_9906]) ).
tcf(c_69029,plain,
( subset(sK5(powerset(sK5(iPr_def_11))),sK18)
| ( sK5(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_3564,c_68870]) ).
tcf(c_69030,plain,
( subset(empty_set,sK18)
| ( sK5(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_3420,c_68870]) ).
tcf(c_69031,plain,
( epsilon_transitive(powerset(sK5(iPr_def_11)))
| subset(sK1(powerset(sK5(iPr_def_11))),sK18)
| ( sK5(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_3566,c_68870]) ).
tcf(c_69032,plain,
( epsilon_connected(powerset(sK5(iPr_def_11)))
| subset(sK3(powerset(sK5(iPr_def_11))),sK18)
| ( sK5(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_3567,c_68870]) ).
tcf(c_69033,plain,
( epsilon_connected(powerset(sK5(iPr_def_11)))
| subset(sK4(powerset(sK5(iPr_def_11))),sK18)
| ( sK5(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_3568,c_68870]) ).
tcf(c_69034,plain,
( epsilon_connected(sK5(iPr_def_11))
| subset(sK3(sK5(iPr_def_11)),sK18)
| ( sK5(iPr_def_11) = sK18 )
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3807,c_68870]) ).
tcf(c_69035,plain,
( epsilon_connected(sK5(iPr_def_11))
| subset(sK4(sK5(iPr_def_11)),sK18)
| ( sK5(iPr_def_11) = sK18 )
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3808,c_68870]) ).
tcf(c_69036,plain,
( empty(sK5(iPr_def_11))
| subset(sK5(sK5(iPr_def_11)),sK18)
| ( sK5(iPr_def_11) = sK18 )
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3899,c_68870]) ).
tcf(c_69037,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK5(iPr_def_11)),sK18)
| in(sK2(X0,X1,sK5(iPr_def_11)),X1)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4330,c_68870]) ).
tcf(c_69038,plain,
( epsilon_connected(powerset(empty_set))
| subset(sK3(powerset(empty_set)),sK18)
| ( sK5(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_4620,c_68870]) ).
tcf(c_69039,plain,
( epsilon_connected(powerset(empty_set))
| subset(sK4(powerset(empty_set)),sK18)
| ( sK5(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_4637,c_68870]) ).
tcf(c_69040,plain,
( subset(sK5(powerset(sK5(powerset(sK5(iPr_def_11))))),sK18)
| ( sK5(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_5196,c_68870]) ).
tcf(c_69041,plain,
( subset(sK5(powerset(sK5(powerset(sK5(powerset(sK5(iPr_def_11))))))),sK18)
| ( sK5(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_5252,c_68870]) ).
tcf(c_69042,plain,
! [X0: $i] :
( subset(X0,sK18)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7244,c_68870]) ).
tcf(c_69109,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK4(iPr_def_11))
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_66184,c_13671]) ).
tcf(c_69110,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK3(iPr_def_11))
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_66184,c_13665]) ).
tcf(c_69111,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(sK18,X0,sK18),X0)
| in(sK2(sK18,X0,sK18),sK5(iPr_def_11))
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_66184,c_13657]) ).
tcf(c_69112,plain,
! [X0: $i,X1: $i] :
( subset(X0,iPr_def_10)
| in(sK2(sK18,X1,sK18),X1)
| ( set_union2(sK18,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(sK18,X1,sK18)) ),
inference(superposition,[status(thm)],[c_66184,c_128]) ).
tcf(c_69114,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66184,c_49877]) ).
tcf(c_69115,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(sK18,X0,sK18))
| in(sK2(sK18,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK18,X0) = sK18 )
| ( sK2(sK18,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66184,c_7260]) ).
tcf(c_69116,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_66184,c_359]) ).
tcf(c_69117,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| element(sK2(sK18,X0,sK18),X1)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_66184,c_358]) ).
tcf(c_69118,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X0)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_66184,c_77]) ).
tcf(c_69119,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| subset(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_66184,c_65]) ).
tcf(c_69120,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(sK18,X0,sK18)) ),
inference(superposition,[status(thm)],[c_66184,c_49]) ).
tcf(c_69123,plain,
! [X0: $i] :
( subset(sK2(sK18,singleton(X0),sK18),iPr_def_10)
| ( set_union2(sK18,singleton(X0)) = sK18 )
| ( sK2(sK18,singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_66184,c_62]) ).
tcf(c_69126,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(sK18,set_union2(X0,X1),sK18))
| in(sK2(sK18,set_union2(X0,X1),sK18),X2)
| ( set_union2(sK18,set_union2(X0,X1)) = sK18 )
| ( sK2(sK18,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_66184,c_4213]) ).
tcf(c_69127,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(sK18,set_union2(X0,X1),sK18))
| in(sK2(sK18,set_union2(X0,X1),sK18),X2)
| ( set_union2(sK18,set_union2(X0,X1)) = sK18 )
| ( sK2(sK18,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_66184,c_4212]) ).
tcf(c_69128,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,set_union2(X0,X1),sK18),iPr_def_10)
| in(sK2(sK18,set_union2(X0,X1),sK18),X1)
| in(sK2(sK18,set_union2(X0,X1),sK18),X0)
| ( set_union2(sK18,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_66184,c_71]) ).
tcf(c_69129,plain,
( subset(sK2(sK18,empty_set,sK18),iPr_def_10)
| ( set_union2(sK18,empty_set) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_66184,c_7097]) ).
tcf(c_69134,plain,
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_66184,c_9540]) ).
tcf(c_69135,plain,
( subset(sK2(sK18,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(sK18,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(sK18,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_66184,c_6289]) ).
tcf(c_69139,plain,
( subset(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_11,sK18),sK18)
| ( set_union2(sK18,iPr_def_11) = sK18 )
| ( sK2(sK18,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_66184,c_33457]) ).
tcf(c_69140,plain,
( subset(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_11,sK18),sK18)
| ( set_union2(sK18,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_66184,c_4035]) ).
tcf(c_69141,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK18,sK5(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(sK18,sK5(iPr_def_11),sK18))
| in(sK2(sK18,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK18,sK5(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66184,c_7243]) ).
tcf(c_69142,plain,
( subset(sK2(sK18,sK5(iPr_def_11),sK18),iPr_def_10)
| ( set_union2(sK18,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK18,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_66184,c_23189]) ).
tcf(c_69143,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK18,sK3(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(sK18,sK3(iPr_def_11),sK18))
| in(sK2(sK18,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK18,sK3(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66184,c_9906]) ).
tcf(c_69144,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK18,sK4(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(sK18,sK4(iPr_def_11),sK18))
| in(sK2(sK18,sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK18,sK4(iPr_def_11)) = sK18 )
| ( sK2(sK18,sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_66184,c_45801]) ).
tcf(c_69326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_union2(X3,X2)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X1)
| in(sK2(X0,X1,set_union2(X2,X3)),X0)
| ( set_union2(X0,X1) = set_union2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_58,c_4337]) ).
tcf(c_69330,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,set_union2(empty_set,X2)),empty_set)
| in(sK2(X0,X1,set_union2(empty_set,X2)),X1)
| in(sK2(X0,X1,set_union2(empty_set,X2)),X0)
| ( set_union2(X0,X1) = set_union2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_3423,c_4337]) ).
tcf(c_69331,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_11),sK18)
| in(sK2(X0,X1,set_union2(iPr_def_10,sK18)),iPr_def_10)
| in(sK2(X0,X1,set_union2(iPr_def_10,sK18)),X1)
| in(sK2(X0,X1,set_union2(iPr_def_10,sK18)),X0)
| ( set_union2(X0,X1) = set_union2(iPr_def_10,sK18) ) ),
inference(superposition,[status(thm)],[c_3424,c_4337]) ).
tcf(c_69332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_union2(X3,X2)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X1)
| in(sK2(X0,X1,set_union2(X2,X3)),X0)
| ( set_union2(X0,X1) = set_union2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_58,c_4337]) ).
tcf(c_69334,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X0)
| in(sK2(X1,X2,set_union2(X0,X0)),X2)
| in(sK2(X1,X2,set_union2(X0,X0)),X1)
| in(sK2(X1,X2,set_union2(X0,X0)),X0)
| ( set_union2(X0,X0) = set_union2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_97,c_4337]) ).
tcf(c_69335,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,set_union2(X2,empty_set)),empty_set)
| in(sK2(X0,X1,set_union2(X2,empty_set)),X1)
| in(sK2(X0,X1,set_union2(X2,empty_set)),X0)
| ( set_union2(X0,X1) = set_union2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_126,c_4337]) ).
tcf(c_69337,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,set_union2(iPr_def_10,sK18)),sK18)
| in(sK2(X0,X1,set_union2(iPr_def_10,sK18)),X1)
| in(sK2(X0,X1,set_union2(iPr_def_10,sK18)),X0)
| ( set_union2(X0,X1) = set_union2(iPr_def_10,sK18) ) ),
inference(superposition,[status(thm)],[c_3424,c_4337]) ).
tcf(c_69338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_union2(X3,X2)),X1)
| in(sK2(X0,X1,set_union2(X2,X3)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X0)
| ( set_union2(X0,X1) = set_union2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_58,c_4337]) ).
tcf(c_69340,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,set_union2(X0,X0)),X1)
| in(sK2(X1,X2,set_union2(X0,X0)),X0)
| ( set_union2(X0,X0) = set_union2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_97,c_4337]) ).
tcf(c_69341,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,set_union2(X2,empty_set)),empty_set)
| in(sK2(X0,X1,set_union2(X2,empty_set)),X2)
| in(sK2(X0,X1,set_union2(X2,empty_set)),X0)
| ( set_union2(X0,X1) = set_union2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_126,c_4337]) ).
tcf(c_69342,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,set_union2(empty_set,X2)),empty_set)
| in(sK2(X0,X1,set_union2(empty_set,X2)),X2)
| in(sK2(X0,X1,set_union2(empty_set,X2)),X0)
| ( set_union2(X0,X1) = set_union2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_3423,c_4337]) ).
tcf(c_69343,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_11),X1)
| in(sK2(X0,X1,set_union2(iPr_def_10,sK18)),iPr_def_10)
| in(sK2(X0,X1,set_union2(iPr_def_10,sK18)),sK18)
| in(sK2(X0,X1,set_union2(iPr_def_10,sK18)),X0)
| ( set_union2(X0,X1) = set_union2(iPr_def_10,sK18) ) ),
inference(superposition,[status(thm)],[c_3424,c_4337]) ).
tcf(c_69344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_union2(X3,X2)),X0)
| in(sK2(X0,X1,set_union2(X2,X3)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X1)
| ( set_union2(X0,X1) = set_union2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_58,c_4337]) ).
tcf(c_69346,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X1)
| in(sK2(X1,X2,set_union2(X0,X0)),X2)
| in(sK2(X1,X2,set_union2(X0,X0)),X0)
| ( set_union2(X0,X0) = set_union2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_97,c_4337]) ).
tcf(c_69347,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,set_union2(X2,empty_set)),empty_set)
| in(sK2(X0,X1,set_union2(X2,empty_set)),X2)
| in(sK2(X0,X1,set_union2(X2,empty_set)),X1)
| ( set_union2(X0,X1) = set_union2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_126,c_4337]) ).
tcf(c_69348,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,set_union2(empty_set,X2)),empty_set)
| in(sK2(X0,X1,set_union2(empty_set,X2)),X2)
| in(sK2(X0,X1,set_union2(empty_set,X2)),X1)
| ( set_union2(X0,X1) = set_union2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_3423,c_4337]) ).
tcf(c_69349,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_11),X0)
| in(sK2(X0,X1,set_union2(iPr_def_10,sK18)),iPr_def_10)
| in(sK2(X0,X1,set_union2(iPr_def_10,sK18)),sK18)
| in(sK2(X0,X1,set_union2(iPr_def_10,sK18)),X1)
| ( set_union2(X0,X1) = set_union2(iPr_def_10,sK18) ) ),
inference(superposition,[status(thm)],[c_3424,c_4337]) ).
tcf(c_69350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X2,X3,set_union2(X1,X0)),X3)
| in(sK2(X2,X3,set_union2(X1,X0)),X2)
| in(sK2(X2,X3,set_union2(X1,X0)),X1)
| in(sK3(iPr_def_11),sK2(X2,X3,set_union2(X1,X0)))
| in(sK2(X2,X3,set_union2(X1,X0)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = set_union2(X2,X3) )
| ( sK2(X2,X3,set_union2(X1,X0)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_49877]) ).
tcf(c_69351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X2,X3,set_union2(X1,X0)),X3)
| in(sK2(X2,X3,set_union2(X1,X0)),X2)
| in(sK2(X2,X3,set_union2(X1,X0)),X1)
| in(sK5(iPr_def_11),sK2(X2,X3,set_union2(X1,X0)))
| in(sK2(X2,X3,set_union2(X1,X0)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = set_union2(X2,X3) )
| ( sK2(X2,X3,set_union2(X1,X0)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_7260]) ).
tcf(c_69352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_union2(X2,X0)),X4)
| in(sK2(X3,X4,set_union2(X2,X0)),X3)
| in(sK2(X3,X4,set_union2(X2,X0)),X2)
| ( set_union2(X2,X0) = set_union2(X3,X4) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4337,c_359]) ).
tcf(c_69353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,set_union2(X2,X0)),X1)
| in(sK2(X3,X4,set_union2(X2,X0)),X4)
| in(sK2(X3,X4,set_union2(X2,X0)),X3)
| in(sK2(X3,X4,set_union2(X2,X0)),X2)
| ( set_union2(X2,X0) = set_union2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4337,c_358]) ).
tcf(c_69354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,sK2(X2,X3,set_union2(X4,X1)))
| in(sK2(X2,X3,set_union2(X4,X1)),X4)
| in(sK2(X2,X3,set_union2(X4,X1)),X3)
| in(sK2(X2,X3,set_union2(X4,X1)),X2)
| in(sK2(X2,X3,set_union2(X4,X1)),X0)
| ( set_union2(X2,X3) = set_union2(X4,X1) )
| ( sK2(X2,X3,set_union2(X4,X1)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4337,c_77]) ).
tcf(c_69355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X3,set_union2(X1,X0)),X0)
| in(sK2(X2,X3,set_union2(X1,X0)),X3)
| in(sK2(X2,X3,set_union2(X1,X0)),X2)
| in(sK2(X2,X3,set_union2(X1,X0)),X1)
| ( set_union2(X1,X0) = set_union2(X2,X3) )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4337,c_65]) ).
tcf(c_69356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,set_union2(X3,X0)),X3)
| in(sK2(X1,X2,set_union2(X3,X0)),X2)
| in(sK2(X1,X2,set_union2(X3,X0)),X1)
| ( set_union2(X1,X2) = set_union2(X3,X0) )
| ~ in(X0,sK2(X1,X2,set_union2(X3,X0))) ),
inference(superposition,[status(thm)],[c_4337,c_49]) ).
tcf(c_69357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_union2(X1,X0)),X3)
| in(sK2(X2,X3,set_union2(X1,X0)),X2)
| in(sK2(X2,X3,set_union2(X1,X0)),X1)
| ( set_union2(X1,X0) = set_union2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4337,c_137]) ).
tcf(c_69358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,set_union2(X2,X3)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X1)
| in(sK2(X0,X1,set_union2(X2,X3)),X0)
| ( set_union2(X0,X1) = set_union2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_4337,c_127]) ).
tcf(c_69359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_union2(X2,singleton(X3))),X2)
| in(sK2(X0,X1,set_union2(X2,singleton(X3))),X1)
| in(sK2(X0,X1,set_union2(X2,singleton(X3))),X0)
| ( set_union2(X2,singleton(X3)) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(X2,singleton(X3))) = X3 ) ),
inference(superposition,[status(thm)],[c_4337,c_62]) ).
tcf(c_69360,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X2,X0)),X2)
| in(sK2(X0,X1,set_union2(X2,X0)),X1)
| in(sK2(X0,X1,set_union2(X2,X0)),X0)
| ( set_union2(X0,X1) = set_union2(X2,X0) )
| ~ in(sK2(X0,X1,set_union2(X2,X0)),set_union2(X2,X0)) ),
inference(superposition,[status(thm)],[c_4337,c_66]) ).
tcf(c_69361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X2,sK2(X3,X4,set_union2(X5,set_union2(X0,X1))))
| in(sK2(X3,X4,set_union2(X5,set_union2(X0,X1))),X5)
| in(sK2(X3,X4,set_union2(X5,set_union2(X0,X1))),X4)
| in(sK2(X3,X4,set_union2(X5,set_union2(X0,X1))),X3)
| in(sK2(X3,X4,set_union2(X5,set_union2(X0,X1))),X2)
| ( set_union2(X5,set_union2(X0,X1)) = set_union2(X3,X4) )
| ( sK2(X3,X4,set_union2(X5,set_union2(X0,X1))) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4337,c_4213]) ).
tcf(c_69362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X2,sK2(X3,X4,set_union2(X5,set_union2(X0,X1))))
| in(sK2(X3,X4,set_union2(X5,set_union2(X0,X1))),X5)
| in(sK2(X3,X4,set_union2(X5,set_union2(X0,X1))),X4)
| in(sK2(X3,X4,set_union2(X5,set_union2(X0,X1))),X3)
| in(sK2(X3,X4,set_union2(X5,set_union2(X0,X1))),X2)
| ( set_union2(X5,set_union2(X0,X1)) = set_union2(X3,X4) )
| ( sK2(X3,X4,set_union2(X5,set_union2(X0,X1))) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4337,c_4212]) ).
tcf(c_69363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_union2(X0,set_union2(X1,X2))),X4)
| in(sK2(X3,X4,set_union2(X0,set_union2(X1,X2))),X3)
| in(sK2(X3,X4,set_union2(X0,set_union2(X1,X2))),X2)
| in(sK2(X3,X4,set_union2(X0,set_union2(X1,X2))),X1)
| in(sK2(X3,X4,set_union2(X0,set_union2(X1,X2))),X0)
| ( set_union2(X0,set_union2(X1,X2)) = set_union2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_4337,c_71]) ).
tcf(c_69364,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X2,empty_set)),X2)
| in(sK2(X0,X1,set_union2(X2,empty_set)),X1)
| in(sK2(X0,X1,set_union2(X2,empty_set)),X0)
| ( set_union2(X0,X1) = set_union2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_4337,c_7097]) ).
tcf(c_69365,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,set_union2(X2,sK18)),iPr_def_11)
| in(sK2(X0,X1,set_union2(X2,sK18)),X2)
| in(sK2(X0,X1,set_union2(X2,sK18)),X1)
| in(sK2(X0,X1,set_union2(X2,sK18)),X0)
| ( set_union2(X0,X1) = set_union2(X2,sK18) ) ),
inference(superposition,[status(thm)],[c_4337,c_12813]) ).
tcf(c_69366,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X2,sK18)),X2)
| in(sK2(X0,X1,set_union2(X2,sK18)),X1)
| in(sK2(X0,X1,set_union2(X2,sK18)),X0)
| ( set_union2(X0,X1) = set_union2(X2,sK18) )
| ~ in(iPr_def_11,sK2(X0,X1,set_union2(X2,sK18))) ),
inference(superposition,[status(thm)],[c_4337,c_6841]) ).
tcf(c_69367,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,set_union2(X2,sK18)),iPr_def_11)
| in(sK2(X0,X1,set_union2(X2,sK18)),X2)
| in(sK2(X0,X1,set_union2(X2,sK18)),X1)
| in(sK2(X0,X1,set_union2(X2,sK18)),X0)
| ( set_union2(X0,X1) = set_union2(X2,sK18) ) ),
inference(superposition,[status(thm)],[c_4337,c_5047]) ).
tcf(c_69368,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X2,sK18)),iPr_def_11)
| in(sK2(X0,X1,set_union2(X2,sK18)),X2)
| in(sK2(X0,X1,set_union2(X2,sK18)),X1)
| in(sK2(X0,X1,set_union2(X2,sK18)),X0)
| ( set_union2(X0,X1) = set_union2(X2,sK18) ) ),
inference(superposition,[status(thm)],[c_4337,c_3640]) ).
tcf(c_69369,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,set_union2(X2,iPr_def_10)),iPr_def_11)
| in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X2)
| in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X1)
| in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X0)
| ( set_union2(X0,X1) = set_union2(X2,iPr_def_10) )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4337,c_9540]) ).
tcf(c_69370,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X2)
| in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X1)
| in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X0)
| ( set_union2(X0,X1) = set_union2(X2,iPr_def_10) )
| ~ in(iPr_def_11,sK2(X0,X1,set_union2(X2,iPr_def_10))) ),
inference(superposition,[status(thm)],[c_4337,c_6289]) ).
tcf(c_69371,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,set_union2(X2,iPr_def_10)),iPr_def_11)
| in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X2)
| in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X1)
| in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X0)
| ( set_union2(X0,X1) = set_union2(X2,iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_4337,c_4912]) ).
tcf(c_69372,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X2)
| in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X1)
| in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X0)
| ( set_union2(X0,X1) = set_union2(X2,iPr_def_10) )
| ( sK2(X0,X1,set_union2(X2,iPr_def_10)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4337,c_3592]) ).
tcf(c_69373,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X2,iPr_def_10)),iPr_def_11)
| in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X2)
| in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X1)
| in(sK2(X0,X1,set_union2(X2,iPr_def_10)),X0)
| ( set_union2(X0,X1) = set_union2(X2,iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_4337,c_3614]) ).
tcf(c_69374,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X2,iPr_def_11)),sK18)
| in(sK2(X0,X1,set_union2(X2,iPr_def_11)),X2)
| in(sK2(X0,X1,set_union2(X2,iPr_def_11)),X1)
| in(sK2(X0,X1,set_union2(X2,iPr_def_11)),X0)
| ( set_union2(X0,X1) = set_union2(X2,iPr_def_11) )
| ( sK2(X0,X1,set_union2(X2,iPr_def_11)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4337,c_33457]) ).
tcf(c_69375,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X2,iPr_def_11)),iPr_def_10)
| in(sK2(X0,X1,set_union2(X2,iPr_def_11)),sK18)
| in(sK2(X0,X1,set_union2(X2,iPr_def_11)),X2)
| in(sK2(X0,X1,set_union2(X2,iPr_def_11)),X1)
| in(sK2(X0,X1,set_union2(X2,iPr_def_11)),X0)
| ( set_union2(X0,X1) = set_union2(X2,iPr_def_11) ) ),
inference(superposition,[status(thm)],[c_4337,c_4035]) ).
tcf(c_69376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_union2(X0,X1),X2,set_union2(X3,X0)),X3)
| in(sK2(set_union2(X0,X1),X2,set_union2(X3,X0)),X2)
| in(sK2(set_union2(X0,X1),X2,set_union2(X3,X0)),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = set_union2(X3,X0) )
| ~ in(sK2(set_union2(X0,X1),X2,set_union2(X3,X0)),set_union2(X3,X0)) ),
inference(superposition,[status(thm)],[c_4337,c_4078]) ).
tcf(c_69379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK2(X1,X2,set_union2(X3,sK5(iPr_def_11))))
| in(sK2(X1,X2,set_union2(X3,sK5(iPr_def_11))),X3)
| in(sK2(X1,X2,set_union2(X3,sK5(iPr_def_11))),X2)
| in(sK2(X1,X2,set_union2(X3,sK5(iPr_def_11))),X1)
| in(sK2(X1,X2,set_union2(X3,sK5(iPr_def_11))),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X3,sK5(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X1,X2,set_union2(X3,sK5(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_7243]) ).
tcf(c_69380,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X2,sK5(iPr_def_11))),X2)
| in(sK2(X0,X1,set_union2(X2,sK5(iPr_def_11))),X1)
| in(sK2(X0,X1,set_union2(X2,sK5(iPr_def_11))),X0)
| ( set_union2(X2,sK5(iPr_def_11)) = set_union2(X0,X1) )
| ~ subset(iPr_def_11,sK2(X0,X1,set_union2(X2,sK5(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_4337,c_23189]) ).
tcf(c_69381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK2(X1,X2,set_union2(X3,sK3(iPr_def_11))))
| in(sK2(X1,X2,set_union2(X3,sK3(iPr_def_11))),X3)
| in(sK2(X1,X2,set_union2(X3,sK3(iPr_def_11))),X2)
| in(sK2(X1,X2,set_union2(X3,sK3(iPr_def_11))),X1)
| in(sK2(X1,X2,set_union2(X3,sK3(iPr_def_11))),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X3,sK3(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X1,X2,set_union2(X3,sK3(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_9906]) ).
tcf(c_69382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK2(X1,X2,set_union2(X3,sK4(iPr_def_11))))
| in(sK2(X1,X2,set_union2(X3,sK4(iPr_def_11))),X3)
| in(sK2(X1,X2,set_union2(X3,sK4(iPr_def_11))),X2)
| in(sK2(X1,X2,set_union2(X3,sK4(iPr_def_11))),X1)
| in(sK2(X1,X2,set_union2(X3,sK4(iPr_def_11))),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X3,sK4(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X1,X2,set_union2(X3,sK4(iPr_def_11))) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_45801]) ).
tcf(c_69383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X2,X3,set_union2(X0,X1)),X3)
| in(sK2(X2,X3,set_union2(X0,X1)),X2)
| in(sK2(X2,X3,set_union2(X0,X1)),X1)
| in(sK3(iPr_def_11),sK2(X2,X3,set_union2(X0,X1)))
| in(sK2(X2,X3,set_union2(X0,X1)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ( sK2(X2,X3,set_union2(X0,X1)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_49877]) ).
tcf(c_69384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X2,X3,set_union2(X0,X1)),X3)
| in(sK2(X2,X3,set_union2(X0,X1)),X2)
| in(sK2(X2,X3,set_union2(X0,X1)),X1)
| in(sK5(iPr_def_11),sK2(X2,X3,set_union2(X0,X1)))
| in(sK2(X2,X3,set_union2(X0,X1)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ( sK2(X2,X3,set_union2(X0,X1)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_7260]) ).
tcf(c_69385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_union2(X0,X2)),X4)
| in(sK2(X3,X4,set_union2(X0,X2)),X3)
| in(sK2(X3,X4,set_union2(X0,X2)),X2)
| ( set_union2(X0,X2) = set_union2(X3,X4) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4337,c_359]) ).
tcf(c_69386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,set_union2(X0,X2)),X1)
| in(sK2(X3,X4,set_union2(X0,X2)),X4)
| in(sK2(X3,X4,set_union2(X0,X2)),X3)
| in(sK2(X3,X4,set_union2(X0,X2)),X2)
| ( set_union2(X0,X2) = set_union2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4337,c_358]) ).
tcf(c_69387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,sK2(X2,X3,set_union2(X1,X4)))
| in(sK2(X2,X3,set_union2(X1,X4)),X4)
| in(sK2(X2,X3,set_union2(X1,X4)),X3)
| in(sK2(X2,X3,set_union2(X1,X4)),X2)
| in(sK2(X2,X3,set_union2(X1,X4)),X0)
| ( set_union2(X1,X4) = set_union2(X2,X3) )
| ( sK2(X2,X3,set_union2(X1,X4)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4337,c_77]) ).
tcf(c_69388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X3,set_union2(X0,X1)),X0)
| in(sK2(X2,X3,set_union2(X0,X1)),X3)
| in(sK2(X2,X3,set_union2(X0,X1)),X2)
| in(sK2(X2,X3,set_union2(X0,X1)),X1)
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4337,c_65]) ).
tcf(c_69389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,set_union2(X0,X3)),X3)
| in(sK2(X1,X2,set_union2(X0,X3)),X2)
| in(sK2(X1,X2,set_union2(X0,X3)),X1)
| ( set_union2(X0,X3) = set_union2(X1,X2) )
| ~ in(X0,sK2(X1,X2,set_union2(X0,X3))) ),
inference(superposition,[status(thm)],[c_4337,c_49]) ).
tcf(c_69390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_union2(X0,X1)),X3)
| in(sK2(X2,X3,set_union2(X0,X1)),X2)
| in(sK2(X2,X3,set_union2(X0,X1)),X1)
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4337,c_137]) ).
tcf(c_69391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,set_union2(X2,X3)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X1)
| in(sK2(X0,X1,set_union2(X2,X3)),X0)
| ( set_union2(X0,X1) = set_union2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_4337,c_127]) ).
tcf(c_69392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_union2(singleton(X2),X3)),X3)
| in(sK2(X0,X1,set_union2(singleton(X2),X3)),X1)
| in(sK2(X0,X1,set_union2(singleton(X2),X3)),X0)
| ( set_union2(singleton(X2),X3) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(singleton(X2),X3)) = X2 ) ),
inference(superposition,[status(thm)],[c_4337,c_62]) ).
tcf(c_69394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X2,sK2(X3,X4,set_union2(set_union2(X0,X1),X5)))
| in(sK2(X3,X4,set_union2(set_union2(X0,X1),X5)),X5)
| in(sK2(X3,X4,set_union2(set_union2(X0,X1),X5)),X4)
| in(sK2(X3,X4,set_union2(set_union2(X0,X1),X5)),X3)
| in(sK2(X3,X4,set_union2(set_union2(X0,X1),X5)),X2)
| ( set_union2(set_union2(X0,X1),X5) = set_union2(X3,X4) )
| ( sK2(X3,X4,set_union2(set_union2(X0,X1),X5)) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4337,c_4213]) ).
tcf(c_69395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X2,sK2(X3,X4,set_union2(set_union2(X0,X1),X5)))
| in(sK2(X3,X4,set_union2(set_union2(X0,X1),X5)),X5)
| in(sK2(X3,X4,set_union2(set_union2(X0,X1),X5)),X4)
| in(sK2(X3,X4,set_union2(set_union2(X0,X1),X5)),X3)
| in(sK2(X3,X4,set_union2(set_union2(X0,X1),X5)),X2)
| ( set_union2(set_union2(X0,X1),X5) = set_union2(X3,X4) )
| ( sK2(X3,X4,set_union2(set_union2(X0,X1),X5)) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4337,c_4212]) ).
tcf(c_69396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_union2(set_union2(X0,X1),X2)),X4)
| in(sK2(X3,X4,set_union2(set_union2(X0,X1),X2)),X3)
| in(sK2(X3,X4,set_union2(set_union2(X0,X1),X2)),X2)
| in(sK2(X3,X4,set_union2(set_union2(X0,X1),X2)),X1)
| in(sK2(X3,X4,set_union2(set_union2(X0,X1),X2)),X0)
| ( set_union2(set_union2(X0,X1),X2) = set_union2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_4337,c_71]) ).
tcf(c_69397,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(empty_set,X2)),X2)
| in(sK2(X0,X1,set_union2(empty_set,X2)),X1)
| in(sK2(X0,X1,set_union2(empty_set,X2)),X0)
| ( set_union2(X0,X1) = set_union2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_4337,c_7097]) ).
tcf(c_69398,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,set_union2(sK18,X2)),iPr_def_11)
| in(sK2(X0,X1,set_union2(sK18,X2)),X2)
| in(sK2(X0,X1,set_union2(sK18,X2)),X1)
| in(sK2(X0,X1,set_union2(sK18,X2)),X0)
| ( set_union2(X0,X1) = set_union2(sK18,X2) ) ),
inference(superposition,[status(thm)],[c_4337,c_12813]) ).
tcf(c_69399,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(sK18,X2)),X2)
| in(sK2(X0,X1,set_union2(sK18,X2)),X1)
| in(sK2(X0,X1,set_union2(sK18,X2)),X0)
| ( set_union2(X0,X1) = set_union2(sK18,X2) )
| ~ in(iPr_def_11,sK2(X0,X1,set_union2(sK18,X2))) ),
inference(superposition,[status(thm)],[c_4337,c_6841]) ).
tcf(c_69400,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,set_union2(sK18,X2)),iPr_def_11)
| in(sK2(X0,X1,set_union2(sK18,X2)),X2)
| in(sK2(X0,X1,set_union2(sK18,X2)),X1)
| in(sK2(X0,X1,set_union2(sK18,X2)),X0)
| ( set_union2(X0,X1) = set_union2(sK18,X2) ) ),
inference(superposition,[status(thm)],[c_4337,c_5047]) ).
tcf(c_69401,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(sK18,X2)),iPr_def_11)
| in(sK2(X0,X1,set_union2(sK18,X2)),X2)
| in(sK2(X0,X1,set_union2(sK18,X2)),X1)
| in(sK2(X0,X1,set_union2(sK18,X2)),X0)
| ( set_union2(X0,X1) = set_union2(sK18,X2) ) ),
inference(superposition,[status(thm)],[c_4337,c_3640]) ).
tcf(c_69402,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,set_union2(iPr_def_10,X2)),iPr_def_11)
| in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X2)
| in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X1)
| in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X0)
| ( set_union2(X0,X1) = set_union2(iPr_def_10,X2) )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4337,c_9540]) ).
tcf(c_69403,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X2)
| in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X1)
| in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X0)
| ( set_union2(X0,X1) = set_union2(iPr_def_10,X2) )
| ~ in(iPr_def_11,sK2(X0,X1,set_union2(iPr_def_10,X2))) ),
inference(superposition,[status(thm)],[c_4337,c_6289]) ).
tcf(c_69404,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,set_union2(iPr_def_10,X2)),iPr_def_11)
| in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X2)
| in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X1)
| in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X0)
| ( set_union2(X0,X1) = set_union2(iPr_def_10,X2) ) ),
inference(superposition,[status(thm)],[c_4337,c_4912]) ).
tcf(c_69405,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X2)
| in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X1)
| in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X0)
| ( set_union2(X0,X1) = set_union2(iPr_def_10,X2) )
| ( sK2(X0,X1,set_union2(iPr_def_10,X2)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4337,c_3592]) ).
tcf(c_69406,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(iPr_def_10,X2)),iPr_def_11)
| in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X2)
| in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X1)
| in(sK2(X0,X1,set_union2(iPr_def_10,X2)),X0)
| ( set_union2(X0,X1) = set_union2(iPr_def_10,X2) ) ),
inference(superposition,[status(thm)],[c_4337,c_3614]) ).
tcf(c_69407,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(iPr_def_11,X2)),sK18)
| in(sK2(X0,X1,set_union2(iPr_def_11,X2)),X2)
| in(sK2(X0,X1,set_union2(iPr_def_11,X2)),X1)
| in(sK2(X0,X1,set_union2(iPr_def_11,X2)),X0)
| ( set_union2(X0,X1) = set_union2(iPr_def_11,X2) )
| ( sK2(X0,X1,set_union2(iPr_def_11,X2)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4337,c_33457]) ).
tcf(c_69408,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(iPr_def_11,X2)),iPr_def_10)
| in(sK2(X0,X1,set_union2(iPr_def_11,X2)),sK18)
| in(sK2(X0,X1,set_union2(iPr_def_11,X2)),X2)
| in(sK2(X0,X1,set_union2(iPr_def_11,X2)),X1)
| in(sK2(X0,X1,set_union2(iPr_def_11,X2)),X0)
| ( set_union2(X0,X1) = set_union2(iPr_def_11,X2) ) ),
inference(superposition,[status(thm)],[c_4337,c_4035]) ).
tcf(c_69409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_union2(X0,X1),X2,set_union2(X0,X3)),X3)
| in(sK2(set_union2(X0,X1),X2,set_union2(X0,X3)),X2)
| in(sK2(set_union2(X0,X1),X2,set_union2(X0,X3)),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = set_union2(X0,X3) )
| ~ in(sK2(set_union2(X0,X1),X2,set_union2(X0,X3)),set_union2(X0,X3)) ),
inference(superposition,[status(thm)],[c_4337,c_4078]) ).
tcf(c_69412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK2(X1,X2,set_union2(sK5(iPr_def_11),X3)))
| in(sK2(X1,X2,set_union2(sK5(iPr_def_11),X3)),X3)
| in(sK2(X1,X2,set_union2(sK5(iPr_def_11),X3)),X2)
| in(sK2(X1,X2,set_union2(sK5(iPr_def_11),X3)),X1)
| in(sK2(X1,X2,set_union2(sK5(iPr_def_11),X3)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X3) = set_union2(X1,X2) )
| ( sK2(X1,X2,set_union2(sK5(iPr_def_11),X3)) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_7243]) ).
tcf(c_69413,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),X2)
| in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),X1)
| in(sK2(X0,X1,set_union2(sK5(iPr_def_11),X2)),X0)
| ( set_union2(sK5(iPr_def_11),X2) = set_union2(X0,X1) )
| ~ subset(iPr_def_11,sK2(X0,X1,set_union2(sK5(iPr_def_11),X2))) ),
inference(superposition,[status(thm)],[c_4337,c_23189]) ).
tcf(c_69414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK2(X1,X2,set_union2(sK3(iPr_def_11),X3)))
| in(sK2(X1,X2,set_union2(sK3(iPr_def_11),X3)),X3)
| in(sK2(X1,X2,set_union2(sK3(iPr_def_11),X3)),X2)
| in(sK2(X1,X2,set_union2(sK3(iPr_def_11),X3)),X1)
| in(sK2(X1,X2,set_union2(sK3(iPr_def_11),X3)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X3) = set_union2(X1,X2) )
| ( sK2(X1,X2,set_union2(sK3(iPr_def_11),X3)) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_9906]) ).
tcf(c_69415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK2(X1,X2,set_union2(sK4(iPr_def_11),X3)))
| in(sK2(X1,X2,set_union2(sK4(iPr_def_11),X3)),X3)
| in(sK2(X1,X2,set_union2(sK4(iPr_def_11),X3)),X2)
| in(sK2(X1,X2,set_union2(sK4(iPr_def_11),X3)),X1)
| in(sK2(X1,X2,set_union2(sK4(iPr_def_11),X3)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X3) = set_union2(X1,X2) )
| ( sK2(X1,X2,set_union2(sK4(iPr_def_11),X3)) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_45801]) ).
tcf(c_69416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X1,X0,set_union2(X2,X3)),X3)
| in(sK2(X1,X0,set_union2(X2,X3)),X2)
| in(sK2(X1,X0,set_union2(X2,X3)),X1)
| in(sK3(iPr_def_11),sK2(X1,X0,set_union2(X2,X3)))
| in(sK2(X1,X0,set_union2(X2,X3)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = set_union2(X2,X3) )
| ( sK2(X1,X0,set_union2(X2,X3)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_49877]) ).
tcf(c_69417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X1,X0,set_union2(X2,X3)),X3)
| in(sK2(X1,X0,set_union2(X2,X3)),X2)
| in(sK2(X1,X0,set_union2(X2,X3)),X1)
| in(sK5(iPr_def_11),sK2(X1,X0,set_union2(X2,X3)))
| in(sK2(X1,X0,set_union2(X2,X3)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = set_union2(X2,X3) )
| ( sK2(X1,X0,set_union2(X2,X3)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_7260]) ).
tcf(c_69418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X0,set_union2(X3,X4)),X4)
| in(sK2(X2,X0,set_union2(X3,X4)),X3)
| in(sK2(X2,X0,set_union2(X3,X4)),X2)
| ( set_union2(X2,X0) = set_union2(X3,X4) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4337,c_359]) ).
tcf(c_69419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,X0,set_union2(X3,X4)),X1)
| in(sK2(X2,X0,set_union2(X3,X4)),X4)
| in(sK2(X2,X0,set_union2(X3,X4)),X3)
| in(sK2(X2,X0,set_union2(X3,X4)),X2)
| ( set_union2(X2,X0) = set_union2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4337,c_358]) ).
tcf(c_69420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,sK2(X2,X1,set_union2(X3,X4)))
| in(sK2(X2,X1,set_union2(X3,X4)),X4)
| in(sK2(X2,X1,set_union2(X3,X4)),X3)
| in(sK2(X2,X1,set_union2(X3,X4)),X2)
| in(sK2(X2,X1,set_union2(X3,X4)),X0)
| ( set_union2(X2,X1) = set_union2(X3,X4) )
| ( sK2(X2,X1,set_union2(X3,X4)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4337,c_77]) ).
tcf(c_69421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X1,X0,set_union2(X2,X3)),X0)
| in(sK2(X1,X0,set_union2(X2,X3)),X3)
| in(sK2(X1,X0,set_union2(X2,X3)),X2)
| in(sK2(X1,X0,set_union2(X2,X3)),X1)
| ( set_union2(X1,X0) = set_union2(X2,X3) )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4337,c_65]) ).
tcf(c_69422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X0,set_union2(X2,X3)),X3)
| in(sK2(X1,X0,set_union2(X2,X3)),X2)
| in(sK2(X1,X0,set_union2(X2,X3)),X1)
| ( set_union2(X1,X0) = set_union2(X2,X3) )
| ~ in(X0,sK2(X1,X0,set_union2(X2,X3))) ),
inference(superposition,[status(thm)],[c_4337,c_49]) ).
tcf(c_69423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X0,set_union2(X2,X3)),X3)
| in(sK2(X1,X0,set_union2(X2,X3)),X2)
| in(sK2(X1,X0,set_union2(X2,X3)),X1)
| ( set_union2(X1,X0) = set_union2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4337,c_137]) ).
tcf(c_69424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,set_union2(X2,X3)),X1)
| in(sK2(X0,X1,set_union2(X2,X3)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X0)
| ( set_union2(X0,X1) = set_union2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_4337,c_127]) ).
tcf(c_69425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,singleton(X1),set_union2(X2,X3)),X3)
| in(sK2(X0,singleton(X1),set_union2(X2,X3)),X2)
| in(sK2(X0,singleton(X1),set_union2(X2,X3)),X0)
| ( set_union2(X0,singleton(X1)) = set_union2(X2,X3) )
| ( sK2(X0,singleton(X1),set_union2(X2,X3)) = X1 ) ),
inference(superposition,[status(thm)],[c_4337,c_62]) ).
tcf(c_69426,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_union2(X1,X2)),X2)
| in(sK2(X0,X0,set_union2(X1,X2)),X1)
| in(sK2(X0,X0,set_union2(X1,X2)),X0)
| ( set_union2(X0,X0) = set_union2(X1,X2) )
| ~ in(sK2(X0,X0,set_union2(X1,X2)),set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_4337,c_66]) ).
tcf(c_69427,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_union2(X1,X2),set_union2(X1,X2)),X2)
| in(sK2(X0,set_union2(X1,X2),set_union2(X1,X2)),X1)
| in(sK2(X0,set_union2(X1,X2),set_union2(X1,X2)),X0)
| ( set_union2(X0,set_union2(X1,X2)) = set_union2(X1,X2) )
| ~ in(sK2(X0,set_union2(X1,X2),set_union2(X1,X2)),set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_4337,c_67]) ).
tcf(c_69428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X2,sK2(X3,set_union2(X0,X1),set_union2(X4,X5)))
| in(sK2(X3,set_union2(X0,X1),set_union2(X4,X5)),X5)
| in(sK2(X3,set_union2(X0,X1),set_union2(X4,X5)),X4)
| in(sK2(X3,set_union2(X0,X1),set_union2(X4,X5)),X3)
| in(sK2(X3,set_union2(X0,X1),set_union2(X4,X5)),X2)
| ( set_union2(X3,set_union2(X0,X1)) = set_union2(X4,X5) )
| ( sK2(X3,set_union2(X0,X1),set_union2(X4,X5)) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4337,c_4213]) ).
tcf(c_69429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X2,sK2(X3,set_union2(X0,X1),set_union2(X4,X5)))
| in(sK2(X3,set_union2(X0,X1),set_union2(X4,X5)),X5)
| in(sK2(X3,set_union2(X0,X1),set_union2(X4,X5)),X4)
| in(sK2(X3,set_union2(X0,X1),set_union2(X4,X5)),X3)
| in(sK2(X3,set_union2(X0,X1),set_union2(X4,X5)),X2)
| ( set_union2(X3,set_union2(X0,X1)) = set_union2(X4,X5) )
| ( sK2(X3,set_union2(X0,X1),set_union2(X4,X5)) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4337,c_4212]) ).
tcf(c_69430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_union2(X1,X2),set_union2(X3,X4)),X4)
| in(sK2(X0,set_union2(X1,X2),set_union2(X3,X4)),X3)
| in(sK2(X0,set_union2(X1,X2),set_union2(X3,X4)),X2)
| in(sK2(X0,set_union2(X1,X2),set_union2(X3,X4)),X1)
| in(sK2(X0,set_union2(X1,X2),set_union2(X3,X4)),X0)
| ( set_union2(X0,set_union2(X1,X2)) = set_union2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_4337,c_71]) ).
tcf(c_69431,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,empty_set,set_union2(X0,X1)),X2)
| in(sK2(X2,empty_set,set_union2(X0,X1)),X1)
| in(sK2(X2,empty_set,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_4337,c_7097]) ).
tcf(c_69432,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,sK18,set_union2(X0,X1)),iPr_def_11)
| in(sK2(X2,sK18,set_union2(X0,X1)),X2)
| in(sK2(X2,sK18,set_union2(X0,X1)),X1)
| in(sK2(X2,sK18,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(X2,sK18) ) ),
inference(superposition,[status(thm)],[c_4337,c_12813]) ).
tcf(c_69433,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK18,set_union2(X1,X2)),X2)
| in(sK2(X0,sK18,set_union2(X1,X2)),X1)
| in(sK2(X0,sK18,set_union2(X1,X2)),X0)
| ( set_union2(X1,X2) = set_union2(X0,sK18) )
| ~ in(iPr_def_11,sK2(X0,sK18,set_union2(X1,X2))) ),
inference(superposition,[status(thm)],[c_4337,c_6841]) ).
tcf(c_69434,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X2,sK18,set_union2(X0,X1)),iPr_def_11)
| in(sK2(X2,sK18,set_union2(X0,X1)),X2)
| in(sK2(X2,sK18,set_union2(X0,X1)),X1)
| in(sK2(X2,sK18,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(X2,sK18) ) ),
inference(superposition,[status(thm)],[c_4337,c_5047]) ).
tcf(c_69435,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,sK18,set_union2(X0,X1)),iPr_def_11)
| in(sK2(X2,sK18,set_union2(X0,X1)),X2)
| in(sK2(X2,sK18,set_union2(X0,X1)),X1)
| in(sK2(X2,sK18,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(X2,sK18) ) ),
inference(superposition,[status(thm)],[c_4337,c_3640]) ).
tcf(c_69436,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,iPr_def_10,set_union2(X0,X1)),iPr_def_11)
| in(sK2(X2,iPr_def_10,set_union2(X0,X1)),X2)
| in(sK2(X2,iPr_def_10,set_union2(X0,X1)),X1)
| in(sK2(X2,iPr_def_10,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(X2,iPr_def_10) )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4337,c_9540]) ).
tcf(c_69437,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,iPr_def_10,set_union2(X1,X2)),X2)
| in(sK2(X0,iPr_def_10,set_union2(X1,X2)),X1)
| in(sK2(X0,iPr_def_10,set_union2(X1,X2)),X0)
| ( set_union2(X1,X2) = set_union2(X0,iPr_def_10) )
| ~ in(iPr_def_11,sK2(X0,iPr_def_10,set_union2(X1,X2))) ),
inference(superposition,[status(thm)],[c_4337,c_6289]) ).
tcf(c_69438,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X2,iPr_def_10,set_union2(X0,X1)),iPr_def_11)
| in(sK2(X2,iPr_def_10,set_union2(X0,X1)),X2)
| in(sK2(X2,iPr_def_10,set_union2(X0,X1)),X1)
| in(sK2(X2,iPr_def_10,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(X2,iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_4337,c_4912]) ).
tcf(c_69439,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,iPr_def_10,set_union2(X1,X2)),X2)
| in(sK2(X0,iPr_def_10,set_union2(X1,X2)),X1)
| in(sK2(X0,iPr_def_10,set_union2(X1,X2)),X0)
| ( set_union2(X1,X2) = set_union2(X0,iPr_def_10) )
| ( sK2(X0,iPr_def_10,set_union2(X1,X2)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4337,c_3592]) ).
tcf(c_69440,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,iPr_def_10,set_union2(X0,X1)),iPr_def_11)
| in(sK2(X2,iPr_def_10,set_union2(X0,X1)),X2)
| in(sK2(X2,iPr_def_10,set_union2(X0,X1)),X1)
| in(sK2(X2,iPr_def_10,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(X2,iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_4337,c_3614]) ).
tcf(c_69441,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,iPr_def_11,set_union2(X1,X2)),sK18)
| in(sK2(X0,iPr_def_11,set_union2(X1,X2)),X2)
| in(sK2(X0,iPr_def_11,set_union2(X1,X2)),X1)
| in(sK2(X0,iPr_def_11,set_union2(X1,X2)),X0)
| ( set_union2(X1,X2) = set_union2(X0,iPr_def_11) )
| ( sK2(X0,iPr_def_11,set_union2(X1,X2)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4337,c_33457]) ).
tcf(c_69442,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,iPr_def_11,set_union2(X0,X1)),iPr_def_10)
| in(sK2(X2,iPr_def_11,set_union2(X0,X1)),sK18)
| in(sK2(X2,iPr_def_11,set_union2(X0,X1)),X2)
| in(sK2(X2,iPr_def_11,set_union2(X0,X1)),X1)
| in(sK2(X2,iPr_def_11,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(X2,iPr_def_11) ) ),
inference(superposition,[status(thm)],[c_4337,c_4035]) ).
tcf(c_69443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_union2(X0,X1),X0,set_union2(X2,X3)),X3)
| in(sK2(set_union2(X0,X1),X0,set_union2(X2,X3)),X2)
| in(sK2(set_union2(X0,X1),X0,set_union2(X2,X3)),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X0) = set_union2(X2,X3) )
| ~ in(sK2(set_union2(X0,X1),X0,set_union2(X2,X3)),set_union2(X2,X3)) ),
inference(superposition,[status(thm)],[c_4337,c_4078]) ).
tcf(c_69444,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_union2(X0,X1),set_union2(X2,X3),set_union2(X2,X3)),X3)
| in(sK2(set_union2(X0,X1),set_union2(X2,X3),set_union2(X2,X3)),X2)
| in(sK2(set_union2(X0,X1),set_union2(X2,X3),set_union2(X2,X3)),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),set_union2(X2,X3)) = set_union2(X2,X3) )
| ~ in(sK2(set_union2(X0,X1),set_union2(X2,X3),set_union2(X2,X3)),X1) ),
inference(superposition,[status(thm)],[c_4337,c_4079]) ).
tcf(c_69447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK2(X1,sK5(iPr_def_11),set_union2(X2,X3)))
| in(sK2(X1,sK5(iPr_def_11),set_union2(X2,X3)),X3)
| in(sK2(X1,sK5(iPr_def_11),set_union2(X2,X3)),X2)
| in(sK2(X1,sK5(iPr_def_11),set_union2(X2,X3)),X1)
| in(sK2(X1,sK5(iPr_def_11),set_union2(X2,X3)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,sK5(iPr_def_11)) = set_union2(X2,X3) )
| ( sK2(X1,sK5(iPr_def_11),set_union2(X2,X3)) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_7243]) ).
tcf(c_69448,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),X2)
| in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),X1)
| in(sK2(X0,sK5(iPr_def_11),set_union2(X1,X2)),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = set_union2(X1,X2) )
| ~ subset(iPr_def_11,sK2(X0,sK5(iPr_def_11),set_union2(X1,X2))) ),
inference(superposition,[status(thm)],[c_4337,c_23189]) ).
tcf(c_69449,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK2(X1,sK3(iPr_def_11),set_union2(X2,X3)))
| in(sK2(X1,sK3(iPr_def_11),set_union2(X2,X3)),X3)
| in(sK2(X1,sK3(iPr_def_11),set_union2(X2,X3)),X2)
| in(sK2(X1,sK3(iPr_def_11),set_union2(X2,X3)),X1)
| in(sK2(X1,sK3(iPr_def_11),set_union2(X2,X3)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,sK3(iPr_def_11)) = set_union2(X2,X3) )
| ( sK2(X1,sK3(iPr_def_11),set_union2(X2,X3)) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_9906]) ).
tcf(c_69450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK2(X1,sK4(iPr_def_11),set_union2(X2,X3)))
| in(sK2(X1,sK4(iPr_def_11),set_union2(X2,X3)),X3)
| in(sK2(X1,sK4(iPr_def_11),set_union2(X2,X3)),X2)
| in(sK2(X1,sK4(iPr_def_11),set_union2(X2,X3)),X1)
| in(sK2(X1,sK4(iPr_def_11),set_union2(X2,X3)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,sK4(iPr_def_11)) = set_union2(X2,X3) )
| ( sK2(X1,sK4(iPr_def_11),set_union2(X2,X3)) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_45801]) ).
tcf(c_69451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X0,X1,set_union2(X2,X3)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X1)
| in(sK3(iPr_def_11),sK2(X0,X1,set_union2(X2,X3)))
| in(sK2(X0,X1,set_union2(X2,X3)),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ( sK2(X0,X1,set_union2(X2,X3)) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_49877]) ).
tcf(c_69452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X0,X1,set_union2(X2,X3)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X1)
| in(sK5(iPr_def_11),sK2(X0,X1,set_union2(X2,X3)))
| in(sK2(X0,X1,set_union2(X2,X3)),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ( sK2(X0,X1,set_union2(X2,X3)) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_7260]) ).
tcf(c_69453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X2,set_union2(X3,X4)),X4)
| in(sK2(X0,X2,set_union2(X3,X4)),X3)
| in(sK2(X0,X2,set_union2(X3,X4)),X2)
| ( set_union2(X0,X2) = set_union2(X3,X4) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4337,c_359]) ).
tcf(c_69454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X2,set_union2(X3,X4)),X1)
| in(sK2(X0,X2,set_union2(X3,X4)),X4)
| in(sK2(X0,X2,set_union2(X3,X4)),X3)
| in(sK2(X0,X2,set_union2(X3,X4)),X2)
| ( set_union2(X0,X2) = set_union2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4337,c_358]) ).
tcf(c_69455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,sK2(X1,X2,set_union2(X3,X4)))
| in(sK2(X1,X2,set_union2(X3,X4)),X4)
| in(sK2(X1,X2,set_union2(X3,X4)),X3)
| in(sK2(X1,X2,set_union2(X3,X4)),X2)
| in(sK2(X1,X2,set_union2(X3,X4)),X0)
| ( set_union2(X1,X2) = set_union2(X3,X4) )
| ( sK2(X1,X2,set_union2(X3,X4)) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4337,c_77]) ).
tcf(c_69456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X0,X1,set_union2(X2,X3)),X0)
| in(sK2(X0,X1,set_union2(X2,X3)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X1)
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4337,c_65]) ).
tcf(c_69457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_union2(X2,X3)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X1)
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ~ in(X0,sK2(X0,X1,set_union2(X2,X3))) ),
inference(superposition,[status(thm)],[c_4337,c_49]) ).
tcf(c_69458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_union2(X2,X3)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X1)
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4337,c_137]) ).
tcf(c_69459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,set_union2(X2,X3)),X0)
| in(sK2(X0,X1,set_union2(X2,X3)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X1)
| ( set_union2(X0,X1) = set_union2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_4337,c_127]) ).
tcf(c_69460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(singleton(X0),X1,set_union2(X2,X3)),X3)
| in(sK2(singleton(X0),X1,set_union2(X2,X3)),X2)
| in(sK2(singleton(X0),X1,set_union2(X2,X3)),X1)
| ( set_union2(singleton(X0),X1) = set_union2(X2,X3) )
| ( sK2(singleton(X0),X1,set_union2(X2,X3)) = X0 ) ),
inference(superposition,[status(thm)],[c_4337,c_62]) ).
tcf(c_69461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_union2(X2,X3)),X3)
| in(sK2(X0,X1,set_union2(X2,X3)),X2)
| in(sK2(X0,X1,set_union2(X2,X3)),X1)
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ~ in(sK2(X0,X1,set_union2(X2,X3)),set_union2(X2,X3)) ),
inference(superposition,[status(thm)],[c_4337,c_66]) ).
tcf(c_69463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X2,sK2(set_union2(X0,X1),X3,set_union2(X4,X5)))
| in(sK2(set_union2(X0,X1),X3,set_union2(X4,X5)),X5)
| in(sK2(set_union2(X0,X1),X3,set_union2(X4,X5)),X4)
| in(sK2(set_union2(X0,X1),X3,set_union2(X4,X5)),X3)
| in(sK2(set_union2(X0,X1),X3,set_union2(X4,X5)),X2)
| ( set_union2(set_union2(X0,X1),X3) = set_union2(X4,X5) )
| ( sK2(set_union2(X0,X1),X3,set_union2(X4,X5)) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4337,c_4213]) ).
tcf(c_69464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X2,sK2(set_union2(X0,X1),X3,set_union2(X4,X5)))
| in(sK2(set_union2(X0,X1),X3,set_union2(X4,X5)),X5)
| in(sK2(set_union2(X0,X1),X3,set_union2(X4,X5)),X4)
| in(sK2(set_union2(X0,X1),X3,set_union2(X4,X5)),X3)
| in(sK2(set_union2(X0,X1),X3,set_union2(X4,X5)),X2)
| ( set_union2(set_union2(X0,X1),X3) = set_union2(X4,X5) )
| ( sK2(set_union2(X0,X1),X3,set_union2(X4,X5)) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4337,c_4212]) ).
tcf(c_69465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_union2(X0,X1),X2,set_union2(X3,X4)),X4)
| in(sK2(set_union2(X0,X1),X2,set_union2(X3,X4)),X3)
| in(sK2(set_union2(X0,X1),X2,set_union2(X3,X4)),X2)
| in(sK2(set_union2(X0,X1),X2,set_union2(X3,X4)),X1)
| in(sK2(set_union2(X0,X1),X2,set_union2(X3,X4)),X0)
| ( set_union2(set_union2(X0,X1),X2) = set_union2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_4337,c_71]) ).
tcf(c_69466,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,set_union2(X0,X1)),X2)
| in(sK2(empty_set,X2,set_union2(X0,X1)),X1)
| in(sK2(empty_set,X2,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_4337,c_7097]) ).
tcf(c_69467,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X2,set_union2(X0,X1)),iPr_def_11)
| in(sK2(sK18,X2,set_union2(X0,X1)),X2)
| in(sK2(sK18,X2,set_union2(X0,X1)),X1)
| in(sK2(sK18,X2,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(sK18,X2) ) ),
inference(superposition,[status(thm)],[c_4337,c_12813]) ).
tcf(c_69468,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK18,X0,set_union2(X1,X2)),X2)
| in(sK2(sK18,X0,set_union2(X1,X2)),X1)
| in(sK2(sK18,X0,set_union2(X1,X2)),X0)
| ( set_union2(X1,X2) = set_union2(sK18,X0) )
| ~ in(iPr_def_11,sK2(sK18,X0,set_union2(X1,X2))) ),
inference(superposition,[status(thm)],[c_4337,c_6841]) ).
tcf(c_69469,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(sK18,X2,set_union2(X0,X1)),iPr_def_11)
| in(sK2(sK18,X2,set_union2(X0,X1)),X2)
| in(sK2(sK18,X2,set_union2(X0,X1)),X1)
| in(sK2(sK18,X2,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(sK18,X2) ) ),
inference(superposition,[status(thm)],[c_4337,c_5047]) ).
tcf(c_69470,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK18,X2,set_union2(X0,X1)),iPr_def_11)
| in(sK2(sK18,X2,set_union2(X0,X1)),X2)
| in(sK2(sK18,X2,set_union2(X0,X1)),X1)
| in(sK2(sK18,X2,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(sK18,X2) ) ),
inference(superposition,[status(thm)],[c_4337,c_3640]) ).
tcf(c_69471,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(iPr_def_10,X2,set_union2(X0,X1)),iPr_def_11)
| in(sK2(iPr_def_10,X2,set_union2(X0,X1)),X2)
| in(sK2(iPr_def_10,X2,set_union2(X0,X1)),X1)
| in(sK2(iPr_def_10,X2,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(iPr_def_10,X2) )
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_4337,c_9540]) ).
tcf(c_69472,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(iPr_def_10,X0,set_union2(X1,X2)),X2)
| in(sK2(iPr_def_10,X0,set_union2(X1,X2)),X1)
| in(sK2(iPr_def_10,X0,set_union2(X1,X2)),X0)
| ( set_union2(X1,X2) = set_union2(iPr_def_10,X0) )
| ~ in(iPr_def_11,sK2(iPr_def_10,X0,set_union2(X1,X2))) ),
inference(superposition,[status(thm)],[c_4337,c_6289]) ).
tcf(c_69473,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(iPr_def_10,X2,set_union2(X0,X1)),iPr_def_11)
| in(sK2(iPr_def_10,X2,set_union2(X0,X1)),X2)
| in(sK2(iPr_def_10,X2,set_union2(X0,X1)),X1)
| in(sK2(iPr_def_10,X2,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(iPr_def_10,X2) ) ),
inference(superposition,[status(thm)],[c_4337,c_4912]) ).
tcf(c_69474,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(iPr_def_10,X0,set_union2(X1,X2)),X2)
| in(sK2(iPr_def_10,X0,set_union2(X1,X2)),X1)
| in(sK2(iPr_def_10,X0,set_union2(X1,X2)),X0)
| ( set_union2(X1,X2) = set_union2(iPr_def_10,X0) )
| ( sK2(iPr_def_10,X0,set_union2(X1,X2)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4337,c_3592]) ).
tcf(c_69475,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(iPr_def_10,X2,set_union2(X0,X1)),iPr_def_11)
| in(sK2(iPr_def_10,X2,set_union2(X0,X1)),X2)
| in(sK2(iPr_def_10,X2,set_union2(X0,X1)),X1)
| in(sK2(iPr_def_10,X2,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(iPr_def_10,X2) ) ),
inference(superposition,[status(thm)],[c_4337,c_3614]) ).
tcf(c_69476,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(iPr_def_11,X0,set_union2(X1,X2)),sK18)
| in(sK2(iPr_def_11,X0,set_union2(X1,X2)),X2)
| in(sK2(iPr_def_11,X0,set_union2(X1,X2)),X1)
| in(sK2(iPr_def_11,X0,set_union2(X1,X2)),X0)
| ( set_union2(X1,X2) = set_union2(iPr_def_11,X0) )
| ( sK2(iPr_def_11,X0,set_union2(X1,X2)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4337,c_33457]) ).
tcf(c_69477,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(iPr_def_11,X2,set_union2(X0,X1)),iPr_def_10)
| in(sK2(iPr_def_11,X2,set_union2(X0,X1)),sK18)
| in(sK2(iPr_def_11,X2,set_union2(X0,X1)),X2)
| in(sK2(iPr_def_11,X2,set_union2(X0,X1)),X1)
| in(sK2(iPr_def_11,X2,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(iPr_def_11,X2) ) ),
inference(superposition,[status(thm)],[c_4337,c_4035]) ).
tcf(c_69481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(X0,sK2(sK5(iPr_def_11),X1,set_union2(X2,X3)))
| in(sK2(sK5(iPr_def_11),X1,set_union2(X2,X3)),X3)
| in(sK2(sK5(iPr_def_11),X1,set_union2(X2,X3)),X2)
| in(sK2(sK5(iPr_def_11),X1,set_union2(X2,X3)),X1)
| in(sK2(sK5(iPr_def_11),X1,set_union2(X2,X3)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X1) = set_union2(X2,X3) )
| ( sK2(sK5(iPr_def_11),X1,set_union2(X2,X3)) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_7243]) ).
tcf(c_69482,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK5(iPr_def_11),X0,set_union2(X1,X2)),X2)
| in(sK2(sK5(iPr_def_11),X0,set_union2(X1,X2)),X1)
| in(sK2(sK5(iPr_def_11),X0,set_union2(X1,X2)),X0)
| ( set_union2(sK5(iPr_def_11),X0) = set_union2(X1,X2) )
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,set_union2(X1,X2))) ),
inference(superposition,[status(thm)],[c_4337,c_23189]) ).
tcf(c_69483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(X0,sK2(sK3(iPr_def_11),X1,set_union2(X2,X3)))
| in(sK2(sK3(iPr_def_11),X1,set_union2(X2,X3)),X3)
| in(sK2(sK3(iPr_def_11),X1,set_union2(X2,X3)),X2)
| in(sK2(sK3(iPr_def_11),X1,set_union2(X2,X3)),X1)
| in(sK2(sK3(iPr_def_11),X1,set_union2(X2,X3)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X1) = set_union2(X2,X3) )
| ( sK2(sK3(iPr_def_11),X1,set_union2(X2,X3)) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_9906]) ).
tcf(c_69484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(X0,sK2(sK4(iPr_def_11),X1,set_union2(X2,X3)))
| in(sK2(sK4(iPr_def_11),X1,set_union2(X2,X3)),X3)
| in(sK2(sK4(iPr_def_11),X1,set_union2(X2,X3)),X2)
| in(sK2(sK4(iPr_def_11),X1,set_union2(X2,X3)),X1)
| in(sK2(sK4(iPr_def_11),X1,set_union2(X2,X3)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X1) = set_union2(X2,X3) )
| ( sK2(sK4(iPr_def_11),X1,set_union2(X2,X3)) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4337,c_45801]) ).
tcf(c_69488,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,set_union2(X0,X0)),X2)
| in(sK2(X1,X2,set_union2(X0,X0)),X1)
| in(sK2(X1,X2,set_union2(X0,X0)),X0)
| ( set_union2(X0,X0) = set_union2(X1,X2) ) ),
inference(equality_factoring,[status(thm)],[c_4337]) ).
tcf(c_69491,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X2,X1)),X2)
| in(sK2(X0,X1,set_union2(X2,X1)),X1)
| in(sK2(X0,X1,set_union2(X2,X1)),X0)
| ( set_union2(X0,X1) = set_union2(X2,X1) ) ),
inference(equality_factoring,[status(thm)],[c_4337]) ).
tcf(c_69492,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X1,X2)),X2)
| in(sK2(X0,X1,set_union2(X1,X2)),X1)
| in(sK2(X0,X1,set_union2(X1,X2)),X0)
| ( set_union2(X0,X1) = set_union2(X1,X2) ) ),
inference(equality_factoring,[status(thm)],[c_4337]) ).
tcf(c_69494,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,set_union2(X0,X1)),X2)
| in(sK2(X1,X2,set_union2(X0,X1)),X1)
| in(sK2(X1,X2,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(X1,X2) ) ),
inference(equality_factoring,[status(thm)],[c_4337]) ).
tcf(c_69495,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X0,X2)),X2)
| in(sK2(X0,X1,set_union2(X0,X2)),X1)
| in(sK2(X0,X1,set_union2(X0,X2)),X0)
| ( set_union2(X0,X1) = set_union2(X0,X2) ) ),
inference(equality_factoring,[status(thm)],[c_4337]) ).
tcf(c_69496,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_union2(X1,X2)),X2)
| in(sK2(X0,X0,set_union2(X1,X2)),X1)
| in(sK2(X0,X0,set_union2(X1,X2)),X0)
| ( set_union2(X0,X0) = set_union2(X1,X2) ) ),
inference(equality_factoring,[status(thm)],[c_4337]) ).
tcf(c_69499,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X2,set_union2(X0,X1)),X2)
| in(sK2(X2,X2,set_union2(X0,X1)),X1)
| in(sK2(X2,X2,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(light_normalisation,[status(thm)],[c_69496,c_97]) ).
tcf(c_69558,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,set_union2(empty_set,X2)),X2)
| in(sK2(X0,X1,set_union2(empty_set,X2)),X1)
| ( set_union2(X0,X1) = set_union2(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_69348,c_7097]) ).
tcf(c_69563,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,set_union2(X2,empty_set)),X2)
| in(sK2(X0,X1,set_union2(X2,empty_set)),X1)
| ( set_union2(X0,X1) = set_union2(X2,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_69347,c_7097]) ).
tcf(c_69569,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,set_union2(empty_set,X2)),X2)
| in(sK2(X0,X1,set_union2(empty_set,X2)),X0)
| ( set_union2(X0,X1) = set_union2(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_69342,c_7097]) ).
tcf(c_69574,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,set_union2(X2,empty_set)),X2)
| in(sK2(X0,X1,set_union2(X2,empty_set)),X0)
| ( set_union2(X0,X1) = set_union2(X2,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_69341,c_7097]) ).
tcf(c_69580,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,set_union2(X2,empty_set)),X1)
| in(sK2(X0,X1,set_union2(X2,empty_set)),X0)
| ( set_union2(X0,X1) = set_union2(X2,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_69335,c_7097]) ).
tcf(c_69587,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,set_union2(empty_set,X2)),X1)
| in(sK2(X0,X1,set_union2(empty_set,X2)),X0)
| ( set_union2(X0,X1) = set_union2(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_69330,c_7097]) ).
tcf(c_69859,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_union2(X1,X2)),X2)
| in(sK2(X0,X0,set_union2(X1,X2)),X1)
| in(sK2(X0,X0,set_union2(X1,X2)),X0)
| ( set_union2(X1,X2) = X0 )
| ~ in(sK2(X0,X0,set_union2(X1,X2)),set_union2(X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_69426,c_97]) ).
tcf(c_71305,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),sK18)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_68821]) ).
tcf(c_71306,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),sK18)
| element(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ~ in(sK18,sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_13652,c_68821]) ).
tcf(c_71311,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),sK18)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(sK18,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_7234,c_68821]) ).
tcf(c_71317,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),sK18)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_71311,c_3400]) ).
tcf(c_71342,plain,
! [X0: $i] :
( epsilon_transitive(sK5(powerset(powerset(X0))))
| subset(sK1(sK5(powerset(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3564,c_18478]) ).
tcf(c_71344,plain,
! [X0: $i] :
( epsilon_transitive(powerset(powerset(X0)))
| epsilon_transitive(sK1(powerset(powerset(X0))))
| subset(sK1(sK1(powerset(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3566,c_18478]) ).
tcf(c_71345,plain,
! [X0: $i] :
( epsilon_connected(powerset(powerset(X0)))
| epsilon_transitive(sK3(powerset(powerset(X0))))
| subset(sK1(sK3(powerset(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3567,c_18478]) ).
tcf(c_71346,plain,
! [X0: $i] :
( epsilon_connected(powerset(powerset(X0)))
| epsilon_transitive(sK4(powerset(powerset(X0))))
| subset(sK1(sK4(powerset(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3568,c_18478]) ).
tcf(c_71347,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| epsilon_transitive(sK3(powerset(X0)))
| subset(sK1(sK3(powerset(X0))),X0)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_3807,c_18478]) ).
tcf(c_71348,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| epsilon_transitive(sK4(powerset(X0)))
| subset(sK1(sK4(powerset(X0))),X0)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_3808,c_18478]) ).
tcf(c_71349,plain,
! [X0: $i] :
( empty(powerset(X0))
| epsilon_transitive(sK5(powerset(X0)))
| subset(sK1(sK5(powerset(X0))),X0)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_3899,c_18478]) ).
tcf(c_71350,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(sK2(X1,X2,powerset(X0)))
| in(sK2(X1,X2,powerset(X0)),X2)
| in(sK2(X1,X2,powerset(X0)),X1)
| subset(sK1(sK2(X1,X2,powerset(X0))),X0)
| ( set_union2(X1,X2) = powerset(X0) )
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_4330,c_18478]) ).
tcf(c_71351,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| epsilon_transitive(sK3(powerset(empty_set)))
| subset(sK1(sK3(powerset(empty_set))),X0) ),
inference(superposition,[status(thm)],[c_4620,c_18478]) ).
tcf(c_71352,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| epsilon_transitive(sK4(powerset(empty_set)))
| subset(sK1(sK4(powerset(empty_set))),X0) ),
inference(superposition,[status(thm)],[c_4637,c_18478]) ).
tcf(c_71353,plain,
! [X0: $i] :
( epsilon_transitive(sK5(powerset(sK5(powerset(powerset(X0))))))
| subset(sK1(sK5(powerset(sK5(powerset(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_5196,c_18478]) ).
tcf(c_71354,plain,
! [X0: $i] :
( epsilon_transitive(sK5(powerset(sK5(powerset(sK5(powerset(powerset(X0))))))))
| subset(sK1(sK5(powerset(sK5(powerset(sK5(powerset(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_5252,c_18478]) ).
tcf(c_71355,plain,
! [X0: $i] :
( epsilon_transitive(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK1(sK5(iPr_def_11)),X0)
| in(powerset(X0),sK5(iPr_def_11))
| ( powerset(X0) = sK5(iPr_def_11) )
| ~ epsilon_transitive(powerset(X0))
| ~ in(powerset(X0),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_18478]) ).
tcf(c_71356,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK1(sK3(iPr_def_11)),X0)
| in(powerset(X0),sK3(iPr_def_11))
| ( powerset(X0) = sK3(iPr_def_11) )
| ~ epsilon_transitive(powerset(X0))
| ~ in(powerset(X0),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_18478]) ).
tcf(c_71357,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_transitive(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK1(sK4(iPr_def_11)),X0)
| in(powerset(X0),sK4(iPr_def_11))
| ( powerset(X0) = sK4(iPr_def_11) )
| ~ epsilon_transitive(powerset(X0))
| ~ in(powerset(X0),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_18478]) ).
tcf(c_71501,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(iPr_def_11))),sK4(iPr_def_11))
| ( sK5(powerset(sK5(iPr_def_11))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_65237,c_13671]) ).
tcf(c_71502,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(iPr_def_11))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(iPr_def_11))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_65237,c_13665]) ).
tcf(c_71503,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(iPr_def_11))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_65237,c_13657]) ).
tcf(c_71504,plain,
! [X0: $i] :
( subset(X0,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK5(powerset(sK5(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_65237,c_128]) ).
tcf(c_71543,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(iPr_def_11))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(iPr_def_11))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_65335,c_13665]) ).
tcf(c_71544,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(iPr_def_11))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK5(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_65335,c_13657]) ).
tcf(c_71545,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK5(powerset(sK5(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_65335,c_128]) ).
tcf(c_71570,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(iPr_def_11))),sK3(iPr_def_11))
| ( sK5(powerset(sK5(iPr_def_11))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(sK5(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_65425,c_13665]) ).
tcf(c_71571,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(powerset(sK5(iPr_def_11))),sK5(iPr_def_11))
| ( sK5(powerset(sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(sK5(powerset(sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_65425,c_13657]) ).
tcf(c_71572,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ subset(X0,sK5(powerset(sK5(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_65425,c_128]) ).
tcf(c_71584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(singleton(set_union2(X0,set_union2(X1,X2))),X3),X1),
inference(superposition,[status(thm)],[c_69,c_68457]) ).
tcf(c_71585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(singleton(set_union2(X0,set_union2(X1,X2))),X3),X2),
inference(superposition,[status(thm)],[c_70,c_68457]) ).
tcf(c_71586,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X1))
| ~ subset(set_union2(singleton(set_union2(X0,powerset(X1))),X2),X1) ),
inference(superposition,[status(thm)],[c_3769,c_68457]) ).
tcf(c_71587,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK5(sK18),set_union2(singleton(set_union2(X0,sK5(sK18))),X1))
| ( set_union2(singleton(set_union2(X0,sK5(sK18))),X1) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(set_union2(singleton(set_union2(X0,sK5(sK18))),X1),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_68457]) ).
tcf(c_71588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),set_union2(singleton(set_union2(X0,sK2(X1,X2,X3))),X4))
| ( set_union2(X1,X2) = X3 )
| ( set_union2(singleton(set_union2(X0,sK2(X1,X2,X3))),X4) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X3)
| ~ in(set_union2(singleton(set_union2(X0,sK2(X1,X2,X3))),X4),X3) ),
inference(superposition,[status(thm)],[c_4329,c_68457]) ).
tcf(c_71589,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_68457]) ).
tcf(c_71590,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_68457]) ).
tcf(c_71591,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_68457]) ).
tcf(c_71592,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_68457]) ).
tcf(c_71593,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ empty(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_68457]) ).
tcf(c_71594,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_68457]) ).
tcf(c_71595,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_68457]) ).
tcf(c_71596,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_7266,c_68457]) ).
tcf(c_71597,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),set_union2(singleton(set_union2(X0,sK1(iPr_def_11))),X1))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(X0,sK1(iPr_def_11))),X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(singleton(set_union2(X0,sK1(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_68457]) ).
tcf(c_71598,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),set_union2(singleton(set_union2(X0,sK1(iPr_def_11))),X1))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(X0,sK1(iPr_def_11))),X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(singleton(set_union2(X0,sK1(iPr_def_11))),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_68457]) ).
tcf(c_71599,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_68457]) ).
tcf(c_71600,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_68457]) ).
tcf(c_71601,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_68457]) ).
tcf(c_71602,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_68457]) ).
tcf(c_71603,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ empty(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_68457]) ).
tcf(c_71604,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_68457]) ).
tcf(c_71605,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_68457]) ).
tcf(c_71606,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_9930,c_68457]) ).
tcf(c_71607,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_68457]) ).
tcf(c_71608,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_68457]) ).
tcf(c_71609,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_68457]) ).
tcf(c_71610,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ empty(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_68457]) ).
tcf(c_71611,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_68457]) ).
tcf(c_71612,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_11214,c_68457]) ).
tcf(c_71620,plain,
! [X0: $i,X1: $i] : ~ in(set_union2(singleton(X0),X1),empty_set),
inference(superposition,[status(thm)],[c_126,c_68457]) ).
tcf(c_71622,plain,
! [X0: $i] : ~ in(set_union2(singleton(iPr_def_11),X0),sK18),
inference(superposition,[status(thm)],[c_3424,c_68457]) ).
tcf(c_71868,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),X0)
| in(sK2(iPr_def_10,X0,sK18),sK4(iPr_def_11))
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(iPr_def_10,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53147,c_13671]) ).
tcf(c_71869,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),X0)
| in(sK2(iPr_def_10,X0,sK18),sK3(iPr_def_11))
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(iPr_def_10,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53147,c_13665]) ).
tcf(c_71870,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),X0)
| in(sK2(iPr_def_10,X0,sK18),sK5(iPr_def_11))
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(iPr_def_10,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53147,c_13657]) ).
tcf(c_71871,plain,
! [X0: $i,X1: $i] :
( subset(X0,iPr_def_10)
| in(sK2(iPr_def_10,X1,sK18),X1)
| ( set_union2(iPr_def_10,X1) = sK18 )
| ( sK2(iPr_def_10,X1,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(iPr_def_10,X1,sK18)) ),
inference(superposition,[status(thm)],[c_53147,c_128]) ).
tcf(c_71872,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| in(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53147,c_3868]) ).
tcf(c_71873,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(iPr_def_10,X0,sK18))
| in(sK2(iPr_def_10,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53147,c_49877]) ).
tcf(c_71874,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(iPr_def_10,X0,sK18))
| in(sK2(iPr_def_10,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53147,c_7260]) ).
tcf(c_71875,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53147,c_359]) ).
tcf(c_71876,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| element(sK2(iPr_def_10,X0,sK18),X1)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53147,c_358]) ).
tcf(c_71877,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X1,sK18),iPr_def_10)
| in(X0,sK2(iPr_def_10,X1,sK18))
| in(sK2(iPr_def_10,X1,sK18),X0)
| ( set_union2(iPr_def_10,X1) = sK18 )
| ( sK2(iPr_def_10,X1,sK18) = sK18 )
| ( sK2(iPr_def_10,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53147,c_77]) ).
tcf(c_71878,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| subset(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53147,c_65]) ).
tcf(c_71879,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(iPr_def_10,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53147,c_49]) ).
tcf(c_71882,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,singleton(X0),sK18),iPr_def_10)
| ( set_union2(iPr_def_10,singleton(X0)) = sK18 )
| ( sK2(iPr_def_10,singleton(X0),sK18) = sK18 )
| ( sK2(iPr_def_10,singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53147,c_62]) ).
tcf(c_71884,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ( sK2(iPr_def_10,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(iPr_def_10,sK18,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53147,c_67]) ).
tcf(c_71885,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(iPr_def_10,set_union2(X0,X1),sK18))
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),X2)
| ( set_union2(iPr_def_10,set_union2(X0,X1)) = sK18 )
| ( sK2(iPr_def_10,set_union2(X0,X1),sK18) = sK18 )
| ( sK2(iPr_def_10,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53147,c_4213]) ).
tcf(c_71886,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(iPr_def_10,set_union2(X0,X1),sK18))
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),X2)
| ( set_union2(iPr_def_10,set_union2(X0,X1)) = sK18 )
| ( sK2(iPr_def_10,set_union2(X0,X1),sK18) = sK18 )
| ( sK2(iPr_def_10,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53147,c_4212]) ).
tcf(c_71887,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,set_union2(X0,X1),sK18),iPr_def_10)
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),X1)
| in(sK2(iPr_def_10,set_union2(X0,X1),sK18),X0)
| ( set_union2(iPr_def_10,set_union2(X0,X1)) = sK18 )
| ( sK2(iPr_def_10,set_union2(X0,X1),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53147,c_71]) ).
tcf(c_71888,plain,
( subset(sK2(iPr_def_10,empty_set,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,empty_set) = sK18 )
| ( sK2(iPr_def_10,empty_set,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53147,c_7097]) ).
tcf(c_71889,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ( sK2(iPr_def_10,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53147,c_12813]) ).
tcf(c_71890,plain,
( subset(sK2(iPr_def_10,sK18,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK18) = sK18 )
| ( sK2(iPr_def_10,sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(iPr_def_10,sK18,sK18)) ),
inference(superposition,[status(thm)],[c_53147,c_6841]) ).
tcf(c_71898,plain,
( subset(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_10)
| in(sK2(iPr_def_10,iPr_def_11,sK18),sK18)
| ( set_union2(iPr_def_10,iPr_def_11) = sK18 )
| ( sK2(iPr_def_10,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53147,c_33457]) ).
tcf(c_71899,plain,
( subset(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_10)
| in(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_10)
| in(sK2(iPr_def_10,iPr_def_11,sK18),sK18)
| ( set_union2(iPr_def_10,iPr_def_11) = sK18 )
| ( sK2(iPr_def_10,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53147,c_4035]) ).
tcf(c_71900,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(iPr_def_10,sK5(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(iPr_def_10,sK5(iPr_def_11),sK18))
| in(sK2(iPr_def_10,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,sK5(iPr_def_11)) = sK18 )
| ( sK2(iPr_def_10,sK5(iPr_def_11),sK18) = sK18 )
| ( sK2(iPr_def_10,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53147,c_7243]) ).
tcf(c_71901,plain,
( subset(sK2(iPr_def_10,sK5(iPr_def_11),sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK5(iPr_def_11)) = sK18 )
| ( sK2(iPr_def_10,sK5(iPr_def_11),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(iPr_def_10,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53147,c_23189]) ).
tcf(c_71902,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(iPr_def_10,sK3(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(iPr_def_10,sK3(iPr_def_11),sK18))
| in(sK2(iPr_def_10,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,sK3(iPr_def_11)) = sK18 )
| ( sK2(iPr_def_10,sK3(iPr_def_11),sK18) = sK18 )
| ( sK2(iPr_def_10,sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53147,c_9906]) ).
tcf(c_71903,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(iPr_def_10,sK4(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(iPr_def_10,sK4(iPr_def_11),sK18))
| in(sK2(iPr_def_10,sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(iPr_def_10,sK4(iPr_def_11)) = sK18 )
| ( sK2(iPr_def_10,sK4(iPr_def_11),sK18) = sK18 )
| ( sK2(iPr_def_10,sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53147,c_45801]) ).
tcf(c_72142,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53096,c_13671]) ).
tcf(c_72143,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53096,c_13665]) ).
tcf(c_72144,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53096,c_13657]) ).
tcf(c_72145,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,iPr_def_10)
| subset(sK2(X1,X2,sK18),X2)
| in(sK2(X1,X2,sK18),X1)
| ( set_union2(X1,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X2)
| ~ subset(X0,sK2(X1,X2,sK18)) ),
inference(superposition,[status(thm)],[c_53096,c_128]) ).
tcf(c_72146,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_11)
| subset(sK2(X1,X0,sK18),X0)
| in(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53096,c_3868]) ).
tcf(c_72147,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK2(X1,X0,sK18),X1)
| subset(sK2(sK2(X1,X0,sK18),X2,sK18),iPr_def_10)
| in(sK2(sK2(X1,X0,sK18),X2,sK18),X2)
| ( set_union2(X1,X0) = sK18 )
| ( set_union2(sK2(X1,X0,sK18),X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53096,c_53126]) ).
tcf(c_72148,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X0,sK18),iPr_def_10)
| in(sK2(X2,X0,sK18),X2)
| subset(sK2(X1,sK2(X2,X0,sK18),sK18),iPr_def_10)
| in(sK2(X1,sK2(X2,X0,sK18),sK18),X1)
| ( set_union2(X2,X0) = sK18 )
| ( set_union2(X1,sK2(X2,X0,sK18)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53096,c_53093]) ).
tcf(c_72149,plain,
! [X0: $i,X1: $i] :
( empty(sK2(X1,X0,sK18))
| subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53096,c_24092]) ).
tcf(c_72150,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK2(X1,X0,sK18))
| subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53096,c_24090]) ).
tcf(c_72151,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK2(X1,X0,sK18))
| subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53096,c_24084]) ).
tcf(c_72152,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ empty(X1)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53096,c_24160]) ).
tcf(c_72153,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ empty(X1)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53096,c_24149]) ).
tcf(c_72154,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ empty(X1)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53096,c_24137]) ).
tcf(c_72155,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X1)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53096,c_13671]) ).
tcf(c_72156,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X1)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53096,c_13665]) ).
tcf(c_72157,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X1)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53096,c_13657]) ).
tcf(c_72158,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| subset(sK2(X1,X2,sK18),iPr_def_10)
| in(sK2(X1,X2,sK18),X1)
| ( set_union2(X1,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X2)
| ~ subset(X0,sK2(X1,X2,sK18)) ),
inference(superposition,[status(thm)],[c_53096,c_128]) ).
tcf(c_72159,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK2(X1,powerset(X0),sK18))
| subset(sK2(X1,powerset(X0),sK18),iPr_def_10)
| in(sK2(X1,powerset(X0),sK18),X1)
| subset(sK1(sK2(X1,powerset(X0),sK18)),X0)
| ( set_union2(X1,powerset(X0)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_53096,c_18478]) ).
tcf(c_72160,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,empty_set,sK18),iPr_def_10)
| subset(sK2(X0,empty_set,sK18),X1)
| in(sK2(X0,empty_set,sK18),X0)
| ( set_union2(X0,empty_set) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(empty_set) ),
inference(superposition,[status(thm)],[c_53096,c_3866]) ).
tcf(c_72163,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK5(powerset(X0)),sK18),iPr_def_10)
| subset(sK2(X1,sK5(powerset(X0)),sK18),X0)
| in(sK2(X1,sK5(powerset(X0)),sK18),X1)
| ( set_union2(X1,sK5(powerset(X0))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(X0))) ),
inference(superposition,[status(thm)],[c_53096,c_3864]) ).
tcf(c_72165,plain,
! [X0: $i] :
( subset(sK2(X0,sK5(powerset(sK18)),sK18),iPr_def_11)
| subset(sK2(X0,sK5(powerset(sK18)),sK18),iPr_def_10)
| in(sK2(X0,sK5(powerset(sK18)),sK18),X0)
| ( set_union2(X0,sK5(powerset(sK18))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(sK18))) ),
inference(superposition,[status(thm)],[c_53096,c_4177]) ).
tcf(c_72166,plain,
! [X0: $i] :
( subset(sK2(X0,sK5(powerset(iPr_def_10)),sK18),iPr_def_11)
| subset(sK2(X0,sK5(powerset(iPr_def_10)),sK18),iPr_def_10)
| in(sK2(X0,sK5(powerset(iPr_def_10)),sK18),X0)
| ( set_union2(X0,sK5(powerset(iPr_def_10))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_53096,c_4574]) ).
tcf(c_72167,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK5(powerset(sK5(powerset(X0)))),sK18),iPr_def_10)
| subset(sK2(X1,sK5(powerset(sK5(powerset(X0)))),sK18),X0)
| in(sK2(X1,sK5(powerset(sK5(powerset(X0)))),sK18),X1)
| ( set_union2(X1,sK5(powerset(sK5(powerset(X0))))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_53096,c_5249]) ).
tcf(c_72168,plain,
! [X0: $i] :
( empty(sK18)
| subset(sK2(X0,sK5(sK18),sK18),iPr_def_10)
| in(sK2(X0,sK5(sK18),sK18),X0)
| ( set_union2(X0,sK5(sK18)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_53096,c_7217]) ).
tcf(c_72169,plain,
! [X0: $i] :
( empty(sK18)
| subset(sK2(X0,sK5(sK18),sK18),iPr_def_11)
| subset(sK2(X0,sK5(sK18),sK18),iPr_def_10)
| in(sK2(X0,sK5(sK18),sK18),X0)
| ( set_union2(X0,sK5(sK18)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_53096,c_5354]) ).
tcf(c_72170,plain,
! [X0: $i] :
( subset(sK2(X0,sK5(powerset(sK5(powerset(sK18)))),sK18),iPr_def_11)
| subset(sK2(X0,sK5(powerset(sK5(powerset(sK18)))),sK18),iPr_def_10)
| in(sK2(X0,sK5(powerset(sK5(powerset(sK18)))),sK18),X0)
| ( set_union2(X0,sK5(powerset(sK5(powerset(sK18))))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK18))))) ),
inference(superposition,[status(thm)],[c_53096,c_5379]) ).
tcf(c_72171,plain,
! [X0: $i] :
( subset(sK2(X0,sK5(powerset(sK5(powerset(iPr_def_10)))),sK18),iPr_def_11)
| subset(sK2(X0,sK5(powerset(sK5(powerset(iPr_def_10)))),sK18),iPr_def_10)
| in(sK2(X0,sK5(powerset(sK5(powerset(iPr_def_10)))),sK18),X0)
| ( set_union2(X0,sK5(powerset(sK5(powerset(iPr_def_10))))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(iPr_def_10))))) ),
inference(superposition,[status(thm)],[c_53096,c_5407]) ).
tcf(c_72172,plain,
! [X0: $i] :
( empty(sK18)
| subset(sK2(X0,sK5(powerset(sK5(sK18))),sK18),iPr_def_11)
| subset(sK2(X0,sK5(powerset(sK5(sK18))),sK18),iPr_def_10)
| in(sK2(X0,sK5(powerset(sK5(sK18))),sK18),X0)
| ( set_union2(X0,sK5(powerset(sK5(sK18)))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_53096,c_5478]) ).
tcf(c_72173,plain,
! [X0: $i] :
( empty(sK18)
| subset(sK2(X0,sK5(powerset(sK5(powerset(sK5(sK18))))),sK18),iPr_def_11)
| subset(sK2(X0,sK5(powerset(sK5(powerset(sK5(sK18))))),sK18),iPr_def_10)
| in(sK2(X0,sK5(powerset(sK5(powerset(sK5(sK18))))),sK18),X0)
| ( set_union2(X0,sK5(powerset(sK5(powerset(sK5(sK18)))))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK5(sK18)))))) ),
inference(superposition,[status(thm)],[c_53096,c_5491]) ).
tcf(c_72174,plain,
! [X0: $i] :
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| subset(sK2(X0,sK1(powerset(sK5(sK18))),sK18),iPr_def_11)
| subset(sK2(X0,sK1(powerset(sK5(sK18))),sK18),iPr_def_10)
| in(sK2(X0,sK1(powerset(sK5(sK18))),sK18),X0)
| ( set_union2(X0,sK1(powerset(sK5(sK18)))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK1(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_53096,c_5502]) ).
tcf(c_72175,plain,
! [X0: $i] :
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK2(X0,sK3(powerset(sK5(sK18))),sK18),iPr_def_11)
| subset(sK2(X0,sK3(powerset(sK5(sK18))),sK18),iPr_def_10)
| in(sK2(X0,sK3(powerset(sK5(sK18))),sK18),X0)
| ( set_union2(X0,sK3(powerset(sK5(sK18)))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK3(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_53096,c_5516]) ).
tcf(c_72176,plain,
! [X0: $i] :
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK2(X0,sK4(powerset(sK5(sK18))),sK18),iPr_def_11)
| subset(sK2(X0,sK4(powerset(sK5(sK18))),sK18),iPr_def_10)
| in(sK2(X0,sK4(powerset(sK5(sK18))),sK18),X0)
| ( set_union2(X0,sK4(powerset(sK5(sK18)))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK4(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_53096,c_5528]) ).
tcf(c_72177,plain,
! [X0: $i] :
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK2(X0,sK3(sK5(sK18)),sK18),iPr_def_11)
| subset(sK2(X0,sK3(sK5(sK18)),sK18),iPr_def_10)
| in(sK2(X0,sK3(sK5(sK18)),sK18),X0)
| ( set_union2(X0,sK3(sK5(sK18))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK3(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_53096,c_5794]) ).
tcf(c_72178,plain,
! [X0: $i] :
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK2(X0,sK4(sK5(sK18)),sK18),iPr_def_11)
| subset(sK2(X0,sK4(sK5(sK18)),sK18),iPr_def_10)
| in(sK2(X0,sK4(sK5(sK18)),sK18),X0)
| ( set_union2(X0,sK4(sK5(sK18))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK4(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_53096,c_5809]) ).
tcf(c_72179,plain,
! [X0: $i] :
( empty(sK18)
| empty(sK5(sK18))
| subset(sK2(X0,sK5(sK5(sK18)),sK18),iPr_def_11)
| subset(sK2(X0,sK5(sK5(sK18)),sK18),iPr_def_10)
| in(sK2(X0,sK5(sK5(sK18)),sK18),X0)
| ( set_union2(X0,sK5(sK5(sK18))) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK5(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_53096,c_5824]) ).
tcf(c_72180,plain,
! [X0: $i] :
( subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| subset(sK2(X0,sK5(iPr_def_11),sK18),sK18)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53096,c_68870]) ).
tcf(c_72181,plain,
! [X0: $i] :
( subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_11)
| subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53096,c_8544]) ).
tcf(c_72183,plain,
! [X0: $i] :
( subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53096,c_7570]) ).
tcf(c_72184,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| subset(sK2(X0,sK5(iPr_def_11),sK18),sK18)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53096,c_7199]) ).
tcf(c_72185,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK3(iPr_def_11),sK18),iPr_def_10)
| subset(sK2(X0,sK3(iPr_def_11),sK18),sK18)
| in(sK2(X0,sK3(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK3(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53096,c_9862]) ).
tcf(c_72186,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| subset(sK2(X0,sK4(iPr_def_11),sK18),sK18)
| in(sK2(X0,sK4(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53096,c_11154]) ).
tcf(c_72187,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X0,X1,sK18),iPr_def_10)
| subset(sK2(X0,X1,sK18),X1)
| in(sK3(iPr_def_11),sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53096,c_49877]) ).
tcf(c_72188,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X0,X1,sK18),iPr_def_10)
| subset(sK2(X0,X1,sK18),X1)
| in(sK5(iPr_def_11),sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53096,c_7260]) ).
tcf(c_72189,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X2,sK18),iPr_def_10)
| subset(sK2(X0,X2,sK18),X2)
| ( set_union2(X0,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53096,c_359]) ).
tcf(c_72190,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X2,sK18),iPr_def_10)
| element(sK2(X0,X2,sK18),X1)
| subset(sK2(X0,X2,sK18),X2)
| ( set_union2(X0,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53096,c_358]) ).
tcf(c_72191,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X2,sK18),iPr_def_10)
| subset(sK2(X1,X2,sK18),X2)
| in(X0,sK2(X1,X2,sK18))
| in(sK2(X1,X2,sK18),X0)
| ( set_union2(X1,X2) = sK18 )
| ( sK2(X1,X2,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53096,c_77]) ).
tcf(c_72192,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| subset(sK2(X1,X0,sK18),X1)
| subset(sK2(X1,X0,sK18),X0)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53096,c_65]) ).
tcf(c_72193,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| subset(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_53096,c_49]) ).
tcf(c_72196,plain,
! [X0: $i,X1: $i] :
( subset(sK2(singleton(X1),X0,sK18),iPr_def_10)
| subset(sK2(singleton(X1),X0,sK18),X0)
| ( set_union2(singleton(X1),X0) = sK18 )
| ( sK2(singleton(X1),X0,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53096,c_62]) ).
tcf(c_72197,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| subset(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53096,c_66]) ).
tcf(c_72199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X0,X1),X3,sK18),iPr_def_10)
| subset(sK2(set_union2(X0,X1),X3,sK18),X3)
| in(X2,sK2(set_union2(X0,X1),X3,sK18))
| in(sK2(set_union2(X0,X1),X3,sK18),X2)
| ( set_union2(set_union2(X0,X1),X3) = sK18 )
| ( sK2(set_union2(X0,X1),X3,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X3)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53096,c_4213]) ).
tcf(c_72200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X0,X1),X3,sK18),iPr_def_10)
| subset(sK2(set_union2(X0,X1),X3,sK18),X3)
| in(X2,sK2(set_union2(X0,X1),X3,sK18))
| in(sK2(set_union2(X0,X1),X3,sK18),X2)
| ( set_union2(set_union2(X0,X1),X3) = sK18 )
| ( sK2(set_union2(X0,X1),X3,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X3)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53096,c_4212]) ).
tcf(c_72201,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X1,X2),X0,sK18),iPr_def_10)
| subset(sK2(set_union2(X1,X2),X0,sK18),X0)
| in(sK2(set_union2(X1,X2),X0,sK18),X2)
| in(sK2(set_union2(X1,X2),X0,sK18),X1)
| ( set_union2(set_union2(X1,X2),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53096,c_71]) ).
tcf(c_72202,plain,
! [X0: $i] :
( subset(sK2(empty_set,X0,sK18),iPr_def_10)
| subset(sK2(empty_set,X0,sK18),X0)
| ( set_union2(empty_set,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53096,c_7097]) ).
tcf(c_72207,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| subset(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53096,c_9540]) ).
tcf(c_72208,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| subset(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ in(iPr_def_11,sK2(iPr_def_10,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53096,c_6289]) ).
tcf(c_72212,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),sK18)
| subset(sK2(iPr_def_11,X0,sK18),X0)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ( sK2(iPr_def_11,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53096,c_33457]) ).
tcf(c_72213,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),sK18)
| subset(sK2(iPr_def_11,X0,sK18),X0)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53096,c_4035]) ).
tcf(c_72214,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK5(iPr_def_11),X1,sK18),iPr_def_10)
| subset(sK2(sK5(iPr_def_11),X1,sK18),X1)
| in(X0,sK2(sK5(iPr_def_11),X1,sK18))
| in(sK2(sK5(iPr_def_11),X1,sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X1) = sK18 )
| ( sK2(sK5(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53096,c_7243]) ).
tcf(c_72215,plain,
! [X0: $i] :
( subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| subset(sK2(sK5(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,sK18)) ),
inference(superposition,[status(thm)],[c_53096,c_23189]) ).
tcf(c_72216,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK3(iPr_def_11),X1,sK18),iPr_def_10)
| subset(sK2(sK3(iPr_def_11),X1,sK18),X1)
| in(X0,sK2(sK3(iPr_def_11),X1,sK18))
| in(sK2(sK3(iPr_def_11),X1,sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X1) = sK18 )
| ( sK2(sK3(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53096,c_9906]) ).
tcf(c_72217,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK4(iPr_def_11),X1,sK18),iPr_def_10)
| subset(sK2(sK4(iPr_def_11),X1,sK18),X1)
| in(X0,sK2(sK4(iPr_def_11),X1,sK18))
| in(sK2(sK4(iPr_def_11),X1,sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X1) = sK18 )
| ( sK2(sK4(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53096,c_45801]) ).
tcf(c_72219,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(equality_factoring,[status(thm)],[c_53096]) ).
tcf(c_72225,plain,
! [X0: $i] :
( subset(sK2(empty_set,X0,sK18),iPr_def_10)
| subset(sK2(empty_set,X0,sK18),X0)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(light_normalisation,[status(thm)],[c_72202,c_3423]) ).
tcf(c_72242,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,empty_set,sK18),iPr_def_10)
| subset(sK2(X0,empty_set,sK18),X1)
| in(sK2(X0,empty_set,sK18),X0)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(empty_set) ),
inference(light_normalisation,[status(thm)],[c_72160,c_126]) ).
tcf(c_72243,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,empty_set,sK18),iPr_def_10)
| subset(sK2(X0,empty_set,sK18),X1)
| in(sK2(X0,empty_set,sK18),X0)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_72242,c_89]) ).
tcf(c_73003,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53129,c_13671]) ).
tcf(c_73004,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53129,c_13665]) ).
tcf(c_73005,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53129,c_13657]) ).
tcf(c_73006,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,iPr_def_10)
| subset(sK2(X1,X2,sK18),X1)
| in(sK2(X1,X2,sK18),X2)
| ( set_union2(X1,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ subset(X0,sK2(X1,X2,sK18)) ),
inference(superposition,[status(thm)],[c_53129,c_128]) ).
tcf(c_73007,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_11)
| subset(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53129,c_3868]) ).
tcf(c_73008,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| subset(sK2(sK2(X0,X1,sK18),X2,sK18),iPr_def_10)
| in(sK2(sK2(X0,X1,sK18),X2,sK18),X2)
| ( set_union2(X0,X1) = sK18 )
| ( set_union2(sK2(X0,X1,sK18),X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53129,c_53126]) ).
tcf(c_73009,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X2,sK18),iPr_def_10)
| in(sK2(X0,X2,sK18),X2)
| subset(sK2(X1,sK2(X0,X2,sK18),sK18),iPr_def_10)
| in(sK2(X1,sK2(X0,X2,sK18),sK18),X1)
| ( set_union2(X0,X2) = sK18 )
| ( set_union2(X1,sK2(X0,X2,sK18)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53129,c_53093]) ).
tcf(c_73010,plain,
! [X0: $i,X1: $i] :
( empty(sK2(X0,X1,sK18))
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53129,c_24092]) ).
tcf(c_73011,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK2(X0,X1,sK18))
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53129,c_24090]) ).
tcf(c_73012,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK2(X0,X1,sK18))
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53129,c_24084]) ).
tcf(c_73013,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53129,c_24160]) ).
tcf(c_73014,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53129,c_24149]) ).
tcf(c_73015,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53129,c_24137]) ).
tcf(c_73016,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53129,c_13671]) ).
tcf(c_73017,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53129,c_13665]) ).
tcf(c_73018,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53129,c_13657]) ).
tcf(c_73019,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X1)
| subset(sK2(X1,X2,sK18),iPr_def_10)
| in(sK2(X1,X2,sK18),X2)
| ( set_union2(X1,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ subset(X0,sK2(X1,X2,sK18)) ),
inference(superposition,[status(thm)],[c_53129,c_128]) ).
tcf(c_73020,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK2(powerset(X0),X1,sK18))
| subset(sK2(powerset(X0),X1,sK18),iPr_def_10)
| in(sK2(powerset(X0),X1,sK18),X1)
| subset(sK1(sK2(powerset(X0),X1,sK18)),X0)
| ( set_union2(powerset(X0),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_53129,c_18478]) ).
tcf(c_73021,plain,
! [X0: $i,X1: $i] :
( subset(sK2(empty_set,X0,sK18),iPr_def_10)
| subset(sK2(empty_set,X0,sK18),X1)
| in(sK2(empty_set,X0,sK18),X0)
| ( set_union2(empty_set,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(empty_set) ),
inference(superposition,[status(thm)],[c_53129,c_3866]) ).
tcf(c_73024,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK5(powerset(X0)),X1,sK18),iPr_def_10)
| subset(sK2(sK5(powerset(X0)),X1,sK18),X0)
| in(sK2(sK5(powerset(X0)),X1,sK18),X1)
| ( set_union2(sK5(powerset(X0)),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(X0))) ),
inference(superposition,[status(thm)],[c_53129,c_3864]) ).
tcf(c_73026,plain,
! [X0: $i] :
( subset(sK2(sK5(powerset(sK18)),X0,sK18),iPr_def_11)
| subset(sK2(sK5(powerset(sK18)),X0,sK18),iPr_def_10)
| in(sK2(sK5(powerset(sK18)),X0,sK18),X0)
| ( set_union2(sK5(powerset(sK18)),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(sK18))) ),
inference(superposition,[status(thm)],[c_53129,c_4177]) ).
tcf(c_73027,plain,
! [X0: $i] :
( subset(sK2(sK5(powerset(iPr_def_10)),X0,sK18),iPr_def_11)
| subset(sK2(sK5(powerset(iPr_def_10)),X0,sK18),iPr_def_10)
| in(sK2(sK5(powerset(iPr_def_10)),X0,sK18),X0)
| ( set_union2(sK5(powerset(iPr_def_10)),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_53129,c_4574]) ).
tcf(c_73028,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK5(powerset(sK5(powerset(X0)))),X1,sK18),iPr_def_10)
| subset(sK2(sK5(powerset(sK5(powerset(X0)))),X1,sK18),X0)
| in(sK2(sK5(powerset(sK5(powerset(X0)))),X1,sK18),X1)
| ( set_union2(sK5(powerset(sK5(powerset(X0)))),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_53129,c_5249]) ).
tcf(c_73029,plain,
! [X0: $i] :
( empty(sK18)
| subset(sK2(sK5(sK18),X0,sK18),iPr_def_10)
| in(sK2(sK5(sK18),X0,sK18),X0)
| ( set_union2(sK5(sK18),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_53129,c_7217]) ).
tcf(c_73030,plain,
! [X0: $i] :
( empty(sK18)
| subset(sK2(sK5(sK18),X0,sK18),iPr_def_11)
| subset(sK2(sK5(sK18),X0,sK18),iPr_def_10)
| in(sK2(sK5(sK18),X0,sK18),X0)
| ( set_union2(sK5(sK18),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_53129,c_5354]) ).
tcf(c_73031,plain,
! [X0: $i] :
( subset(sK2(sK5(powerset(sK5(powerset(sK18)))),X0,sK18),iPr_def_11)
| subset(sK2(sK5(powerset(sK5(powerset(sK18)))),X0,sK18),iPr_def_10)
| in(sK2(sK5(powerset(sK5(powerset(sK18)))),X0,sK18),X0)
| ( set_union2(sK5(powerset(sK5(powerset(sK18)))),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK18))))) ),
inference(superposition,[status(thm)],[c_53129,c_5379]) ).
tcf(c_73032,plain,
! [X0: $i] :
( subset(sK2(sK5(powerset(sK5(powerset(iPr_def_10)))),X0,sK18),iPr_def_11)
| subset(sK2(sK5(powerset(sK5(powerset(iPr_def_10)))),X0,sK18),iPr_def_10)
| in(sK2(sK5(powerset(sK5(powerset(iPr_def_10)))),X0,sK18),X0)
| ( set_union2(sK5(powerset(sK5(powerset(iPr_def_10)))),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(iPr_def_10))))) ),
inference(superposition,[status(thm)],[c_53129,c_5407]) ).
tcf(c_73033,plain,
! [X0: $i] :
( empty(sK18)
| subset(sK2(sK5(powerset(sK5(sK18))),X0,sK18),iPr_def_11)
| subset(sK2(sK5(powerset(sK5(sK18))),X0,sK18),iPr_def_10)
| in(sK2(sK5(powerset(sK5(sK18))),X0,sK18),X0)
| ( set_union2(sK5(powerset(sK5(sK18))),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_53129,c_5478]) ).
tcf(c_73034,plain,
! [X0: $i] :
( empty(sK18)
| subset(sK2(sK5(powerset(sK5(powerset(sK5(sK18))))),X0,sK18),iPr_def_11)
| subset(sK2(sK5(powerset(sK5(powerset(sK5(sK18))))),X0,sK18),iPr_def_10)
| in(sK2(sK5(powerset(sK5(powerset(sK5(sK18))))),X0,sK18),X0)
| ( set_union2(sK5(powerset(sK5(powerset(sK5(sK18))))),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK5(sK18)))))) ),
inference(superposition,[status(thm)],[c_53129,c_5491]) ).
tcf(c_73035,plain,
! [X0: $i] :
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| subset(sK2(sK1(powerset(sK5(sK18))),X0,sK18),iPr_def_11)
| subset(sK2(sK1(powerset(sK5(sK18))),X0,sK18),iPr_def_10)
| in(sK2(sK1(powerset(sK5(sK18))),X0,sK18),X0)
| ( set_union2(sK1(powerset(sK5(sK18))),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK1(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_53129,c_5502]) ).
tcf(c_73036,plain,
! [X0: $i] :
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK2(sK3(powerset(sK5(sK18))),X0,sK18),iPr_def_11)
| subset(sK2(sK3(powerset(sK5(sK18))),X0,sK18),iPr_def_10)
| in(sK2(sK3(powerset(sK5(sK18))),X0,sK18),X0)
| ( set_union2(sK3(powerset(sK5(sK18))),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK3(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_53129,c_5516]) ).
tcf(c_73037,plain,
! [X0: $i] :
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK2(sK4(powerset(sK5(sK18))),X0,sK18),iPr_def_11)
| subset(sK2(sK4(powerset(sK5(sK18))),X0,sK18),iPr_def_10)
| in(sK2(sK4(powerset(sK5(sK18))),X0,sK18),X0)
| ( set_union2(sK4(powerset(sK5(sK18))),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK4(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_53129,c_5528]) ).
tcf(c_73038,plain,
! [X0: $i] :
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK2(sK3(sK5(sK18)),X0,sK18),iPr_def_11)
| subset(sK2(sK3(sK5(sK18)),X0,sK18),iPr_def_10)
| in(sK2(sK3(sK5(sK18)),X0,sK18),X0)
| ( set_union2(sK3(sK5(sK18)),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK3(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_53129,c_5794]) ).
tcf(c_73039,plain,
! [X0: $i] :
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK2(sK4(sK5(sK18)),X0,sK18),iPr_def_11)
| subset(sK2(sK4(sK5(sK18)),X0,sK18),iPr_def_10)
| in(sK2(sK4(sK5(sK18)),X0,sK18),X0)
| ( set_union2(sK4(sK5(sK18)),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK4(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_53129,c_5809]) ).
tcf(c_73040,plain,
! [X0: $i] :
( empty(sK18)
| empty(sK5(sK18))
| subset(sK2(sK5(sK5(sK18)),X0,sK18),iPr_def_11)
| subset(sK2(sK5(sK5(sK18)),X0,sK18),iPr_def_10)
| in(sK2(sK5(sK5(sK18)),X0,sK18),X0)
| ( set_union2(sK5(sK5(sK18)),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK5(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_53129,c_5824]) ).
tcf(c_73041,plain,
! [X0: $i] :
( subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| subset(sK2(sK5(iPr_def_11),X0,sK18),sK18)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53129,c_68870]) ).
tcf(c_73042,plain,
! [X0: $i] :
( subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_11)
| subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53129,c_8544]) ).
tcf(c_73044,plain,
! [X0: $i] :
( subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53129,c_7570]) ).
tcf(c_73045,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| subset(sK2(sK5(iPr_def_11),X0,sK18),sK18)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53129,c_7199]) ).
tcf(c_73046,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(sK3(iPr_def_11),X0,sK18),iPr_def_10)
| subset(sK2(sK3(iPr_def_11),X0,sK18),sK18)
| in(sK2(sK3(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK3(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53129,c_9862]) ).
tcf(c_73047,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| subset(sK2(sK4(iPr_def_11),X0,sK18),sK18)
| in(sK2(sK4(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53129,c_11154]) ).
tcf(c_73048,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X1,X0,sK18),iPr_def_10)
| subset(sK2(X1,X0,sK18),X1)
| in(sK3(iPr_def_11),sK2(X1,X0,sK18))
| in(sK2(X1,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = sK18 )
| ( sK2(X1,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53129,c_49877]) ).
tcf(c_73049,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X1,X0,sK18),iPr_def_10)
| subset(sK2(X1,X0,sK18),X1)
| in(sK5(iPr_def_11),sK2(X1,X0,sK18))
| in(sK2(X1,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = sK18 )
| ( sK2(X1,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53129,c_7260]) ).
tcf(c_73050,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X0,sK18),iPr_def_10)
| subset(sK2(X2,X0,sK18),X2)
| ( set_union2(X2,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53129,c_359]) ).
tcf(c_73051,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X0,sK18),iPr_def_10)
| element(sK2(X2,X0,sK18),X1)
| subset(sK2(X2,X0,sK18),X2)
| ( set_union2(X2,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53129,c_358]) ).
tcf(c_73052,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X1,sK18),iPr_def_10)
| subset(sK2(X2,X1,sK18),X2)
| in(X0,sK2(X2,X1,sK18))
| in(sK2(X2,X1,sK18),X0)
| ( set_union2(X2,X1) = sK18 )
| ( sK2(X2,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53129,c_77]) ).
tcf(c_73053,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| subset(sK2(X0,X1,sK18),X1)
| subset(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53129,c_65]) ).
tcf(c_73054,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| subset(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK2(X1,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53129,c_49]) ).
tcf(c_73057,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,singleton(X1),sK18),iPr_def_10)
| subset(sK2(X0,singleton(X1),sK18),X0)
| ( set_union2(X0,singleton(X1)) = sK18 )
| ( sK2(X0,singleton(X1),sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53129,c_62]) ).
tcf(c_73058,plain,
! [X0: $i] :
( subset(sK2(X0,X0,sK18),iPr_def_10)
| subset(sK2(X0,X0,sK18),X0)
| ( set_union2(X0,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ in(sK2(X0,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53129,c_66]) ).
tcf(c_73060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,set_union2(X0,X1),sK18),iPr_def_10)
| subset(sK2(X3,set_union2(X0,X1),sK18),X3)
| in(X2,sK2(X3,set_union2(X0,X1),sK18))
| in(sK2(X3,set_union2(X0,X1),sK18),X2)
| ( set_union2(X3,set_union2(X0,X1)) = sK18 )
| ( sK2(X3,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X3)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53129,c_4213]) ).
tcf(c_73061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,set_union2(X0,X1),sK18),iPr_def_10)
| subset(sK2(X3,set_union2(X0,X1),sK18),X3)
| in(X2,sK2(X3,set_union2(X0,X1),sK18))
| in(sK2(X3,set_union2(X0,X1),sK18),X2)
| ( set_union2(X3,set_union2(X0,X1)) = sK18 )
| ( sK2(X3,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X3)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53129,c_4212]) ).
tcf(c_73062,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,set_union2(X1,X2),sK18),iPr_def_10)
| subset(sK2(X0,set_union2(X1,X2),sK18),X0)
| in(sK2(X0,set_union2(X1,X2),sK18),X2)
| in(sK2(X0,set_union2(X1,X2),sK18),X1)
| ( set_union2(X0,set_union2(X1,X2)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53129,c_71]) ).
tcf(c_73063,plain,
! [X0: $i] :
( subset(sK2(X0,empty_set,sK18),iPr_def_10)
| subset(sK2(X0,empty_set,sK18),X0)
| ( set_union2(X0,empty_set) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53129,c_7097]) ).
tcf(c_73068,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| subset(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53129,c_9540]) ).
tcf(c_73069,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| subset(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ in(iPr_def_11,sK2(X0,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53129,c_6289]) ).
tcf(c_73073,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),sK18)
| subset(sK2(X0,iPr_def_11,sK18),X0)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ( sK2(X0,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53129,c_33457]) ).
tcf(c_73074,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),sK18)
| subset(sK2(X0,iPr_def_11,sK18),X0)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_53129,c_4035]) ).
tcf(c_73075,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| subset(sK2(set_union2(X0,X1),X0,sK18),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53129,c_4078]) ).
tcf(c_73076,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_10)
| subset(sK2(set_union2(X0,X1),sK18,sK18),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ in(sK2(set_union2(X0,X1),sK18,sK18),X1) ),
inference(superposition,[status(thm)],[c_53129,c_4079]) ).
tcf(c_73077,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(X1,sK5(iPr_def_11),sK18),iPr_def_10)
| subset(sK2(X1,sK5(iPr_def_11),sK18),X1)
| in(X0,sK2(X1,sK5(iPr_def_11),sK18))
| in(sK2(X1,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,sK5(iPr_def_11)) = sK18 )
| ( sK2(X1,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53129,c_7243]) ).
tcf(c_73078,plain,
! [X0: $i] :
( subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| subset(sK2(X0,sK5(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ subset(iPr_def_11,sK2(X0,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53129,c_23189]) ).
tcf(c_73079,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(X1,sK3(iPr_def_11),sK18),iPr_def_10)
| subset(sK2(X1,sK3(iPr_def_11),sK18),X1)
| in(X0,sK2(X1,sK3(iPr_def_11),sK18))
| in(sK2(X1,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,sK3(iPr_def_11)) = sK18 )
| ( sK2(X1,sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53129,c_9906]) ).
tcf(c_73080,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(X1,sK4(iPr_def_11),sK18),iPr_def_10)
| subset(sK2(X1,sK4(iPr_def_11),sK18),X1)
| in(X0,sK2(X1,sK4(iPr_def_11),sK18))
| in(sK2(X1,sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,sK4(iPr_def_11)) = sK18 )
| ( sK2(X1,sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53129,c_45801]) ).
tcf(c_73082,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(equality_factoring,[status(thm)],[c_53129]) ).
tcf(c_73088,plain,
! [X0: $i] :
( subset(sK2(X0,empty_set,sK18),iPr_def_10)
| subset(sK2(X0,empty_set,sK18),X0)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(light_normalisation,[status(thm)],[c_73063,c_126]) ).
tcf(c_73105,plain,
! [X0: $i,X1: $i] :
( subset(sK2(empty_set,X0,sK18),iPr_def_10)
| subset(sK2(empty_set,X0,sK18),X1)
| in(sK2(empty_set,X0,sK18),X0)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(empty_set) ),
inference(light_normalisation,[status(thm)],[c_73021,c_3423]) ).
tcf(c_73106,plain,
! [X0: $i,X1: $i] :
( subset(sK2(empty_set,X0,sK18),iPr_def_10)
| subset(sK2(empty_set,X0,sK18),X1)
| in(sK2(empty_set,X0,sK18),X0)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_73105,c_89]) ).
tcf(c_73124,plain,
! [X0: $i] :
( subset(sK2(X0,X0,sK18),iPr_def_10)
| subset(sK2(X0,X0,sK18),X0)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ in(sK2(X0,X0,sK18),sK18) ),
inference(light_normalisation,[status(thm)],[c_73058,c_97]) ).
tcf(c_74108,plain,
( ~ empty(sK18)
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_68864,c_43126]) ).
tcf(c_74109,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(renaming,[status(thm)],[c_74108]) ).
tcf(c_74117,plain,
! [X0: $i] :
( element(sK4(iPr_def_11),X0)
| ~ empty(sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_74109,c_358]) ).
tcf(c_74118,plain,
! [X0: $i] :
( in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_74109,c_77]) ).
tcf(c_74119,plain,
( subset(sK4(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74109,c_65]) ).
tcf(c_74120,plain,
( ~ empty(sK18)
| ~ in(iPr_def_10,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_74109,c_49]) ).
tcf(c_74122,plain,
( element(sK4(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74109,c_127]) ).
tcf(c_74123,plain,
( subset(sK4(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74109,c_9540]) ).
tcf(c_74124,plain,
( ~ empty(sK18)
| ~ in(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_74109,c_6289]) ).
tcf(c_74125,plain,
( element(sK4(iPr_def_11),iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74109,c_4912]) ).
tcf(c_74126,plain,
( ( sK4(iPr_def_11) = sK18 )
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74109,c_3592]) ).
tcf(c_74127,plain,
( in(sK4(iPr_def_11),iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74109,c_3614]) ).
tcf(c_74155,plain,
( ~ empty(sK18)
| in(sK3(iPr_def_11),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_68865,c_43064]) ).
tcf(c_74156,plain,
( in(sK3(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(renaming,[status(thm)],[c_74155]) ).
tcf(c_74164,plain,
! [X0: $i] :
( element(sK3(iPr_def_11),X0)
| ~ empty(sK18)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_74156,c_358]) ).
tcf(c_74165,plain,
! [X0: $i] :
( in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK18)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_74156,c_77]) ).
tcf(c_74166,plain,
( subset(sK3(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74156,c_65]) ).
tcf(c_74167,plain,
( ~ empty(sK18)
| ~ in(iPr_def_10,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_74156,c_49]) ).
tcf(c_74169,plain,
( element(sK3(iPr_def_11),iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74156,c_127]) ).
tcf(c_74170,plain,
( subset(sK3(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74156,c_9540]) ).
tcf(c_74171,plain,
( ~ empty(sK18)
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_74156,c_6289]) ).
tcf(c_74172,plain,
( element(sK3(iPr_def_11),iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74156,c_4912]) ).
tcf(c_74173,plain,
( ( sK3(iPr_def_11) = sK18 )
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74156,c_3592]) ).
tcf(c_74174,plain,
( in(sK3(iPr_def_11),iPr_def_11)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74156,c_3614]) ).
tcf(c_74202,plain,
! [X0: $i] : ~ in(set_union2(X0,singleton(iPr_def_11)),sK18),
inference(superposition,[status(thm)],[c_58,c_71622]) ).
tcf(c_74233,plain,
! [X0: $i] :
( element(sK4(iPr_def_11),X0)
| ~ empty(sK18)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_74127,c_358]) ).
tcf(c_74234,plain,
! [X0: $i] :
( in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ empty(sK18)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_74127,c_77]) ).
tcf(c_74240,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK18)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74127,c_4035]) ).
tcf(c_74325,plain,
! [X0: $i] :
( element(sK3(iPr_def_11),X0)
| ~ empty(sK18)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_74174,c_358]) ).
tcf(c_74326,plain,
! [X0: $i] :
( in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ empty(sK18)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_74174,c_77]) ).
tcf(c_74332,plain,
( in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK18)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74174,c_4035]) ).
tcf(c_74359,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| subset(sK5(powerset(sK2(X0,X1,sK18))),iPr_def_10)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3564,c_53089]) ).
tcf(c_74360,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3420,c_53089]) ).
tcf(c_74361,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(powerset(sK2(X0,X1,sK18)))
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| subset(sK1(powerset(sK2(X0,X1,sK18))),iPr_def_10)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3566,c_53089]) ).
tcf(c_74362,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(sK2(X0,X1,sK18)))
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| subset(sK3(powerset(sK2(X0,X1,sK18))),iPr_def_10)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3567,c_53089]) ).
tcf(c_74363,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(sK2(X0,X1,sK18)))
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| subset(sK4(powerset(sK2(X0,X1,sK18))),iPr_def_10)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3568,c_53089]) ).
tcf(c_74364,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| subset(sK3(sK2(X0,X1,sK18)),iPr_def_10)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_3807,c_53089]) ).
tcf(c_74365,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| subset(sK4(sK2(X0,X1,sK18)),iPr_def_10)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_3808,c_53089]) ).
tcf(c_74366,plain,
! [X0: $i,X1: $i] :
( empty(sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| subset(sK5(sK2(X0,X1,sK18)),iPr_def_10)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_3899,c_53089]) ).
tcf(c_74367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| subset(sK2(X2,X3,sK2(X0,X1,sK18)),iPr_def_10)
| in(sK2(X2,X3,sK2(X0,X1,sK18)),X3)
| in(sK2(X2,X3,sK2(X0,X1,sK18)),X2)
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = set_union2(X2,X3) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_4330,c_53089]) ).
tcf(c_74368,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(empty_set))
| subset(sK3(powerset(empty_set)),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4620,c_53089]) ).
tcf(c_74369,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(empty_set))
| subset(sK4(powerset(empty_set)),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4637,c_53089]) ).
tcf(c_74370,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| subset(sK5(powerset(sK5(powerset(sK2(X0,X1,sK18))))),iPr_def_10)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5196,c_53089]) ).
tcf(c_74371,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK2(X0,X1,sK18))))))),iPr_def_10)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5252,c_53089]) ).
tcf(c_74372,plain,
! [X0: $i,X1: $i] :
( subset(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK2(X0,X1,sK18))
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_53089]) ).
tcf(c_74373,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK2(X0,X1,sK18))
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_53089]) ).
tcf(c_74374,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK2(X0,X1,sK18))
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_53089]) ).
tcf(c_74375,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| subset(sK2(X2,sK2(X0,X1,sK18),sK18),iPr_def_10)
| in(sK2(X2,sK2(X0,X1,sK18),sK18),X2)
| ( set_union2(X0,X1) = sK18 )
| ( set_union2(X2,sK2(X0,X1,sK18)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_53096,c_53089]) ).
tcf(c_74376,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| subset(sK2(sK2(X0,X1,sK18),X2,sK18),iPr_def_10)
| in(sK2(sK2(X0,X1,sK18),X2,sK18),X2)
| ( set_union2(X0,X1) = sK18 )
| ( set_union2(sK2(X0,X1,sK18),X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_53129,c_53089]) ).
tcf(c_74529,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| subset(sK2(X2,X0,sK18),iPr_def_10)
| in(sK2(X2,X0,sK18),X2)
| in(sK2(X2,X0,sK18),X1)
| ( set_union2(X2,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_131]) ).
tcf(c_74530,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X0,sK18),iPr_def_10)
| subset(sK2(X2,X0,sK18),X1)
| in(sK2(X2,X0,sK18),X2)
| ( set_union2(X2,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_53094,c_133]) ).
tcf(c_74531,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| subset(sK2(X2,X0,sK18),iPr_def_10)
| element(sK2(X2,X0,sK18),X1)
| in(sK3(iPr_def_11),sK2(X2,X0,sK18))
| in(sK2(X2,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X2,X0) = sK18 )
| ( sK2(X2,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X2)
| ~ in(X2,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_49877]) ).
tcf(c_74532,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| subset(sK2(X2,X0,sK18),iPr_def_10)
| element(sK2(X2,X0,sK18),X1)
| in(sK5(iPr_def_11),sK2(X2,X0,sK18))
| in(sK2(X2,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X2,X0) = sK18 )
| ( sK2(X2,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X2)
| ~ in(X2,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_7260]) ).
tcf(c_74533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X0,sK18),iPr_def_10)
| element(sK2(X2,X0,sK18),X1)
| ( set_union2(X2,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_359]) ).
tcf(c_74534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X0,sK18),iPr_def_10)
| element(sK2(X2,X0,sK18),X3)
| element(sK2(X2,X0,sK18),X1)
| ( set_union2(X2,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_358]) ).
tcf(c_74535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X1,X2,sK18),iPr_def_10)
| element(sK2(X1,X2,sK18),X3)
| in(X0,sK2(X1,X2,sK18))
| in(sK2(X1,X2,sK18),X0)
| ( set_union2(X1,X2) = sK18 )
| ( sK2(X1,X2,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ subset(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_77]) ).
tcf(c_74537,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| element(sK2(X0,X1,sK18),X2)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X1,X2)
| ~ in(X0,sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_53094,c_49]) ).
tcf(c_74540,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(singleton(X2),X0,sK18),iPr_def_10)
| element(sK2(singleton(X2),X0,sK18),X1)
| ( set_union2(singleton(X2),X0) = sK18 )
| ( sK2(singleton(X2),X0,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_62]) ).
tcf(c_74541,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| element(sK2(X0,X1,sK18),X2)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X1,X2)
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53094,c_66]) ).
tcf(c_74543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(set_union2(X0,X1),X3,sK18),iPr_def_10)
| element(sK2(set_union2(X0,X1),X3,sK18),X4)
| in(X2,sK2(set_union2(X0,X1),X3,sK18))
| in(sK2(set_union2(X0,X1),X3,sK18),X2)
| ( set_union2(set_union2(X0,X1),X3) = sK18 )
| ( sK2(set_union2(X0,X1),X3,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X3,X4)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53094,c_4213]) ).
tcf(c_74544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(set_union2(X0,X1),X3,sK18),iPr_def_10)
| element(sK2(set_union2(X0,X1),X3,sK18),X4)
| in(X2,sK2(set_union2(X0,X1),X3,sK18))
| in(sK2(set_union2(X0,X1),X3,sK18),X2)
| ( set_union2(set_union2(X0,X1),X3) = sK18 )
| ( sK2(set_union2(X0,X1),X3,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X3,X4)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53094,c_4212]) ).
tcf(c_74545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X2,X3),X0,sK18),iPr_def_10)
| element(sK2(set_union2(X2,X3),X0,sK18),X1)
| in(sK2(set_union2(X2,X3),X0,sK18),X3)
| in(sK2(set_union2(X2,X3),X0,sK18),X2)
| ( set_union2(set_union2(X2,X3),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_71]) ).
tcf(c_74546,plain,
! [X0: $i,X1: $i] :
( subset(sK2(empty_set,X0,sK18),iPr_def_10)
| element(sK2(empty_set,X0,sK18),X1)
| ( set_union2(empty_set,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_7097]) ).
tcf(c_74551,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| element(sK2(iPr_def_10,X0,sK18),X1)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_9540]) ).
tcf(c_74552,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| element(sK2(iPr_def_10,X0,sK18),X1)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1)
| ~ in(iPr_def_11,sK2(iPr_def_10,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53094,c_6289]) ).
tcf(c_74556,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),sK18)
| element(sK2(iPr_def_11,X0,sK18),X1)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ( sK2(iPr_def_11,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_33457]) ).
tcf(c_74557,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),sK18)
| element(sK2(iPr_def_11,X0,sK18),X1)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_4035]) ).
tcf(c_74558,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X2)
| subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| element(sK2(sK5(iPr_def_11),X0,sK18),X1)
| in(X2,sK2(sK5(iPr_def_11),X0,sK18))
| in(sK2(sK5(iPr_def_11),X0,sK18),X2)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ( sK2(sK5(iPr_def_11),X0,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X2,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_7243]) ).
tcf(c_74559,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_10)
| element(sK2(sK5(iPr_def_11),X0,sK18),X1)
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,sK18)) ),
inference(superposition,[status(thm)],[c_53094,c_23189]) ).
tcf(c_74560,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X2)
| subset(sK2(sK3(iPr_def_11),X0,sK18),iPr_def_10)
| element(sK2(sK3(iPr_def_11),X0,sK18),X1)
| in(X2,sK2(sK3(iPr_def_11),X0,sK18))
| in(sK2(sK3(iPr_def_11),X0,sK18),X2)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(sK3(iPr_def_11),X0) = sK18 )
| ( sK2(sK3(iPr_def_11),X0,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X2,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_9906]) ).
tcf(c_74561,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X2)
| subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| element(sK2(sK4(iPr_def_11),X0,sK18),X1)
| in(X2,sK2(sK4(iPr_def_11),X0,sK18))
| in(sK2(sK4(iPr_def_11),X0,sK18),X2)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ( sK2(sK4(iPr_def_11),X0,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X2,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53094,c_45801]) ).
tcf(c_74563,plain,
! [X0: $i,X1: $i] :
( subset(sK2(empty_set,X0,sK18),iPr_def_10)
| element(sK2(empty_set,X0,sK18),X1)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_74546,c_3423]) ).
tcf(c_74897,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| subset(sK2(X0,X2,sK18),iPr_def_10)
| in(sK2(X0,X2,sK18),X2)
| in(sK2(X0,X2,sK18),X1)
| ( set_union2(X0,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_131]) ).
tcf(c_74898,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X2,sK18),iPr_def_10)
| subset(sK2(X0,X2,sK18),X1)
| in(sK2(X0,X2,sK18),X2)
| ( set_union2(X0,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_53127,c_133]) ).
tcf(c_74899,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| subset(sK2(X0,X2,sK18),iPr_def_10)
| element(sK2(X0,X2,sK18),X1)
| in(sK3(iPr_def_11),sK2(X0,X2,sK18))
| in(sK2(X0,X2,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,X2) = sK18 )
| ( sK2(X0,X2,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X2)
| ~ in(X2,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_49877]) ).
tcf(c_74900,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| subset(sK2(X0,X2,sK18),iPr_def_10)
| element(sK2(X0,X2,sK18),X1)
| in(sK5(iPr_def_11),sK2(X0,X2,sK18))
| in(sK2(X0,X2,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,X2) = sK18 )
| ( sK2(X0,X2,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X2)
| ~ in(X2,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_7260]) ).
tcf(c_74901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X0,X2,sK18),iPr_def_10)
| element(sK2(X0,X2,sK18),X1)
| ( set_union2(X0,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_359]) ).
tcf(c_74902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X0,X2,sK18),iPr_def_10)
| element(sK2(X0,X2,sK18),X3)
| element(sK2(X0,X2,sK18),X1)
| ( set_union2(X0,X2) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_358]) ).
tcf(c_74903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X1,sK18),iPr_def_10)
| element(sK2(X2,X1,sK18),X3)
| in(X0,sK2(X2,X1,sK18))
| in(sK2(X2,X1,sK18),X0)
| ( set_union2(X2,X1) = sK18 )
| ( sK2(X2,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ subset(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_77]) ).
tcf(c_74905,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| element(sK2(X1,X0,sK18),X2)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X1,X2)
| ~ in(X0,sK2(X1,X0,sK18)) ),
inference(superposition,[status(thm)],[c_53127,c_49]) ).
tcf(c_74908,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,singleton(X2),sK18),iPr_def_10)
| element(sK2(X0,singleton(X2),sK18),X1)
| ( set_union2(X0,singleton(X2)) = sK18 )
| ( sK2(X0,singleton(X2),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_62]) ).
tcf(c_74909,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X0,sK18),iPr_def_10)
| element(sK2(X0,X0,sK18),X1)
| ( set_union2(X0,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1)
| ~ in(sK2(X0,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53127,c_66]) ).
tcf(c_74911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(X3,set_union2(X0,X1),sK18),iPr_def_10)
| element(sK2(X3,set_union2(X0,X1),sK18),X4)
| in(X2,sK2(X3,set_union2(X0,X1),sK18))
| in(sK2(X3,set_union2(X0,X1),sK18),X2)
| ( set_union2(X3,set_union2(X0,X1)) = sK18 )
| ( sK2(X3,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X3,X4)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53127,c_4213]) ).
tcf(c_74912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(X3,set_union2(X0,X1),sK18),iPr_def_10)
| element(sK2(X3,set_union2(X0,X1),sK18),X4)
| in(X2,sK2(X3,set_union2(X0,X1),sK18))
| in(sK2(X3,set_union2(X0,X1),sK18),X2)
| ( set_union2(X3,set_union2(X0,X1)) = sK18 )
| ( sK2(X3,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X3,X4)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53127,c_4212]) ).
tcf(c_74913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X0,set_union2(X2,X3),sK18),iPr_def_10)
| element(sK2(X0,set_union2(X2,X3),sK18),X1)
| in(sK2(X0,set_union2(X2,X3),sK18),X3)
| in(sK2(X0,set_union2(X2,X3),sK18),X2)
| ( set_union2(X0,set_union2(X2,X3)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_71]) ).
tcf(c_74914,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,empty_set,sK18),iPr_def_10)
| element(sK2(X0,empty_set,sK18),X1)
| ( set_union2(X0,empty_set) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_7097]) ).
tcf(c_74919,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| element(sK2(X0,iPr_def_10,sK18),X1)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_9540]) ).
tcf(c_74920,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| element(sK2(X0,iPr_def_10,sK18),X1)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1)
| ~ in(iPr_def_11,sK2(X0,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53127,c_6289]) ).
tcf(c_74924,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),sK18)
| element(sK2(X0,iPr_def_11,sK18),X1)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ( sK2(X0,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_33457]) ).
tcf(c_74925,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),sK18)
| element(sK2(X0,iPr_def_11,sK18),X1)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_4035]) ).
tcf(c_74926,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| element(sK2(set_union2(X0,X1),X0,sK18),X2)
| ( set_union2(set_union2(X0,X1),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(set_union2(X0,X1),X2)
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53127,c_4078]) ).
tcf(c_74927,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_10)
| element(sK2(set_union2(X0,X1),sK18,sK18),X2)
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(set_union2(X0,X1),X2)
| ~ in(sK2(set_union2(X0,X1),sK18,sK18),X1) ),
inference(superposition,[status(thm)],[c_53127,c_4079]) ).
tcf(c_74928,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X2)
| subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| element(sK2(X0,sK5(iPr_def_11),sK18),X1)
| in(X2,sK2(X0,sK5(iPr_def_11),sK18))
| in(sK2(X0,sK5(iPr_def_11),sK18),X2)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ( sK2(X0,sK5(iPr_def_11),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X2,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_7243]) ).
tcf(c_74929,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_10)
| element(sK2(X0,sK5(iPr_def_11),sK18),X1)
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1)
| ~ subset(iPr_def_11,sK2(X0,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53127,c_23189]) ).
tcf(c_74930,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X2)
| subset(sK2(X0,sK3(iPr_def_11),sK18),iPr_def_10)
| element(sK2(X0,sK3(iPr_def_11),sK18),X1)
| in(X2,sK2(X0,sK3(iPr_def_11),sK18))
| in(sK2(X0,sK3(iPr_def_11),sK18),X2)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,sK3(iPr_def_11)) = sK18 )
| ( sK2(X0,sK3(iPr_def_11),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X2,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_9906]) ).
tcf(c_74931,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X2)
| subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| element(sK2(X0,sK4(iPr_def_11),sK18),X1)
| in(X2,sK2(X0,sK4(iPr_def_11),sK18))
| in(sK2(X0,sK4(iPr_def_11),sK18),X2)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ( sK2(X0,sK4(iPr_def_11),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X2,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53127,c_45801]) ).
tcf(c_74933,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,empty_set,sK18),iPr_def_10)
| element(sK2(X0,empty_set,sK18),X1)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_74914,c_126]) ).
tcf(c_74945,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X0,sK18),iPr_def_10)
| element(sK2(X0,X0,sK18),X1)
| ( X0 = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1)
| ~ in(sK2(X0,X0,sK18),sK18) ),
inference(light_normalisation,[status(thm)],[c_74909,c_97]) ).
tcf(c_75168,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,singleton(sK18),sK18),X0)
| ( set_union2(X0,singleton(sK18)) = sK18 )
| ( sK2(X0,singleton(sK18),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_2420,c_53100]) ).
tcf(c_75169,plain,
! [X0: $i] :
( in(sK2(X0,iPr_def_10,sK18),X0)
| subset(sK2(X0,singleton(sK18),sK18),iPr_def_10)
| ( set_union2(X0,singleton(sK18)) = sK18 )
| ( sK2(X0,singleton(sK18),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_2420,c_53100]) ).
tcf(c_75178,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,singleton(X1),sK18),X0)
| in(sK2(X0,singleton(X1),sK18),sK4(iPr_def_11))
| ( set_union2(X0,singleton(X1)) = sK18 )
| ( sK2(X0,singleton(X1),sK18) = X1 )
| ( sK2(X0,singleton(X1),sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,singleton(X1),sK18),sK18) ),
inference(superposition,[status(thm)],[c_53100,c_13671]) ).
tcf(c_75179,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,singleton(X1),sK18),X0)
| in(sK2(X0,singleton(X1),sK18),sK3(iPr_def_11))
| ( set_union2(X0,singleton(X1)) = sK18 )
| ( sK2(X0,singleton(X1),sK18) = X1 )
| ( sK2(X0,singleton(X1),sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,singleton(X1),sK18),sK18) ),
inference(superposition,[status(thm)],[c_53100,c_13665]) ).
tcf(c_75180,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,singleton(X1),sK18),X0)
| in(sK2(X0,singleton(X1),sK18),sK5(iPr_def_11))
| ( set_union2(X0,singleton(X1)) = sK18 )
| ( sK2(X0,singleton(X1),sK18) = X1 )
| ( sK2(X0,singleton(X1),sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,singleton(X1),sK18),sK18) ),
inference(superposition,[status(thm)],[c_53100,c_13657]) ).
tcf(c_75181,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,iPr_def_10)
| in(sK2(X1,singleton(X2),sK18),X1)
| ( set_union2(X1,singleton(X2)) = sK18 )
| ( sK2(X1,singleton(X2),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(X1,singleton(X2),sK18)) ),
inference(superposition,[status(thm)],[c_53100,c_128]) ).
tcf(c_75182,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,singleton(X1),sK18),iPr_def_11)
| in(sK2(X0,singleton(X1),sK18),X0)
| ( set_union2(X0,singleton(X1)) = sK18 )
| ( sK2(X0,singleton(X1),sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53100,c_3868]) ).
tcf(c_75183,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X0,singleton(X1),sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(X0,singleton(X1),sK18))
| in(sK2(X0,singleton(X1),sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,singleton(X1)) = sK18 )
| ( sK2(X0,singleton(X1),sK18) = X1 )
| ( sK2(X0,singleton(X1),sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53100,c_49877]) ).
tcf(c_75184,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X0,singleton(X1),sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(X0,singleton(X1),sK18))
| in(sK2(X0,singleton(X1),sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,singleton(X1)) = sK18 )
| ( sK2(X0,singleton(X1),sK18) = X1 )
| ( sK2(X0,singleton(X1),sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53100,c_7260]) ).
tcf(c_75185,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,singleton(X2),sK18),iPr_def_10)
| ( set_union2(X0,singleton(X2)) = sK18 )
| ( sK2(X0,singleton(X2),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53100,c_359]) ).
tcf(c_75187,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,singleton(X2),sK18),iPr_def_10)
| in(X0,sK2(X1,singleton(X2),sK18))
| in(sK2(X1,singleton(X2),sK18),X0)
| ( set_union2(X1,singleton(X2)) = sK18 )
| ( sK2(X1,singleton(X2),sK18) = X2 )
| ( sK2(X1,singleton(X2),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53100,c_77]) ).
tcf(c_75189,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,singleton(X1),sK18),iPr_def_10)
| ( set_union2(X0,singleton(X1)) = sK18 )
| ( sK2(X0,singleton(X1),sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X0,singleton(X1),sK18)) ),
inference(superposition,[status(thm)],[c_53100,c_49]) ).
tcf(c_75192,plain,
! [X0: $i,X1: $i] :
( subset(sK2(singleton(X0),singleton(X1),sK18),iPr_def_10)
| ( set_union2(singleton(X0),singleton(X1)) = sK18 )
| ( sK2(singleton(X0),singleton(X1),sK18) = X1 )
| ( sK2(singleton(X0),singleton(X1),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53100,c_62]) ).
tcf(c_75193,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,singleton(X1),sK18),iPr_def_10)
| ( set_union2(X0,singleton(X1)) = sK18 )
| ( sK2(X0,singleton(X1),sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,singleton(X1),sK18),sK18) ),
inference(superposition,[status(thm)],[c_53100,c_66]) ).
tcf(c_75195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X0,X1),singleton(X3),sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),singleton(X3),sK18))
| in(sK2(set_union2(X0,X1),singleton(X3),sK18),X2)
| ( set_union2(set_union2(X0,X1),singleton(X3)) = sK18 )
| ( sK2(set_union2(X0,X1),singleton(X3),sK18) = X3 )
| ( sK2(set_union2(X0,X1),singleton(X3),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53100,c_4213]) ).
tcf(c_75196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X0,X1),singleton(X3),sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),singleton(X3),sK18))
| in(sK2(set_union2(X0,X1),singleton(X3),sK18),X2)
| ( set_union2(set_union2(X0,X1),singleton(X3)) = sK18 )
| ( sK2(set_union2(X0,X1),singleton(X3),sK18) = X3 )
| ( sK2(set_union2(X0,X1),singleton(X3),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53100,c_4212]) ).
tcf(c_75197,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),singleton(X2),sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),singleton(X2),sK18),X1)
| in(sK2(set_union2(X0,X1),singleton(X2),sK18),X0)
| ( set_union2(set_union2(X0,X1),singleton(X2)) = sK18 )
| ( sK2(set_union2(X0,X1),singleton(X2),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53100,c_71]) ).
tcf(c_75198,plain,
! [X0: $i] :
( subset(sK2(empty_set,singleton(X0),sK18),iPr_def_10)
| ( set_union2(empty_set,singleton(X0)) = sK18 )
| ( sK2(empty_set,singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53100,c_7097]) ).
tcf(c_75203,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,singleton(X0),sK18),iPr_def_11)
| subset(sK2(iPr_def_10,singleton(X0),sK18),iPr_def_10)
| ( set_union2(iPr_def_10,singleton(X0)) = sK18 )
| ( sK2(iPr_def_10,singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53100,c_9540]) ).
tcf(c_75204,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,singleton(X0),sK18),iPr_def_10)
| ( set_union2(iPr_def_10,singleton(X0)) = sK18 )
| ( sK2(iPr_def_10,singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(iPr_def_10,singleton(X0),sK18)) ),
inference(superposition,[status(thm)],[c_53100,c_6289]) ).
tcf(c_75208,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,singleton(X0),sK18),iPr_def_10)
| in(sK2(iPr_def_11,singleton(X0),sK18),sK18)
| ( set_union2(iPr_def_11,singleton(X0)) = sK18 )
| ( sK2(iPr_def_11,singleton(X0),sK18) = sK18 )
| ( sK2(iPr_def_11,singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53100,c_33457]) ).
tcf(c_75209,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,singleton(X0),sK18),iPr_def_10)
| in(sK2(iPr_def_11,singleton(X0),sK18),iPr_def_10)
| in(sK2(iPr_def_11,singleton(X0),sK18),sK18)
| ( set_union2(iPr_def_11,singleton(X0)) = sK18 )
| ( sK2(iPr_def_11,singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53100,c_4035]) ).
tcf(c_75210,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK5(iPr_def_11),singleton(X1),sK18),iPr_def_10)
| in(X0,sK2(sK5(iPr_def_11),singleton(X1),sK18))
| in(sK2(sK5(iPr_def_11),singleton(X1),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),singleton(X1)) = sK18 )
| ( sK2(sK5(iPr_def_11),singleton(X1),sK18) = X1 )
| ( sK2(sK5(iPr_def_11),singleton(X1),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53100,c_7243]) ).
tcf(c_75211,plain,
! [X0: $i] :
( subset(sK2(sK5(iPr_def_11),singleton(X0),sK18),iPr_def_10)
| ( set_union2(sK5(iPr_def_11),singleton(X0)) = sK18 )
| ( sK2(sK5(iPr_def_11),singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),singleton(X0),sK18)) ),
inference(superposition,[status(thm)],[c_53100,c_23189]) ).
tcf(c_75212,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK3(iPr_def_11),singleton(X1),sK18),iPr_def_10)
| in(X0,sK2(sK3(iPr_def_11),singleton(X1),sK18))
| in(sK2(sK3(iPr_def_11),singleton(X1),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),singleton(X1)) = sK18 )
| ( sK2(sK3(iPr_def_11),singleton(X1),sK18) = X1 )
| ( sK2(sK3(iPr_def_11),singleton(X1),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53100,c_9906]) ).
tcf(c_75213,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK4(iPr_def_11),singleton(X1),sK18),iPr_def_10)
| in(X0,sK2(sK4(iPr_def_11),singleton(X1),sK18))
| in(sK2(sK4(iPr_def_11),singleton(X1),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),singleton(X1)) = sK18 )
| ( sK2(sK4(iPr_def_11),singleton(X1),sK18) = X1 )
| ( sK2(sK4(iPr_def_11),singleton(X1),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53100,c_45801]) ).
tcf(c_75757,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(singleton(sK18),X0,sK18),X0)
| ( set_union2(singleton(sK18),X0) = sK18 )
| ( sK2(singleton(sK18),X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_2420,c_53133]) ).
tcf(c_75758,plain,
! [X0: $i] :
( in(sK2(iPr_def_10,X0,sK18),X0)
| subset(sK2(singleton(sK18),X0,sK18),iPr_def_10)
| ( set_union2(singleton(sK18),X0) = sK18 )
| ( sK2(singleton(sK18),X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_2420,c_53133]) ).
tcf(c_75767,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(singleton(X0),X1,sK18),X1)
| in(sK2(singleton(X0),X1,sK18),sK4(iPr_def_11))
| ( set_union2(singleton(X0),X1) = sK18 )
| ( sK2(singleton(X0),X1,sK18) = X0 )
| ( sK2(singleton(X0),X1,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(singleton(X0),X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53133,c_13671]) ).
tcf(c_75768,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(singleton(X0),X1,sK18),X1)
| in(sK2(singleton(X0),X1,sK18),sK3(iPr_def_11))
| ( set_union2(singleton(X0),X1) = sK18 )
| ( sK2(singleton(X0),X1,sK18) = X0 )
| ( sK2(singleton(X0),X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(singleton(X0),X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53133,c_13665]) ).
tcf(c_75769,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(singleton(X0),X1,sK18),X1)
| in(sK2(singleton(X0),X1,sK18),sK5(iPr_def_11))
| ( set_union2(singleton(X0),X1) = sK18 )
| ( sK2(singleton(X0),X1,sK18) = X0 )
| ( sK2(singleton(X0),X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(singleton(X0),X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_53133,c_13657]) ).
tcf(c_75770,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,iPr_def_10)
| in(sK2(singleton(X1),X2,sK18),X2)
| ( set_union2(singleton(X1),X2) = sK18 )
| ( sK2(singleton(X1),X2,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(singleton(X1),X2,sK18)) ),
inference(superposition,[status(thm)],[c_53133,c_128]) ).
tcf(c_75771,plain,
! [X0: $i,X1: $i] :
( subset(sK2(singleton(X0),X1,sK18),iPr_def_11)
| in(sK2(singleton(X0),X1,sK18),X1)
| ( set_union2(singleton(X0),X1) = sK18 )
| ( sK2(singleton(X0),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53133,c_3868]) ).
tcf(c_75772,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(singleton(X1),X0,sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(singleton(X1),X0,sK18))
| in(sK2(singleton(X1),X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(singleton(X1),X0) = sK18 )
| ( sK2(singleton(X1),X0,sK18) = X1 )
| ( sK2(singleton(X1),X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53133,c_49877]) ).
tcf(c_75773,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(singleton(X1),X0,sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(singleton(X1),X0,sK18))
| in(sK2(singleton(X1),X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(singleton(X1),X0) = sK18 )
| ( sK2(singleton(X1),X0,sK18) = X1 )
| ( sK2(singleton(X1),X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53133,c_7260]) ).
tcf(c_75774,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(singleton(X2),X0,sK18),iPr_def_10)
| ( set_union2(singleton(X2),X0) = sK18 )
| ( sK2(singleton(X2),X0,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53133,c_359]) ).
tcf(c_75776,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(singleton(X2),X1,sK18),iPr_def_10)
| in(X0,sK2(singleton(X2),X1,sK18))
| in(sK2(singleton(X2),X1,sK18),X0)
| ( set_union2(singleton(X2),X1) = sK18 )
| ( sK2(singleton(X2),X1,sK18) = X2 )
| ( sK2(singleton(X2),X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_53133,c_77]) ).
tcf(c_75778,plain,
! [X0: $i,X1: $i] :
( subset(sK2(singleton(X1),X0,sK18),iPr_def_10)
| ( set_union2(singleton(X1),X0) = sK18 )
| ( sK2(singleton(X1),X0,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(singleton(X1),X0,sK18)) ),
inference(superposition,[status(thm)],[c_53133,c_49]) ).
tcf(c_75782,plain,
! [X0: $i] :
( subset(sK2(singleton(X0),singleton(X0),sK18),iPr_def_10)
| ( set_union2(singleton(X0),singleton(X0)) = sK18 )
| ( sK2(singleton(X0),singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(singleton(X0),singleton(X0),sK18),sK18) ),
inference(superposition,[status(thm)],[c_53133,c_66]) ).
tcf(c_75784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(singleton(X3),set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(singleton(X3),set_union2(X0,X1),sK18))
| in(sK2(singleton(X3),set_union2(X0,X1),sK18),X2)
| ( set_union2(singleton(X3),set_union2(X0,X1)) = sK18 )
| ( sK2(singleton(X3),set_union2(X0,X1),sK18) = X3 )
| ( sK2(singleton(X3),set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53133,c_4213]) ).
tcf(c_75785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(singleton(X3),set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(singleton(X3),set_union2(X0,X1),sK18))
| in(sK2(singleton(X3),set_union2(X0,X1),sK18),X2)
| ( set_union2(singleton(X3),set_union2(X0,X1)) = sK18 )
| ( sK2(singleton(X3),set_union2(X0,X1),sK18) = X3 )
| ( sK2(singleton(X3),set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53133,c_4212]) ).
tcf(c_75786,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(singleton(X0),set_union2(X1,X2),sK18),iPr_def_10)
| in(sK2(singleton(X0),set_union2(X1,X2),sK18),X2)
| in(sK2(singleton(X0),set_union2(X1,X2),sK18),X1)
| ( set_union2(singleton(X0),set_union2(X1,X2)) = sK18 )
| ( sK2(singleton(X0),set_union2(X1,X2),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53133,c_71]) ).
tcf(c_75787,plain,
! [X0: $i] :
( subset(sK2(singleton(X0),empty_set,sK18),iPr_def_10)
| ( set_union2(singleton(X0),empty_set) = sK18 )
| ( sK2(singleton(X0),empty_set,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53133,c_7097]) ).
tcf(c_75792,plain,
! [X0: $i] :
( subset(sK2(singleton(X0),iPr_def_10,sK18),iPr_def_11)
| subset(sK2(singleton(X0),iPr_def_10,sK18),iPr_def_10)
| ( set_union2(singleton(X0),iPr_def_10) = sK18 )
| ( sK2(singleton(X0),iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53133,c_9540]) ).
tcf(c_75793,plain,
! [X0: $i] :
( subset(sK2(singleton(X0),iPr_def_10,sK18),iPr_def_10)
| ( set_union2(singleton(X0),iPr_def_10) = sK18 )
| ( sK2(singleton(X0),iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(singleton(X0),iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53133,c_6289]) ).
tcf(c_75797,plain,
! [X0: $i] :
( subset(sK2(singleton(X0),iPr_def_11,sK18),iPr_def_10)
| in(sK2(singleton(X0),iPr_def_11,sK18),sK18)
| ( set_union2(singleton(X0),iPr_def_11) = sK18 )
| ( sK2(singleton(X0),iPr_def_11,sK18) = sK18 )
| ( sK2(singleton(X0),iPr_def_11,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53133,c_33457]) ).
tcf(c_75798,plain,
! [X0: $i] :
( subset(sK2(singleton(X0),iPr_def_11,sK18),iPr_def_10)
| in(sK2(singleton(X0),iPr_def_11,sK18),iPr_def_10)
| in(sK2(singleton(X0),iPr_def_11,sK18),sK18)
| ( set_union2(singleton(X0),iPr_def_11) = sK18 )
| ( sK2(singleton(X0),iPr_def_11,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53133,c_4035]) ).
tcf(c_75799,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(singleton(X1),sK5(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(singleton(X1),sK5(iPr_def_11),sK18))
| in(sK2(singleton(X1),sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(singleton(X1),sK5(iPr_def_11)) = sK18 )
| ( sK2(singleton(X1),sK5(iPr_def_11),sK18) = X1 )
| ( sK2(singleton(X1),sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53133,c_7243]) ).
tcf(c_75800,plain,
! [X0: $i] :
( subset(sK2(singleton(X0),sK5(iPr_def_11),sK18),iPr_def_10)
| ( set_union2(singleton(X0),sK5(iPr_def_11)) = sK18 )
| ( sK2(singleton(X0),sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(singleton(X0),sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53133,c_23189]) ).
tcf(c_75801,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(singleton(X1),sK3(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(singleton(X1),sK3(iPr_def_11),sK18))
| in(sK2(singleton(X1),sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(singleton(X1),sK3(iPr_def_11)) = sK18 )
| ( sK2(singleton(X1),sK3(iPr_def_11),sK18) = X1 )
| ( sK2(singleton(X1),sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53133,c_9906]) ).
tcf(c_75802,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(singleton(X1),sK4(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(singleton(X1),sK4(iPr_def_11),sK18))
| in(sK2(singleton(X1),sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(singleton(X1),sK4(iPr_def_11)) = sK18 )
| ( sK2(singleton(X1),sK4(iPr_def_11),sK18) = X1 )
| ( sK2(singleton(X1),sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_53133,c_45801]) ).
tcf(c_76127,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X2,sK18),X0)
| in(sK2(X1,X2,sK18),X2)
| in(sK2(X1,X2,sK18),X1)
| ( set_union2(X1,X2) = sK18 )
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_4339,c_358]) ).
tcf(c_76128,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X1,X2,sK18))
| in(sK2(X1,X2,sK18),X2)
| in(sK2(X1,X2,sK18),X1)
| in(sK2(X1,X2,sK18),X0)
| ( set_union2(X1,X2) = sK18 )
| ( sK2(X1,X2,sK18) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4339,c_77]) ).
tcf(c_76134,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK18),sK18)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK18 ) ),
inference(superposition,[status(thm)],[c_4339,c_33457]) ).
tcf(c_76135,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),sK18)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 ) ),
inference(superposition,[status(thm)],[c_4339,c_4035]) ).
tcf(c_76136,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_union2(iPr_def_11,X0),X1,sK18),X1)
| in(sK2(set_union2(iPr_def_11,X0),X1,sK18),set_union2(iPr_def_11,X0))
| ( set_union2(set_union2(iPr_def_11,X0),X1) = sK18 )
| ~ in(sK2(set_union2(iPr_def_11,X0),X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_4339,c_4078]) ).
tcf(c_76137,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X1,X0,sK18),iPr_def_11)
| in(sK2(X1,X0,sK18),X1)
| in(sK3(iPr_def_11),sK2(X1,X0,sK18))
| in(sK2(X1,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = sK18 )
| ( sK2(X1,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4339,c_49877]) ).
tcf(c_76138,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X1,X0,sK18),iPr_def_11)
| in(sK2(X1,X0,sK18),X1)
| in(sK5(iPr_def_11),sK2(X1,X0,sK18))
| in(sK2(X1,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = sK18 )
| ( sK2(X1,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4339,c_7260]) ).
tcf(c_76139,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X0,sK18),iPr_def_11)
| in(sK2(X2,X0,sK18),X2)
| ( set_union2(X2,X0) = sK18 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4339,c_359]) ).
tcf(c_76140,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X0,sK18),iPr_def_11)
| element(sK2(X2,X0,sK18),X1)
| in(sK2(X2,X0,sK18),X2)
| ( set_union2(X2,X0) = sK18 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4339,c_358]) ).
tcf(c_76141,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X1,sK18),iPr_def_11)
| in(X0,sK2(X2,X1,sK18))
| in(sK2(X2,X1,sK18),X2)
| in(sK2(X2,X1,sK18),X0)
| ( set_union2(X2,X1) = sK18 )
| ( sK2(X2,X1,sK18) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4339,c_77]) ).
tcf(c_76142,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,sK18),iPr_def_11)
| subset(sK2(X1,X0,sK18),X0)
| in(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4339,c_65]) ).
tcf(c_76143,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,sK18),iPr_def_11)
| in(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ in(X0,sK2(X1,X0,sK18)) ),
inference(superposition,[status(thm)],[c_4339,c_49]) ).
tcf(c_76144,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,sK18),iPr_def_11)
| in(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4339,c_137]) ).
tcf(c_76145,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK18),iPr_def_11)
| element(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 ) ),
inference(superposition,[status(thm)],[c_4339,c_127]) ).
tcf(c_76146,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,singleton(X1),sK18),iPr_def_11)
| in(sK2(X0,singleton(X1),sK18),X0)
| ( set_union2(X0,singleton(X1)) = sK18 )
| ( sK2(X0,singleton(X1),sK18) = X1 ) ),
inference(superposition,[status(thm)],[c_4339,c_62]) ).
tcf(c_76147,plain,
! [X0: $i] :
( in(sK2(X0,X0,sK18),iPr_def_11)
| in(sK2(X0,X0,sK18),X0)
| ( set_union2(X0,X0) = sK18 )
| ~ in(sK2(X0,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_4339,c_66]) ).
tcf(c_76149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,set_union2(X0,X1),sK18),iPr_def_11)
| in(X2,sK2(X3,set_union2(X0,X1),sK18))
| in(sK2(X3,set_union2(X0,X1),sK18),X3)
| in(sK2(X3,set_union2(X0,X1),sK18),X2)
| ( set_union2(X3,set_union2(X0,X1)) = sK18 )
| ( sK2(X3,set_union2(X0,X1),sK18) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4339,c_4213]) ).
tcf(c_76150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,set_union2(X0,X1),sK18),iPr_def_11)
| in(X2,sK2(X3,set_union2(X0,X1),sK18))
| in(sK2(X3,set_union2(X0,X1),sK18),X3)
| in(sK2(X3,set_union2(X0,X1),sK18),X2)
| ( set_union2(X3,set_union2(X0,X1)) = sK18 )
| ( sK2(X3,set_union2(X0,X1),sK18) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4339,c_4212]) ).
tcf(c_76151,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_union2(X1,X2),sK18),iPr_def_11)
| in(sK2(X0,set_union2(X1,X2),sK18),X2)
| in(sK2(X0,set_union2(X1,X2),sK18),X1)
| in(sK2(X0,set_union2(X1,X2),sK18),X0)
| ( set_union2(X0,set_union2(X1,X2)) = sK18 ) ),
inference(superposition,[status(thm)],[c_4339,c_71]) ).
tcf(c_76152,plain,
! [X0: $i] :
( in(sK2(X0,empty_set,sK18),iPr_def_11)
| in(sK2(X0,empty_set,sK18),X0)
| ( set_union2(X0,empty_set) = sK18 ) ),
inference(superposition,[status(thm)],[c_4339,c_7097]) ).
tcf(c_76156,plain,
! [X0: $i] :
( in(sK2(X0,sK18,sK18),iPr_def_11)
| in(sK2(X0,sK18,sK18),X0)
| ( set_union2(X0,sK18) = sK18 ) ),
inference(superposition,[status(thm)],[c_4339,c_3640]) ).
tcf(c_76161,plain,
! [X0: $i] :
( in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| in(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 ) ),
inference(superposition,[status(thm)],[c_4339,c_3614]) ).
tcf(c_76164,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_union2(X0,X1),X0,sK18),iPr_def_11)
| in(sK2(set_union2(X0,X1),X0,sK18),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X0) = sK18 )
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_4339,c_4078]) ).
tcf(c_76165,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_union2(X0,X1),sK18,sK18),iPr_def_11)
| in(sK2(set_union2(X0,X1),sK18,sK18),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),sK18) = sK18 )
| ~ in(sK2(set_union2(X0,X1),sK18,sK18),X1) ),
inference(superposition,[status(thm)],[c_4339,c_4079]) ).
tcf(c_76166,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(sK2(X1,sK5(iPr_def_11),sK18),iPr_def_11)
| in(X0,sK2(X1,sK5(iPr_def_11),sK18))
| in(sK2(X1,sK5(iPr_def_11),sK18),X1)
| in(sK2(X1,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,sK5(iPr_def_11)) = sK18 )
| ( sK2(X1,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4339,c_7243]) ).
tcf(c_76167,plain,
! [X0: $i] :
( in(sK2(X0,sK5(iPr_def_11),sK18),iPr_def_11)
| in(sK2(X0,sK5(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = sK18 )
| ~ subset(iPr_def_11,sK2(X0,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_4339,c_23189]) ).
tcf(c_76168,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(sK2(X1,sK3(iPr_def_11),sK18),iPr_def_11)
| in(X0,sK2(X1,sK3(iPr_def_11),sK18))
| in(sK2(X1,sK3(iPr_def_11),sK18),X1)
| in(sK2(X1,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,sK3(iPr_def_11)) = sK18 )
| ( sK2(X1,sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4339,c_9906]) ).
tcf(c_76169,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(sK2(X1,sK4(iPr_def_11),sK18),iPr_def_11)
| in(X0,sK2(X1,sK4(iPr_def_11),sK18))
| in(sK2(X1,sK4(iPr_def_11),sK18),X1)
| in(sK2(X1,sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,sK4(iPr_def_11)) = sK18 )
| ( sK2(X1,sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4339,c_45801]) ).
tcf(c_76171,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X0,X1,sK18),iPr_def_11)
| in(sK2(X0,X1,sK18),X1)
| in(sK3(iPr_def_11),sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4339,c_49877]) ).
tcf(c_76172,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X0,X1,sK18),iPr_def_11)
| in(sK2(X0,X1,sK18),X1)
| in(sK5(iPr_def_11),sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4339,c_7260]) ).
tcf(c_76173,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,sK18),iPr_def_11)
| in(sK2(X0,X2,sK18),X2)
| ( set_union2(X0,X2) = sK18 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4339,c_359]) ).
tcf(c_76174,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,sK18),iPr_def_11)
| element(sK2(X0,X2,sK18),X1)
| in(sK2(X0,X2,sK18),X2)
| ( set_union2(X0,X2) = sK18 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4339,c_358]) ).
tcf(c_76175,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,sK18),iPr_def_11)
| in(X0,sK2(X1,X2,sK18))
| in(sK2(X1,X2,sK18),X2)
| in(sK2(X1,X2,sK18),X0)
| ( set_union2(X1,X2) = sK18 )
| ( sK2(X1,X2,sK18) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4339,c_77]) ).
tcf(c_76176,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK18),iPr_def_11)
| subset(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4339,c_65]) ).
tcf(c_76177,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK18),iPr_def_11)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ in(X0,sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_4339,c_49]) ).
tcf(c_76178,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK18),iPr_def_11)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4339,c_137]) ).
tcf(c_76179,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK18),iPr_def_11)
| element(sK2(X0,X1,sK18),X0)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 ) ),
inference(superposition,[status(thm)],[c_4339,c_127]) ).
tcf(c_76180,plain,
! [X0: $i,X1: $i] :
( in(sK2(singleton(X0),X1,sK18),iPr_def_11)
| in(sK2(singleton(X0),X1,sK18),X1)
| ( set_union2(singleton(X0),X1) = sK18 )
| ( sK2(singleton(X0),X1,sK18) = X0 ) ),
inference(superposition,[status(thm)],[c_4339,c_62]) ).
tcf(c_76181,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK18),iPr_def_11)
| in(sK2(X0,X1,sK18),X1)
| ( set_union2(X0,X1) = sK18 )
| ~ in(sK2(X0,X1,sK18),sK18) ),
inference(superposition,[status(thm)],[c_4339,c_66]) ).
tcf(c_76183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_union2(X0,X1),X3,sK18),iPr_def_11)
| in(X2,sK2(set_union2(X0,X1),X3,sK18))
| in(sK2(set_union2(X0,X1),X3,sK18),X3)
| in(sK2(set_union2(X0,X1),X3,sK18),X2)
| ( set_union2(set_union2(X0,X1),X3) = sK18 )
| ( sK2(set_union2(X0,X1),X3,sK18) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4339,c_4213]) ).
tcf(c_76184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_union2(X0,X1),X3,sK18),iPr_def_11)
| in(X2,sK2(set_union2(X0,X1),X3,sK18))
| in(sK2(set_union2(X0,X1),X3,sK18),X3)
| in(sK2(set_union2(X0,X1),X3,sK18),X2)
| ( set_union2(set_union2(X0,X1),X3) = sK18 )
| ( sK2(set_union2(X0,X1),X3,sK18) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4339,c_4212]) ).
tcf(c_76185,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_union2(X0,X1),X2,sK18),iPr_def_11)
| in(sK2(set_union2(X0,X1),X2,sK18),X2)
| in(sK2(set_union2(X0,X1),X2,sK18),X1)
| in(sK2(set_union2(X0,X1),X2,sK18),X0)
| ( set_union2(set_union2(X0,X1),X2) = sK18 ) ),
inference(superposition,[status(thm)],[c_4339,c_71]) ).
tcf(c_76186,plain,
! [X0: $i] :
( in(sK2(empty_set,X0,sK18),iPr_def_11)
| in(sK2(empty_set,X0,sK18),X0)
| ( set_union2(empty_set,X0) = sK18 ) ),
inference(superposition,[status(thm)],[c_4339,c_7097]) ).
tcf(c_76190,plain,
! [X0: $i] :
( in(sK2(sK18,X0,sK18),iPr_def_11)
| in(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 ) ),
inference(superposition,[status(thm)],[c_4339,c_3640]) ).
tcf(c_76195,plain,
! [X0: $i] :
( in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| in(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 ) ),
inference(superposition,[status(thm)],[c_4339,c_3614]) ).
tcf(c_76198,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(sK2(sK5(iPr_def_11),X1,sK18),iPr_def_11)
| in(X0,sK2(sK5(iPr_def_11),X1,sK18))
| in(sK2(sK5(iPr_def_11),X1,sK18),X1)
| in(sK2(sK5(iPr_def_11),X1,sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X1) = sK18 )
| ( sK2(sK5(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4339,c_7243]) ).
tcf(c_76199,plain,
! [X0: $i] :
( in(sK2(sK5(iPr_def_11),X0,sK18),iPr_def_11)
| in(sK2(sK5(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK5(iPr_def_11),X0) = sK18 )
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,sK18)) ),
inference(superposition,[status(thm)],[c_4339,c_23189]) ).
tcf(c_76200,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(sK2(sK3(iPr_def_11),X1,sK18),iPr_def_11)
| in(X0,sK2(sK3(iPr_def_11),X1,sK18))
| in(sK2(sK3(iPr_def_11),X1,sK18),X1)
| in(sK2(sK3(iPr_def_11),X1,sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X1) = sK18 )
| ( sK2(sK3(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4339,c_9906]) ).
tcf(c_76201,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(sK2(sK4(iPr_def_11),X1,sK18),iPr_def_11)
| in(X0,sK2(sK4(iPr_def_11),X1,sK18))
| in(sK2(sK4(iPr_def_11),X1,sK18),X1)
| in(sK2(sK4(iPr_def_11),X1,sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X1) = sK18 )
| ( sK2(sK4(iPr_def_11),X1,sK18) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4339,c_45801]) ).
tcf(c_76205,plain,
! [X0: $i] :
( in(sK2(X0,iPr_def_11,sK18),iPr_def_11)
| in(sK2(X0,iPr_def_11,sK18),X0)
| ( set_union2(X0,iPr_def_11) = sK18 ) ),
inference(equality_factoring,[status(thm)],[c_4339]) ).
tcf(c_76207,plain,
! [X0: $i] :
( in(sK2(iPr_def_11,X0,sK18),iPr_def_11)
| in(sK2(iPr_def_11,X0,sK18),X0)
| ( set_union2(iPr_def_11,X0) = sK18 ) ),
inference(equality_factoring,[status(thm)],[c_4339]) ).
tcf(c_76208,plain,
! [X0: $i] :
( in(sK2(X0,X0,sK18),iPr_def_11)
| in(sK2(X0,X0,sK18),X0)
| ( set_union2(X0,X0) = sK18 ) ),
inference(equality_factoring,[status(thm)],[c_4339]) ).
tcf(c_76209,plain,
! [X0: $i] :
( in(sK2(X0,X0,sK18),iPr_def_11)
| in(sK2(X0,X0,sK18),X0)
| ( X0 = sK18 ) ),
inference(light_normalisation,[status(thm)],[c_76208,c_97]) ).
tcf(c_76225,plain,
! [X0: $i] :
( in(sK2(empty_set,X0,sK18),iPr_def_11)
| in(sK2(empty_set,X0,sK18),X0)
| ( X0 = sK18 ) ),
inference(light_normalisation,[status(thm)],[c_76186,c_3423]) ).
tcf(c_76235,plain,
! [X0: $i] :
( in(sK2(X0,empty_set,sK18),iPr_def_11)
| in(sK2(X0,empty_set,sK18),X0)
| ( X0 = sK18 ) ),
inference(light_normalisation,[status(thm)],[c_76152,c_126]) ).
tcf(c_76784,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = iPr_def_10 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK18)
| ~ in(iPr_def_10,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_74167]) ).
tcf(c_76810,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_74119,c_13665]) ).
tcf(c_76811,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_74119,c_13657]) ).
tcf(c_76812,plain,
! [X0: $i] :
( subset(X0,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18)
| ~ subset(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_74119,c_128]) ).
tcf(c_76813,plain,
( subset(sK4(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74119,c_3868]) ).
tcf(c_76815,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_74119,c_13674]) ).
tcf(c_76862,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_74166,c_13671]) ).
tcf(c_76864,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_74166,c_13657]) ).
tcf(c_76865,plain,
! [X0: $i] :
( subset(X0,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18)
| ~ subset(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_74166,c_128]) ).
tcf(c_76866,plain,
( subset(sK3(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_74166,c_3868]) ).
tcf(c_76868,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_74166,c_13668]) ).
tcf(c_76999,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = iPr_def_11 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ empty(sK18)
| ~ in(iPr_def_11,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_48071,c_74171]) ).
tcf(c_77034,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),X0)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53117,c_65,c_66161]) ).
tcf(c_77055,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),X0)
| in(sK2(X0,iPr_def_11,sK18),sK4(iPr_def_11))
| ( set_union2(X0,iPr_def_11) = sK18 )
| ( sK2(X0,iPr_def_11,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,iPr_def_11,sK18),sK18) ),
inference(superposition,[status(thm)],[c_77034,c_13671]) ).
tcf(c_77056,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),X0)
| in(sK2(X0,iPr_def_11,sK18),sK3(iPr_def_11))
| ( set_union2(X0,iPr_def_11) = sK18 )
| ( sK2(X0,iPr_def_11,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,iPr_def_11,sK18),sK18) ),
inference(superposition,[status(thm)],[c_77034,c_13665]) ).
tcf(c_77057,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),X0)
| in(sK2(X0,iPr_def_11,sK18),sK5(iPr_def_11))
| ( set_union2(X0,iPr_def_11) = sK18 )
| ( sK2(X0,iPr_def_11,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,iPr_def_11,sK18),sK18) ),
inference(superposition,[status(thm)],[c_77034,c_13657]) ).
tcf(c_77058,plain,
! [X0: $i,X1: $i] :
( subset(X0,iPr_def_10)
| in(sK2(X1,iPr_def_11,sK18),X1)
| ( set_union2(X1,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(X1,iPr_def_11,sK18)) ),
inference(superposition,[status(thm)],[c_77034,c_128]) ).
tcf(c_77059,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_11)
| in(sK2(X0,iPr_def_11,sK18),X0)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77034,c_3868]) ).
tcf(c_77060,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(X0,iPr_def_11,sK18))
| in(sK2(X0,iPr_def_11,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,iPr_def_11) = sK18 )
| ( sK2(X0,iPr_def_11,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_77034,c_49877]) ).
tcf(c_77061,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(X0,iPr_def_11,sK18))
| in(sK2(X0,iPr_def_11,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,iPr_def_11) = sK18 )
| ( sK2(X0,iPr_def_11,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_77034,c_7260]) ).
tcf(c_77062,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_77034,c_359]) ).
tcf(c_77063,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| element(sK2(X0,iPr_def_11,sK18),X1)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_77034,c_358]) ).
tcf(c_77064,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,iPr_def_11,sK18),iPr_def_10)
| in(X0,sK2(X1,iPr_def_11,sK18))
| in(sK2(X1,iPr_def_11,sK18),X0)
| ( set_union2(X1,iPr_def_11) = sK18 )
| ( sK2(X1,iPr_def_11,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_77034,c_77]) ).
tcf(c_77065,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| subset(sK2(X0,iPr_def_11,sK18),X0)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_77034,c_65]) ).
tcf(c_77066,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X0,iPr_def_11,sK18)) ),
inference(superposition,[status(thm)],[c_77034,c_49]) ).
tcf(c_77067,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_77034,c_137]) ).
tcf(c_77068,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| element(sK2(X0,iPr_def_11,sK18),X0)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77034,c_127]) ).
tcf(c_77069,plain,
! [X0: $i] :
( subset(sK2(singleton(X0),iPr_def_11,sK18),iPr_def_10)
| ( set_union2(singleton(X0),iPr_def_11) = sK18 )
| ( sK2(singleton(X0),iPr_def_11,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77034,c_62]) ).
tcf(c_77070,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,iPr_def_11,sK18),sK18) ),
inference(superposition,[status(thm)],[c_77034,c_66]) ).
tcf(c_77072,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),iPr_def_11,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),iPr_def_11,sK18))
| in(sK2(set_union2(X0,X1),iPr_def_11,sK18),X2)
| ( set_union2(set_union2(X0,X1),iPr_def_11) = sK18 )
| ( sK2(set_union2(X0,X1),iPr_def_11,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_77034,c_4213]) ).
tcf(c_77073,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),iPr_def_11,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),iPr_def_11,sK18))
| in(sK2(set_union2(X0,X1),iPr_def_11,sK18),X2)
| ( set_union2(set_union2(X0,X1),iPr_def_11) = sK18 )
| ( sK2(set_union2(X0,X1),iPr_def_11,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_77034,c_4212]) ).
tcf(c_77074,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),iPr_def_11,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),iPr_def_11,sK18),X1)
| in(sK2(set_union2(X0,X1),iPr_def_11,sK18),X0)
| ( set_union2(set_union2(X0,X1),iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77034,c_71]) ).
tcf(c_77075,plain,
( subset(sK2(empty_set,iPr_def_11,sK18),iPr_def_10)
| ( set_union2(empty_set,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77034,c_7097]) ).
tcf(c_77079,plain,
( subset(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| in(sK2(sK18,iPr_def_11,sK18),iPr_def_11)
| ( set_union2(sK18,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77034,c_3640]) ).
tcf(c_77080,plain,
( subset(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77034,c_9540]) ).
tcf(c_77081,plain,
( subset(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(iPr_def_10,iPr_def_11,sK18)) ),
inference(superposition,[status(thm)],[c_77034,c_6289]) ).
tcf(c_77082,plain,
( element(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_11)
| subset(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77034,c_4912]) ).
tcf(c_77083,plain,
( subset(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,iPr_def_11) = sK18 )
| ( sK2(iPr_def_10,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77034,c_3592]) ).
tcf(c_77084,plain,
( subset(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_10)
| in(sK2(iPr_def_10,iPr_def_11,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77034,c_3614]) ).
tcf(c_77085,plain,
( subset(sK2(iPr_def_11,iPr_def_11,sK18),iPr_def_10)
| in(sK2(iPr_def_11,iPr_def_11,sK18),sK18)
| ( set_union2(iPr_def_11,iPr_def_11) = sK18 )
| ( sK2(iPr_def_11,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77034,c_33457]) ).
tcf(c_77086,plain,
( subset(sK2(iPr_def_11,iPr_def_11,sK18),iPr_def_10)
| in(sK2(iPr_def_11,iPr_def_11,sK18),iPr_def_10)
| in(sK2(iPr_def_11,iPr_def_11,sK18),sK18)
| ( set_union2(iPr_def_11,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77034,c_4035]) ).
tcf(c_77087,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK5(iPr_def_11),iPr_def_11,sK18),iPr_def_10)
| in(X0,sK2(sK5(iPr_def_11),iPr_def_11,sK18))
| in(sK2(sK5(iPr_def_11),iPr_def_11,sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),iPr_def_11) = sK18 )
| ( sK2(sK5(iPr_def_11),iPr_def_11,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_77034,c_7243]) ).
tcf(c_77088,plain,
( subset(sK2(sK5(iPr_def_11),iPr_def_11,sK18),iPr_def_10)
| ( set_union2(sK5(iPr_def_11),iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),iPr_def_11,sK18)) ),
inference(superposition,[status(thm)],[c_77034,c_23189]) ).
tcf(c_77089,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK3(iPr_def_11),iPr_def_11,sK18),iPr_def_10)
| in(X0,sK2(sK3(iPr_def_11),iPr_def_11,sK18))
| in(sK2(sK3(iPr_def_11),iPr_def_11,sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),iPr_def_11) = sK18 )
| ( sK2(sK3(iPr_def_11),iPr_def_11,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_77034,c_9906]) ).
tcf(c_77090,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK4(iPr_def_11),iPr_def_11,sK18),iPr_def_10)
| in(X0,sK2(sK4(iPr_def_11),iPr_def_11,sK18))
| in(sK2(sK4(iPr_def_11),iPr_def_11,sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),iPr_def_11) = sK18 )
| ( sK2(sK4(iPr_def_11),iPr_def_11,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_77034,c_45801]) ).
tcf(c_77091,plain,
( subset(sK2(sK18,iPr_def_11,sK18),iPr_def_10)
| ( set_union2(sK18,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77034,c_66161]) ).
tcf(c_77535,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),X0)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53150,c_65,c_66161]) ).
tcf(c_77556,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),X0)
| in(sK2(iPr_def_11,X0,sK18),sK4(iPr_def_11))
| ( set_union2(iPr_def_11,X0) = sK18 )
| ( sK2(iPr_def_11,X0,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(iPr_def_11,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_77535,c_13671]) ).
tcf(c_77557,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),X0)
| in(sK2(iPr_def_11,X0,sK18),sK3(iPr_def_11))
| ( set_union2(iPr_def_11,X0) = sK18 )
| ( sK2(iPr_def_11,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(iPr_def_11,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_77535,c_13665]) ).
tcf(c_77558,plain,
! [X0: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(iPr_def_11,X0,sK18),X0)
| in(sK2(iPr_def_11,X0,sK18),sK5(iPr_def_11))
| ( set_union2(iPr_def_11,X0) = sK18 )
| ( sK2(iPr_def_11,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(iPr_def_11,X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_77535,c_13657]) ).
tcf(c_77559,plain,
! [X0: $i,X1: $i] :
( subset(X0,iPr_def_10)
| in(sK2(iPr_def_11,X1,sK18),X1)
| ( set_union2(iPr_def_11,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(iPr_def_11,X1,sK18)) ),
inference(superposition,[status(thm)],[c_77535,c_128]) ).
tcf(c_77560,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_11)
| in(sK2(iPr_def_11,X0,sK18),X0)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77535,c_3868]) ).
tcf(c_77561,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(iPr_def_11,X0,sK18))
| in(sK2(iPr_def_11,X0,sK18),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(iPr_def_11,X0) = sK18 )
| ( sK2(iPr_def_11,X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_77535,c_49877]) ).
tcf(c_77562,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(iPr_def_11,X0,sK18))
| in(sK2(iPr_def_11,X0,sK18),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(iPr_def_11,X0) = sK18 )
| ( sK2(iPr_def_11,X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_77535,c_7260]) ).
tcf(c_77563,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_77535,c_359]) ).
tcf(c_77564,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| element(sK2(iPr_def_11,X0,sK18),X1)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_77535,c_358]) ).
tcf(c_77565,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_11,X1,sK18),iPr_def_10)
| in(X0,sK2(iPr_def_11,X1,sK18))
| in(sK2(iPr_def_11,X1,sK18),X0)
| ( set_union2(iPr_def_11,X1) = sK18 )
| ( sK2(iPr_def_11,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_77535,c_77]) ).
tcf(c_77566,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| subset(sK2(iPr_def_11,X0,sK18),X0)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_77535,c_65]) ).
tcf(c_77567,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(iPr_def_11,X0,sK18)) ),
inference(superposition,[status(thm)],[c_77535,c_49]) ).
tcf(c_77568,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_77535,c_137]) ).
tcf(c_77569,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,X0,sK18),iPr_def_10)
| element(sK2(iPr_def_11,X0,sK18),X0)
| ( set_union2(iPr_def_11,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77535,c_127]) ).
tcf(c_77570,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,singleton(X0),sK18),iPr_def_10)
| ( set_union2(iPr_def_11,singleton(X0)) = sK18 )
| ( sK2(iPr_def_11,singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77535,c_62]) ).
tcf(c_77571,plain,
( subset(sK2(iPr_def_11,iPr_def_11,sK18),iPr_def_10)
| ( set_union2(iPr_def_11,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(iPr_def_11,iPr_def_11,sK18),sK18) ),
inference(superposition,[status(thm)],[c_77535,c_66]) ).
tcf(c_77573,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(iPr_def_11,set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(iPr_def_11,set_union2(X0,X1),sK18))
| in(sK2(iPr_def_11,set_union2(X0,X1),sK18),X2)
| ( set_union2(iPr_def_11,set_union2(X0,X1)) = sK18 )
| ( sK2(iPr_def_11,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_77535,c_4213]) ).
tcf(c_77574,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(iPr_def_11,set_union2(X0,X1),sK18),iPr_def_10)
| in(X2,sK2(iPr_def_11,set_union2(X0,X1),sK18))
| in(sK2(iPr_def_11,set_union2(X0,X1),sK18),X2)
| ( set_union2(iPr_def_11,set_union2(X0,X1)) = sK18 )
| ( sK2(iPr_def_11,set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_77535,c_4212]) ).
tcf(c_77575,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_11,set_union2(X0,X1),sK18),iPr_def_10)
| in(sK2(iPr_def_11,set_union2(X0,X1),sK18),X1)
| in(sK2(iPr_def_11,set_union2(X0,X1),sK18),X0)
| ( set_union2(iPr_def_11,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77535,c_71]) ).
tcf(c_77576,plain,
( subset(sK2(iPr_def_11,empty_set,sK18),iPr_def_10)
| ( set_union2(iPr_def_11,empty_set) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77535,c_7097]) ).
tcf(c_77580,plain,
( subset(sK2(iPr_def_11,sK18,sK18),iPr_def_10)
| in(sK2(iPr_def_11,sK18,sK18),iPr_def_11)
| ( set_union2(iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77535,c_3640]) ).
tcf(c_77581,plain,
( subset(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(iPr_def_11,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77535,c_9540]) ).
tcf(c_77582,plain,
( subset(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(iPr_def_11,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(iPr_def_11,iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_77535,c_6289]) ).
tcf(c_77583,plain,
( element(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| ( set_union2(iPr_def_11,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77535,c_4912]) ).
tcf(c_77585,plain,
( subset(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(iPr_def_11,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77535,c_3614]) ).
tcf(c_77588,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(iPr_def_11,sK5(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(iPr_def_11,sK5(iPr_def_11),sK18))
| in(sK2(iPr_def_11,sK5(iPr_def_11),sK18),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(iPr_def_11,sK5(iPr_def_11)) = sK18 )
| ( sK2(iPr_def_11,sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_77535,c_7243]) ).
tcf(c_77589,plain,
( subset(sK2(iPr_def_11,sK5(iPr_def_11),sK18),iPr_def_10)
| ( set_union2(iPr_def_11,sK5(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(iPr_def_11,sK5(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_77535,c_23189]) ).
tcf(c_77590,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(iPr_def_11,sK3(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(iPr_def_11,sK3(iPr_def_11),sK18))
| in(sK2(iPr_def_11,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(iPr_def_11,sK3(iPr_def_11)) = sK18 )
| ( sK2(iPr_def_11,sK3(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_77535,c_9906]) ).
tcf(c_77591,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(iPr_def_11,sK4(iPr_def_11),sK18),iPr_def_10)
| in(X0,sK2(iPr_def_11,sK4(iPr_def_11),sK18))
| in(sK2(iPr_def_11,sK4(iPr_def_11),sK18),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(iPr_def_11,sK4(iPr_def_11)) = sK18 )
| ( sK2(iPr_def_11,sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_77535,c_45801]) ).
tcf(c_77592,plain,
( subset(sK2(iPr_def_11,sK18,sK18),iPr_def_10)
| ( set_union2(iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_77535,c_66161]) ).
tcf(c_78014,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X2,iPr_def_10),X0)
| in(sK2(X1,X2,iPr_def_10),X2)
| in(sK2(X1,X2,iPr_def_10),X1)
| ( set_union2(X1,X2) = iPr_def_10 )
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_4340,c_358]) ).
tcf(c_78015,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X1,X2,iPr_def_10))
| in(sK2(X1,X2,iPr_def_10),X2)
| in(sK2(X1,X2,iPr_def_10),X1)
| in(sK2(X1,X2,iPr_def_10),X0)
| ( set_union2(X1,X2) = iPr_def_10 )
| ( sK2(X1,X2,iPr_def_10) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4340,c_77]) ).
tcf(c_78022,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_10),iPr_def_10)
| in(sK2(X0,X1,iPr_def_10),sK18)
| in(sK2(X0,X1,iPr_def_10),X1)
| in(sK2(X0,X1,iPr_def_10),X0)
| ( set_union2(X0,X1) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4340,c_4035]) ).
tcf(c_78023,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_union2(iPr_def_11,X0),X1,iPr_def_10),X1)
| in(sK2(set_union2(iPr_def_11,X0),X1,iPr_def_10),set_union2(iPr_def_11,X0))
| ( set_union2(set_union2(iPr_def_11,X0),X1) = iPr_def_10 )
| ~ in(sK2(set_union2(iPr_def_11,X0),X1,iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4340,c_4078]) ).
tcf(c_78024,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X1,X0,iPr_def_10),iPr_def_11)
| in(sK2(X1,X0,iPr_def_10),X1)
| in(sK3(iPr_def_11),sK2(X1,X0,iPr_def_10))
| in(sK2(X1,X0,iPr_def_10),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = iPr_def_10 )
| ( sK2(X1,X0,iPr_def_10) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4340,c_49877]) ).
tcf(c_78025,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X1,X0,iPr_def_10),iPr_def_11)
| in(sK2(X1,X0,iPr_def_10),X1)
| in(sK5(iPr_def_11),sK2(X1,X0,iPr_def_10))
| in(sK2(X1,X0,iPr_def_10),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,X0) = iPr_def_10 )
| ( sK2(X1,X0,iPr_def_10) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4340,c_7260]) ).
tcf(c_78026,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X0,iPr_def_10),iPr_def_11)
| in(sK2(X2,X0,iPr_def_10),X2)
| ( set_union2(X2,X0) = iPr_def_10 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4340,c_359]) ).
tcf(c_78027,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X0,iPr_def_10),iPr_def_11)
| element(sK2(X2,X0,iPr_def_10),X1)
| in(sK2(X2,X0,iPr_def_10),X2)
| ( set_union2(X2,X0) = iPr_def_10 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4340,c_358]) ).
tcf(c_78028,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X1,iPr_def_10),iPr_def_11)
| in(X0,sK2(X2,X1,iPr_def_10))
| in(sK2(X2,X1,iPr_def_10),X2)
| in(sK2(X2,X1,iPr_def_10),X0)
| ( set_union2(X2,X1) = iPr_def_10 )
| ( sK2(X2,X1,iPr_def_10) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4340,c_77]) ).
tcf(c_78029,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,iPr_def_10),iPr_def_11)
| subset(sK2(X1,X0,iPr_def_10),X0)
| in(sK2(X1,X0,iPr_def_10),X1)
| ( set_union2(X1,X0) = iPr_def_10 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4340,c_65]) ).
tcf(c_78030,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,iPr_def_10),iPr_def_11)
| in(sK2(X1,X0,iPr_def_10),X1)
| ( set_union2(X1,X0) = iPr_def_10 )
| ~ in(X0,sK2(X1,X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4340,c_49]) ).
tcf(c_78031,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,iPr_def_10),iPr_def_11)
| in(sK2(X1,X0,iPr_def_10),X1)
| ( set_union2(X1,X0) = iPr_def_10 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4340,c_137]) ).
tcf(c_78032,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_10),iPr_def_11)
| element(sK2(X0,X1,iPr_def_10),X1)
| in(sK2(X0,X1,iPr_def_10),X0)
| ( set_union2(X0,X1) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4340,c_127]) ).
tcf(c_78033,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,singleton(X1),iPr_def_10),iPr_def_11)
| in(sK2(X0,singleton(X1),iPr_def_10),X0)
| ( set_union2(X0,singleton(X1)) = iPr_def_10 )
| ( sK2(X0,singleton(X1),iPr_def_10) = X1 ) ),
inference(superposition,[status(thm)],[c_4340,c_62]) ).
tcf(c_78034,plain,
! [X0: $i] :
( in(sK2(X0,X0,iPr_def_10),iPr_def_11)
| in(sK2(X0,X0,iPr_def_10),X0)
| ( set_union2(X0,X0) = iPr_def_10 )
| ~ in(sK2(X0,X0,iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4340,c_66]) ).
tcf(c_78036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,set_union2(X0,X1),iPr_def_10),iPr_def_11)
| in(X2,sK2(X3,set_union2(X0,X1),iPr_def_10))
| in(sK2(X3,set_union2(X0,X1),iPr_def_10),X3)
| in(sK2(X3,set_union2(X0,X1),iPr_def_10),X2)
| ( set_union2(X3,set_union2(X0,X1)) = iPr_def_10 )
| ( sK2(X3,set_union2(X0,X1),iPr_def_10) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4340,c_4213]) ).
tcf(c_78037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,set_union2(X0,X1),iPr_def_10),iPr_def_11)
| in(X2,sK2(X3,set_union2(X0,X1),iPr_def_10))
| in(sK2(X3,set_union2(X0,X1),iPr_def_10),X3)
| in(sK2(X3,set_union2(X0,X1),iPr_def_10),X2)
| ( set_union2(X3,set_union2(X0,X1)) = iPr_def_10 )
| ( sK2(X3,set_union2(X0,X1),iPr_def_10) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4340,c_4212]) ).
tcf(c_78038,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_union2(X1,X2),iPr_def_10),iPr_def_11)
| in(sK2(X0,set_union2(X1,X2),iPr_def_10),X2)
| in(sK2(X0,set_union2(X1,X2),iPr_def_10),X1)
| in(sK2(X0,set_union2(X1,X2),iPr_def_10),X0)
| ( set_union2(X0,set_union2(X1,X2)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4340,c_71]) ).
tcf(c_78039,plain,
! [X0: $i] :
( in(sK2(X0,empty_set,iPr_def_10),iPr_def_11)
| in(sK2(X0,empty_set,iPr_def_10),X0)
| ( set_union2(X0,empty_set) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4340,c_7097]) ).
tcf(c_78043,plain,
! [X0: $i] :
( in(sK2(X0,sK18,iPr_def_10),iPr_def_11)
| in(sK2(X0,sK18,iPr_def_10),X0)
| ( set_union2(X0,sK18) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4340,c_3640]) ).
tcf(c_78048,plain,
! [X0: $i] :
( in(sK2(X0,iPr_def_10,iPr_def_10),iPr_def_11)
| in(sK2(X0,iPr_def_10,iPr_def_10),X0)
| ( set_union2(X0,iPr_def_10) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4340,c_3614]) ).
tcf(c_78049,plain,
! [X0: $i] :
( in(sK2(X0,iPr_def_11,iPr_def_10),iPr_def_11)
| in(sK2(X0,iPr_def_11,iPr_def_10),sK18)
| in(sK2(X0,iPr_def_11,iPr_def_10),X0)
| ( set_union2(X0,iPr_def_11) = iPr_def_10 )
| ( sK2(X0,iPr_def_11,iPr_def_10) = sK18 ) ),
inference(superposition,[status(thm)],[c_4340,c_33457]) ).
tcf(c_78051,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_union2(X0,X1),X0,iPr_def_10),iPr_def_11)
| in(sK2(set_union2(X0,X1),X0,iPr_def_10),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X0) = iPr_def_10 )
| ~ in(sK2(set_union2(X0,X1),X0,iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4340,c_4078]) ).
tcf(c_78052,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_union2(X0,X1),iPr_def_10,iPr_def_10),iPr_def_11)
| in(sK2(set_union2(X0,X1),iPr_def_10,iPr_def_10),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),iPr_def_10) = iPr_def_10 )
| ~ in(sK2(set_union2(X0,X1),iPr_def_10,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_4340,c_4079]) ).
tcf(c_78053,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(sK2(X1,sK5(iPr_def_11),iPr_def_10),iPr_def_11)
| in(X0,sK2(X1,sK5(iPr_def_11),iPr_def_10))
| in(sK2(X1,sK5(iPr_def_11),iPr_def_10),X1)
| in(sK2(X1,sK5(iPr_def_11),iPr_def_10),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,sK5(iPr_def_11)) = iPr_def_10 )
| ( sK2(X1,sK5(iPr_def_11),iPr_def_10) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4340,c_7243]) ).
tcf(c_78054,plain,
! [X0: $i] :
( in(sK2(X0,sK5(iPr_def_11),iPr_def_10),iPr_def_11)
| in(sK2(X0,sK5(iPr_def_11),iPr_def_10),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = iPr_def_10 )
| ~ subset(iPr_def_11,sK2(X0,sK5(iPr_def_11),iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4340,c_23189]) ).
tcf(c_78055,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(sK2(X1,sK3(iPr_def_11),iPr_def_10),iPr_def_11)
| in(X0,sK2(X1,sK3(iPr_def_11),iPr_def_10))
| in(sK2(X1,sK3(iPr_def_11),iPr_def_10),X1)
| in(sK2(X1,sK3(iPr_def_11),iPr_def_10),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,sK3(iPr_def_11)) = iPr_def_10 )
| ( sK2(X1,sK3(iPr_def_11),iPr_def_10) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4340,c_9906]) ).
tcf(c_78056,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(sK2(X1,sK4(iPr_def_11),iPr_def_10),iPr_def_11)
| in(X0,sK2(X1,sK4(iPr_def_11),iPr_def_10))
| in(sK2(X1,sK4(iPr_def_11),iPr_def_10),X1)
| in(sK2(X1,sK4(iPr_def_11),iPr_def_10),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,sK4(iPr_def_11)) = iPr_def_10 )
| ( sK2(X1,sK4(iPr_def_11),iPr_def_10) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4340,c_45801]) ).
tcf(c_78057,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK2(X0,X1,iPr_def_10),iPr_def_11)
| in(sK2(X0,X1,iPr_def_10),X1)
| in(sK3(iPr_def_11),sK2(X0,X1,iPr_def_10))
| in(sK2(X0,X1,iPr_def_10),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = iPr_def_10 )
| ( sK2(X0,X1,iPr_def_10) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4340,c_49877]) ).
tcf(c_78058,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK2(X0,X1,iPr_def_10),iPr_def_11)
| in(sK2(X0,X1,iPr_def_10),X1)
| in(sK5(iPr_def_11),sK2(X0,X1,iPr_def_10))
| in(sK2(X0,X1,iPr_def_10),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = iPr_def_10 )
| ( sK2(X0,X1,iPr_def_10) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4340,c_7260]) ).
tcf(c_78059,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,iPr_def_10),iPr_def_11)
| in(sK2(X0,X2,iPr_def_10),X2)
| ( set_union2(X0,X2) = iPr_def_10 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4340,c_359]) ).
tcf(c_78060,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,iPr_def_10),iPr_def_11)
| element(sK2(X0,X2,iPr_def_10),X1)
| in(sK2(X0,X2,iPr_def_10),X2)
| ( set_union2(X0,X2) = iPr_def_10 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4340,c_358]) ).
tcf(c_78061,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,iPr_def_10),iPr_def_11)
| in(X0,sK2(X1,X2,iPr_def_10))
| in(sK2(X1,X2,iPr_def_10),X2)
| in(sK2(X1,X2,iPr_def_10),X0)
| ( set_union2(X1,X2) = iPr_def_10 )
| ( sK2(X1,X2,iPr_def_10) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4340,c_77]) ).
tcf(c_78062,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_10),iPr_def_11)
| subset(sK2(X0,X1,iPr_def_10),X0)
| in(sK2(X0,X1,iPr_def_10),X1)
| ( set_union2(X0,X1) = iPr_def_10 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4340,c_65]) ).
tcf(c_78063,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_10),iPr_def_11)
| in(sK2(X0,X1,iPr_def_10),X1)
| ( set_union2(X0,X1) = iPr_def_10 )
| ~ in(X0,sK2(X0,X1,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4340,c_49]) ).
tcf(c_78064,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_10),iPr_def_11)
| in(sK2(X0,X1,iPr_def_10),X1)
| ( set_union2(X0,X1) = iPr_def_10 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4340,c_137]) ).
tcf(c_78065,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_10),iPr_def_11)
| element(sK2(X0,X1,iPr_def_10),X0)
| in(sK2(X0,X1,iPr_def_10),X1)
| ( set_union2(X0,X1) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4340,c_127]) ).
tcf(c_78066,plain,
! [X0: $i,X1: $i] :
( in(sK2(singleton(X0),X1,iPr_def_10),iPr_def_11)
| in(sK2(singleton(X0),X1,iPr_def_10),X1)
| ( set_union2(singleton(X0),X1) = iPr_def_10 )
| ( sK2(singleton(X0),X1,iPr_def_10) = X0 ) ),
inference(superposition,[status(thm)],[c_4340,c_62]) ).
tcf(c_78067,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,iPr_def_10),iPr_def_11)
| in(sK2(X0,X1,iPr_def_10),X1)
| ( set_union2(X0,X1) = iPr_def_10 )
| ~ in(sK2(X0,X1,iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4340,c_66]) ).
tcf(c_78069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_union2(X0,X1),X3,iPr_def_10),iPr_def_11)
| in(X2,sK2(set_union2(X0,X1),X3,iPr_def_10))
| in(sK2(set_union2(X0,X1),X3,iPr_def_10),X3)
| in(sK2(set_union2(X0,X1),X3,iPr_def_10),X2)
| ( set_union2(set_union2(X0,X1),X3) = iPr_def_10 )
| ( sK2(set_union2(X0,X1),X3,iPr_def_10) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4340,c_4213]) ).
tcf(c_78070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_union2(X0,X1),X3,iPr_def_10),iPr_def_11)
| in(X2,sK2(set_union2(X0,X1),X3,iPr_def_10))
| in(sK2(set_union2(X0,X1),X3,iPr_def_10),X3)
| in(sK2(set_union2(X0,X1),X3,iPr_def_10),X2)
| ( set_union2(set_union2(X0,X1),X3) = iPr_def_10 )
| ( sK2(set_union2(X0,X1),X3,iPr_def_10) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4340,c_4212]) ).
tcf(c_78071,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_union2(X0,X1),X2,iPr_def_10),iPr_def_11)
| in(sK2(set_union2(X0,X1),X2,iPr_def_10),X2)
| in(sK2(set_union2(X0,X1),X2,iPr_def_10),X1)
| in(sK2(set_union2(X0,X1),X2,iPr_def_10),X0)
| ( set_union2(set_union2(X0,X1),X2) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4340,c_71]) ).
tcf(c_78072,plain,
! [X0: $i] :
( in(sK2(empty_set,X0,iPr_def_10),iPr_def_11)
| in(sK2(empty_set,X0,iPr_def_10),X0)
| ( set_union2(empty_set,X0) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4340,c_7097]) ).
tcf(c_78076,plain,
! [X0: $i] :
( in(sK2(sK18,X0,iPr_def_10),iPr_def_11)
| in(sK2(sK18,X0,iPr_def_10),X0)
| ( set_union2(sK18,X0) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4340,c_3640]) ).
tcf(c_78081,plain,
! [X0: $i] :
( in(sK2(iPr_def_10,X0,iPr_def_10),iPr_def_11)
| in(sK2(iPr_def_10,X0,iPr_def_10),X0)
| ( set_union2(iPr_def_10,X0) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_4340,c_3614]) ).
tcf(c_78082,plain,
! [X0: $i] :
( in(sK2(iPr_def_11,X0,iPr_def_10),iPr_def_11)
| in(sK2(iPr_def_11,X0,iPr_def_10),sK18)
| in(sK2(iPr_def_11,X0,iPr_def_10),X0)
| ( set_union2(iPr_def_11,X0) = iPr_def_10 )
| ( sK2(iPr_def_11,X0,iPr_def_10) = sK18 ) ),
inference(superposition,[status(thm)],[c_4340,c_33457]) ).
tcf(c_78084,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(sK2(sK5(iPr_def_11),X1,iPr_def_10),iPr_def_11)
| in(X0,sK2(sK5(iPr_def_11),X1,iPr_def_10))
| in(sK2(sK5(iPr_def_11),X1,iPr_def_10),X1)
| in(sK2(sK5(iPr_def_11),X1,iPr_def_10),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X1) = iPr_def_10 )
| ( sK2(sK5(iPr_def_11),X1,iPr_def_10) = X0 )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4340,c_7243]) ).
tcf(c_78085,plain,
! [X0: $i] :
( in(sK2(sK5(iPr_def_11),X0,iPr_def_10),iPr_def_11)
| in(sK2(sK5(iPr_def_11),X0,iPr_def_10),X0)
| ( set_union2(sK5(iPr_def_11),X0) = iPr_def_10 )
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4340,c_23189]) ).
tcf(c_78086,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(sK2(sK3(iPr_def_11),X1,iPr_def_10),iPr_def_11)
| in(X0,sK2(sK3(iPr_def_11),X1,iPr_def_10))
| in(sK2(sK3(iPr_def_11),X1,iPr_def_10),X1)
| in(sK2(sK3(iPr_def_11),X1,iPr_def_10),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X1) = iPr_def_10 )
| ( sK2(sK3(iPr_def_11),X1,iPr_def_10) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4340,c_9906]) ).
tcf(c_78087,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(sK2(sK4(iPr_def_11),X1,iPr_def_10),iPr_def_11)
| in(X0,sK2(sK4(iPr_def_11),X1,iPr_def_10))
| in(sK2(sK4(iPr_def_11),X1,iPr_def_10),X1)
| in(sK2(sK4(iPr_def_11),X1,iPr_def_10),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X1) = iPr_def_10 )
| ( sK2(sK4(iPr_def_11),X1,iPr_def_10) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4340,c_45801]) ).
tcf(c_78090,plain,
! [X0: $i] :
( in(sK2(X0,iPr_def_11,iPr_def_10),iPr_def_11)
| in(sK2(X0,iPr_def_11,iPr_def_10),X0)
| ( set_union2(X0,iPr_def_11) = iPr_def_10 ) ),
inference(equality_factoring,[status(thm)],[c_4340]) ).
tcf(c_78092,plain,
! [X0: $i] :
( in(sK2(iPr_def_11,X0,iPr_def_10),iPr_def_11)
| in(sK2(iPr_def_11,X0,iPr_def_10),X0)
| ( set_union2(iPr_def_11,X0) = iPr_def_10 ) ),
inference(equality_factoring,[status(thm)],[c_4340]) ).
tcf(c_78093,plain,
! [X0: $i] :
( in(sK2(X0,X0,iPr_def_10),iPr_def_11)
| in(sK2(X0,X0,iPr_def_10),X0)
| ( set_union2(X0,X0) = iPr_def_10 ) ),
inference(equality_factoring,[status(thm)],[c_4340]) ).
tcf(c_78094,plain,
! [X0: $i] :
( in(sK2(X0,X0,iPr_def_10),iPr_def_11)
| in(sK2(X0,X0,iPr_def_10),X0)
| ( X0 = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_78093,c_97]) ).
tcf(c_78110,plain,
! [X0: $i] :
( in(sK2(empty_set,X0,iPr_def_10),iPr_def_11)
| in(sK2(empty_set,X0,iPr_def_10),X0)
| ( X0 = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_78072,c_3423]) ).
tcf(c_78120,plain,
! [X0: $i] :
( in(sK2(X0,empty_set,iPr_def_10),iPr_def_11)
| in(sK2(X0,empty_set,iPr_def_10),X0)
| ( X0 = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_78039,c_126]) ).
tcf(c_79373,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(powerset(X0))))
| subset(sK3(sK5(powerset(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3564,c_19389]) ).
tcf(c_79375,plain,
! [X0: $i] :
( epsilon_transitive(powerset(powerset(X0)))
| epsilon_connected(sK1(powerset(powerset(X0))))
| subset(sK3(sK1(powerset(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3566,c_19389]) ).
tcf(c_79376,plain,
! [X0: $i] :
( epsilon_connected(powerset(powerset(X0)))
| epsilon_connected(sK3(powerset(powerset(X0))))
| subset(sK3(sK3(powerset(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3567,c_19389]) ).
tcf(c_79377,plain,
! [X0: $i] :
( epsilon_connected(powerset(powerset(X0)))
| epsilon_connected(sK4(powerset(powerset(X0))))
| subset(sK3(sK4(powerset(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3568,c_19389]) ).
tcf(c_79378,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| epsilon_connected(sK3(powerset(X0)))
| subset(sK3(sK3(powerset(X0))),X0)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_3807,c_19389]) ).
tcf(c_79379,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| epsilon_connected(sK4(powerset(X0)))
| subset(sK3(sK4(powerset(X0))),X0)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_3808,c_19389]) ).
tcf(c_79380,plain,
! [X0: $i] :
( empty(powerset(X0))
| epsilon_connected(sK5(powerset(X0)))
| subset(sK3(sK5(powerset(X0))),X0)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_3899,c_19389]) ).
tcf(c_79381,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(sK2(X1,X2,powerset(X0)))
| in(sK2(X1,X2,powerset(X0)),X2)
| in(sK2(X1,X2,powerset(X0)),X1)
| subset(sK3(sK2(X1,X2,powerset(X0))),X0)
| ( set_union2(X1,X2) = powerset(X0) )
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_4330,c_19389]) ).
tcf(c_79382,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| epsilon_connected(sK3(powerset(empty_set)))
| subset(sK3(sK3(powerset(empty_set))),X0) ),
inference(superposition,[status(thm)],[c_4620,c_19389]) ).
tcf(c_79383,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| epsilon_connected(sK4(powerset(empty_set)))
| subset(sK3(sK4(powerset(empty_set))),X0) ),
inference(superposition,[status(thm)],[c_4637,c_19389]) ).
tcf(c_79384,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(sK5(powerset(powerset(X0))))))
| subset(sK3(sK5(powerset(sK5(powerset(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_5196,c_19389]) ).
tcf(c_79385,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(sK5(powerset(sK5(powerset(powerset(X0))))))))
| subset(sK3(sK5(powerset(sK5(powerset(sK5(powerset(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_5252,c_19389]) ).
tcf(c_79386,plain,
! [X0: $i] :
( epsilon_connected(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK3(sK5(iPr_def_11)),X0)
| in(powerset(X0),sK5(iPr_def_11))
| ( powerset(X0) = sK5(iPr_def_11) )
| ~ epsilon_transitive(powerset(X0))
| ~ in(powerset(X0),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_19389]) ).
tcf(c_79387,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(sK3(iPr_def_11)),X0)
| in(powerset(X0),sK3(iPr_def_11))
| ( powerset(X0) = sK3(iPr_def_11) )
| ~ epsilon_transitive(powerset(X0))
| ~ in(powerset(X0),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_19389]) ).
tcf(c_79388,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK3(sK4(iPr_def_11)),X0)
| in(powerset(X0),sK4(iPr_def_11))
| ( powerset(X0) = sK4(iPr_def_11) )
| ~ epsilon_transitive(powerset(X0))
| ~ in(powerset(X0),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_19389]) ).
tcf(c_79389,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK2(X1,powerset(X0),sK18))
| subset(sK2(X1,powerset(X0),sK18),iPr_def_10)
| in(sK2(X1,powerset(X0),sK18),X1)
| subset(sK3(sK2(X1,powerset(X0),sK18)),X0)
| ( set_union2(X1,powerset(X0)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_53096,c_19389]) ).
tcf(c_79390,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK2(powerset(X0),X1,sK18))
| subset(sK2(powerset(X0),X1,sK18),iPr_def_10)
| in(sK2(powerset(X0),X1,sK18),X1)
| subset(sK3(sK2(powerset(X0),X1,sK18)),X0)
| ( set_union2(powerset(X0),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_53129,c_19389]) ).
tcf(c_79490,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(powerset(X0))))
| subset(sK4(sK5(powerset(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3564,c_19404]) ).
tcf(c_79492,plain,
! [X0: $i] :
( epsilon_transitive(powerset(powerset(X0)))
| epsilon_connected(sK1(powerset(powerset(X0))))
| subset(sK4(sK1(powerset(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3566,c_19404]) ).
tcf(c_79493,plain,
! [X0: $i] :
( epsilon_connected(powerset(powerset(X0)))
| epsilon_connected(sK3(powerset(powerset(X0))))
| subset(sK4(sK3(powerset(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3567,c_19404]) ).
tcf(c_79494,plain,
! [X0: $i] :
( epsilon_connected(powerset(powerset(X0)))
| epsilon_connected(sK4(powerset(powerset(X0))))
| subset(sK4(sK4(powerset(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3568,c_19404]) ).
tcf(c_79495,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| epsilon_connected(sK3(powerset(X0)))
| subset(sK4(sK3(powerset(X0))),X0)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_3807,c_19404]) ).
tcf(c_79496,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| epsilon_connected(sK4(powerset(X0)))
| subset(sK4(sK4(powerset(X0))),X0)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_3808,c_19404]) ).
tcf(c_79497,plain,
! [X0: $i] :
( empty(powerset(X0))
| epsilon_connected(sK5(powerset(X0)))
| subset(sK4(sK5(powerset(X0))),X0)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_3899,c_19404]) ).
tcf(c_79498,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(sK2(X1,X2,powerset(X0)))
| in(sK2(X1,X2,powerset(X0)),X2)
| in(sK2(X1,X2,powerset(X0)),X1)
| subset(sK4(sK2(X1,X2,powerset(X0))),X0)
| ( set_union2(X1,X2) = powerset(X0) )
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_4330,c_19404]) ).
tcf(c_79499,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| epsilon_connected(sK3(powerset(empty_set)))
| subset(sK4(sK3(powerset(empty_set))),X0) ),
inference(superposition,[status(thm)],[c_4620,c_19404]) ).
tcf(c_79500,plain,
! [X0: $i] :
( epsilon_connected(powerset(empty_set))
| epsilon_connected(sK4(powerset(empty_set)))
| subset(sK4(sK4(powerset(empty_set))),X0) ),
inference(superposition,[status(thm)],[c_4637,c_19404]) ).
tcf(c_79501,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(sK5(powerset(powerset(X0))))))
| subset(sK4(sK5(powerset(sK5(powerset(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_5196,c_19404]) ).
tcf(c_79502,plain,
! [X0: $i] :
( epsilon_connected(sK5(powerset(sK5(powerset(sK5(powerset(powerset(X0))))))))
| subset(sK4(sK5(powerset(sK5(powerset(sK5(powerset(powerset(X0)))))))),X0) ),
inference(superposition,[status(thm)],[c_5252,c_19404]) ).
tcf(c_79503,plain,
! [X0: $i] :
( epsilon_connected(sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| subset(sK4(sK5(iPr_def_11)),X0)
| in(powerset(X0),sK5(iPr_def_11))
| ( powerset(X0) = sK5(iPr_def_11) )
| ~ epsilon_transitive(powerset(X0))
| ~ in(powerset(X0),sK18) ),
inference(superposition,[status(thm)],[c_7261,c_19404]) ).
tcf(c_79504,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK4(sK3(iPr_def_11)),X0)
| in(powerset(X0),sK3(iPr_def_11))
| ( powerset(X0) = sK3(iPr_def_11) )
| ~ epsilon_transitive(powerset(X0))
| ~ in(powerset(X0),sK18) ),
inference(superposition,[status(thm)],[c_9925,c_19404]) ).
tcf(c_79505,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| epsilon_connected(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(sK4(iPr_def_11)),X0)
| in(powerset(X0),sK4(iPr_def_11))
| ( powerset(X0) = sK4(iPr_def_11) )
| ~ epsilon_transitive(powerset(X0))
| ~ in(powerset(X0),sK18) ),
inference(superposition,[status(thm)],[c_11209,c_19404]) ).
tcf(c_79506,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK2(X1,powerset(X0),sK18))
| subset(sK2(X1,powerset(X0),sK18),iPr_def_10)
| in(sK2(X1,powerset(X0),sK18),X1)
| subset(sK4(sK2(X1,powerset(X0),sK18)),X0)
| ( set_union2(X1,powerset(X0)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_53096,c_19404]) ).
tcf(c_79507,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK2(powerset(X0),X1,sK18))
| subset(sK2(powerset(X0),X1,sK18),iPr_def_10)
| in(sK2(powerset(X0),X1,sK18),X1)
| subset(sK4(sK2(powerset(X0),X1,sK18)),X0)
| ( set_union2(powerset(X0),X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_53129,c_19404]) ).
tcf(c_79634,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ subset(iPr_def_11,X0)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_23188,c_13671]) ).
tcf(c_79635,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X0)
| ~ subset(iPr_def_11,X0)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_23188,c_13665]) ).
tcf(c_79637,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ subset(iPr_def_11,X1)
| ~ subset(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_23188,c_128]) ).
tcf(c_79638,plain,
! [X0: $i] :
( epsilon_connected(sK5(iPr_def_11))
| subset(sK4(sK5(iPr_def_11)),X0)
| ~ epsilon_transitive(powerset(X0))
| ~ subset(iPr_def_11,powerset(X0)) ),
inference(superposition,[status(thm)],[c_23188,c_19404]) ).
tcf(c_79639,plain,
! [X0: $i] :
( epsilon_connected(sK5(iPr_def_11))
| subset(sK3(sK5(iPr_def_11)),X0)
| ~ epsilon_transitive(powerset(X0))
| ~ subset(iPr_def_11,powerset(X0)) ),
inference(superposition,[status(thm)],[c_23188,c_19389]) ).
tcf(c_79640,plain,
! [X0: $i] :
( epsilon_transitive(sK5(iPr_def_11))
| subset(sK1(sK5(iPr_def_11)),X0)
| ~ epsilon_transitive(powerset(X0))
| ~ subset(iPr_def_11,powerset(X0)) ),
inference(superposition,[status(thm)],[c_23188,c_18478]) ).
tcf(c_79643,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(sK18)
| ~ subset(iPr_def_11,sK18) ),
inference(superposition,[status(thm)],[c_23188,c_3867]) ).
tcf(c_79644,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),X0)
| ~ epsilon_transitive(sK5(powerset(X0)))
| ~ subset(iPr_def_11,sK5(powerset(X0))) ),
inference(superposition,[status(thm)],[c_23188,c_3864]) ).
tcf(c_79646,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK18)))
| ~ subset(iPr_def_11,sK5(powerset(sK18))) ),
inference(superposition,[status(thm)],[c_23188,c_4177]) ).
tcf(c_79647,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(iPr_def_10)))
| ~ subset(iPr_def_11,sK5(powerset(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_23188,c_4574]) ).
tcf(c_79648,plain,
! [X0: $i] :
( subset(sK5(iPr_def_11),X0)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(X0)))))
| ~ subset(iPr_def_11,sK5(powerset(sK5(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_23188,c_5249]) ).
tcf(c_79650,plain,
( empty(sK18)
| subset(sK5(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ subset(iPr_def_11,sK5(sK18)) ),
inference(superposition,[status(thm)],[c_23188,c_5354]) ).
tcf(c_79651,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK18)))))
| ~ subset(iPr_def_11,sK5(powerset(sK5(powerset(sK18))))) ),
inference(superposition,[status(thm)],[c_23188,c_5379]) ).
tcf(c_79652,plain,
( subset(sK5(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(iPr_def_10)))))
| ~ subset(iPr_def_11,sK5(powerset(sK5(powerset(iPr_def_10))))) ),
inference(superposition,[status(thm)],[c_23188,c_5407]) ).
tcf(c_79653,plain,
( empty(sK18)
| subset(sK5(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(sK18))))
| ~ subset(iPr_def_11,sK5(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_23188,c_5478]) ).
tcf(c_79654,plain,
( empty(sK18)
| subset(sK5(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK5(sK18))))))
| ~ subset(iPr_def_11,sK5(powerset(sK5(powerset(sK5(sK18)))))) ),
inference(superposition,[status(thm)],[c_23188,c_5491]) ).
tcf(c_79655,plain,
( empty(sK18)
| subset(sK5(iPr_def_11),iPr_def_11)
| epsilon_transitive(powerset(sK5(sK18)))
| ~ epsilon_transitive(sK1(powerset(sK5(sK18))))
| ~ subset(iPr_def_11,sK1(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_23188,c_5502]) ).
tcf(c_79656,plain,
( empty(sK18)
| subset(sK5(iPr_def_11),iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| ~ epsilon_transitive(sK3(powerset(sK5(sK18))))
| ~ subset(iPr_def_11,sK3(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_23188,c_5516]) ).
tcf(c_79657,plain,
( empty(sK18)
| subset(sK5(iPr_def_11),iPr_def_11)
| epsilon_connected(powerset(sK5(sK18)))
| ~ epsilon_transitive(sK4(powerset(sK5(sK18))))
| ~ subset(iPr_def_11,sK4(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_23188,c_5528]) ).
tcf(c_79658,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK5(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK3(sK5(sK18)))
| ~ subset(iPr_def_11,sK3(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_23188,c_5794]) ).
tcf(c_79659,plain,
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK5(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK4(sK5(sK18)))
| ~ subset(iPr_def_11,sK4(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_23188,c_5809]) ).
tcf(c_79660,plain,
( empty(sK18)
| empty(sK5(sK18))
| subset(sK5(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK5(sK5(sK18)))
| ~ subset(iPr_def_11,sK5(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_23188,c_5824]) ).
tcf(c_79666,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(X1)
| ~ empty(X1)
| ~ subset(iPr_def_11,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_23188,c_24142]) ).
tcf(c_79667,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ~ epsilon_transitive(X1)
| ~ subset(iPr_def_11,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_23188,c_13661]) ).
tcf(c_79668,plain,
( epsilon_connected(iPr_def_11)
| subset(sK5(iPr_def_11),sK18)
| in(sK3(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ subset(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_23188,c_9862]) ).
tcf(c_79669,plain,
( epsilon_connected(iPr_def_11)
| subset(sK5(iPr_def_11),sK18)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ subset(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_23188,c_11154]) ).
tcf(c_79670,plain,
! [X0: $i,X1: $i] :
( subset(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK2(X0,X1,sK18))
| ~ subset(iPr_def_11,sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_23188,c_53089]) ).
tcf(c_79867,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(set_union2(X1,X2),X0))
| ~ subset(sK1(set_union2(X0,set_union2(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_3863,c_29457]) ).
tcf(c_79868,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(set_union2(X1,X2),X0))
| ~ epsilon_transitive(set_union2(X1,X2))
| ~ in(sK1(set_union2(X0,set_union2(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_3806,c_29457]) ).
tcf(c_79869,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(set_union2(X1,X2),X0))
| ~ epsilon_transitive(set_union2(X1,X2))
| ~ in(sK1(set_union2(X0,set_union2(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_3805,c_29457]) ).
tcf(c_79870,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(set_union2(X1,X2),X0))
| ~ subset(sK1(set_union2(X0,set_union2(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_3865,c_29457]) ).
tcf(c_79871,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| epsilon_transitive(set_union2(sK5(iPr_def_11),X0))
| in(sK5(iPr_def_11),sK1(set_union2(X0,sK5(iPr_def_11))))
| ( sK1(set_union2(X0,sK5(iPr_def_11))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(sK1(set_union2(X0,sK5(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_7244,c_29457]) ).
tcf(c_79872,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| epsilon_transitive(set_union2(sK3(iPr_def_11),X0))
| in(sK3(iPr_def_11),sK1(set_union2(X0,sK3(iPr_def_11))))
| ( sK1(set_union2(X0,sK3(iPr_def_11))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(sK1(set_union2(X0,sK3(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_9907,c_29457]) ).
tcf(c_79873,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| epsilon_transitive(set_union2(sK4(iPr_def_11),X0))
| in(sK4(iPr_def_11),sK1(set_union2(X0,sK4(iPr_def_11))))
| ( sK1(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(sK1(set_union2(X0,sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_11191,c_29457]) ).
tcf(c_79879,plain,
( epsilon_transitive(set_union2(sK18,iPr_def_10))
| ~ subset(sK1(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_3424,c_29457]) ).
tcf(c_79926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(singleton(set_union2(set_union2(X0,X1),X2)),X3),X0),
inference(superposition,[status(thm)],[c_69,c_68458]) ).
tcf(c_79927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(singleton(set_union2(set_union2(X0,X1),X2)),X3),X1),
inference(superposition,[status(thm)],[c_70,c_68458]) ).
tcf(c_79928,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X0))
| ~ subset(set_union2(singleton(set_union2(powerset(X0),X1)),X2),X0) ),
inference(superposition,[status(thm)],[c_3769,c_68458]) ).
tcf(c_79929,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK5(sK18),set_union2(singleton(set_union2(sK5(sK18),X0)),X1))
| ( set_union2(singleton(set_union2(sK5(sK18),X0)),X1) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(set_union2(singleton(set_union2(sK5(sK18),X0)),X1),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_68458]) ).
tcf(c_79930,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),set_union2(singleton(set_union2(sK2(X0,X1,X2),X3)),X4))
| ( set_union2(X0,X1) = X2 )
| ( set_union2(singleton(set_union2(sK2(X0,X1,X2),X3)),X4) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X2)
| ~ in(set_union2(singleton(set_union2(sK2(X0,X1,X2),X3)),X4),X2) ),
inference(superposition,[status(thm)],[c_4329,c_68458]) ).
tcf(c_79931,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_68458]) ).
tcf(c_79932,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_68458]) ).
tcf(c_79933,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_68458]) ).
tcf(c_79934,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_68458]) ).
tcf(c_79935,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ empty(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_68458]) ).
tcf(c_79936,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_68458]) ).
tcf(c_79937,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_68458]) ).
tcf(c_79938,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_7266,c_68458]) ).
tcf(c_79939,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),set_union2(singleton(set_union2(sK1(iPr_def_11),X0)),X1))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(sK1(iPr_def_11),X0)),X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(singleton(set_union2(sK1(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_68458]) ).
tcf(c_79940,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),set_union2(singleton(set_union2(sK1(iPr_def_11),X0)),X1))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(sK1(iPr_def_11),X0)),X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(singleton(set_union2(sK1(iPr_def_11),X0)),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_68458]) ).
tcf(c_79941,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_68458]) ).
tcf(c_79942,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_68458]) ).
tcf(c_79943,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_68458]) ).
tcf(c_79944,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_68458]) ).
tcf(c_79945,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ empty(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_68458]) ).
tcf(c_79946,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_68458]) ).
tcf(c_79947,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_68458]) ).
tcf(c_79948,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_9930,c_68458]) ).
tcf(c_79949,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_68458]) ).
tcf(c_79950,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_68458]) ).
tcf(c_79951,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_68458]) ).
tcf(c_79952,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ empty(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_68458]) ).
tcf(c_79953,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_68458]) ).
tcf(c_79954,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_11214,c_68458]) ).
tcf(c_79964,plain,
! [X0: $i] : ~ in(set_union2(singleton(iPr_def_11),X0),iPr_def_10),
inference(superposition,[status(thm)],[c_3424,c_68458]) ).
tcf(c_80336,plain,
! [X0: $i] : ~ in(set_union2(X0,singleton(iPr_def_11)),iPr_def_10),
inference(superposition,[status(thm)],[c_58,c_79964]) ).
tcf(c_80345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(X0,singleton(set_union2(X1,set_union2(X2,X3)))),X2),
inference(superposition,[status(thm)],[c_69,c_68567]) ).
tcf(c_80346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(X0,singleton(set_union2(X1,set_union2(X2,X3)))),X3),
inference(superposition,[status(thm)],[c_70,c_68567]) ).
tcf(c_80347,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X2))
| ~ subset(set_union2(X0,singleton(set_union2(X1,powerset(X2)))),X2) ),
inference(superposition,[status(thm)],[c_3769,c_68567]) ).
tcf(c_80348,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK5(sK18),set_union2(X0,singleton(set_union2(X1,sK5(sK18)))))
| ( set_union2(X0,singleton(set_union2(X1,sK5(sK18)))) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(sK18)))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_68567]) ).
tcf(c_80349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X4),X3)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X2,X3,X4),set_union2(X0,singleton(set_union2(X1,sK2(X2,X3,X4)))))
| ( set_union2(X2,X3) = X4 )
| ( set_union2(X0,singleton(set_union2(X1,sK2(X2,X3,X4)))) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X4)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK2(X2,X3,X4)))),X4) ),
inference(superposition,[status(thm)],[c_4329,c_68567]) ).
tcf(c_80350,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_68567]) ).
tcf(c_80351,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_68567]) ).
tcf(c_80352,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_68567]) ).
tcf(c_80353,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_68567]) ).
tcf(c_80354,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ empty(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_68567]) ).
tcf(c_80355,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_68567]) ).
tcf(c_80356,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_68567]) ).
tcf(c_80357,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(sK5(iPr_def_11),singleton(set_union2(X1,sK5(iPr_def_11))))
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_7266,c_68567]) ).
tcf(c_80358,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK1(iPr_def_11)))))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(X1,sK1(iPr_def_11)))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK1(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_68567]) ).
tcf(c_80359,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK1(iPr_def_11)))))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(X1,sK1(iPr_def_11)))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK1(iPr_def_11)))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_68567]) ).
tcf(c_80360,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_68567]) ).
tcf(c_80361,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_68567]) ).
tcf(c_80362,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_68567]) ).
tcf(c_80363,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_68567]) ).
tcf(c_80364,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ empty(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_68567]) ).
tcf(c_80365,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_68567]) ).
tcf(c_80366,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_68567]) ).
tcf(c_80367,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),singleton(set_union2(X1,sK3(iPr_def_11))))
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_9930,c_68567]) ).
tcf(c_80368,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_68567]) ).
tcf(c_80369,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_68567]) ).
tcf(c_80370,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_68567]) ).
tcf(c_80371,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ empty(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_68567]) ).
tcf(c_80372,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_68567]) ).
tcf(c_80373,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),singleton(set_union2(X1,sK4(iPr_def_11))))
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_11214,c_68567]) ).
tcf(c_80381,plain,
! [X0: $i,X1: $i] : ~ in(set_union2(X0,singleton(X1)),empty_set),
inference(superposition,[status(thm)],[c_126,c_68567]) ).
tcf(c_80546,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ( sK2(X0,iPr_def_11,sK18) = sK18 )
| ( set_union2(X0,iPr_def_11) = sK18 )
| in(sK2(X0,iPr_def_11,sK18),X0) ),
inference(global_subsumption_just,[status(thm)],[c_53116,c_53116,c_77070]) ).
tcf(c_80547,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_11,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_11,sK18),X0)
| ( set_union2(X0,iPr_def_11) = sK18 )
| ( sK2(X0,iPr_def_11,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(renaming,[status(thm)],[c_80546]) ).
tcf(c_80557,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X1,singleton(set_union2(X0,sK5(iPr_def_11)))))
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_71594]) ).
tcf(c_80559,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),singleton(set_union2(X0,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),singleton(set_union2(X0,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_71594]) ).
tcf(c_80560,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),empty_set) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),empty_set),sK18) ),
inference(superposition,[status(thm)],[c_126,c_71594]) ).
tcf(c_80561,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_71594]) ).
tcf(c_80563,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(singleton(sK5(iPr_def_11)),X0))
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),sK5(iPr_def_11))),X0) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),sK5(iPr_def_11))),X0),sK18) ),
inference(superposition,[status(thm)],[c_97,c_71594]) ).
tcf(c_80564,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(singleton(sK5(iPr_def_11)),X0))
| ( set_union2(singleton(set_union2(empty_set,sK5(iPr_def_11))),X0) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(empty_set,sK5(iPr_def_11))),X0),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_71594]) ).
tcf(c_80565,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71594,c_49877]) ).
tcf(c_80567,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ empty(X2)
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18)
| ~ subset(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),X2) ),
inference(superposition,[status(thm)],[c_71594,c_359]) ).
tcf(c_80568,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X2)
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18)
| ~ subset(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),X2) ),
inference(superposition,[status(thm)],[c_71594,c_358]) ).
tcf(c_80569,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(singleton(set_union2(X1,sK5(iPr_def_11))),X2) = sK5(iPr_def_11) )
| ~ epsilon_connected(set_union2(singleton(set_union2(X1,sK5(iPr_def_11))),X2))
| ~ in(set_union2(singleton(set_union2(X1,sK5(iPr_def_11))),X2),sK18)
| ~ in(X0,set_union2(singleton(set_union2(X1,sK5(iPr_def_11))),X2)) ),
inference(superposition,[status(thm)],[c_71594,c_77]) ).
tcf(c_80570,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ epsilon_transitive(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71594,c_65]) ).
tcf(c_80571,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18)
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_71594,c_49]) ).
tcf(c_80573,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71594,c_127]) ).
tcf(c_80574,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71594,c_4213]) ).
tcf(c_80575,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ~ in(X2,singleton(set_union2(X0,sK5(iPr_def_11))))
| ~ epsilon_connected(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71594,c_4212]) ).
tcf(c_80665,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X1,singleton(set_union2(sK5(iPr_def_11),X0))))
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_79936]) ).
tcf(c_80667,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),singleton(set_union2(sK5(iPr_def_11),X0))) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),singleton(set_union2(sK5(iPr_def_11),X0))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_79936]) ).
tcf(c_80668,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),empty_set) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),empty_set),sK18) ),
inference(superposition,[status(thm)],[c_126,c_79936]) ).
tcf(c_80669,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(singleton(set_union2(X0,sK5(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_79936]) ).
tcf(c_80672,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(singleton(sK5(iPr_def_11)),X0))
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),empty_set)),X0) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),empty_set)),X0),sK18) ),
inference(superposition,[status(thm)],[c_126,c_79936]) ).
tcf(c_80673,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79936,c_49877]) ).
tcf(c_80675,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ empty(X2)
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18)
| ~ subset(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),X2) ),
inference(superposition,[status(thm)],[c_79936,c_359]) ).
tcf(c_80676,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X2)
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18)
| ~ subset(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),X2) ),
inference(superposition,[status(thm)],[c_79936,c_358]) ).
tcf(c_80677,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X1)),X2) = sK5(iPr_def_11) )
| ~ epsilon_connected(set_union2(singleton(set_union2(sK5(iPr_def_11),X1)),X2))
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X1)),X2),sK18)
| ~ in(X0,set_union2(singleton(set_union2(sK5(iPr_def_11),X1)),X2)) ),
inference(superposition,[status(thm)],[c_79936,c_77]) ).
tcf(c_80678,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ epsilon_transitive(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79936,c_65]) ).
tcf(c_80679,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18)
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_79936,c_49]) ).
tcf(c_80681,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79936,c_127]) ).
tcf(c_80682,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79936,c_4213]) ).
tcf(c_80683,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ~ in(X2,singleton(set_union2(sK5(iPr_def_11),X0)))
| ~ epsilon_connected(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK5(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79936,c_4212]) ).
tcf(c_80773,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(singleton(set_union2(X1,sK5(iPr_def_11))),X0))
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_80355]) ).
tcf(c_80776,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(X0,sK5(iPr_def_11))))
| ( set_union2(empty_set,singleton(set_union2(X0,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(set_union2(empty_set,singleton(set_union2(X0,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_80355]) ).
tcf(c_80777,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_80355]) ).
tcf(c_80779,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,singleton(sK5(iPr_def_11))))
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_80355]) ).
tcf(c_80780,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,singleton(sK5(iPr_def_11))))
| ( set_union2(X0,singleton(set_union2(empty_set,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(empty_set,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_80355]) ).
tcf(c_80781,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80355,c_49877]) ).
tcf(c_80783,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ empty(X2)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18)
| ~ subset(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),X2) ),
inference(superposition,[status(thm)],[c_80355,c_359]) ).
tcf(c_80784,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X2)
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18)
| ~ subset(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),X2) ),
inference(superposition,[status(thm)],[c_80355,c_358]) ).
tcf(c_80785,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,singleton(set_union2(X2,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ epsilon_connected(set_union2(X1,singleton(set_union2(X2,sK5(iPr_def_11)))))
| ~ in(set_union2(X1,singleton(set_union2(X2,sK5(iPr_def_11)))),sK18)
| ~ in(X0,set_union2(X1,singleton(set_union2(X2,sK5(iPr_def_11))))) ),
inference(superposition,[status(thm)],[c_80355,c_77]) ).
tcf(c_80786,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80355,c_65]) ).
tcf(c_80787,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_80355,c_49]) ).
tcf(c_80789,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80355,c_127]) ).
tcf(c_80790,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(X2,singleton(set_union2(X1,sK5(iPr_def_11))))
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80355,c_4213]) ).
tcf(c_80791,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))) = sK5(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80355,c_4212]) ).
tcf(c_81005,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X1,singleton(set_union2(X0,sK3(iPr_def_11)))))
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_71604]) ).
tcf(c_81007,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),singleton(set_union2(X0,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),singleton(set_union2(X0,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_71604]) ).
tcf(c_81008,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),empty_set) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),empty_set),sK18) ),
inference(superposition,[status(thm)],[c_126,c_71604]) ).
tcf(c_81009,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_71604]) ).
tcf(c_81011,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(singleton(sK3(iPr_def_11)),X0))
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),sK3(iPr_def_11))),X0) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),sK3(iPr_def_11))),X0),sK18) ),
inference(superposition,[status(thm)],[c_97,c_71604]) ).
tcf(c_81012,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(singleton(sK3(iPr_def_11)),X0))
| ( set_union2(singleton(set_union2(empty_set,sK3(iPr_def_11))),X0) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(empty_set,sK3(iPr_def_11))),X0),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_71604]) ).
tcf(c_81014,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71604,c_7260]) ).
tcf(c_81015,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ empty(X2)
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18)
| ~ subset(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),X2) ),
inference(superposition,[status(thm)],[c_71604,c_359]) ).
tcf(c_81016,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X2)
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18)
| ~ subset(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),X2) ),
inference(superposition,[status(thm)],[c_71604,c_358]) ).
tcf(c_81017,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(singleton(set_union2(X1,sK3(iPr_def_11))),X2) = sK3(iPr_def_11) )
| ~ epsilon_connected(set_union2(singleton(set_union2(X1,sK3(iPr_def_11))),X2))
| ~ in(set_union2(singleton(set_union2(X1,sK3(iPr_def_11))),X2),sK18)
| ~ in(X0,set_union2(singleton(set_union2(X1,sK3(iPr_def_11))),X2)) ),
inference(superposition,[status(thm)],[c_71604,c_77]) ).
tcf(c_81018,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ epsilon_transitive(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71604,c_65]) ).
tcf(c_81019,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18)
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_71604,c_49]) ).
tcf(c_81021,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71604,c_127]) ).
tcf(c_81022,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71604,c_4213]) ).
tcf(c_81023,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1) = sK3(iPr_def_11) )
| ~ in(X2,singleton(set_union2(X0,sK3(iPr_def_11))))
| ~ epsilon_connected(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71604,c_4212]) ).
tcf(c_81127,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X1,singleton(set_union2(X0,sK4(iPr_def_11)))))
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_71611]) ).
tcf(c_81129,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),singleton(set_union2(X0,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),singleton(set_union2(X0,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_71611]) ).
tcf(c_81130,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),empty_set) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),empty_set),sK18) ),
inference(superposition,[status(thm)],[c_126,c_71611]) ).
tcf(c_81131,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_71611]) ).
tcf(c_81133,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(sK4(iPr_def_11)),X0))
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),sK4(iPr_def_11))),X0) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),sK4(iPr_def_11))),X0),sK18) ),
inference(superposition,[status(thm)],[c_97,c_71611]) ).
tcf(c_81134,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(sK4(iPr_def_11)),X0))
| ( set_union2(singleton(set_union2(empty_set,sK4(iPr_def_11))),X0) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(empty_set,sK4(iPr_def_11))),X0),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_71611]) ).
tcf(c_81136,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK5(iPr_def_11) )
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ epsilon_connected(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71611,c_7260]) ).
tcf(c_81137,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ empty(X2)
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18)
| ~ subset(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),X2) ),
inference(superposition,[status(thm)],[c_71611,c_359]) ).
tcf(c_81138,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X2)
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18)
| ~ subset(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),X2) ),
inference(superposition,[status(thm)],[c_71611,c_358]) ).
tcf(c_81139,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(singleton(set_union2(X1,sK4(iPr_def_11))),X2) = sK4(iPr_def_11) )
| ~ epsilon_connected(set_union2(singleton(set_union2(X1,sK4(iPr_def_11))),X2))
| ~ in(set_union2(singleton(set_union2(X1,sK4(iPr_def_11))),X2),sK18)
| ~ in(X0,set_union2(singleton(set_union2(X1,sK4(iPr_def_11))),X2)) ),
inference(superposition,[status(thm)],[c_71611,c_77]) ).
tcf(c_81140,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ epsilon_transitive(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71611,c_65]) ).
tcf(c_81141,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18)
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_71611,c_49]) ).
tcf(c_81143,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71611,c_127]) ).
tcf(c_81144,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71611,c_4213]) ).
tcf(c_81145,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ in(X2,singleton(set_union2(X0,sK4(iPr_def_11))))
| ~ epsilon_connected(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1))
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_71611,c_4212]) ).
tcf(c_81255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X3,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X3)
| in(sK2(X0,X1,X2),X3)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X3 )
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X3 )
| ( sK2(X0,X1,X2) = sK3(iPr_def_11) )
| ~ epsilon_connected(X1)
| ~ in(X3,X1)
| ~ epsilon_connected(sK2(X0,X1,X2))
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4341,c_49877]) ).
tcf(c_81256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X3,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X3)
| in(sK2(X0,X1,X2),X3)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X3 )
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X3 )
| ( sK2(X0,X1,X2) = sK5(iPr_def_11) )
| ~ epsilon_connected(X1)
| ~ in(X3,X1)
| ~ epsilon_connected(sK2(X0,X1,X2))
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4341,c_7260]) ).
tcf(c_81257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X4)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X4 )
| ~ epsilon_connected(X1)
| ~ empty(X3)
| ~ in(X4,X1)
| ~ subset(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_4341,c_359]) ).
tcf(c_81258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(X4,X3)
| in(sK2(X0,X1,X2),X4)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X4 )
| ~ epsilon_connected(X1)
| ~ in(X4,X1)
| ~ subset(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_4341,c_358]) ).
tcf(c_81259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X4,X0)
| in(X0,X4)
| in(sK2(X1,X2,X3),X4)
| in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X1)
| ( X0 = X4 )
| ( set_union2(X1,X2) = X3 )
| ( sK2(X1,X2,X3) = X4 )
| ~ epsilon_connected(X2)
| ~ in(X4,X2)
| ~ epsilon_connected(sK2(X1,X2,X3))
| ~ in(X0,sK2(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_4341,c_77]) ).
tcf(c_81260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X3)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X3 )
| ~ epsilon_connected(X1)
| ~ in(X3,X1)
| ~ epsilon_transitive(sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4341,c_65]) ).
tcf(c_81262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,X2),X3)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X3 )
| ~ epsilon_connected(X1)
| ~ in(X3,X1)
| ~ empty(sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4341,c_137]) ).
tcf(c_81263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X0,sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),X3)
| in(sK2(X2,X1,X3),X2)
| in(sK2(X2,X1,X3),X0)
| ( set_union2(X2,X1) = X3 )
| ( sK2(X2,X1,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_127]) ).
tcf(c_81264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK2(sK2(X0,X1,X2),X3,X4))
| ( set_union2(X0,X1) = X2 )
| ( set_union2(sK2(X0,X1,X2),X3) = X4 )
| ( sK2(sK2(X0,X1,X2),X3,X4) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X1)
| ~ in(sK2(sK2(X0,X1,X2),X3,X4),X4)
| ~ in(sK2(sK2(X0,X1,X2),X3,X4),X1) ),
inference(superposition,[status(thm)],[c_4341,c_66]) ).
tcf(c_81265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X4),X4)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X2,X3,X4),sK2(X0,X1,sK2(X2,X3,X4)))
| ( set_union2(X2,X3) = X4 )
| ( sK2(X2,X3,X4) = set_union2(X0,X1) )
| ( sK2(X0,X1,sK2(X2,X3,X4)) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X3)
| ~ in(sK2(X0,X1,sK2(X2,X3,X4)),X3)
| ~ in(sK2(X0,X1,sK2(X2,X3,X4)),X1) ),
inference(superposition,[status(thm)],[c_4341,c_67]) ).
tcf(c_81266,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),singleton(sK2(X0,X1,X2)))
| ( set_union2(X0,X1) = X2 )
| ( singleton(sK2(X0,X1,X2)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X1)
| ~ in(singleton(sK2(X0,X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_4341,c_3522]) ).
tcf(c_81267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),set_union2(X4,X3))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = set_union2(X4,X3) )
| ~ epsilon_connected(X1)
| ~ in(set_union2(X4,X3),X1)
| ~ in(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_4341,c_3641]) ).
tcf(c_81268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),set_union2(X3,X4))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = set_union2(X3,X4) )
| ~ epsilon_connected(X1)
| ~ in(set_union2(X3,X4),X1)
| ~ in(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_4341,c_3615]) ).
tcf(c_81269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),singleton(set_union2(sK2(X0,X1,X2),X3)))
| ( set_union2(X0,X1) = X2 )
| ( singleton(set_union2(sK2(X0,X1,X2),X3)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X1)
| ~ in(singleton(set_union2(sK2(X0,X1,X2),X3)),X1) ),
inference(superposition,[status(thm)],[c_4341,c_3618]) ).
tcf(c_81270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),singleton(set_union2(X0,sK2(X1,X2,X3))))
| ( set_union2(X1,X2) = X3 )
| ( singleton(set_union2(X0,sK2(X1,X2,X3))) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X2)
| ~ in(singleton(set_union2(X0,sK2(X1,X2,X3))),X2) ),
inference(superposition,[status(thm)],[c_4341,c_3644]) ).
tcf(c_81271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),singleton(set_union2(set_union2(sK2(X0,X1,X2),X3),X4)))
| ( set_union2(X0,X1) = X2 )
| ( singleton(set_union2(set_union2(sK2(X0,X1,X2),X3),X4)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X1)
| ~ in(singleton(set_union2(set_union2(sK2(X0,X1,X2),X3),X4)),X1) ),
inference(superposition,[status(thm)],[c_4341,c_3944]) ).
tcf(c_81272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),singleton(set_union2(set_union2(X0,sK2(X1,X2,X3)),X4)))
| ( set_union2(X1,X2) = X3 )
| ( singleton(set_union2(set_union2(X0,sK2(X1,X2,X3)),X4)) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X2)
| ~ in(singleton(set_union2(set_union2(X0,sK2(X1,X2,X3)),X4)),X2) ),
inference(superposition,[status(thm)],[c_4341,c_3945]) ).
tcf(c_81273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK2(set_union2(sK2(X0,X1,X2),X3),X4,X5))
| ( set_union2(X0,X1) = X2 )
| ( set_union2(set_union2(sK2(X0,X1,X2),X3),X4) = X5 )
| ( sK2(set_union2(sK2(X0,X1,X2),X3),X4,X5) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X1)
| ~ in(sK2(set_union2(sK2(X0,X1,X2),X3),X4,X5),X5)
| ~ in(sK2(set_union2(sK2(X0,X1,X2),X3),X4,X5),X1) ),
inference(superposition,[status(thm)],[c_4341,c_4078]) ).
tcf(c_81274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,X4,X5),X5)
| in(sK2(X3,X4,X5),X3)
| in(sK2(X3,X4,X5),sK2(set_union2(X0,X1),X2,sK2(X3,X4,X5)))
| ( set_union2(X3,X4) = X5 )
| ( set_union2(set_union2(X0,X1),X2) = sK2(X3,X4,X5) )
| ( sK2(set_union2(X0,X1),X2,sK2(X3,X4,X5)) = sK2(X3,X4,X5) )
| ~ epsilon_connected(X4)
| ~ in(sK2(set_union2(X0,X1),X2,sK2(X3,X4,X5)),X4)
| ~ in(sK2(set_union2(X0,X1),X2,sK2(X3,X4,X5)),X1) ),
inference(superposition,[status(thm)],[c_4341,c_4079]) ).
tcf(c_81275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,X3,X4),X4)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X2,X3,X4),sK2(X0,X1,set_union2(sK2(X2,X3,X4),X5)))
| ( set_union2(X2,X3) = X4 )
| ( set_union2(sK2(X2,X3,X4),X5) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK2(X2,X3,X4),X5)) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X3)
| ~ in(sK2(X0,X1,set_union2(sK2(X2,X3,X4),X5)),X3)
| ~ in(sK2(X0,X1,set_union2(sK2(X2,X3,X4),X5)),X1) ),
inference(superposition,[status(thm)],[c_4341,c_4095]) ).
tcf(c_81276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),sK2(X0,sK2(X1,X2,X3),set_union2(X4,X5)))
| ( set_union2(X1,X2) = X3 )
| ( set_union2(X0,sK2(X1,X2,X3)) = set_union2(X4,X5) )
| ( sK2(X0,sK2(X1,X2,X3),set_union2(X4,X5)) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X2)
| ~ in(sK2(X0,sK2(X1,X2,X3),set_union2(X4,X5)),X5)
| ~ in(sK2(X0,sK2(X1,X2,X3),set_union2(X4,X5)),X2) ),
inference(superposition,[status(thm)],[c_4341,c_4096]) ).
tcf(c_81277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),singleton(set_union2(X0,set_union2(sK2(X1,X2,X3),X4))))
| ( set_union2(X1,X2) = X3 )
| ( singleton(set_union2(X0,set_union2(sK2(X1,X2,X3),X4))) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X2)
| ~ in(singleton(set_union2(X0,set_union2(sK2(X1,X2,X3),X4))),X2) ),
inference(superposition,[status(thm)],[c_4341,c_4131]) ).
tcf(c_81278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X4),X4)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X2,X3,X4),singleton(set_union2(X0,set_union2(X1,sK2(X2,X3,X4)))))
| ( set_union2(X2,X3) = X4 )
| ( singleton(set_union2(X0,set_union2(X1,sK2(X2,X3,X4)))) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X3)
| ~ in(singleton(set_union2(X0,set_union2(X1,sK2(X2,X3,X4)))),X3) ),
inference(superposition,[status(thm)],[c_4341,c_4132]) ).
tcf(c_81279,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X1,X0),X2)
| in(sK2(X2,X1,X0),X1)
| in(sK2(X2,X1,X0),X0)
| ( set_union2(X2,X1) = X0 )
| ( sK2(X2,X1,X0) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_4331]) ).
tcf(c_81280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),singleton(set_union2(set_union2(set_union2(sK2(X0,X1,X2),X3),X4),X5)))
| ( set_union2(X0,X1) = X2 )
| ( singleton(set_union2(set_union2(set_union2(sK2(X0,X1,X2),X3),X4),X5)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X1)
| ~ in(singleton(set_union2(set_union2(set_union2(sK2(X0,X1,X2),X3),X4),X5)),X1) ),
inference(superposition,[status(thm)],[c_4341,c_5325]) ).
tcf(c_81281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),singleton(set_union2(set_union2(set_union2(X0,sK2(X1,X2,X3)),X4),X5)))
| ( set_union2(X1,X2) = X3 )
| ( singleton(set_union2(set_union2(set_union2(X0,sK2(X1,X2,X3)),X4),X5)) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X2)
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK2(X1,X2,X3)),X4),X5)),X2) ),
inference(superposition,[status(thm)],[c_4341,c_5326]) ).
tcf(c_81282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),singleton(set_union2(set_union2(X0,set_union2(sK2(X1,X2,X3),X4)),X5)))
| ( set_union2(X1,X2) = X3 )
| ( singleton(set_union2(set_union2(X0,set_union2(sK2(X1,X2,X3),X4)),X5)) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X2)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK2(X1,X2,X3),X4)),X5)),X2) ),
inference(superposition,[status(thm)],[c_4341,c_5547]) ).
tcf(c_81283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,X3,X4),X4)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X2,X3,X4),singleton(set_union2(set_union2(X0,set_union2(X1,sK2(X2,X3,X4))),X5)))
| ( set_union2(X2,X3) = X4 )
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK2(X2,X3,X4))),X5)) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X3)
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK2(X2,X3,X4))),X5)),X3) ),
inference(superposition,[status(thm)],[c_4341,c_5548]) ).
tcf(c_81284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),singleton(set_union2(X0,set_union2(set_union2(sK2(X1,X2,X3),X4),X5))))
| ( set_union2(X1,X2) = X3 )
| ( singleton(set_union2(X0,set_union2(set_union2(sK2(X1,X2,X3),X4),X5))) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X2)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK2(X1,X2,X3),X4),X5))),X2) ),
inference(superposition,[status(thm)],[c_4341,c_5584]) ).
tcf(c_81285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,X3,X4),X4)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X2,X3,X4),singleton(set_union2(X0,set_union2(set_union2(X1,sK2(X2,X3,X4)),X5))))
| ( set_union2(X2,X3) = X4 )
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK2(X2,X3,X4)),X5))) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X3)
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK2(X2,X3,X4)),X5))),X3) ),
inference(superposition,[status(thm)],[c_4341,c_5585]) ).
tcf(c_81286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,X3,X4),X4)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X2,X3,X4),singleton(set_union2(X0,set_union2(X1,set_union2(sK2(X2,X3,X4),X5)))))
| ( set_union2(X2,X3) = X4 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK2(X2,X3,X4),X5)))) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X3)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK2(X2,X3,X4),X5)))),X3) ),
inference(superposition,[status(thm)],[c_4341,c_5597]) ).
tcf(c_81287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,X4,X5),X5)
| in(sK2(X3,X4,X5),X3)
| in(sK2(X3,X4,X5),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK2(X3,X4,X5))))))
| ( set_union2(X3,X4) = X5 )
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK2(X3,X4,X5))))) = sK2(X3,X4,X5) )
| ~ epsilon_connected(X4)
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK2(X3,X4,X5))))),X4) ),
inference(superposition,[status(thm)],[c_4341,c_5598]) ).
tcf(c_81288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),set_union2(singleton(sK2(X0,X1,X2)),X3))
| ( set_union2(X0,X1) = X2 )
| ( set_union2(singleton(sK2(X0,X1,X2)),X3) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X1)
| ~ in(set_union2(singleton(sK2(X0,X1,X2)),X3),X1) ),
inference(superposition,[status(thm)],[c_4341,c_68451]) ).
tcf(c_81289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),set_union2(X0,singleton(sK2(X1,X2,X3))))
| ( set_union2(X1,X2) = X3 )
| ( set_union2(X0,singleton(sK2(X1,X2,X3))) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X2)
| ~ in(set_union2(X0,singleton(sK2(X1,X2,X3))),X2) ),
inference(superposition,[status(thm)],[c_4341,c_68561]) ).
tcf(c_81290,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK2(X1,X0,sK18),sK18)
| in(sK2(X1,X0,sK18),X1)
| in(sK2(X1,X0,sK18),X0)
| ( set_union2(X1,X0) = sK18 )
| ( sK2(X1,X0,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,X0) ),
inference(superposition,[status(thm)],[c_4341,c_53097]) ).
tcf(c_81291,plain,
! [X0: $i] :
( subset(sK2(X0,iPr_def_10,sK18),iPr_def_10)
| in(sK2(X0,iPr_def_10,sK18),iPr_def_11)
| in(sK2(X0,iPr_def_10,sK18),sK18)
| in(sK2(X0,iPr_def_10,sK18),X0)
| ( set_union2(X0,iPr_def_10) = sK18 )
| ( sK2(X0,iPr_def_10,sK18) = iPr_def_11 )
| ~ epsilon_connected(iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4341,c_53112]) ).
tcf(c_81292,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),iPr_def_10)
| in(sK2(X0,X1,sK18),sK18)
| in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_53130]) ).
tcf(c_81293,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_11)
| in(sK2(iPr_def_10,X0,sK18),iPr_def_10)
| in(sK2(iPr_def_10,X0,sK18),sK18)
| in(sK2(iPr_def_10,X0,sK18),X0)
| ( set_union2(iPr_def_10,X0) = sK18 )
| ( sK2(iPr_def_10,X0,sK18) = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_4341,c_53145]) ).
tcf(c_81294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),set_union2(singleton(set_union2(X0,sK2(X1,X2,X3))),X4))
| ( set_union2(X1,X2) = X3 )
| ( set_union2(singleton(set_union2(X0,sK2(X1,X2,X3))),X4) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X2)
| ~ in(set_union2(singleton(set_union2(X0,sK2(X1,X2,X3))),X4),X2) ),
inference(superposition,[status(thm)],[c_4341,c_68457]) ).
tcf(c_81295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),set_union2(singleton(set_union2(sK2(X0,X1,X2),X3)),X4))
| ( set_union2(X0,X1) = X2 )
| ( set_union2(singleton(set_union2(sK2(X0,X1,X2),X3)),X4) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X1)
| ~ in(set_union2(singleton(set_union2(sK2(X0,X1,X2),X3)),X4),X1) ),
inference(superposition,[status(thm)],[c_4341,c_68458]) ).
tcf(c_81296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X4),X4)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X2,X3,X4),set_union2(X0,singleton(set_union2(X1,sK2(X2,X3,X4)))))
| ( set_union2(X2,X3) = X4 )
| ( set_union2(X0,singleton(set_union2(X1,sK2(X2,X3,X4)))) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X3)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK2(X2,X3,X4)))),X3) ),
inference(superposition,[status(thm)],[c_4341,c_68567]) ).
tcf(c_81297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(X0,sK2(X3,X1,X2))
| in(sK2(X3,X1,X2),X3)
| in(sK2(X3,X1,X2),X0)
| in(sK3(iPr_def_11),sK2(X3,X1,X2))
| in(sK2(X3,X1,X2),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X3,X1) = X2 )
| ( sK2(X3,X1,X2) = X0 )
| ( sK2(X3,X1,X2) = sK3(iPr_def_11) )
| ~ epsilon_connected(X2)
| ~ epsilon_connected(X1)
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_49877]) ).
tcf(c_81298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(X0,sK2(X3,X1,X2))
| in(sK2(X3,X1,X2),X3)
| in(sK2(X3,X1,X2),X0)
| in(sK5(iPr_def_11),sK2(X3,X1,X2))
| in(sK2(X3,X1,X2),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X3,X1) = X2 )
| ( sK2(X3,X1,X2) = X0 )
| ( sK2(X3,X1,X2) = sK5(iPr_def_11) )
| ~ epsilon_connected(X2)
| ~ epsilon_connected(X1)
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_7260]) ).
tcf(c_81299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,sK2(X4,X1,X2))
| in(sK2(X4,X1,X2),X4)
| in(sK2(X4,X1,X2),X0)
| ( set_union2(X4,X1) = X2 )
| ( sK2(X4,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_359]) ).
tcf(c_81300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X1,X2),X3)
| in(X0,sK2(X4,X1,X2))
| in(sK2(X4,X1,X2),X4)
| in(sK2(X4,X1,X2),X0)
| ( set_union2(X4,X1) = X2 )
| ( sK2(X4,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ subset(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_358]) ).
tcf(c_81301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(X4,X1,X3))
| in(X0,sK2(X4,X1,X3))
| in(sK2(X4,X1,X3),X4)
| in(sK2(X4,X1,X3),X2)
| in(sK2(X4,X1,X3),X0)
| ( set_union2(X4,X1) = X3 )
| ( sK2(X4,X1,X3) = X2 )
| ( sK2(X4,X1,X3) = X0 )
| ~ epsilon_connected(X3)
| ~ epsilon_connected(X1)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_77]) ).
tcf(c_81303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),X3)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ( sK2(X1,X2,X0) = X3 )
| ~ epsilon_connected(X2)
| ~ in(X3,X2)
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_4341,c_49]) ).
tcf(c_81308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X3)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X3 )
| ~ epsilon_connected(X1)
| ~ in(X3,X1)
| ~ in(sK2(X0,X1,X2),X1) ),
inference(superposition,[status(thm)],[c_4341,c_67]) ).
tcf(c_81309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X4,sK2(X5,X3,set_union2(X0,X1)))
| in(X2,sK2(X5,X3,set_union2(X0,X1)))
| in(sK2(X5,X3,set_union2(X0,X1)),X5)
| in(sK2(X5,X3,set_union2(X0,X1)),X4)
| in(sK2(X5,X3,set_union2(X0,X1)),X2)
| ( set_union2(X0,X1) = set_union2(X5,X3) )
| ( sK2(X5,X3,set_union2(X0,X1)) = X4 )
| ( sK2(X5,X3,set_union2(X0,X1)) = X2 )
| ~ epsilon_connected(X3)
| ~ in(X4,X1)
| ~ in(X2,X3)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4341,c_4213]) ).
tcf(c_81310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X4,sK2(X5,X3,set_union2(X0,X1)))
| in(X2,sK2(X5,X3,set_union2(X0,X1)))
| in(sK2(X5,X3,set_union2(X0,X1)),X5)
| in(sK2(X5,X3,set_union2(X0,X1)),X4)
| in(sK2(X5,X3,set_union2(X0,X1)),X2)
| ( set_union2(X0,X1) = set_union2(X5,X3) )
| ( sK2(X5,X3,set_union2(X0,X1)) = X4 )
| ( sK2(X5,X3,set_union2(X0,X1)) = X2 )
| ~ epsilon_connected(X3)
| ~ in(X4,X0)
| ~ in(X2,X3)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4341,c_4212]) ).
tcf(c_81312,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X2,X1,empty_set))
| in(sK2(X2,X1,empty_set),X2)
| in(sK2(X2,X1,empty_set),X0)
| ( set_union2(X2,X1) = empty_set )
| ( sK2(X2,X1,empty_set) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_7097]) ).
tcf(c_81313,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X1,sK18),iPr_def_11)
| in(X0,sK2(X2,X1,sK18))
| in(sK2(X2,X1,sK18),X2)
| in(sK2(X2,X1,sK18),X0)
| ( set_union2(X2,X1) = sK18 )
| ( sK2(X2,X1,sK18) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_12813]) ).
tcf(c_81314,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(X0,X1,sK18))
| in(sK2(X0,X1,sK18),X2)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ( sK2(X0,X1,sK18) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ in(iPr_def_11,sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_4341,c_6841]) ).
tcf(c_81315,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X2,X1,sK18),iPr_def_11)
| in(X0,sK2(X2,X1,sK18))
| in(sK2(X2,X1,sK18),X2)
| in(sK2(X2,X1,sK18),X0)
| ( set_union2(X2,X1) = sK18 )
| ( sK2(X2,X1,sK18) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_5047]) ).
tcf(c_81317,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X1,iPr_def_10),iPr_def_11)
| in(X0,sK2(X2,X1,iPr_def_10))
| in(sK2(X2,X1,iPr_def_10),X2)
| in(sK2(X2,X1,iPr_def_10),X0)
| ( set_union2(X2,X1) = iPr_def_10 )
| ( sK2(X2,X1,iPr_def_10) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_9540]) ).
tcf(c_81318,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(X0,X1,iPr_def_10))
| in(sK2(X0,X1,iPr_def_10),X2)
| in(sK2(X0,X1,iPr_def_10),X0)
| ( set_union2(X0,X1) = iPr_def_10 )
| ( sK2(X0,X1,iPr_def_10) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ in(iPr_def_11,sK2(X0,X1,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4341,c_6289]) ).
tcf(c_81319,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X2,X1,iPr_def_10),iPr_def_11)
| in(X0,sK2(X2,X1,iPr_def_10))
| in(sK2(X2,X1,iPr_def_10),X2)
| in(sK2(X2,X1,iPr_def_10),X0)
| ( set_union2(X2,X1) = iPr_def_10 )
| ( sK2(X2,X1,iPr_def_10) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_4912]) ).
tcf(c_81320,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X2,X1,iPr_def_10))
| in(sK2(X2,X1,iPr_def_10),X2)
| in(sK2(X2,X1,iPr_def_10),X0)
| ( set_union2(X2,X1) = iPr_def_10 )
| ( sK2(X2,X1,iPr_def_10) = sK18 )
| ( sK2(X2,X1,iPr_def_10) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_3592]) ).
tcf(c_81322,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X1,iPr_def_11),sK18)
| in(X0,sK2(X2,X1,iPr_def_11))
| in(sK2(X2,X1,iPr_def_11),X2)
| in(sK2(X2,X1,iPr_def_11),X0)
| ( set_union2(X2,X1) = iPr_def_11 )
| ( sK2(X2,X1,iPr_def_11) = sK18 )
| ( sK2(X2,X1,iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_33457]) ).
tcf(c_81323,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X1,iPr_def_11),iPr_def_10)
| in(sK2(X2,X1,iPr_def_11),sK18)
| in(X0,sK2(X2,X1,iPr_def_11))
| in(sK2(X2,X1,iPr_def_11),X2)
| in(sK2(X2,X1,iPr_def_11),X0)
| ( set_union2(X2,X1) = iPr_def_11 )
| ( sK2(X2,X1,iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_4035]) ).
tcf(c_81324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(set_union2(X0,X1),X2,X0))
| in(sK2(set_union2(X0,X1),X2,X0),X3)
| in(sK2(set_union2(X0,X1),X2,X0),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = X0 )
| ( sK2(set_union2(X0,X1),X2,X0) = X3 )
| ~ epsilon_connected(X2)
| ~ in(X3,X2)
| ~ in(sK2(set_union2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_4341,c_4078]) ).
tcf(c_81325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X4,sK2(set_union2(X0,X1),X2,X3))
| in(sK2(set_union2(X0,X1),X2,X3),X4)
| in(sK2(set_union2(X0,X1),X2,X3),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = X3 )
| ( sK2(set_union2(X0,X1),X2,X3) = X4 )
| ~ epsilon_connected(X2)
| ~ in(X4,X2)
| ~ in(sK2(set_union2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_4341,c_4079]) ).
tcf(c_81326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(X0,set_union2(X1,X2),set_union2(X1,X2)))
| in(sK2(X0,set_union2(X1,X2),set_union2(X1,X2)),X3)
| in(sK2(X0,set_union2(X1,X2),set_union2(X1,X2)),X0)
| ( set_union2(X0,set_union2(X1,X2)) = set_union2(X1,X2) )
| ( sK2(X0,set_union2(X1,X2),set_union2(X1,X2)) = X3 )
| ~ epsilon_connected(set_union2(X1,X2))
| ~ in(X3,set_union2(X1,X2))
| ~ in(sK2(X0,set_union2(X1,X2),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4341,c_4096]) ).
tcf(c_81327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X2)
| in(X2,sK2(X3,X1,sK5(iPr_def_11)))
| in(X0,sK2(X3,X1,sK5(iPr_def_11)))
| in(sK2(X3,X1,sK5(iPr_def_11)),X3)
| in(sK2(X3,X1,sK5(iPr_def_11)),X2)
| in(sK2(X3,X1,sK5(iPr_def_11)),X0)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X3,X1) = sK5(iPr_def_11) )
| ( sK2(X3,X1,sK5(iPr_def_11)) = X2 )
| ( sK2(X3,X1,sK5(iPr_def_11)) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_7243]) ).
tcf(c_81328,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(X0,X1,sK5(iPr_def_11)))
| in(sK2(X0,X1,sK5(iPr_def_11)),X2)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( sK2(X0,X1,sK5(iPr_def_11)) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ subset(iPr_def_11,sK2(X0,X1,sK5(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_4341,c_23189]) ).
tcf(c_81329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X2)
| in(X2,sK2(X3,X1,sK3(iPr_def_11)))
| in(X0,sK2(X3,X1,sK3(iPr_def_11)))
| in(sK2(X3,X1,sK3(iPr_def_11)),X3)
| in(sK2(X3,X1,sK3(iPr_def_11)),X2)
| in(sK2(X3,X1,sK3(iPr_def_11)),X0)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X3,X1) = sK3(iPr_def_11) )
| ( sK2(X3,X1,sK3(iPr_def_11)) = X2 )
| ( sK2(X3,X1,sK3(iPr_def_11)) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_9906]) ).
tcf(c_81330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X2)
| in(X2,sK2(X3,X1,sK4(iPr_def_11)))
| in(X0,sK2(X3,X1,sK4(iPr_def_11)))
| in(sK2(X3,X1,sK4(iPr_def_11)),X3)
| in(sK2(X3,X1,sK4(iPr_def_11)),X2)
| in(sK2(X3,X1,sK4(iPr_def_11)),X0)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X3,X1) = sK4(iPr_def_11) )
| ( sK2(X3,X1,sK4(iPr_def_11)) = X2 )
| ( sK2(X3,X1,sK4(iPr_def_11)) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_45801]) ).
tcf(c_81332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(X0,sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),X3)
| in(sK2(X2,X1,X3),X0)
| in(sK3(iPr_def_11),sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X2,X1) = X3 )
| ( sK2(X2,X1,X3) = X0 )
| ( sK2(X2,X1,X3) = sK3(iPr_def_11) )
| ~ epsilon_connected(X2)
| ~ epsilon_connected(X1)
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_49877]) ).
tcf(c_81333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(X0,sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),X3)
| in(sK2(X2,X1,X3),X0)
| in(sK5(iPr_def_11),sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X2,X1) = X3 )
| ( sK2(X2,X1,X3) = X0 )
| ( sK2(X2,X1,X3) = sK5(iPr_def_11) )
| ~ epsilon_connected(X2)
| ~ epsilon_connected(X1)
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_7260]) ).
tcf(c_81334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,sK2(X2,X1,X4))
| in(sK2(X2,X1,X4),X4)
| in(sK2(X2,X1,X4),X0)
| ( set_union2(X2,X1) = X4 )
| ( sK2(X2,X1,X4) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_359]) ).
tcf(c_81335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,X1,X4),X3)
| in(X0,sK2(X2,X1,X4))
| in(sK2(X2,X1,X4),X4)
| in(sK2(X2,X1,X4),X0)
| ( set_union2(X2,X1) = X4 )
| ( sK2(X2,X1,X4) = X0 )
| ~ epsilon_connected(X1)
| ~ subset(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_358]) ).
tcf(c_81336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(X3,X1,X4))
| in(X0,sK2(X3,X1,X4))
| in(sK2(X3,X1,X4),X4)
| in(sK2(X3,X1,X4),X2)
| in(sK2(X3,X1,X4),X0)
| ( set_union2(X3,X1) = X4 )
| ( sK2(X3,X1,X4) = X2 )
| ( sK2(X3,X1,X4) = X0 )
| ~ epsilon_connected(X3)
| ~ epsilon_connected(X1)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_77]) ).
tcf(c_81337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X1,X3),X2)
| in(X0,sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),X3)
| in(sK2(X2,X1,X3),X0)
| ( set_union2(X2,X1) = X3 )
| ( sK2(X2,X1,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_65]) ).
tcf(c_81338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X3)
| in(sK2(X0,X1,X2),X2)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X3 )
| ~ epsilon_connected(X1)
| ~ in(X3,X1)
| ~ in(X0,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4341,c_49]) ).
tcf(c_81339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),X3)
| in(sK2(X2,X1,X3),X0)
| ( set_union2(X2,X1) = X3 )
| ( sK2(X2,X1,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_137]) ).
tcf(c_81340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X1,X3),X2)
| in(X0,sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),X3)
| in(sK2(X2,X1,X3),X0)
| ( set_union2(X2,X1) = X3 )
| ( sK2(X2,X1,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_127]) ).
tcf(c_81341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(singleton(X2),X1,X3))
| in(sK2(singleton(X2),X1,X3),X3)
| in(sK2(singleton(X2),X1,X3),X0)
| ( set_union2(singleton(X2),X1) = X3 )
| ( sK2(singleton(X2),X1,X3) = X2 )
| ( sK2(singleton(X2),X1,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_62]) ).
tcf(c_81344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X4,sK2(set_union2(X0,X1),X3,X5))
| in(X2,sK2(set_union2(X0,X1),X3,X5))
| in(sK2(set_union2(X0,X1),X3,X5),X5)
| in(sK2(set_union2(X0,X1),X3,X5),X4)
| in(sK2(set_union2(X0,X1),X3,X5),X2)
| ( set_union2(set_union2(X0,X1),X3) = X5 )
| ( sK2(set_union2(X0,X1),X3,X5) = X4 )
| ( sK2(set_union2(X0,X1),X3,X5) = X2 )
| ~ epsilon_connected(X3)
| ~ in(X4,X1)
| ~ in(X2,X3)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4341,c_4213]) ).
tcf(c_81345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X4,sK2(set_union2(X0,X1),X3,X5))
| in(X2,sK2(set_union2(X0,X1),X3,X5))
| in(sK2(set_union2(X0,X1),X3,X5),X5)
| in(sK2(set_union2(X0,X1),X3,X5),X4)
| in(sK2(set_union2(X0,X1),X3,X5),X2)
| ( set_union2(set_union2(X0,X1),X3) = X5 )
| ( sK2(set_union2(X0,X1),X3,X5) = X4 )
| ( sK2(set_union2(X0,X1),X3,X5) = X2 )
| ~ epsilon_connected(X3)
| ~ in(X4,X0)
| ~ in(X2,X3)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4341,c_4212]) ).
tcf(c_81346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,sK2(set_union2(X2,X3),X1,X4))
| in(sK2(set_union2(X2,X3),X1,X4),X4)
| in(sK2(set_union2(X2,X3),X1,X4),X3)
| in(sK2(set_union2(X2,X3),X1,X4),X2)
| in(sK2(set_union2(X2,X3),X1,X4),X0)
| ( set_union2(set_union2(X2,X3),X1) = X4 )
| ( sK2(set_union2(X2,X3),X1,X4) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_71]) ).
tcf(c_81347,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(empty_set,X1,X2))
| in(sK2(empty_set,X1,X2),X2)
| in(sK2(empty_set,X1,X2),X0)
| ( set_union2(empty_set,X1) = X2 )
| ( sK2(empty_set,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_7097]) ).
tcf(c_81348,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(sK18,X1,X2),iPr_def_11)
| in(X0,sK2(sK18,X1,X2))
| in(sK2(sK18,X1,X2),X2)
| in(sK2(sK18,X1,X2),X0)
| ( set_union2(sK18,X1) = X2 )
| ( sK2(sK18,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_12813]) ).
tcf(c_81349,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(sK18,X0,X1))
| in(sK2(sK18,X0,X1),X2)
| in(sK2(sK18,X0,X1),X1)
| ( set_union2(sK18,X0) = X1 )
| ( sK2(sK18,X0,X1) = X2 )
| ~ epsilon_connected(X0)
| ~ in(X2,X0)
| ~ in(iPr_def_11,sK2(sK18,X0,X1)) ),
inference(superposition,[status(thm)],[c_4341,c_6841]) ).
tcf(c_81350,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(sK18,X1,X2),iPr_def_11)
| in(X0,sK2(sK18,X1,X2))
| in(sK2(sK18,X1,X2),X2)
| in(sK2(sK18,X1,X2),X0)
| ( set_union2(sK18,X1) = X2 )
| ( sK2(sK18,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_5047]) ).
tcf(c_81351,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK18,X1,X2),iPr_def_11)
| in(X0,sK2(sK18,X1,X2))
| in(sK2(sK18,X1,X2),X2)
| in(sK2(sK18,X1,X2),X0)
| ( set_union2(sK18,X1) = X2 )
| ( sK2(sK18,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_3640]) ).
tcf(c_81352,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(iPr_def_10,X1,X2),iPr_def_11)
| in(X0,sK2(iPr_def_10,X1,X2))
| in(sK2(iPr_def_10,X1,X2),X2)
| in(sK2(iPr_def_10,X1,X2),X0)
| ( set_union2(iPr_def_10,X1) = X2 )
| ( sK2(iPr_def_10,X1,X2) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_9540]) ).
tcf(c_81353,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(iPr_def_10,X0,X1))
| in(sK2(iPr_def_10,X0,X1),X2)
| in(sK2(iPr_def_10,X0,X1),X1)
| ( set_union2(iPr_def_10,X0) = X1 )
| ( sK2(iPr_def_10,X0,X1) = X2 )
| ~ epsilon_connected(X0)
| ~ in(X2,X0)
| ~ in(iPr_def_11,sK2(iPr_def_10,X0,X1)) ),
inference(superposition,[status(thm)],[c_4341,c_6289]) ).
tcf(c_81354,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(iPr_def_10,X1,X2),iPr_def_11)
| in(X0,sK2(iPr_def_10,X1,X2))
| in(sK2(iPr_def_10,X1,X2),X2)
| in(sK2(iPr_def_10,X1,X2),X0)
| ( set_union2(iPr_def_10,X1) = X2 )
| ( sK2(iPr_def_10,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_4912]) ).
tcf(c_81355,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(iPr_def_10,X1,X2))
| in(sK2(iPr_def_10,X1,X2),X2)
| in(sK2(iPr_def_10,X1,X2),X0)
| ( set_union2(iPr_def_10,X1) = X2 )
| ( sK2(iPr_def_10,X1,X2) = sK18 )
| ( sK2(iPr_def_10,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_3592]) ).
tcf(c_81356,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(iPr_def_10,X1,X2),iPr_def_11)
| in(X0,sK2(iPr_def_10,X1,X2))
| in(sK2(iPr_def_10,X1,X2),X2)
| in(sK2(iPr_def_10,X1,X2),X0)
| ( set_union2(iPr_def_10,X1) = X2 )
| ( sK2(iPr_def_10,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_3614]) ).
tcf(c_81357,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(iPr_def_11,X1,X2),sK18)
| in(X0,sK2(iPr_def_11,X1,X2))
| in(sK2(iPr_def_11,X1,X2),X2)
| in(sK2(iPr_def_11,X1,X2),X0)
| ( set_union2(iPr_def_11,X1) = X2 )
| ( sK2(iPr_def_11,X1,X2) = sK18 )
| ( sK2(iPr_def_11,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_33457]) ).
tcf(c_81358,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(iPr_def_11,X1,X2),iPr_def_10)
| in(sK2(iPr_def_11,X1,X2),sK18)
| in(X0,sK2(iPr_def_11,X1,X2))
| in(sK2(iPr_def_11,X1,X2),X2)
| in(sK2(iPr_def_11,X1,X2),X0)
| ( set_union2(iPr_def_11,X1) = X2 )
| ( sK2(iPr_def_11,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_4035]) ).
tcf(c_81359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(set_union2(X0,X1),X2,set_union2(X0,X1)))
| in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X3)
| in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = set_union2(X0,X1) )
| ( sK2(set_union2(X0,X1),X2,set_union2(X0,X1)) = X3 )
| ~ epsilon_connected(X2)
| ~ in(X3,X2)
| ~ in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_4341,c_4079]) ).
tcf(c_81360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(X0,X1,set_union2(X0,X2)))
| in(sK2(X0,X1,set_union2(X0,X2)),X3)
| in(sK2(X0,X1,set_union2(X0,X2)),set_union2(X0,X2))
| ( set_union2(X0,X1) = set_union2(X0,X2) )
| ( sK2(X0,X1,set_union2(X0,X2)) = X3 )
| ~ epsilon_connected(X1)
| ~ in(X3,X1)
| ~ in(sK2(X0,X1,set_union2(X0,X2)),X1) ),
inference(superposition,[status(thm)],[c_4341,c_4095]) ).
tcf(c_81361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(X0,X0,set_union2(X1,X2)))
| in(sK2(X0,X0,set_union2(X1,X2)),X3)
| in(sK2(X0,X0,set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X0,X0) = set_union2(X1,X2) )
| ( sK2(X0,X0,set_union2(X1,X2)) = X3 )
| ~ epsilon_connected(X0)
| ~ in(X3,X0)
| ~ in(sK2(X0,X0,set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4341,c_4096]) ).
tcf(c_81362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X2)
| in(X2,sK2(sK5(iPr_def_11),X1,X3))
| in(X0,sK2(sK5(iPr_def_11),X1,X3))
| in(sK2(sK5(iPr_def_11),X1,X3),X3)
| in(sK2(sK5(iPr_def_11),X1,X3),X2)
| in(sK2(sK5(iPr_def_11),X1,X3),X0)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(sK5(iPr_def_11),X1) = X3 )
| ( sK2(sK5(iPr_def_11),X1,X3) = X2 )
| ( sK2(sK5(iPr_def_11),X1,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_7243]) ).
tcf(c_81363,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(sK5(iPr_def_11),X0,X1))
| in(sK2(sK5(iPr_def_11),X0,X1),X2)
| in(sK2(sK5(iPr_def_11),X0,X1),X1)
| ( set_union2(sK5(iPr_def_11),X0) = X1 )
| ( sK2(sK5(iPr_def_11),X0,X1) = X2 )
| ~ epsilon_connected(X0)
| ~ in(X2,X0)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,X1)) ),
inference(superposition,[status(thm)],[c_4341,c_23189]) ).
tcf(c_81364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X2)
| in(X2,sK2(sK3(iPr_def_11),X1,X3))
| in(X0,sK2(sK3(iPr_def_11),X1,X3))
| in(sK2(sK3(iPr_def_11),X1,X3),X3)
| in(sK2(sK3(iPr_def_11),X1,X3),X2)
| in(sK2(sK3(iPr_def_11),X1,X3),X0)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(sK3(iPr_def_11),X1) = X3 )
| ( sK2(sK3(iPr_def_11),X1,X3) = X2 )
| ( sK2(sK3(iPr_def_11),X1,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_9906]) ).
tcf(c_81365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X2)
| in(X2,sK2(sK4(iPr_def_11),X1,X3))
| in(X0,sK2(sK4(iPr_def_11),X1,X3))
| in(sK2(sK4(iPr_def_11),X1,X3),X3)
| in(sK2(sK4(iPr_def_11),X1,X3),X2)
| in(sK2(sK4(iPr_def_11),X1,X3),X0)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(sK4(iPr_def_11),X1) = X3 )
| ( sK2(sK4(iPr_def_11),X1,X3) = X2 )
| ( sK2(sK4(iPr_def_11),X1,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X2,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_45801]) ).
tcf(c_81366,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X1,sK18),iPr_def_10)
| in(sK2(sK18,X1,sK18),sK18)
| in(X0,sK2(sK18,X1,sK18))
| in(sK2(sK18,X1,sK18),X0)
| ( set_union2(sK18,X1) = sK18 )
| ( sK2(sK18,X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_66161]) ).
tcf(c_81367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(X0,sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),X3)
| in(sK2(X2,X1,X3),X2)
| in(sK3(iPr_def_11),sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X2,X1) = X3 )
| ( sK2(X2,X1,X3) = X0 )
| ( sK2(X2,X1,X3) = sK3(iPr_def_11) )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_49877]) ).
tcf(c_81368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(X0,sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),X3)
| in(sK2(X2,X1,X3),X2)
| in(sK5(iPr_def_11),sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X2,X1) = X3 )
| ( sK2(X2,X1,X3) = X0 )
| ( sK2(X2,X1,X3) = sK5(iPr_def_11) )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_7260]) ).
tcf(c_81369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,sK2(X3,X1,X4))
| in(sK2(X3,X1,X4),X4)
| in(sK2(X3,X1,X4),X3)
| ( set_union2(X3,X1) = X4 )
| ( sK2(X3,X1,X4) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(X2)
| ~ subset(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_359]) ).
tcf(c_81370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X1,X4),X2)
| in(X0,sK2(X3,X1,X4))
| in(sK2(X3,X1,X4),X4)
| in(sK2(X3,X1,X4),X3)
| ( set_union2(X3,X1) = X4 )
| ( sK2(X3,X1,X4) = X0 )
| ~ epsilon_connected(X1)
| ~ subset(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_358]) ).
tcf(c_81371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,sK2(X3,X1,X4))
| in(X0,sK2(X3,X1,X4))
| in(sK2(X3,X1,X4),X4)
| in(sK2(X3,X1,X4),X3)
| in(sK2(X3,X1,X4),X2)
| ( set_union2(X3,X1) = X4 )
| ( sK2(X3,X1,X4) = X2 )
| ( sK2(X3,X1,X4) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_connected(X0)
| ~ in(X2,X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_77]) ).
tcf(c_81372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X1,X3),X0)
| in(X0,sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),X3)
| in(sK2(X2,X1,X3),X2)
| ( set_union2(X2,X1) = X3 )
| ( sK2(X2,X1,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_65]) ).
tcf(c_81374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),X3)
| in(sK2(X2,X1,X3),X2)
| ( set_union2(X2,X1) = X3 )
| ( sK2(X2,X1,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ empty(X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_137]) ).
tcf(c_81375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X1,X3),X0)
| in(X0,sK2(X2,X1,X3))
| in(sK2(X2,X1,X3),X3)
| in(sK2(X2,X1,X3),X2)
| ( set_union2(X2,X1) = X3 )
| ( sK2(X2,X1,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4341,c_127]) ).
tcf(c_81376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X1,X3),X3)
| in(sK2(X2,X1,X3),X2)
| in(singleton(X0),sK2(X2,X1,X3))
| ( set_union2(X2,X1) = X3 )
| ( sK2(X2,X1,X3) = X0 )
| ( sK2(X2,X1,X3) = singleton(X0) )
| ~ epsilon_connected(X1)
| ~ in(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_4341,c_62]) ).
tcf(c_81379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X3,sK2(X4,X2,X5))
| in(sK2(X4,X2,X5),X5)
| in(sK2(X4,X2,X5),X4)
| in(sK2(X4,X2,X5),X3)
| in(set_union2(X0,X1),sK2(X4,X2,X5))
| ( set_union2(X4,X2) = X5 )
| ( sK2(X4,X2,X5) = X3 )
| ( sK2(X4,X2,X5) = set_union2(X0,X1) )
| ~ epsilon_connected(X2)
| ~ in(X3,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_4341,c_4213]) ).
tcf(c_81380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X3,sK2(X4,X2,X5))
| in(sK2(X4,X2,X5),X5)
| in(sK2(X4,X2,X5),X4)
| in(sK2(X4,X2,X5),X3)
| in(set_union2(X0,X1),sK2(X4,X2,X5))
| ( set_union2(X4,X2) = X5 )
| ( sK2(X4,X2,X5) = X3 )
| ( sK2(X4,X2,X5) = set_union2(X0,X1) )
| ~ epsilon_connected(X2)
| ~ in(X3,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_4341,c_4212]) ).
tcf(c_81381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X2,X4),X4)
| in(sK2(X3,X2,X4),X3)
| in(sK2(X3,X2,X4),X1)
| in(sK2(X3,X2,X4),X0)
| in(set_union2(X0,X1),sK2(X3,X2,X4))
| ( set_union2(X3,X2) = X4 )
| ( sK2(X3,X2,X4) = set_union2(X0,X1) )
| ~ epsilon_connected(X2)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_4341,c_71]) ).
tcf(c_81382,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(empty_set,sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = empty_set )
| ~ epsilon_connected(X0)
| ~ in(empty_set,X0) ),
inference(superposition,[status(thm)],[c_4341,c_7097]) ).
tcf(c_81383,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X0,X2),iPr_def_11)
| in(sK18,sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = sK18 )
| ~ epsilon_connected(X0)
| ~ in(sK18,X0) ),
inference(superposition,[status(thm)],[c_4341,c_12813]) ).
tcf(c_81384,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK18 )
| ~ epsilon_connected(X1)
| ~ in(sK18,X1)
| ~ in(iPr_def_11,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4341,c_6841]) ).
tcf(c_81385,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X0,X2),iPr_def_11)
| in(sK18,sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = sK18 )
| ~ epsilon_connected(X0)
| ~ in(sK18,X0) ),
inference(superposition,[status(thm)],[c_4341,c_5047]) ).
tcf(c_81386,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK18,sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),iPr_def_11)
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = sK18 )
| ~ epsilon_connected(X0)
| ~ in(sK18,X0) ),
inference(superposition,[status(thm)],[c_4341,c_3640]) ).
tcf(c_81387,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK1(sK2(X0,X1,X2)),sK2(X0,X1,X2))
| ( set_union2(X0,X1) = X2 )
| ( sK1(sK2(X0,X1,X2)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X1)
| ~ in(sK1(sK2(X0,X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_4341,c_3523]) ).
tcf(c_81388,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK3(sK2(X0,X1,X2)),sK2(X0,X1,X2))
| ( set_union2(X0,X1) = X2 )
| ( sK3(sK2(X0,X1,X2)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X1)
| ~ in(sK3(sK2(X0,X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_4341,c_3524]) ).
tcf(c_81389,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK4(sK2(X0,X1,X2)),sK2(X0,X1,X2))
| ( set_union2(X0,X1) = X2 )
| ( sK4(sK2(X0,X1,X2)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X1)
| ~ in(sK4(sK2(X0,X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_4341,c_3525]) ).
tcf(c_81390,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X0,X2),iPr_def_11)
| in(iPr_def_10,sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = iPr_def_10 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_connected(X0)
| ~ in(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4341,c_9540]) ).
tcf(c_81391,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(iPr_def_10,sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = iPr_def_10 )
| ~ epsilon_connected(X1)
| ~ in(iPr_def_10,X1)
| ~ in(iPr_def_11,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4341,c_6289]) ).
tcf(c_81392,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X0,X2),iPr_def_11)
| in(iPr_def_10,sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = iPr_def_10 )
| ~ epsilon_connected(X0)
| ~ in(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4341,c_4912]) ).
tcf(c_81393,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(iPr_def_10,sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = iPr_def_10 )
| ( sK2(X1,X0,X2) = sK18 )
| ~ epsilon_connected(X0)
| ~ in(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4341,c_3592]) ).
tcf(c_81394,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(iPr_def_10,sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),iPr_def_11)
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = iPr_def_10 )
| ~ epsilon_connected(X0)
| ~ in(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4341,c_3614]) ).
tcf(c_81395,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(iPr_def_11,sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),sK18)
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = iPr_def_11 )
| ( sK2(X1,X0,X2) = sK18 )
| ~ epsilon_connected(X0)
| ~ in(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_4341,c_33457]) ).
tcf(c_81396,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(iPr_def_11,sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),iPr_def_10)
| in(sK2(X1,X0,X2),sK18)
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = iPr_def_11 )
| ~ epsilon_connected(X0)
| ~ in(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_4341,c_4035]) ).
tcf(c_81397,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK5(sK2(X0,X1,X2)),sK2(X0,X1,X2))
| ( set_union2(X0,X1) = X2 )
| ( sK5(sK2(X0,X1,X2)) = sK2(X0,X1,X2) )
| ~ epsilon_connected(X1)
| ~ in(sK5(sK2(X0,X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_4341,c_3900]) ).
tcf(c_81400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,sK2(X0,X1,set_union2(X2,X3)))
| in(sK2(X0,X1,set_union2(X2,X3)),X0)
| in(sK2(X0,X1,set_union2(X2,X3)),set_union2(X2,X3))
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ( sK2(X0,X1,set_union2(X2,X3)) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ in(sK2(X0,X1,set_union2(X2,X3)),X1) ),
inference(superposition,[status(thm)],[c_4341,c_4095]) ).
tcf(c_81401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,sK2(X0,X1,set_union2(X2,X3)))
| in(sK2(X0,X1,set_union2(X2,X3)),X0)
| in(sK2(X0,X1,set_union2(X2,X3)),set_union2(X2,X3))
| ( set_union2(X0,X1) = set_union2(X2,X3) )
| ( sK2(X0,X1,set_union2(X2,X3)) = X1 )
| ~ epsilon_connected(X1)
| ~ in(X1,X1)
| ~ in(sK2(X0,X1,set_union2(X2,X3)),X3) ),
inference(superposition,[status(thm)],[c_4341,c_4096]) ).
tcf(c_81402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X4),X4)
| in(sK2(X2,X3,X4),X2)
| in(sK2(X0,X1,sK2(X2,X3,X4)),X1)
| in(sK2(X0,X1,sK2(X2,X3,X4)),X0)
| in(sK2(X0,X1,sK2(X2,X3,X4)),sK2(X2,X3,X4))
| ( set_union2(X2,X3) = X4 )
| ( sK2(X2,X3,X4) = set_union2(X0,X1) )
| ( sK2(X0,X1,sK2(X2,X3,X4)) = sK2(X2,X3,X4) )
| ~ epsilon_connected(X3)
| ~ in(sK2(X0,X1,sK2(X2,X3,X4)),X3) ),
inference(superposition,[status(thm)],[c_4341,c_4331]) ).
tcf(c_81403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X1)
| in(X1,sK2(X2,X0,X3))
| in(sK2(X2,X0,X3),X3)
| in(sK2(X2,X0,X3),X2)
| in(sK2(X2,X0,X3),X1)
| in(sK5(iPr_def_11),sK2(X2,X0,X3))
| ( sK5(iPr_def_11) = X1 )
| ( set_union2(X2,X0) = X3 )
| ( sK2(X2,X0,X3) = X1 )
| ( sK2(X2,X0,X3) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(sK5(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_4341,c_7243]) ).
tcf(c_81404,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK5(iPr_def_11),sK2(X0,X1,X2))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK5(iPr_def_11) )
| ~ epsilon_connected(X1)
| ~ in(sK5(iPr_def_11),X1)
| ~ subset(iPr_def_11,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4341,c_23189]) ).
tcf(c_81405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X1)
| in(X1,sK2(X2,X0,X3))
| in(sK2(X2,X0,X3),X3)
| in(sK2(X2,X0,X3),X2)
| in(sK2(X2,X0,X3),X1)
| in(sK3(iPr_def_11),sK2(X2,X0,X3))
| ( sK3(iPr_def_11) = X1 )
| ( set_union2(X2,X0) = X3 )
| ( sK2(X2,X0,X3) = X1 )
| ( sK2(X2,X0,X3) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_4341,c_9906]) ).
tcf(c_81406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(X1,sK2(X2,X0,X3))
| in(sK2(X2,X0,X3),X3)
| in(sK2(X2,X0,X3),X2)
| in(sK2(X2,X0,X3),X1)
| in(sK4(iPr_def_11),sK2(X2,X0,X3))
| ( sK4(iPr_def_11) = X1 )
| ( set_union2(X2,X0) = X3 )
| ( sK2(X2,X0,X3) = X1 )
| ( sK2(X2,X0,X3) = sK4(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_4341,c_45801]) ).
tcf(c_81407,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_10)
| in(sK18,sK2(X1,X0,sK18))
| in(sK2(X1,X0,sK18),sK18)
| in(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ( sK2(X1,X0,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(sK18,X0) ),
inference(superposition,[status(thm)],[c_4341,c_66161]) ).
tcf(c_81408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X1)
| subset(sK2(X0,sK2(X1,X2,X3),sK18),iPr_def_10)
| in(sK2(X0,sK2(X1,X2,X3),sK18),X0)
| in(sK2(X0,sK2(X1,X2,X3),sK18),sK2(X1,X2,X3))
| ( set_union2(X1,X2) = X3 )
| ( set_union2(X0,sK2(X1,X2,X3)) = sK18 )
| ( sK2(X0,sK2(X1,X2,X3),sK18) = sK2(X1,X2,X3) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X2)
| ~ in(sK2(X0,sK2(X1,X2,X3),sK18),X2) ),
inference(superposition,[status(thm)],[c_4341,c_53097]) ).
tcf(c_81409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| subset(sK2(sK2(X0,X1,X2),X3,sK18),iPr_def_10)
| in(sK2(sK2(X0,X1,X2),X3,sK18),X3)
| in(sK2(sK2(X0,X1,X2),X3,sK18),sK2(X0,X1,X2))
| ( set_union2(X0,X1) = X2 )
| ( set_union2(sK2(X0,X1,X2),X3) = sK18 )
| ( sK2(sK2(X0,X1,X2),X3,sK18) = sK2(X0,X1,X2) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(sK2(sK2(X0,X1,X2),X3,sK18),X1) ),
inference(superposition,[status(thm)],[c_4341,c_53130]) ).
tcf(c_81413,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X2,X1,X2))
| in(sK2(X2,X1,X2),X2)
| in(sK2(X2,X1,X2),X0)
| ( set_union2(X2,X1) = X2 )
| ( sK2(X2,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_4341]) ).
tcf(c_81416,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X2,X1,X0))
| in(sK2(X2,X1,X0),X2)
| in(sK2(X2,X1,X0),X0)
| ( set_union2(X2,X1) = X0 )
| ( sK2(X2,X1,X0) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_4341]) ).
tcf(c_81417,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_4341]) ).
tcf(c_82101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,sK2(X0,X0,set_union2(X1,X2)))
| in(sK2(X0,X0,set_union2(X1,X2)),X3)
| in(sK2(X0,X0,set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X1,X2) = X0 )
| ( sK2(X0,X0,set_union2(X1,X2)) = X3 )
| ~ epsilon_connected(X0)
| ~ in(X3,X0)
| ~ in(sK2(X0,X0,set_union2(X1,X2)),X2) ),
inference(light_normalisation,[status(thm)],[c_81361,c_97]) ).
tcf(c_82996,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X2,set_union2(X0,X1)))
| ~ subset(sK1(set_union2(set_union2(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_3863,c_30452]) ).
tcf(c_82997,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X2,set_union2(X0,X1)))
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ in(sK1(set_union2(set_union2(X0,X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_3806,c_30452]) ).
tcf(c_82998,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X2,set_union2(X0,X1)))
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ in(sK1(set_union2(set_union2(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_3805,c_30452]) ).
tcf(c_82999,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(set_union2(X2,set_union2(X0,X1)))
| ~ subset(sK1(set_union2(set_union2(X0,X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_3865,c_30452]) ).
tcf(c_83000,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| epsilon_transitive(set_union2(X0,sK5(iPr_def_11)))
| in(sK5(iPr_def_11),sK1(set_union2(sK5(iPr_def_11),X0)))
| ( sK1(set_union2(sK5(iPr_def_11),X0)) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK5(iPr_def_11))
| ~ in(sK1(set_union2(sK5(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_7244,c_30452]) ).
tcf(c_83001,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| epsilon_transitive(set_union2(X0,sK3(iPr_def_11)))
| in(sK3(iPr_def_11),sK1(set_union2(sK3(iPr_def_11),X0)))
| ( sK1(set_union2(sK3(iPr_def_11),X0)) = sK3(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11))
| ~ in(sK1(set_union2(sK3(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_9907,c_30452]) ).
tcf(c_83002,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| epsilon_transitive(set_union2(X0,sK4(iPr_def_11)))
| in(sK4(iPr_def_11),sK1(set_union2(sK4(iPr_def_11),X0)))
| ( sK1(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(sK1(set_union2(sK4(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_11191,c_30452]) ).
tcf(c_83008,plain,
( epsilon_transitive(set_union2(sK18,iPr_def_10))
| ~ subset(sK1(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3424,c_30452]) ).
tcf(c_83105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(X0,singleton(set_union2(set_union2(X1,X2),X3))),X1),
inference(superposition,[status(thm)],[c_69,c_68568]) ).
tcf(c_83106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ in(set_union2(X0,singleton(set_union2(set_union2(X1,X2),X3))),X2),
inference(superposition,[status(thm)],[c_70,c_68568]) ).
tcf(c_83107,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(X1))
| ~ subset(set_union2(X0,singleton(set_union2(powerset(X1),X2))),X1) ),
inference(superposition,[status(thm)],[c_3769,c_68568]) ).
tcf(c_83108,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK5(sK18),set_union2(X0,singleton(set_union2(sK5(sK18),X1))))
| ( set_union2(X0,singleton(set_union2(sK5(sK18),X1))) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(set_union2(X0,singleton(set_union2(sK5(sK18),X1))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_68568]) ).
tcf(c_83109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),set_union2(X0,singleton(set_union2(sK2(X1,X2,X3),X4))))
| ( set_union2(X1,X2) = X3 )
| ( set_union2(X0,singleton(set_union2(sK2(X1,X2,X3),X4))) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X3)
| ~ in(set_union2(X0,singleton(set_union2(sK2(X1,X2,X3),X4))),X3) ),
inference(superposition,[status(thm)],[c_4329,c_68568]) ).
tcf(c_83110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X1,X2,X3),set_union2(X0,singleton(set_union2(sK2(X1,X2,X3),X4))))
| ( set_union2(X1,X2) = X3 )
| ( set_union2(X0,singleton(set_union2(sK2(X1,X2,X3),X4))) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X2)
| ~ in(set_union2(X0,singleton(set_union2(sK2(X1,X2,X3),X4))),X2) ),
inference(superposition,[status(thm)],[c_4341,c_68568]) ).
tcf(c_83111,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_68568]) ).
tcf(c_83112,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_68568]) ).
tcf(c_83113,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_68568]) ).
tcf(c_83114,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_68568]) ).
tcf(c_83115,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ empty(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7263,c_68568]) ).
tcf(c_83116,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_68568]) ).
tcf(c_83117,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_68568]) ).
tcf(c_83118,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X1)))
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_7266,c_68568]) ).
tcf(c_83119,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),set_union2(X0,singleton(set_union2(sK1(iPr_def_11),X1))))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(sK1(iPr_def_11),X1))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(X0,singleton(set_union2(sK1(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_68568]) ).
tcf(c_83120,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK1(iPr_def_11),set_union2(X0,singleton(set_union2(sK1(iPr_def_11),X1))))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(sK1(iPr_def_11),X1))) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(X0,singleton(set_union2(sK1(iPr_def_11),X1))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_68568]) ).
tcf(c_83121,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_68568]) ).
tcf(c_83122,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_68568]) ).
tcf(c_83123,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_68568]) ).
tcf(c_83124,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_68568]) ).
tcf(c_83125,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ empty(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_9927,c_68568]) ).
tcf(c_83126,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_68568]) ).
tcf(c_83127,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_68568]) ).
tcf(c_83128,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X1)))
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_9930,c_68568]) ).
tcf(c_83129,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),X2)
| in(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_13646,c_68568]) ).
tcf(c_83130,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))))
| ( sK4(iPr_def_11) = sK18 )
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_11188,c_68568]) ).
tcf(c_83131,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_11185,c_68568]) ).
tcf(c_83132,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ empty(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_11211,c_68568]) ).
tcf(c_83133,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_11035,c_68568]) ).
tcf(c_83134,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X1)))
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_11214,c_68568]) ).
tcf(c_83356,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_68824,c_13665]) ).
tcf(c_83358,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ( sK5(iPr_def_11) = sK18 )
| ~ subset(X0,sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_68824,c_128]) ).
tcf(c_83360,plain,
! [X0: $i] :
( element(X0,iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_68824,c_13661]) ).
tcf(c_83422,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),iPr_def_11) ),
inference(global_subsumption_just,[status(thm)],[c_11007,c_63759]) ).
tcf(c_83423,plain,
( element(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(renaming,[status(thm)],[c_83422]) ).
tcf(c_83426,plain,
element(sK4(iPr_def_11),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_83423,c_4912]) ).
tcf(c_83427,plain,
( empty(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_11) ),
inference(superposition,[status(thm)],[c_83426,c_131]) ).
tcf(c_83428,plain,
in(sK4(iPr_def_11),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_83427,c_3417]) ).
tcf(c_83432,plain,
! [X0: $i] :
( element(sK4(iPr_def_11),X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_83428,c_358]) ).
tcf(c_83433,plain,
! [X0: $i] :
( in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_11)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_83428,c_77]) ).
tcf(c_83434,plain,
( subset(sK4(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(iPr_def_11) ),
inference(superposition,[status(thm)],[c_83428,c_65]) ).
tcf(c_83435,plain,
~ in(iPr_def_11,sK4(iPr_def_11)),
inference(superposition,[status(thm)],[c_83428,c_49]) ).
tcf(c_83438,plain,
( in(sK4(iPr_def_11),sK18)
| ( sK4(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_83428,c_33457]) ).
tcf(c_83439,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_83428,c_4035]) ).
tcf(c_83462,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(singleton(set_union2(sK5(iPr_def_11),X1)),X0))
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_83116]) ).
tcf(c_83465,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),singleton(set_union2(sK5(iPr_def_11),X0)))
| ( set_union2(empty_set,singleton(set_union2(sK5(iPr_def_11),X0))) = sK5(iPr_def_11) )
| ~ in(set_union2(empty_set,singleton(set_union2(sK5(iPr_def_11),X0))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_83116]) ).
tcf(c_83466,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK5(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_83116]) ).
tcf(c_83469,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),set_union2(X0,singleton(sK5(iPr_def_11))))
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),empty_set))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),empty_set))),sK18) ),
inference(superposition,[status(thm)],[c_126,c_83116]) ).
tcf(c_83470,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83116,c_49877]) ).
tcf(c_83472,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ empty(X2)
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18)
| ~ subset(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),X2) ),
inference(superposition,[status(thm)],[c_83116,c_359]) ).
tcf(c_83473,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X2)
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18)
| ~ subset(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),X2) ),
inference(superposition,[status(thm)],[c_83116,c_358]) ).
tcf(c_83474,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,singleton(set_union2(sK5(iPr_def_11),X2))) = sK5(iPr_def_11) )
| ~ epsilon_connected(set_union2(X1,singleton(set_union2(sK5(iPr_def_11),X2))))
| ~ in(set_union2(X1,singleton(set_union2(sK5(iPr_def_11),X2))),sK18)
| ~ in(X0,set_union2(X1,singleton(set_union2(sK5(iPr_def_11),X2)))) ),
inference(superposition,[status(thm)],[c_83116,c_77]) ).
tcf(c_83475,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ epsilon_transitive(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83116,c_65]) ).
tcf(c_83476,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18)
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_83116,c_49]) ).
tcf(c_83478,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83116,c_127]) ).
tcf(c_83479,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(X2,singleton(set_union2(sK5(iPr_def_11),X1)))
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83116,c_4213]) ).
tcf(c_83480,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK5(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83116,c_4212]) ).
tcf(c_83567,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X1,singleton(set_union2(sK3(iPr_def_11),X0))))
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_79946]) ).
tcf(c_83569,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),singleton(set_union2(sK3(iPr_def_11),X0))) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),singleton(set_union2(sK3(iPr_def_11),X0))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_79946]) ).
tcf(c_83570,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),empty_set) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),empty_set),sK18) ),
inference(superposition,[status(thm)],[c_126,c_79946]) ).
tcf(c_83571,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(X0,sK3(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_79946]) ).
tcf(c_83574,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(singleton(sK3(iPr_def_11)),X0))
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),empty_set)),X0) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),empty_set)),X0),sK18) ),
inference(superposition,[status(thm)],[c_126,c_79946]) ).
tcf(c_83576,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79946,c_7260]) ).
tcf(c_83577,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ empty(X2)
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18)
| ~ subset(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),X2) ),
inference(superposition,[status(thm)],[c_79946,c_359]) ).
tcf(c_83578,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X2)
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18)
| ~ subset(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),X2) ),
inference(superposition,[status(thm)],[c_79946,c_358]) ).
tcf(c_83579,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X1)),X2) = sK3(iPr_def_11) )
| ~ epsilon_connected(set_union2(singleton(set_union2(sK3(iPr_def_11),X1)),X2))
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X1)),X2),sK18)
| ~ in(X0,set_union2(singleton(set_union2(sK3(iPr_def_11),X1)),X2)) ),
inference(superposition,[status(thm)],[c_79946,c_77]) ).
tcf(c_83580,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ epsilon_transitive(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79946,c_65]) ).
tcf(c_83581,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18)
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_79946,c_49]) ).
tcf(c_83583,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79946,c_127]) ).
tcf(c_83584,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79946,c_4213]) ).
tcf(c_83585,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1) = sK3(iPr_def_11) )
| ~ in(X2,singleton(set_union2(sK3(iPr_def_11),X0)))
| ~ epsilon_connected(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK3(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79946,c_4212]) ).
tcf(c_83748,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X1,singleton(set_union2(sK4(iPr_def_11),X0))))
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_79953]) ).
tcf(c_83750,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),singleton(set_union2(sK4(iPr_def_11),X0))) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),singleton(set_union2(sK4(iPr_def_11),X0))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_79953]) ).
tcf(c_83751,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),empty_set) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),empty_set),sK18) ),
inference(superposition,[status(thm)],[c_126,c_79953]) ).
tcf(c_83752,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_58,c_79953]) ).
tcf(c_83755,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(sK4(iPr_def_11)),X0))
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),empty_set)),X0) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),empty_set)),X0),sK18) ),
inference(superposition,[status(thm)],[c_126,c_79953]) ).
tcf(c_83757,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK5(iPr_def_11) )
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ epsilon_connected(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79953,c_7260]) ).
tcf(c_83758,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ empty(X2)
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18)
| ~ subset(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),X2) ),
inference(superposition,[status(thm)],[c_79953,c_359]) ).
tcf(c_83759,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X2)
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18)
| ~ subset(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),X2) ),
inference(superposition,[status(thm)],[c_79953,c_358]) ).
tcf(c_83760,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X1)),X2) = sK4(iPr_def_11) )
| ~ epsilon_connected(set_union2(singleton(set_union2(sK4(iPr_def_11),X1)),X2))
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X1)),X2),sK18)
| ~ in(X0,set_union2(singleton(set_union2(sK4(iPr_def_11),X1)),X2)) ),
inference(superposition,[status(thm)],[c_79953,c_77]) ).
tcf(c_83761,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ epsilon_transitive(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79953,c_65]) ).
tcf(c_83762,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18)
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_79953,c_49]) ).
tcf(c_83764,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79953,c_127]) ).
tcf(c_83765,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79953,c_4213]) ).
tcf(c_83766,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ in(X2,singleton(set_union2(sK4(iPr_def_11),X0)))
| ~ epsilon_connected(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1))
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_79953,c_4212]) ).
tcf(c_83897,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(X1,sK3(iPr_def_11))),X0))
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_80365]) ).
tcf(c_83900,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(X0,sK3(iPr_def_11))))
| ( set_union2(empty_set,singleton(set_union2(X0,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(set_union2(empty_set,singleton(set_union2(X0,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_80365]) ).
tcf(c_83901,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_80365]) ).
tcf(c_83903,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,singleton(sK3(iPr_def_11))))
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_80365]) ).
tcf(c_83904,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,singleton(sK3(iPr_def_11))))
| ( set_union2(X0,singleton(set_union2(empty_set,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(empty_set,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_80365]) ).
tcf(c_83906,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK5(iPr_def_11) )
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80365,c_7260]) ).
tcf(c_83907,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ empty(X2)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18)
| ~ subset(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),X2) ),
inference(superposition,[status(thm)],[c_80365,c_359]) ).
tcf(c_83908,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X2)
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18)
| ~ subset(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),X2) ),
inference(superposition,[status(thm)],[c_80365,c_358]) ).
tcf(c_83909,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,singleton(set_union2(X2,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ epsilon_connected(set_union2(X1,singleton(set_union2(X2,sK3(iPr_def_11)))))
| ~ in(set_union2(X1,singleton(set_union2(X2,sK3(iPr_def_11)))),sK18)
| ~ in(X0,set_union2(X1,singleton(set_union2(X2,sK3(iPr_def_11))))) ),
inference(superposition,[status(thm)],[c_80365,c_77]) ).
tcf(c_83910,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80365,c_65]) ).
tcf(c_83911,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_80365,c_49]) ).
tcf(c_83913,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80365,c_127]) ).
tcf(c_83914,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(X2,singleton(set_union2(X1,sK3(iPr_def_11))))
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80365,c_4213]) ).
tcf(c_83915,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))) = sK3(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80365,c_4212]) ).
tcf(c_84036,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(set_union2(X1,sK4(iPr_def_11))),X0))
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_80372]) ).
tcf(c_84039,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( set_union2(empty_set,singleton(set_union2(X0,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(set_union2(empty_set,singleton(set_union2(X0,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_80372]) ).
tcf(c_84040,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_80372]) ).
tcf(c_84042,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,singleton(sK4(iPr_def_11))))
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_97,c_80372]) ).
tcf(c_84043,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,singleton(sK4(iPr_def_11))))
| ( set_union2(X0,singleton(set_union2(empty_set,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(empty_set,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_80372]) ).
tcf(c_84045,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK5(iPr_def_11) )
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80372,c_7260]) ).
tcf(c_84046,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ empty(X2)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18)
| ~ subset(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),X2) ),
inference(superposition,[status(thm)],[c_80372,c_359]) ).
tcf(c_84047,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X2)
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18)
| ~ subset(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),X2) ),
inference(superposition,[status(thm)],[c_80372,c_358]) ).
tcf(c_84048,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,singleton(set_union2(X2,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ epsilon_connected(set_union2(X1,singleton(set_union2(X2,sK4(iPr_def_11)))))
| ~ in(set_union2(X1,singleton(set_union2(X2,sK4(iPr_def_11)))),sK18)
| ~ in(X0,set_union2(X1,singleton(set_union2(X2,sK4(iPr_def_11))))) ),
inference(superposition,[status(thm)],[c_80372,c_77]) ).
tcf(c_84049,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80372,c_65]) ).
tcf(c_84050,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18)
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_80372,c_49]) ).
tcf(c_84052,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80372,c_127]) ).
tcf(c_84053,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(X2,singleton(set_union2(X1,sK4(iPr_def_11))))
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80372,c_4213]) ).
tcf(c_84054,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))))
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_80372,c_4212]) ).
tcf(c_84244,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(singleton(set_union2(sK3(iPr_def_11),X1)),X0))
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_83126]) ).
tcf(c_84247,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),singleton(set_union2(sK3(iPr_def_11),X0)))
| ( set_union2(empty_set,singleton(set_union2(sK3(iPr_def_11),X0))) = sK3(iPr_def_11) )
| ~ in(set_union2(empty_set,singleton(set_union2(sK3(iPr_def_11),X0))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_83126]) ).
tcf(c_84248,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK3(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_83126]) ).
tcf(c_84251,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),set_union2(X0,singleton(sK3(iPr_def_11))))
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),empty_set))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),empty_set))),sK18) ),
inference(superposition,[status(thm)],[c_126,c_83126]) ).
tcf(c_84253,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83126,c_7260]) ).
tcf(c_84254,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ empty(X2)
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18)
| ~ subset(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),X2) ),
inference(superposition,[status(thm)],[c_83126,c_359]) ).
tcf(c_84255,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X2)
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18)
| ~ subset(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),X2) ),
inference(superposition,[status(thm)],[c_83126,c_358]) ).
tcf(c_84256,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,singleton(set_union2(sK3(iPr_def_11),X2))) = sK3(iPr_def_11) )
| ~ epsilon_connected(set_union2(X1,singleton(set_union2(sK3(iPr_def_11),X2))))
| ~ in(set_union2(X1,singleton(set_union2(sK3(iPr_def_11),X2))),sK18)
| ~ in(X0,set_union2(X1,singleton(set_union2(sK3(iPr_def_11),X2)))) ),
inference(superposition,[status(thm)],[c_83126,c_77]) ).
tcf(c_84257,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ epsilon_transitive(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83126,c_65]) ).
tcf(c_84258,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18)
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_83126,c_49]) ).
tcf(c_84260,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83126,c_127]) ).
tcf(c_84261,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(X2,singleton(set_union2(sK3(iPr_def_11),X1)))
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83126,c_4213]) ).
tcf(c_84262,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))) = sK3(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK3(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83126,c_4212]) ).
tcf(c_84431,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(set_union2(sK4(iPr_def_11),X1)),X0))
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_83133]) ).
tcf(c_84434,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( set_union2(empty_set,singleton(set_union2(sK4(iPr_def_11),X0))) = sK4(iPr_def_11) )
| ~ in(set_union2(empty_set,singleton(set_union2(sK4(iPr_def_11),X0))),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_83133]) ).
tcf(c_84435,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_58,c_83133]) ).
tcf(c_84438,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,singleton(sK4(iPr_def_11))))
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),empty_set))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),empty_set))),sK18) ),
inference(superposition,[status(thm)],[c_126,c_83133]) ).
tcf(c_84440,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK5(iPr_def_11) )
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83133,c_7260]) ).
tcf(c_84441,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ empty(X2)
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18)
| ~ subset(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),X2) ),
inference(superposition,[status(thm)],[c_83133,c_359]) ).
tcf(c_84442,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X2)
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18)
| ~ subset(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),X2) ),
inference(superposition,[status(thm)],[c_83133,c_358]) ).
tcf(c_84443,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,singleton(set_union2(sK4(iPr_def_11),X2))) = sK4(iPr_def_11) )
| ~ epsilon_connected(set_union2(X1,singleton(set_union2(sK4(iPr_def_11),X2))))
| ~ in(set_union2(X1,singleton(set_union2(sK4(iPr_def_11),X2))),sK18)
| ~ in(X0,set_union2(X1,singleton(set_union2(sK4(iPr_def_11),X2)))) ),
inference(superposition,[status(thm)],[c_83133,c_77]) ).
tcf(c_84444,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ epsilon_transitive(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83133,c_65]) ).
tcf(c_84445,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18)
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_83133,c_49]) ).
tcf(c_84447,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83133,c_127]) ).
tcf(c_84448,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(X2,singleton(set_union2(sK4(iPr_def_11),X1)))
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83133,c_4213]) ).
tcf(c_84449,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))))
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_83133,c_4212]) ).
tcf(c_84647,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),X0,sK18),set_union2(X0,X1))
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(demodulation,[status(thm)],[c_53118,c_58]) ).
tcf(c_84669,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| in(sK2(set_union2(X1,X0),X0,sK18),set_union2(X1,X0))
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_58,c_84647]) ).
tcf(c_84671,plain,
! [X0: $i] :
( in(sK2(X0,X0,sK18),X0)
| subset(sK2(set_union2(X0,X0),X0,sK18),iPr_def_10)
| ( set_union2(X0,set_union2(X0,X0)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X0),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_97,c_84647]) ).
tcf(c_84672,plain,
! [X0: $i] :
( in(sK2(X0,X0,sK18),X0)
| subset(sK2(set_union2(X0,empty_set),X0,sK18),iPr_def_10)
| ( set_union2(X0,set_union2(X0,empty_set)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,empty_set),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_126,c_84647]) ).
tcf(c_84673,plain,
! [X0: $i] :
( in(sK2(X0,empty_set,sK18),X0)
| subset(sK2(set_union2(empty_set,X0),empty_set,sK18),iPr_def_10)
| ( set_union2(empty_set,set_union2(empty_set,X0)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(empty_set,X0),empty_set,sK18),sK18) ),
inference(superposition,[status(thm)],[c_3423,c_84647]) ).
tcf(c_84674,plain,
( in(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_11)
| subset(sK2(set_union2(iPr_def_10,sK18),iPr_def_10,sK18),iPr_def_10)
| ( set_union2(iPr_def_10,set_union2(iPr_def_10,sK18)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(iPr_def_10,sK18),iPr_def_10,sK18),sK18) ),
inference(superposition,[status(thm)],[c_3424,c_84647]) ).
tcf(c_84675,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(set_union2(X0,X1),sK3(iPr_def_11))
| subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| in(sK3(iPr_def_11),sK2(set_union2(X0,X1),X0,sK18))
| in(sK2(set_union2(X0,X1),X0,sK18),sK3(iPr_def_11))
| ( set_union2(X0,X1) = sK3(iPr_def_11) )
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ( sK2(set_union2(X0,X1),X0,sK18) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18)
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_84647,c_49877]) ).
tcf(c_84676,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(set_union2(X0,X1),sK5(iPr_def_11))
| subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| in(sK5(iPr_def_11),sK2(set_union2(X0,X1),X0,sK18))
| in(sK2(set_union2(X0,X1),X0,sK18),sK5(iPr_def_11))
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ( sK2(set_union2(X0,X1),X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18)
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_84647,c_7260]) ).
tcf(c_84677,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X2)
| ~ subset(set_union2(X0,X1),X2)
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_84647,c_359]) ).
tcf(c_84678,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| element(sK2(set_union2(X0,X1),X0,sK18),X2)
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(set_union2(X0,X1),X2)
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_84647,c_358]) ).
tcf(c_84679,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),X0,sK18))
| in(sK2(set_union2(X0,X1),X0,sK18),X2)
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ( sK2(set_union2(X0,X1),X0,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(X2,set_union2(X0,X1))
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_84647,c_77]) ).
tcf(c_84680,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| subset(sK2(set_union2(X0,X1),X0,sK18),set_union2(X0,X1))
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(set_union2(X0,X1))
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_84647,c_65]) ).
tcf(c_84681,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18)
| ~ in(set_union2(X0,X1),sK2(set_union2(X0,X1),X0,sK18)) ),
inference(superposition,[status(thm)],[c_84647,c_49]) ).
tcf(c_84682,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(set_union2(X0,X1))
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_84647,c_137]) ).
tcf(c_84683,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| element(sK2(set_union2(X0,X1),X0,sK18),set_union2(X0,X1))
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_84647,c_127]) ).
tcf(c_84684,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ( set_union2(set_union2(X0,X1),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_84647,c_66]) ).
tcf(c_84685,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),X0,sK18))
| in(sK2(set_union2(X0,X1),X0,sK18),X2)
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ( sK2(set_union2(X0,X1),X0,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_84647,c_4213]) ).
tcf(c_84686,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),X0,sK18))
| in(sK2(set_union2(X0,X1),X0,sK18),X2)
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ( sK2(set_union2(X0,X1),X0,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_84647,c_4212]) ).
tcf(c_84687,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),X0,sK18),iPr_def_10)
| in(sK2(set_union2(X0,X1),X0,sK18),X1)
| in(sK2(set_union2(X0,X1),X0,sK18),X0)
| ( set_union2(X0,set_union2(X0,X1)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_84647,c_71]) ).
tcf(c_84693,plain,
( subset(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_10)
| in(sK2(iPr_def_11,iPr_def_10,sK18),iPr_def_11)
| ( set_union2(iPr_def_10,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(iPr_def_11,iPr_def_10,sK18),sK18) ),
inference(light_normalisation,[status(thm)],[c_84674,c_3424]) ).
tcf(c_84918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| subset(sK2(sK2(X1,X0,X2),X3,sK18),iPr_def_10)
| in(sK2(sK2(X1,X0,X2),X3,sK18),X3)
| ( set_union2(X1,X0) = X2 )
| ( set_union2(sK2(X1,X0,X2),X3) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4342,c_53126]) ).
tcf(c_84919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X0,X3),X3)
| in(sK2(X2,X0,X3),X2)
| subset(sK2(X1,sK2(X2,X0,X3),sK18),iPr_def_10)
| in(sK2(X1,sK2(X2,X0,X3),sK18),X1)
| ( set_union2(X2,X0) = X3 )
| ( set_union2(X1,sK2(X2,X0,X3)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4342,c_53093]) ).
tcf(c_84920,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4342,c_24092]) ).
tcf(c_84921,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4342,c_24090]) ).
tcf(c_84922,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| ( set_union2(X1,X0) = X2 )
| ~ epsilon_transitive(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4342,c_24084]) ).
tcf(c_84923,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK4(iPr_def_11))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK4(iPr_def_11) )
| ~ epsilon_transitive(X1)
| ~ empty(X1)
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4342,c_24160]) ).
tcf(c_84924,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK3(iPr_def_11))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK3(iPr_def_11) )
| ~ epsilon_transitive(X1)
| ~ empty(X1)
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4342,c_24149]) ).
tcf(c_84925,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK5(iPr_def_11))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X1)
| ~ empty(X1)
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4342,c_24137]) ).
tcf(c_84926,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X1)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK4(iPr_def_11))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK4(iPr_def_11) )
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4342,c_13671]) ).
tcf(c_84927,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK3(iPr_def_11),X1)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK3(iPr_def_11))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK3(iPr_def_11) )
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4342,c_13665]) ).
tcf(c_84928,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X1)
| in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),sK5(iPr_def_11))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X1,X2),sK18) ),
inference(superposition,[status(thm)],[c_4342,c_13657]) ).
tcf(c_84929,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X2)
| in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X1)
| ( set_union2(X1,X2) = X3 )
| ~ epsilon_transitive(X2)
| ~ subset(X0,sK2(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_4342,c_128]) ).
tcf(c_84930,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(sK2(X1,powerset(X0),X2))
| in(sK2(X1,powerset(X0),X2),X2)
| in(sK2(X1,powerset(X0),X2),X1)
| subset(sK4(sK2(X1,powerset(X0),X2)),X0)
| ( set_union2(X1,powerset(X0)) = X2 )
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_4342,c_19404]) ).
tcf(c_84931,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(sK2(X1,powerset(X0),X2))
| in(sK2(X1,powerset(X0),X2),X2)
| in(sK2(X1,powerset(X0),X2),X1)
| subset(sK3(sK2(X1,powerset(X0),X2)),X0)
| ( set_union2(X1,powerset(X0)) = X2 )
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_4342,c_19389]) ).
tcf(c_84932,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(sK2(X1,powerset(X0),X2))
| in(sK2(X1,powerset(X0),X2),X2)
| in(sK2(X1,powerset(X0),X2),X1)
| subset(sK1(sK2(X1,powerset(X0),X2)),X0)
| ( set_union2(X1,powerset(X0)) = X2 )
| ~ epsilon_transitive(powerset(X0)) ),
inference(superposition,[status(thm)],[c_4342,c_18478]) ).
tcf(c_84933,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,empty_set,X1),X2)
| in(sK2(X0,empty_set,X1),X1)
| in(sK2(X0,empty_set,X1),X0)
| ( set_union2(X0,empty_set) = X1 )
| ~ epsilon_transitive(empty_set) ),
inference(superposition,[status(thm)],[c_4342,c_3866]) ).
tcf(c_84934,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,X1),iPr_def_10)
| in(sK2(X0,sK18,X1),X1)
| in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_4342,c_3931]) ).
tcf(c_84936,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,sK5(powerset(X0)),X2),X0)
| in(sK2(X1,sK5(powerset(X0)),X2),X2)
| in(sK2(X1,sK5(powerset(X0)),X2),X1)
| ( set_union2(X1,sK5(powerset(X0))) = X2 )
| ~ epsilon_transitive(sK5(powerset(X0))) ),
inference(superposition,[status(thm)],[c_4342,c_3864]) ).
tcf(c_84937,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,iPr_def_10,X1),iPr_def_11)
| in(sK2(X0,iPr_def_10,X1),X1)
| in(sK2(X0,iPr_def_10,X1),X0)
| ( set_union2(X0,iPr_def_10) = X1 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4342,c_3868]) ).
tcf(c_84938,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK5(powerset(sK18)),X1),iPr_def_11)
| in(sK2(X0,sK5(powerset(sK18)),X1),X1)
| in(sK2(X0,sK5(powerset(sK18)),X1),X0)
| ( set_union2(X0,sK5(powerset(sK18))) = X1 )
| ~ epsilon_transitive(sK5(powerset(sK18))) ),
inference(superposition,[status(thm)],[c_4342,c_4177]) ).
tcf(c_84939,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK5(powerset(iPr_def_10)),X1),iPr_def_11)
| in(sK2(X0,sK5(powerset(iPr_def_10)),X1),X1)
| in(sK2(X0,sK5(powerset(iPr_def_10)),X1),X0)
| ( set_union2(X0,sK5(powerset(iPr_def_10))) = X1 )
| ~ epsilon_transitive(sK5(powerset(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_4342,c_4574]) ).
tcf(c_84940,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,sK5(powerset(sK5(powerset(X0)))),X2),X0)
| in(sK2(X1,sK5(powerset(sK5(powerset(X0)))),X2),X2)
| in(sK2(X1,sK5(powerset(sK5(powerset(X0)))),X2),X1)
| ( set_union2(X1,sK5(powerset(sK5(powerset(X0))))) = X2 )
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_4342,c_5249]) ).
tcf(c_84941,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| subset(sK2(X0,sK5(sK18),X1),iPr_def_10)
| in(sK2(X0,sK5(sK18),X1),X1)
| in(sK2(X0,sK5(sK18),X1),X0)
| ( set_union2(X0,sK5(sK18)) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_4342,c_7217]) ).
tcf(c_84942,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| subset(sK2(X0,sK5(sK18),X1),iPr_def_11)
| in(sK2(X0,sK5(sK18),X1),X1)
| in(sK2(X0,sK5(sK18),X1),X0)
| ( set_union2(X0,sK5(sK18)) = X1 )
| ~ epsilon_transitive(sK5(sK18)) ),
inference(superposition,[status(thm)],[c_4342,c_5354]) ).
tcf(c_84943,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK5(powerset(sK5(powerset(sK18)))),X1),iPr_def_11)
| in(sK2(X0,sK5(powerset(sK5(powerset(sK18)))),X1),X1)
| in(sK2(X0,sK5(powerset(sK5(powerset(sK18)))),X1),X0)
| ( set_union2(X0,sK5(powerset(sK5(powerset(sK18))))) = X1 )
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK18))))) ),
inference(superposition,[status(thm)],[c_4342,c_5379]) ).
tcf(c_84944,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK5(powerset(sK5(powerset(iPr_def_10)))),X1),iPr_def_11)
| in(sK2(X0,sK5(powerset(sK5(powerset(iPr_def_10)))),X1),X1)
| in(sK2(X0,sK5(powerset(sK5(powerset(iPr_def_10)))),X1),X0)
| ( set_union2(X0,sK5(powerset(sK5(powerset(iPr_def_10))))) = X1 )
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(iPr_def_10))))) ),
inference(superposition,[status(thm)],[c_4342,c_5407]) ).
tcf(c_84945,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| subset(sK2(X0,sK5(powerset(sK5(sK18))),X1),iPr_def_11)
| in(sK2(X0,sK5(powerset(sK5(sK18))),X1),X1)
| in(sK2(X0,sK5(powerset(sK5(sK18))),X1),X0)
| ( set_union2(X0,sK5(powerset(sK5(sK18)))) = X1 )
| ~ epsilon_transitive(sK5(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_4342,c_5478]) ).
tcf(c_84946,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| subset(sK2(X0,sK5(powerset(sK5(powerset(sK5(sK18))))),X1),iPr_def_11)
| in(sK2(X0,sK5(powerset(sK5(powerset(sK5(sK18))))),X1),X1)
| in(sK2(X0,sK5(powerset(sK5(powerset(sK5(sK18))))),X1),X0)
| ( set_union2(X0,sK5(powerset(sK5(powerset(sK5(sK18)))))) = X1 )
| ~ epsilon_transitive(sK5(powerset(sK5(powerset(sK5(sK18)))))) ),
inference(superposition,[status(thm)],[c_4342,c_5491]) ).
tcf(c_84947,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| epsilon_transitive(powerset(sK5(sK18)))
| subset(sK2(X0,sK1(powerset(sK5(sK18))),X1),iPr_def_11)
| in(sK2(X0,sK1(powerset(sK5(sK18))),X1),X1)
| in(sK2(X0,sK1(powerset(sK5(sK18))),X1),X0)
| ( set_union2(X0,sK1(powerset(sK5(sK18)))) = X1 )
| ~ epsilon_transitive(sK1(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_4342,c_5502]) ).
tcf(c_84948,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK2(X0,sK3(powerset(sK5(sK18))),X1),iPr_def_11)
| in(sK2(X0,sK3(powerset(sK5(sK18))),X1),X1)
| in(sK2(X0,sK3(powerset(sK5(sK18))),X1),X0)
| ( set_union2(X0,sK3(powerset(sK5(sK18)))) = X1 )
| ~ epsilon_transitive(sK3(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_4342,c_5516]) ).
tcf(c_84949,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| epsilon_connected(powerset(sK5(sK18)))
| subset(sK2(X0,sK4(powerset(sK5(sK18))),X1),iPr_def_11)
| in(sK2(X0,sK4(powerset(sK5(sK18))),X1),X1)
| in(sK2(X0,sK4(powerset(sK5(sK18))),X1),X0)
| ( set_union2(X0,sK4(powerset(sK5(sK18)))) = X1 )
| ~ epsilon_transitive(sK4(powerset(sK5(sK18)))) ),
inference(superposition,[status(thm)],[c_4342,c_5528]) ).
tcf(c_84950,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK2(X0,sK3(sK5(sK18)),X1),iPr_def_11)
| in(sK2(X0,sK3(sK5(sK18)),X1),X1)
| in(sK2(X0,sK3(sK5(sK18)),X1),X0)
| ( set_union2(X0,sK3(sK5(sK18))) = X1 )
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK3(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_4342,c_5794]) ).
tcf(c_84951,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| epsilon_connected(sK5(sK18))
| subset(sK2(X0,sK4(sK5(sK18)),X1),iPr_def_11)
| in(sK2(X0,sK4(sK5(sK18)),X1),X1)
| in(sK2(X0,sK4(sK5(sK18)),X1),X0)
| ( set_union2(X0,sK4(sK5(sK18))) = X1 )
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK4(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_4342,c_5809]) ).
tcf(c_84952,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| empty(sK5(sK18))
| subset(sK2(X0,sK5(sK5(sK18)),X1),iPr_def_11)
| in(sK2(X0,sK5(sK5(sK18)),X1),X1)
| in(sK2(X0,sK5(sK5(sK18)),X1),X0)
| ( set_union2(X0,sK5(sK5(sK18))) = X1 )
| ~ epsilon_transitive(sK5(sK18))
| ~ epsilon_transitive(sK5(sK5(sK18))) ),
inference(superposition,[status(thm)],[c_4342,c_5824]) ).
tcf(c_84953,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK5(iPr_def_11),X1),sK18)
| in(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4342,c_68870]) ).
tcf(c_84954,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK5(iPr_def_11),X1),iPr_def_11)
| in(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4342,c_8544]) ).
tcf(c_84955,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK5(iPr_def_11),X1),iPr_def_11)
| in(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4342,c_7902]) ).
tcf(c_84956,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK5(iPr_def_11),X1),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4342,c_7570]) ).
tcf(c_84957,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK5(iPr_def_11),X1),sK18)
| in(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ~ epsilon_transitive(sK5(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4342,c_7199]) ).
tcf(c_84958,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK3(iPr_def_11),X1),sK18)
| in(sK2(X0,sK3(iPr_def_11),X1),X1)
| in(sK2(X0,sK3(iPr_def_11),X1),X0)
| ( set_union2(X0,sK3(iPr_def_11)) = X1 )
| ~ epsilon_transitive(sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4342,c_9862]) ).
tcf(c_84959,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK4(iPr_def_11),X1),sK18)
| in(sK2(X0,sK4(iPr_def_11),X1),X1)
| in(sK2(X0,sK4(iPr_def_11),X1),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = X1 )
| ~ epsilon_transitive(sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4342,c_11154]) ).
tcf(c_84960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| subset(sK2(X2,sK2(X0,X1,sK18),X3),iPr_def_10)
| in(sK2(X2,sK2(X0,X1,sK18),X3),X3)
| in(sK2(X2,sK2(X0,X1,sK18),X3),X2)
| ( set_union2(X0,X1) = sK18 )
| ( set_union2(X2,sK2(X0,X1,sK18)) = X3 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_4342,c_53089]) ).
tcf(c_84961,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X2,X1,X0),X1)
| in(sK2(X2,X1,X0),X2)
| in(sK3(iPr_def_11),sK2(X2,X1,X0))
| in(sK2(X2,X1,X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X2,X1) = X0 )
| ( sK2(X2,X1,X0) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4342,c_49877]) ).
tcf(c_84962,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X2,X1,X0),X1)
| in(sK2(X2,X1,X0),X2)
| in(sK5(iPr_def_11),sK2(X2,X1,X0))
| in(sK2(X2,X1,X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X2,X1) = X0 )
| ( sK2(X2,X1,X0) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4342,c_7260]) ).
tcf(c_84963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,X2,X0),X2)
| in(sK2(X3,X2,X0),X3)
| ( set_union2(X3,X2) = X0 )
| ~ epsilon_transitive(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4342,c_359]) ).
tcf(c_84964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X3,X2,X0),X1)
| subset(sK2(X3,X2,X0),X2)
| in(sK2(X3,X2,X0),X3)
| ( set_union2(X3,X2) = X0 )
| ~ epsilon_transitive(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4342,c_358]) ).
tcf(c_84966,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,X0,X1),X1)
| subset(sK2(X2,X0,X1),X0)
| in(sK2(X2,X0,X1),X2)
| ( set_union2(X2,X0) = X1 )
| ~ epsilon_transitive(X1)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_65]) ).
tcf(c_84967,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,X0),X1)
| ( set_union2(X1,X2) = X0 )
| ~ epsilon_transitive(X2)
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_4342,c_49]) ).
tcf(c_84972,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 )
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X1,X2),X1) ),
inference(superposition,[status(thm)],[c_4342,c_67]) ).
tcf(c_84973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(X4,X3,set_union2(X0,X1)),X3)
| in(X2,sK2(X4,X3,set_union2(X0,X1)))
| in(sK2(X4,X3,set_union2(X0,X1)),X4)
| in(sK2(X4,X3,set_union2(X0,X1)),X2)
| ( set_union2(X0,X1) = set_union2(X4,X3) )
| ( sK2(X4,X3,set_union2(X0,X1)) = X2 )
| ~ epsilon_transitive(X3)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4342,c_4213]) ).
tcf(c_84974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(X4,X3,set_union2(X0,X1)),X3)
| in(X2,sK2(X4,X3,set_union2(X0,X1)))
| in(sK2(X4,X3,set_union2(X0,X1)),X4)
| in(sK2(X4,X3,set_union2(X0,X1)),X2)
| ( set_union2(X0,X1) = set_union2(X4,X3) )
| ( sK2(X4,X3,set_union2(X0,X1)) = X2 )
| ~ epsilon_transitive(X3)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4342,c_4212]) ).
tcf(c_84976,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,empty_set),X0)
| in(sK2(X1,X0,empty_set),X1)
| ( set_union2(X1,X0) = empty_set )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_7097]) ).
tcf(c_84977,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,sK18),iPr_def_11)
| subset(sK2(X1,X0,sK18),X0)
| in(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_12813]) ).
tcf(c_84978,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK18),X1)
| in(sK2(X0,X1,sK18),X0)
| ( set_union2(X0,X1) = sK18 )
| ~ epsilon_transitive(X1)
| ~ in(iPr_def_11,sK2(X0,X1,sK18)) ),
inference(superposition,[status(thm)],[c_4342,c_6841]) ).
tcf(c_84979,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,X0,sK18),iPr_def_11)
| subset(sK2(X1,X0,sK18),X0)
| in(sK2(X1,X0,sK18),X1)
| ( set_union2(X1,X0) = sK18 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_5047]) ).
tcf(c_84981,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,iPr_def_10),iPr_def_11)
| subset(sK2(X1,X0,iPr_def_10),X0)
| in(sK2(X1,X0,iPr_def_10),X1)
| ( set_union2(X1,X0) = iPr_def_10 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_9540]) ).
tcf(c_84982,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,iPr_def_10),X1)
| in(sK2(X0,X1,iPr_def_10),X0)
| ( set_union2(X0,X1) = iPr_def_10 )
| ~ epsilon_transitive(X1)
| ~ in(iPr_def_11,sK2(X0,X1,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4342,c_6289]) ).
tcf(c_84983,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,X0,iPr_def_10),iPr_def_11)
| subset(sK2(X1,X0,iPr_def_10),X0)
| in(sK2(X1,X0,iPr_def_10),X1)
| ( set_union2(X1,X0) = iPr_def_10 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_4912]) ).
tcf(c_84984,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,iPr_def_10),X0)
| in(sK2(X1,X0,iPr_def_10),X1)
| ( set_union2(X1,X0) = iPr_def_10 )
| ( sK2(X1,X0,iPr_def_10) = sK18 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_3592]) ).
tcf(c_84986,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,iPr_def_11),sK18)
| subset(sK2(X1,X0,iPr_def_11),X0)
| in(sK2(X1,X0,iPr_def_11),X1)
| ( set_union2(X1,X0) = iPr_def_11 )
| ( sK2(X1,X0,iPr_def_11) = sK18 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_33457]) ).
tcf(c_84987,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,iPr_def_11),iPr_def_10)
| in(sK2(X1,X0,iPr_def_11),sK18)
| subset(sK2(X1,X0,iPr_def_11),X0)
| in(sK2(X1,X0,iPr_def_11),X1)
| ( set_union2(X1,X0) = iPr_def_11 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_4035]) ).
tcf(c_84988,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),X2,X0),X2)
| in(sK2(set_union2(X0,X1),X2,X0),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = X0 )
| ~ epsilon_transitive(X2)
| ~ in(sK2(set_union2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_4342,c_4078]) ).
tcf(c_84989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X0,X1),X2,X3),X2)
| in(sK2(set_union2(X0,X1),X2,X3),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = X3 )
| ~ epsilon_transitive(X2)
| ~ in(sK2(set_union2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_4342,c_4079]) ).
tcf(c_84990,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_union2(X1,X2),set_union2(X1,X2)),X0)
| subset(sK2(X0,set_union2(X1,X2),set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X0,set_union2(X1,X2)) = set_union2(X1,X2) )
| ~ epsilon_transitive(set_union2(X1,X2))
| ~ in(sK2(X0,set_union2(X1,X2),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4342,c_4096]) ).
tcf(c_84991,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(X2,X1,sK5(iPr_def_11)),X1)
| in(X0,sK2(X2,X1,sK5(iPr_def_11)))
| in(sK2(X2,X1,sK5(iPr_def_11)),X2)
| in(sK2(X2,X1,sK5(iPr_def_11)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X2,X1) = sK5(iPr_def_11) )
| ( sK2(X2,X1,sK5(iPr_def_11)) = X0 )
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4342,c_7243]) ).
tcf(c_84992,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK5(iPr_def_11)),X1)
| in(sK2(X0,X1,sK5(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK5(iPr_def_11) )
| ~ epsilon_transitive(X1)
| ~ subset(iPr_def_11,sK2(X0,X1,sK5(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_4342,c_23189]) ).
tcf(c_84993,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(X2,X1,sK3(iPr_def_11)),X1)
| in(X0,sK2(X2,X1,sK3(iPr_def_11)))
| in(sK2(X2,X1,sK3(iPr_def_11)),X2)
| in(sK2(X2,X1,sK3(iPr_def_11)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X2,X1) = sK3(iPr_def_11) )
| ( sK2(X2,X1,sK3(iPr_def_11)) = X0 )
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4342,c_9906]) ).
tcf(c_84994,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(X2,X1,sK4(iPr_def_11)),X1)
| in(X0,sK2(X2,X1,sK4(iPr_def_11)))
| in(sK2(X2,X1,sK4(iPr_def_11)),X2)
| in(sK2(X2,X1,sK4(iPr_def_11)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X2,X1) = sK4(iPr_def_11) )
| ( sK2(X2,X1,sK4(iPr_def_11)) = X0 )
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4342,c_45801]) ).
tcf(c_84996,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2)
| in(sK3(iPr_def_11),sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK3(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4342,c_49877]) ).
tcf(c_84997,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2)
| in(sK5(iPr_def_11),sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4342,c_7260]) ).
tcf(c_84998,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X0,X2,X3),X2)
| in(sK2(X0,X2,X3),X3)
| ( set_union2(X0,X2) = X3 )
| ~ epsilon_transitive(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4342,c_359]) ).
tcf(c_84999,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X2,X3),X1)
| subset(sK2(X0,X2,X3),X2)
| in(sK2(X0,X2,X3),X3)
| ( set_union2(X0,X2) = X3 )
| ~ epsilon_transitive(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4342,c_358]) ).
tcf(c_85000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X1,X2,X3),X2)
| in(X0,sK2(X1,X2,X3))
| in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X0)
| ( set_union2(X1,X2) = X3 )
| ( sK2(X1,X2,X3) = X0 )
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4342,c_77]) ).
tcf(c_85001,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X0,X2),X1)
| subset(sK2(X1,X0,X2),X0)
| in(sK2(X1,X0,X2),X2)
| ( set_union2(X1,X0) = X2 )
| ~ epsilon_transitive(X1)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_65]) ).
tcf(c_85002,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2)
| ( set_union2(X0,X1) = X2 )
| ~ epsilon_transitive(X1)
| ~ in(X0,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4342,c_49]) ).
tcf(c_85003,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2)
| ( set_union2(X0,X1) = X2 )
| ~ epsilon_transitive(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4342,c_137]) ).
tcf(c_85004,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X0,X2),X1)
| subset(sK2(X1,X0,X2),X0)
| in(sK2(X1,X0,X2),X2)
| ( set_union2(X1,X0) = X2 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_127]) ).
tcf(c_85005,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(singleton(X1),X0,X2),X0)
| in(sK2(singleton(X1),X0,X2),X2)
| ( set_union2(singleton(X1),X0) = X2 )
| ( sK2(singleton(X1),X0,X2) = X1 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_62]) ).
tcf(c_85008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(set_union2(X0,X1),X3,X4),X3)
| in(X2,sK2(set_union2(X0,X1),X3,X4))
| in(sK2(set_union2(X0,X1),X3,X4),X4)
| in(sK2(set_union2(X0,X1),X3,X4),X2)
| ( set_union2(set_union2(X0,X1),X3) = X4 )
| ( sK2(set_union2(X0,X1),X3,X4) = X2 )
| ~ epsilon_transitive(X3)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4342,c_4213]) ).
tcf(c_85009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(set_union2(X0,X1),X3,X4),X3)
| in(X2,sK2(set_union2(X0,X1),X3,X4))
| in(sK2(set_union2(X0,X1),X3,X4),X4)
| in(sK2(set_union2(X0,X1),X3,X4),X2)
| ( set_union2(set_union2(X0,X1),X3) = X4 )
| ( sK2(set_union2(X0,X1),X3,X4) = X2 )
| ~ epsilon_transitive(X3)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_4342,c_4212]) ).
tcf(c_85010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X1,X2),X0,X3),X0)
| in(sK2(set_union2(X1,X2),X0,X3),X3)
| in(sK2(set_union2(X1,X2),X0,X3),X2)
| in(sK2(set_union2(X1,X2),X0,X3),X1)
| ( set_union2(set_union2(X1,X2),X0) = X3 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_71]) ).
tcf(c_85011,plain,
! [X0: $i,X1: $i] :
( subset(sK2(empty_set,X0,X1),X0)
| in(sK2(empty_set,X0,X1),X1)
| ( set_union2(empty_set,X0) = X1 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_7097]) ).
tcf(c_85012,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,X1),iPr_def_11)
| subset(sK2(sK18,X0,X1),X0)
| in(sK2(sK18,X0,X1),X1)
| ( set_union2(sK18,X0) = X1 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_12813]) ).
tcf(c_85013,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,X0,X1),X0)
| in(sK2(sK18,X0,X1),X1)
| ( set_union2(sK18,X0) = X1 )
| ~ epsilon_transitive(X0)
| ~ in(iPr_def_11,sK2(sK18,X0,X1)) ),
inference(superposition,[status(thm)],[c_4342,c_6841]) ).
tcf(c_85014,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK18,X0,X1),iPr_def_11)
| subset(sK2(sK18,X0,X1),X0)
| in(sK2(sK18,X0,X1),X1)
| ( set_union2(sK18,X0) = X1 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_5047]) ).
tcf(c_85015,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK18,X0,X1),iPr_def_11)
| subset(sK2(sK18,X0,X1),X0)
| in(sK2(sK18,X0,X1),X1)
| ( set_union2(sK18,X0) = X1 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_3640]) ).
tcf(c_85016,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X0,X1),iPr_def_11)
| subset(sK2(iPr_def_10,X0,X1),X0)
| in(sK2(iPr_def_10,X0,X1),X1)
| ( set_union2(iPr_def_10,X0) = X1 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_9540]) ).
tcf(c_85017,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X0,X1),X0)
| in(sK2(iPr_def_10,X0,X1),X1)
| ( set_union2(iPr_def_10,X0) = X1 )
| ~ epsilon_transitive(X0)
| ~ in(iPr_def_11,sK2(iPr_def_10,X0,X1)) ),
inference(superposition,[status(thm)],[c_4342,c_6289]) ).
tcf(c_85018,plain,
! [X0: $i,X1: $i] :
( element(sK2(iPr_def_10,X0,X1),iPr_def_11)
| subset(sK2(iPr_def_10,X0,X1),X0)
| in(sK2(iPr_def_10,X0,X1),X1)
| ( set_union2(iPr_def_10,X0) = X1 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_4912]) ).
tcf(c_85019,plain,
! [X0: $i,X1: $i] :
( subset(sK2(iPr_def_10,X0,X1),X0)
| in(sK2(iPr_def_10,X0,X1),X1)
| ( set_union2(iPr_def_10,X0) = X1 )
| ( sK2(iPr_def_10,X0,X1) = sK18 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_3592]) ).
tcf(c_85020,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_10,X0,X1),iPr_def_11)
| subset(sK2(iPr_def_10,X0,X1),X0)
| in(sK2(iPr_def_10,X0,X1),X1)
| ( set_union2(iPr_def_10,X0) = X1 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_3614]) ).
tcf(c_85021,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_11,X0,X1),sK18)
| subset(sK2(iPr_def_11,X0,X1),X0)
| in(sK2(iPr_def_11,X0,X1),X1)
| ( set_union2(iPr_def_11,X0) = X1 )
| ( sK2(iPr_def_11,X0,X1) = sK18 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_33457]) ).
tcf(c_85022,plain,
! [X0: $i,X1: $i] :
( in(sK2(iPr_def_11,X0,X1),iPr_def_10)
| in(sK2(iPr_def_11,X0,X1),sK18)
| subset(sK2(iPr_def_11,X0,X1),X0)
| in(sK2(iPr_def_11,X0,X1),X1)
| ( set_union2(iPr_def_11,X0) = X1 )
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_4035]) ).
tcf(c_85023,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X2)
| in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),X2) = set_union2(X0,X1) )
| ~ epsilon_transitive(X2)
| ~ in(sK2(set_union2(X0,X1),X2,set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_4342,c_4079]) ).
tcf(c_85024,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,set_union2(X0,X2)),X1)
| in(sK2(X0,X1,set_union2(X0,X2)),set_union2(X0,X2))
| ( set_union2(X0,X1) = set_union2(X0,X2) )
| ~ epsilon_transitive(X1)
| ~ in(sK2(X0,X1,set_union2(X0,X2)),X1) ),
inference(superposition,[status(thm)],[c_4342,c_4095]) ).
tcf(c_85025,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X0,set_union2(X1,X2)),X0)
| in(sK2(X0,X0,set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X0,X0) = set_union2(X1,X2) )
| ~ epsilon_transitive(X0)
| ~ in(sK2(X0,X0,set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4342,c_4096]) ).
tcf(c_85026,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK5(iPr_def_11),X1,X2),X1)
| in(X0,sK2(sK5(iPr_def_11),X1,X2))
| in(sK2(sK5(iPr_def_11),X1,X2),X2)
| in(sK2(sK5(iPr_def_11),X1,X2),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),X1) = X2 )
| ( sK2(sK5(iPr_def_11),X1,X2) = X0 )
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4342,c_7243]) ).
tcf(c_85027,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK5(iPr_def_11),X0,X1),X0)
| in(sK2(sK5(iPr_def_11),X0,X1),X1)
| ( set_union2(sK5(iPr_def_11),X0) = X1 )
| ~ epsilon_transitive(X0)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),X0,X1)) ),
inference(superposition,[status(thm)],[c_4342,c_23189]) ).
tcf(c_85028,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK3(iPr_def_11),X1,X2),X1)
| in(X0,sK2(sK3(iPr_def_11),X1,X2))
| in(sK2(sK3(iPr_def_11),X1,X2),X2)
| in(sK2(sK3(iPr_def_11),X1,X2),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),X1) = X2 )
| ( sK2(sK3(iPr_def_11),X1,X2) = X0 )
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4342,c_9906]) ).
tcf(c_85029,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK4(iPr_def_11),X1,X2),X1)
| in(X0,sK2(sK4(iPr_def_11),X1,X2))
| in(sK2(sK4(iPr_def_11),X1,X2),X2)
| in(sK2(sK4(iPr_def_11),X1,X2),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),X1) = X2 )
| ( sK2(sK4(iPr_def_11),X1,X2) = X0 )
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_4342,c_45801]) ).
tcf(c_85030,plain,
! [X0: $i] :
( subset(sK2(sK18,X0,sK18),iPr_def_10)
| in(sK2(sK18,X0,sK18),sK18)
| subset(sK2(sK18,X0,sK18),X0)
| ( set_union2(sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_4342,c_66161]) ).
tcf(c_85031,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,X0,X1),X0)
| in(sK2(X1,X0,X1),X1)
| ( set_union2(X1,X0) = X1 )
| ~ epsilon_transitive(X0) ),
inference(equality_factoring,[status(thm)],[c_4342]) ).
tcf(c_85037,plain,
! [X0: $i,X1: $i] :
( subset(sK2(empty_set,X0,X1),X0)
| in(sK2(empty_set,X0,X1),X1)
| ( X0 = X1 )
| ~ epsilon_transitive(X0) ),
inference(light_normalisation,[status(thm)],[c_85011,c_3423]) ).
tcf(c_85101,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,empty_set,X1),X2)
| in(sK2(X0,empty_set,X1),X1)
| in(sK2(X0,empty_set,X1),X0)
| ( X0 = X1 )
| ~ epsilon_transitive(empty_set) ),
inference(light_normalisation,[status(thm)],[c_84933,c_126]) ).
tcf(c_85213,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,X1),iPr_def_10)
| in(sK2(X0,sK18,X1),X1)
| in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_84934,c_2426]) ).
tcf(c_85334,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X0,set_union2(X1,X2)),X0)
| in(sK2(X0,X0,set_union2(X1,X2)),set_union2(X1,X2))
| ( set_union2(X1,X2) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(sK2(X0,X0,set_union2(X1,X2)),X2) ),
inference(light_normalisation,[status(thm)],[c_85025,c_97]) ).
tcf(c_85991,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_83434,c_13665]) ).
tcf(c_85992,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_83434,c_13657]) ).
tcf(c_85993,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| ~ epsilon_transitive(iPr_def_11)
| ~ subset(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_83434,c_128]) ).
tcf(c_86020,plain,
( epsilon_connected(iPr_def_11)
| in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_33470,c_7260]) ).
tcf(c_86021,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| ( sK3(iPr_def_11) = sK18 )
| ~ empty(X0)
| ~ subset(sK18,X0) ),
inference(superposition,[status(thm)],[c_33470,c_359]) ).
tcf(c_86022,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ~ subset(sK18,X0) ),
inference(superposition,[status(thm)],[c_33470,c_358]) ).
tcf(c_86023,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_33470,c_77]) ).
tcf(c_86024,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),sK18)
| ( sK3(iPr_def_11) = sK18 )
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_33470,c_65]) ).
tcf(c_86025,plain,
( epsilon_connected(iPr_def_11)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(sK18,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_33470,c_49]) ).
tcf(c_86027,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),sK18)
| ( sK3(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_33470,c_127]) ).
tcf(c_86028,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_11)
| ( sK3(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_33470,c_12813]) ).
tcf(c_86029,plain,
( epsilon_connected(iPr_def_11)
| ( sK3(iPr_def_11) = sK18 )
| ~ in(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_33470,c_6841]) ).
tcf(c_86030,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_11)
| ( sK3(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_33470,c_5047]) ).
tcf(c_86031,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_11)
| ( sK3(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_33470,c_3640]) ).
tcf(c_86032,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 ) ),
inference(superposition,[status(thm)],[c_33470,c_11771]) ).
tcf(c_86054,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),sK18)
| ( sK3(iPr_def_11) = sK18 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86024,c_2426]) ).
tcf(c_86083,plain,
! [X0: $i] :
( empty(X0)
| in(sK4(iPr_def_11),X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_83432,c_131]) ).
tcf(c_86084,plain,
! [X0: $i] :
( subset(sK4(iPr_def_11),X0)
| ~ subset(iPr_def_11,powerset(X0)) ),
inference(superposition,[status(thm)],[c_83432,c_133]) ).
tcf(c_86095,plain,
( in(sK18,sK3(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_83439,c_49877]) ).
tcf(c_86096,plain,
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK18)
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_83439,c_7260]) ).
tcf(c_86097,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| ~ empty(X0)
| ~ subset(sK18,X0) ),
inference(superposition,[status(thm)],[c_83439,c_359]) ).
tcf(c_86098,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| ~ subset(sK18,X0) ),
inference(superposition,[status(thm)],[c_83439,c_358]) ).
tcf(c_86099,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_83439,c_77]) ).
tcf(c_86100,plain,
( subset(sK4(iPr_def_11),sK18)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_83439,c_65]) ).
tcf(c_86103,plain,
( element(sK4(iPr_def_11),sK18)
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_83439,c_127]) ).
tcf(c_86104,plain,
( subset(sK4(iPr_def_11),iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_83439,c_12813]) ).
tcf(c_86113,plain,
( subset(sK4(iPr_def_11),sK18)
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86100,c_2426]) ).
tcf(c_86122,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86099,c_2427]) ).
tcf(c_86128,plain,
( in(sK18,sK5(iPr_def_11))
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86096,c_2427]) ).
tcf(c_86137,plain,
( in(sK18,sK3(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86095,c_2427]) ).
tcf(c_86167,plain,
( element(sK5(iPr_def_11),iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_86104,c_13657]) ).
tcf(c_86168,plain,
! [X0: $i] :
( subset(X0,iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ subset(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_86104,c_128]) ).
tcf(c_86178,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK4(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_86113,c_53126]) ).
tcf(c_86179,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK4(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_86113,c_53093]) ).
tcf(c_86185,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_86113,c_24137]) ).
tcf(c_86189,plain,
! [X0: $i] :
( subset(X0,sK18)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ subset(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_86113,c_128]) ).
tcf(c_86190,plain,
( subset(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_86113,c_3931]) ).
tcf(c_86226,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK2(sK3(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK3(iPr_def_11),X0,sK18),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(sK3(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_86054,c_53126]) ).
tcf(c_86227,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(sK2(X0,sK3(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK3(iPr_def_11),sK18),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(X0,sK3(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(sK18) ),
inference(superposition,[status(thm)],[c_86054,c_53093]) ).
tcf(c_86231,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ empty(sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_86054,c_24160]) ).
tcf(c_86233,plain,
( epsilon_connected(iPr_def_11)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK18)
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_86054,c_24137]) ).
tcf(c_86237,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| subset(X0,sK18)
| ( sK3(iPr_def_11) = sK18 )
| ~ subset(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_86054,c_128]) ).
tcf(c_86238,plain,
( epsilon_connected(iPr_def_11)
| subset(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_86054,c_3931]) ).
tcf(c_86240,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ empty(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86054,c_24154]) ).
tcf(c_86241,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(X0,sK18)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86054,c_13668]) ).
tcf(c_86400,plain,
! [X0: $i,X1: $i] :
( in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_359]) ).
tcf(c_86401,plain,
! [X0: $i,X1: $i] :
( element(sK4(iPr_def_11),X1)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ subset(iPr_def_10,X1)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_358]) ).
tcf(c_86402,plain,
! [X0: $i,X1: $i] :
( in(X1,sK4(iPr_def_11))
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X1,iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_77]) ).
tcf(c_86403,plain,
! [X0: $i] :
( subset(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_65]) ).
tcf(c_86404,plain,
! [X0: $i] :
( in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ in(iPr_def_10,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_86122,c_49]) ).
tcf(c_86406,plain,
! [X0: $i] :
( element(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_127]) ).
tcf(c_86407,plain,
! [X0: $i] :
( subset(sK4(iPr_def_11),iPr_def_11)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_9540]) ).
tcf(c_86410,plain,
! [X0: $i] :
( in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_3592]) ).
tcf(c_86412,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_49877]) ).
tcf(c_86414,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ~ empty(X0)
| ~ in(X1,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_86122,c_359]) ).
tcf(c_86415,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| ( sK4(iPr_def_11) = X1 )
| ~ in(X1,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_86122,c_358]) ).
tcf(c_86417,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| subset(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_65]) ).
tcf(c_86419,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ empty(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_137]) ).
tcf(c_86420,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| element(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_127]) ).
tcf(c_86421,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(sK4(iPr_def_11),X0,X1))
| ( set_union2(sK4(iPr_def_11),X0) = X1 )
| ( sK2(sK4(iPr_def_11),X0,X1) = sK4(iPr_def_11) )
| ~ in(sK2(sK4(iPr_def_11),X0,X1),sK18)
| ~ in(sK2(sK4(iPr_def_11),X0,X1),X1) ),
inference(superposition,[status(thm)],[c_86122,c_66]) ).
tcf(c_86422,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(X0,X1,sK4(iPr_def_11)))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ( sK2(X0,X1,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),sK18)
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_86122,c_67]) ).
tcf(c_86424,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(sK4(iPr_def_11)))
| ( singleton(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(singleton(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_3522]) ).
tcf(c_86426,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),X1)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_3641]) ).
tcf(c_86427,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,X1))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(sK4(iPr_def_11),X0)
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_3615]) ).
tcf(c_86428,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(sK4(iPr_def_11),X0)))
| ( singleton(set_union2(sK4(iPr_def_11),X0)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(sK4(iPr_def_11),X0)),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_3618]) ).
tcf(c_86429,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,sK4(iPr_def_11))))
| ( singleton(set_union2(X0,sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_3644]) ).
tcf(c_86430,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)))
| ( singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(sK4(iPr_def_11),X0),X1)),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_3944]) ).
tcf(c_86431,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)))
| ( singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,sK4(iPr_def_11)),X1)),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_3945]) ).
tcf(c_86432,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(set_union2(sK4(iPr_def_11),X0),X1,X2))
| ( set_union2(set_union2(sK4(iPr_def_11),X0),X1) = X2 )
| ( sK2(set_union2(sK4(iPr_def_11),X0),X1,X2) = sK4(iPr_def_11) )
| ~ in(sK2(set_union2(sK4(iPr_def_11),X0),X1,X2),sK18)
| ~ in(sK2(set_union2(sK4(iPr_def_11),X0),X1,X2),X2) ),
inference(superposition,[status(thm)],[c_86122,c_4078]) ).
tcf(c_86433,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)))
| ( set_union2(set_union2(X0,X1),X2) = sK4(iPr_def_11) )
| ( sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)),sK18)
| ~ in(sK2(set_union2(X0,X1),X2,sK4(iPr_def_11)),X1) ),
inference(superposition,[status(thm)],[c_86122,c_4079]) ).
tcf(c_86434,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)))
| ( set_union2(sK4(iPr_def_11),X2) = set_union2(X0,X1) )
| ( sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),sK18)
| ~ in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),X1) ),
inference(superposition,[status(thm)],[c_86122,c_4095]) ).
tcf(c_86435,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)))
| ( set_union2(X0,sK4(iPr_def_11)) = set_union2(X1,X2) )
| ( sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),sK18)
| ~ in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_86122,c_4096]) ).
tcf(c_86436,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))))
| ( singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_4131]) ).
tcf(c_86437,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))))
| ( singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_4132]) ).
tcf(c_86438,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(sK4(iPr_def_11),X0),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_5325]) ).
tcf(c_86439,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)))
| ( singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(set_union2(X0,sK4(iPr_def_11)),X1),X2)),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_5326]) ).
tcf(c_86440,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(sK4(iPr_def_11),X1)),X2)),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_5547]) ).
tcf(c_86441,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)))
| ( singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(set_union2(X0,set_union2(X1,sK4(iPr_def_11))),X2)),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_5548]) ).
tcf(c_86442,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(sK4(iPr_def_11),X1),X2))),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_5584]) ).
tcf(c_86443,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))))
| ( singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(set_union2(X1,sK4(iPr_def_11)),X2))),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_5585]) ).
tcf(c_86444,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(sK4(iPr_def_11),X2)))),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_5597]) ).
tcf(c_86445,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))))
| ( singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))) = sK4(iPr_def_11) )
| ~ in(singleton(set_union2(X0,set_union2(X1,set_union2(X2,sK4(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_5598]) ).
tcf(c_86446,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(sK4(iPr_def_11)),X0))
| ( set_union2(singleton(sK4(iPr_def_11)),X0) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(sK4(iPr_def_11)),X0),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_68451]) ).
tcf(c_86447,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,singleton(sK4(iPr_def_11))))
| ( set_union2(X0,singleton(sK4(iPr_def_11))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_68561]) ).
tcf(c_86448,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ( X0 = X1 )
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X1,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_45801]) ).
tcf(c_86453,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1))
| ( set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(X0,sK4(iPr_def_11))),X1),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_68457]) ).
tcf(c_86454,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1))
| ( set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1) = sK4(iPr_def_11) )
| ~ in(set_union2(singleton(set_union2(sK4(iPr_def_11),X0)),X1),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_68458]) ).
tcf(c_86455,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))))
| ( set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(X1,sK4(iPr_def_11)))),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_68567]) ).
tcf(c_86456,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))))
| ( set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,singleton(set_union2(sK4(iPr_def_11),X1))),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_68568]) ).
tcf(c_86457,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(X0,sK3(iPr_def_11))
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_49877]) ).
tcf(c_86458,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(X0,sK4(iPr_def_11))
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_7260]) ).
tcf(c_86459,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X1)
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_86122,c_359]) ).
tcf(c_86460,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X1)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_86122,c_358]) ).
tcf(c_86461,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X1,sK4(iPr_def_11))
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X1 )
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X1,sK18)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_86122,c_77]) ).
tcf(c_86462,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),X0)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_transitive(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_65]) ).
tcf(c_86464,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ empty(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_137]) ).
tcf(c_86465,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| in(X0,sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_127]) ).
tcf(c_86466,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(singleton(X0),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X0 )
| ( singleton(X0) = sK4(iPr_def_11) )
| ~ in(singleton(X0),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_62]) ).
tcf(c_86467,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_4213]) ).
tcf(c_86468,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = X2 )
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_4212]) ).
tcf(c_86469,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| in(set_union2(X0,X1),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ in(set_union2(X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_71]) ).
tcf(c_86471,plain,
( in(empty_set,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = empty_set )
| ~ in(empty_set,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_7097]) ).
tcf(c_86472,plain,
( subset(sK4(iPr_def_11),iPr_def_11)
| in(sK18,sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK18 )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_12813]) ).
tcf(c_86476,plain,
( epsilon_transitive(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK1(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK1(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK1(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_3523]) ).
tcf(c_86477,plain,
( epsilon_connected(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK3(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK3(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_3524]) ).
tcf(c_86478,plain,
( epsilon_connected(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK4(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK4(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_3525]) ).
tcf(c_86486,plain,
( empty(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(sK4(iPr_def_11)),sK4(iPr_def_11))
| ( sK5(sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK5(sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_3900]) ).
tcf(c_86487,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,X1,sK4(iPr_def_11)),X1)
| in(sK2(X0,X1,sK4(iPr_def_11)),X0)
| in(sK2(X0,X1,sK4(iPr_def_11)),sK4(iPr_def_11))
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ( sK2(X0,X1,sK4(iPr_def_11)) = sK4(iPr_def_11) )
| ~ in(sK2(X0,X1,sK4(iPr_def_11)),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_4331]) ).
tcf(c_86489,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18)
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_7243]) ).
tcf(c_86490,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ subset(iPr_def_11,sK4(iPr_def_11))
| ~ in(sK5(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_23189]) ).
tcf(c_86493,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK4(iPr_def_11),sK18),X0)
| in(sK2(X0,sK4(iPr_def_11),sK18),sK4(iPr_def_11))
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ( sK2(X0,sK4(iPr_def_11),sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK4(iPr_def_11),sK18),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_53097]) ).
tcf(c_86494,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK4(iPr_def_11),X0,sK18),X0)
| in(sK2(sK4(iPr_def_11),X0,sK18),sK4(iPr_def_11))
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ( sK2(sK4(iPr_def_11),X0,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK4(iPr_def_11),X0,sK18),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_53130]) ).
tcf(c_86979,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK18,X1),X1)
| in(sK2(X0,sK18,X1),X0)
| in(sK2(X0,sK18,X1),sK3(iPr_def_11))
| ( set_union2(X0,sK18) = X1 )
| ( sK2(X0,sK18,X1) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,X1),sK18) ),
inference(superposition,[status(thm)],[c_85213,c_13665]) ).
tcf(c_86980,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK18,X1),X1)
| in(sK2(X0,sK18,X1),X0)
| in(sK2(X0,sK18,X1),sK5(iPr_def_11))
| ( set_union2(X0,sK18) = X1 )
| ( sK2(X0,sK18,X1) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,X1),sK18) ),
inference(superposition,[status(thm)],[c_85213,c_13657]) ).
tcf(c_86981,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,iPr_def_10)
| in(sK2(X1,sK18,X2),X2)
| in(sK2(X1,sK18,X2),X1)
| ( set_union2(X1,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK2(X1,sK18,X2)) ),
inference(superposition,[status(thm)],[c_85213,c_128]) ).
tcf(c_86983,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X1,sK18,X0),iPr_def_10)
| in(sK2(X1,sK18,X0),X1)
| in(sK3(iPr_def_11),sK2(X1,sK18,X0))
| in(sK2(X1,sK18,X0),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,sK18) = X0 )
| ( sK2(X1,sK18,X0) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_85213,c_49877]) ).
tcf(c_86984,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X1,sK18,X0),iPr_def_10)
| in(sK2(X1,sK18,X0),X1)
| in(sK5(iPr_def_11),sK2(X1,sK18,X0))
| in(sK2(X1,sK18,X0),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,sK18) = X0 )
| ( sK2(X1,sK18,X0) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_85213,c_7260]) ).
tcf(c_86985,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,sK18,X0),iPr_def_10)
| in(sK2(X2,sK18,X0),X2)
| ( set_union2(X2,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_85213,c_359]) ).
tcf(c_86986,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,sK18,X0),iPr_def_10)
| element(sK2(X2,sK18,X0),X1)
| in(sK2(X2,sK18,X0),X2)
| ( set_union2(X2,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_85213,c_358]) ).
tcf(c_86987,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,sK18,X1),iPr_def_10)
| in(X0,sK2(X2,sK18,X1))
| in(sK2(X2,sK18,X1),X2)
| in(sK2(X2,sK18,X1),X0)
| ( set_union2(X2,sK18) = X1 )
| ( sK2(X2,sK18,X1) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_85213,c_77]) ).
tcf(c_86988,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK18,X0),iPr_def_10)
| subset(sK2(X1,sK18,X0),X0)
| in(sK2(X1,sK18,X0),X1)
| ( set_union2(X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_85213,c_65]) ).
tcf(c_86989,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK18,X0),iPr_def_10)
| in(sK2(X1,sK18,X0),X1)
| ( set_union2(X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X1,sK18,X0)) ),
inference(superposition,[status(thm)],[c_85213,c_49]) ).
tcf(c_86990,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,sK18,X0),iPr_def_10)
| in(sK2(X1,sK18,X0),X1)
| ( set_union2(X1,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_85213,c_137]) ).
tcf(c_86991,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,X1),iPr_def_10)
| element(sK2(X0,sK18,X1),X1)
| in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_127]) ).
tcf(c_86992,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,singleton(X1)),iPr_def_10)
| in(sK2(X0,sK18,singleton(X1)),X0)
| ( set_union2(X0,sK18) = singleton(X1) )
| ( sK2(X0,sK18,singleton(X1)) = X1 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_62]) ).
tcf(c_86994,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,X1),iPr_def_10)
| in(sK2(X0,sK18,X1),X0)
| ( set_union2(X0,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,X1),sK18) ),
inference(superposition,[status(thm)],[c_85213,c_67]) ).
tcf(c_86995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,sK18,set_union2(X0,X1)),iPr_def_10)
| in(X2,sK2(X3,sK18,set_union2(X0,X1)))
| in(sK2(X3,sK18,set_union2(X0,X1)),X3)
| in(sK2(X3,sK18,set_union2(X0,X1)),X2)
| ( set_union2(X0,X1) = set_union2(X3,sK18) )
| ( sK2(X3,sK18,set_union2(X0,X1)) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_85213,c_4213]) ).
tcf(c_86996,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X3,sK18,set_union2(X0,X1)),iPr_def_10)
| in(X2,sK2(X3,sK18,set_union2(X0,X1)))
| in(sK2(X3,sK18,set_union2(X0,X1)),X3)
| in(sK2(X3,sK18,set_union2(X0,X1)),X2)
| ( set_union2(X0,X1) = set_union2(X3,sK18) )
| ( sK2(X3,sK18,set_union2(X0,X1)) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_85213,c_4212]) ).
tcf(c_86997,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X2,sK18,set_union2(X0,X1)),iPr_def_10)
| in(sK2(X2,sK18,set_union2(X0,X1)),X2)
| in(sK2(X2,sK18,set_union2(X0,X1)),X1)
| in(sK2(X2,sK18,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = set_union2(X2,sK18) )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_71]) ).
tcf(c_86998,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,empty_set),iPr_def_10)
| in(sK2(X0,sK18,empty_set),X0)
| ( set_union2(X0,sK18) = empty_set )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_7097]) ).
tcf(c_87003,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,iPr_def_10),iPr_def_11)
| subset(sK2(X0,sK18,iPr_def_10),iPr_def_10)
| in(sK2(X0,sK18,iPr_def_10),X0)
| ( set_union2(X0,sK18) = iPr_def_10 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_9540]) ).
tcf(c_87004,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,iPr_def_10),iPr_def_10)
| in(sK2(X0,sK18,iPr_def_10),X0)
| ( set_union2(X0,sK18) = iPr_def_10 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(X0,sK18,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_85213,c_6289]) ).
tcf(c_87005,plain,
! [X0: $i] :
( element(sK2(X0,sK18,iPr_def_10),iPr_def_11)
| subset(sK2(X0,sK18,iPr_def_10),iPr_def_10)
| in(sK2(X0,sK18,iPr_def_10),X0)
| ( set_union2(X0,sK18) = iPr_def_10 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_4912]) ).
tcf(c_87006,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,iPr_def_10),iPr_def_10)
| in(sK2(X0,sK18,iPr_def_10),X0)
| ( set_union2(X0,sK18) = iPr_def_10 )
| ( sK2(X0,sK18,iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_3592]) ).
tcf(c_87008,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,iPr_def_11),iPr_def_10)
| in(sK2(X0,sK18,iPr_def_11),sK18)
| in(sK2(X0,sK18,iPr_def_11),X0)
| ( set_union2(X0,sK18) = iPr_def_11 )
| ( sK2(X0,sK18,iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_33457]) ).
tcf(c_87009,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,iPr_def_11),iPr_def_10)
| in(sK2(X0,sK18,iPr_def_11),iPr_def_10)
| in(sK2(X0,sK18,iPr_def_11),sK18)
| in(sK2(X0,sK18,iPr_def_11),X0)
| ( set_union2(X0,sK18) = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_4035]) ).
tcf(c_87010,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),sK18,X0),iPr_def_10)
| in(sK2(set_union2(X0,X1),sK18,X0),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),sK18,X0),X0) ),
inference(superposition,[status(thm)],[c_85213,c_4078]) ).
tcf(c_87011,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),sK18,X2),iPr_def_10)
| in(sK2(set_union2(X0,X1),sK18,X2),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),sK18,X2),X1) ),
inference(superposition,[status(thm)],[c_85213,c_4079]) ).
tcf(c_87012,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(X1,sK18,sK5(iPr_def_11)),iPr_def_10)
| in(X0,sK2(X1,sK18,sK5(iPr_def_11)))
| in(sK2(X1,sK18,sK5(iPr_def_11)),X1)
| in(sK2(X1,sK18,sK5(iPr_def_11)),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X1,sK18) = sK5(iPr_def_11) )
| ( sK2(X1,sK18,sK5(iPr_def_11)) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_85213,c_7243]) ).
tcf(c_87013,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK5(iPr_def_11)),iPr_def_10)
| in(sK2(X0,sK18,sK5(iPr_def_11)),X0)
| ( set_union2(X0,sK18) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(X0,sK18,sK5(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_85213,c_23189]) ).
tcf(c_87014,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(X1,sK18,sK3(iPr_def_11)),iPr_def_10)
| in(X0,sK2(X1,sK18,sK3(iPr_def_11)))
| in(sK2(X1,sK18,sK3(iPr_def_11)),X1)
| in(sK2(X1,sK18,sK3(iPr_def_11)),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X1,sK18) = sK3(iPr_def_11) )
| ( sK2(X1,sK18,sK3(iPr_def_11)) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_85213,c_9906]) ).
tcf(c_87015,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(X1,sK18,sK4(iPr_def_11)),iPr_def_10)
| in(X0,sK2(X1,sK18,sK4(iPr_def_11)))
| in(sK2(X1,sK18,sK4(iPr_def_11)),X1)
| in(sK2(X1,sK18,sK4(iPr_def_11)),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(X1,sK18) = sK4(iPr_def_11) )
| ( sK2(X1,sK18,sK4(iPr_def_11)) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_85213,c_45801]) ).
tcf(c_87017,plain,
! [X0: $i,X1: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| subset(sK2(X0,sK18,X1),iPr_def_10)
| in(sK2(X0,sK18,X1),X1)
| in(sK3(iPr_def_11),sK2(X0,sK18,X1))
| in(sK2(X0,sK18,X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(X0,sK18) = X1 )
| ( sK2(X0,sK18,X1) = sK3(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_85213,c_49877]) ).
tcf(c_87018,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| subset(sK2(X0,sK18,X1),iPr_def_10)
| in(sK2(X0,sK18,X1),X1)
| in(sK5(iPr_def_11),sK2(X0,sK18,X1))
| in(sK2(X0,sK18,X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(X0,sK18) = X1 )
| ( sK2(X0,sK18,X1) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_85213,c_7260]) ).
tcf(c_87019,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,sK18,X2),iPr_def_10)
| in(sK2(X0,sK18,X2),X2)
| ( set_union2(X0,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_85213,c_359]) ).
tcf(c_87020,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,sK18,X2),iPr_def_10)
| element(sK2(X0,sK18,X2),X1)
| in(sK2(X0,sK18,X2),X2)
| ( set_union2(X0,sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_85213,c_358]) ).
tcf(c_87021,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,sK18,X2),iPr_def_10)
| in(X0,sK2(X1,sK18,X2))
| in(sK2(X1,sK18,X2),X2)
| in(sK2(X1,sK18,X2),X0)
| ( set_union2(X1,sK18) = X2 )
| ( sK2(X1,sK18,X2) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_85213,c_77]) ).
tcf(c_87022,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,X1),iPr_def_10)
| subset(sK2(X0,sK18,X1),X0)
| in(sK2(X0,sK18,X1),X1)
| ( set_union2(X0,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0) ),
inference(superposition,[status(thm)],[c_85213,c_65]) ).
tcf(c_87023,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,X1),iPr_def_10)
| in(sK2(X0,sK18,X1),X1)
| ( set_union2(X0,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X0,sK2(X0,sK18,X1)) ),
inference(superposition,[status(thm)],[c_85213,c_49]) ).
tcf(c_87024,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,X1),iPr_def_10)
| in(sK2(X0,sK18,X1),X1)
| ( set_union2(X0,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_85213,c_137]) ).
tcf(c_87025,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,X1),iPr_def_10)
| element(sK2(X0,sK18,X1),X0)
| in(sK2(X0,sK18,X1),X1)
| ( set_union2(X0,sK18) = X1 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_127]) ).
tcf(c_87026,plain,
! [X0: $i,X1: $i] :
( subset(sK2(singleton(X0),sK18,X1),iPr_def_10)
| in(sK2(singleton(X0),sK18,X1),X1)
| ( set_union2(singleton(X0),sK18) = X1 )
| ( sK2(singleton(X0),sK18,X1) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_62]) ).
tcf(c_87029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X0,X1),sK18,X3),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),sK18,X3))
| in(sK2(set_union2(X0,X1),sK18,X3),X3)
| in(sK2(set_union2(X0,X1),sK18,X3),X2)
| ( set_union2(set_union2(X0,X1),sK18) = X3 )
| ( sK2(set_union2(X0,X1),sK18,X3) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_85213,c_4213]) ).
tcf(c_87030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_union2(X0,X1),sK18,X3),iPr_def_10)
| in(X2,sK2(set_union2(X0,X1),sK18,X3))
| in(sK2(set_union2(X0,X1),sK18,X3),X3)
| in(sK2(set_union2(X0,X1),sK18,X3),X2)
| ( set_union2(set_union2(X0,X1),sK18) = X3 )
| ( sK2(set_union2(X0,X1),sK18,X3) = X2 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_85213,c_4212]) ).
tcf(c_87031,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(set_union2(X0,X1),sK18,X2),iPr_def_10)
| in(sK2(set_union2(X0,X1),sK18,X2),X2)
| in(sK2(set_union2(X0,X1),sK18,X2),X1)
| in(sK2(set_union2(X0,X1),sK18,X2),X0)
| ( set_union2(set_union2(X0,X1),sK18) = X2 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_71]) ).
tcf(c_87032,plain,
! [X0: $i] :
( subset(sK2(empty_set,sK18,X0),iPr_def_10)
| in(sK2(empty_set,sK18,X0),X0)
| ( set_union2(empty_set,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_7097]) ).
tcf(c_87033,plain,
! [X0: $i] :
( subset(sK2(sK18,sK18,X0),iPr_def_11)
| subset(sK2(sK18,sK18,X0),iPr_def_10)
| in(sK2(sK18,sK18,X0),X0)
| ( set_union2(sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_12813]) ).
tcf(c_87034,plain,
! [X0: $i] :
( subset(sK2(sK18,sK18,X0),iPr_def_10)
| in(sK2(sK18,sK18,X0),X0)
| ( set_union2(sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(sK18,sK18,X0)) ),
inference(superposition,[status(thm)],[c_85213,c_6841]) ).
tcf(c_87035,plain,
! [X0: $i] :
( element(sK2(sK18,sK18,X0),iPr_def_11)
| subset(sK2(sK18,sK18,X0),iPr_def_10)
| in(sK2(sK18,sK18,X0),X0)
| ( set_union2(sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_5047]) ).
tcf(c_87036,plain,
! [X0: $i] :
( subset(sK2(sK18,sK18,X0),iPr_def_10)
| in(sK2(sK18,sK18,X0),iPr_def_11)
| in(sK2(sK18,sK18,X0),X0)
| ( set_union2(sK18,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_3640]) ).
tcf(c_87037,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,sK18,X0),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,X0),iPr_def_10)
| in(sK2(iPr_def_10,sK18,X0),X0)
| ( set_union2(iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_9540]) ).
tcf(c_87038,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,sK18,X0),iPr_def_10)
| in(sK2(iPr_def_10,sK18,X0),X0)
| ( set_union2(iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(iPr_def_10,sK18,X0)) ),
inference(superposition,[status(thm)],[c_85213,c_6289]) ).
tcf(c_87039,plain,
! [X0: $i] :
( element(sK2(iPr_def_10,sK18,X0),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,X0),iPr_def_10)
| in(sK2(iPr_def_10,sK18,X0),X0)
| ( set_union2(iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_4912]) ).
tcf(c_87040,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,sK18,X0),iPr_def_10)
| in(sK2(iPr_def_10,sK18,X0),X0)
| ( set_union2(iPr_def_10,sK18) = X0 )
| ( sK2(iPr_def_10,sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_3592]) ).
tcf(c_87041,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,sK18,X0),iPr_def_10)
| in(sK2(iPr_def_10,sK18,X0),iPr_def_11)
| in(sK2(iPr_def_10,sK18,X0),X0)
| ( set_union2(iPr_def_10,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_3614]) ).
tcf(c_87042,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,sK18,X0),iPr_def_10)
| in(sK2(iPr_def_11,sK18,X0),sK18)
| in(sK2(iPr_def_11,sK18,X0),X0)
| ( set_union2(iPr_def_11,sK18) = X0 )
| ( sK2(iPr_def_11,sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_33457]) ).
tcf(c_87043,plain,
! [X0: $i] :
( subset(sK2(iPr_def_11,sK18,X0),iPr_def_10)
| in(sK2(iPr_def_11,sK18,X0),iPr_def_10)
| in(sK2(iPr_def_11,sK18,X0),sK18)
| in(sK2(iPr_def_11,sK18,X0),X0)
| ( set_union2(iPr_def_11,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_4035]) ).
tcf(c_87044,plain,
! [X0: $i,X1: $i] :
( subset(sK2(set_union2(X0,X1),sK18,set_union2(X0,X1)),iPr_def_10)
| in(sK2(set_union2(X0,X1),sK18,set_union2(X0,X1)),set_union2(X0,X1))
| ( set_union2(set_union2(X0,X1),sK18) = set_union2(X0,X1) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(set_union2(X0,X1),sK18,set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_85213,c_4079]) ).
tcf(c_87045,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK18,set_union2(X0,X1)),iPr_def_10)
| in(sK2(X0,sK18,set_union2(X0,X1)),set_union2(X0,X1))
| ( set_union2(X0,X1) = set_union2(X0,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(X0,sK18,set_union2(X0,X1)),sK18) ),
inference(superposition,[status(thm)],[c_85213,c_4095]) ).
tcf(c_87046,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK18,sK18,set_union2(X0,X1)),iPr_def_10)
| in(sK2(sK18,sK18,set_union2(X0,X1)),set_union2(X0,X1))
| ( set_union2(X0,X1) = set_union2(sK18,sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK2(sK18,sK18,set_union2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_85213,c_4096]) ).
tcf(c_87047,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),X0)
| subset(sK2(sK5(iPr_def_11),sK18,X1),iPr_def_10)
| in(X0,sK2(sK5(iPr_def_11),sK18,X1))
| in(sK2(sK5(iPr_def_11),sK18,X1),X1)
| in(sK2(sK5(iPr_def_11),sK18,X1),X0)
| ( sK5(iPr_def_11) = X0 )
| ( set_union2(sK5(iPr_def_11),sK18) = X1 )
| ( sK2(sK5(iPr_def_11),sK18,X1) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK5(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_85213,c_7243]) ).
tcf(c_87048,plain,
! [X0: $i] :
( subset(sK2(sK5(iPr_def_11),sK18,X0),iPr_def_10)
| in(sK2(sK5(iPr_def_11),sK18,X0),X0)
| ( set_union2(sK5(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK5(iPr_def_11),sK18,X0)) ),
inference(superposition,[status(thm)],[c_85213,c_23189]) ).
tcf(c_87049,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),X0)
| subset(sK2(sK3(iPr_def_11),sK18,X1),iPr_def_10)
| in(X0,sK2(sK3(iPr_def_11),sK18,X1))
| in(sK2(sK3(iPr_def_11),sK18,X1),X1)
| in(sK2(sK3(iPr_def_11),sK18,X1),X0)
| ( sK3(iPr_def_11) = X0 )
| ( set_union2(sK3(iPr_def_11),sK18) = X1 )
| ( sK2(sK3(iPr_def_11),sK18,X1) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_85213,c_9906]) ).
tcf(c_87050,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| subset(sK2(sK4(iPr_def_11),sK18,X1),iPr_def_10)
| in(X0,sK2(sK4(iPr_def_11),sK18,X1))
| in(sK2(sK4(iPr_def_11),sK18,X1),X1)
| in(sK2(sK4(iPr_def_11),sK18,X1),X0)
| ( sK4(iPr_def_11) = X0 )
| ( set_union2(sK4(iPr_def_11),sK18) = X1 )
| ( sK2(sK4(iPr_def_11),sK18,X1) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_85213,c_45801]) ).
tcf(c_87051,plain,
( subset(sK2(sK18,sK18,sK18),iPr_def_10)
| in(sK2(sK18,sK18,sK18),sK18)
| ( set_union2(sK18,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_85213,c_66161]) ).
tcf(c_87052,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,X0),iPr_def_10)
| in(sK2(X0,sK18,X0),X0)
| ( set_union2(X0,sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(equality_factoring,[status(thm)],[c_85213]) ).
tcf(c_87076,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,sK18,X0),iPr_def_10)
| in(sK2(iPr_def_10,sK18,X0),iPr_def_11)
| in(sK2(iPr_def_10,sK18,X0),X0)
| ( X0 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_87041,c_3424]) ).
tcf(c_87082,plain,
! [X0: $i] :
( element(sK2(iPr_def_10,sK18,X0),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,X0),iPr_def_10)
| in(sK2(iPr_def_10,sK18,X0),X0)
| ( X0 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_87039,c_3424]) ).
tcf(c_87118,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,sK18,X0),iPr_def_10)
| in(sK2(iPr_def_10,sK18,X0),X0)
| ( X0 = iPr_def_11 )
| ( sK2(iPr_def_10,sK18,X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_87040,c_3424]) ).
tcf(c_87124,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,sK18,X0),iPr_def_10)
| in(sK2(iPr_def_10,sK18,X0),X0)
| ( X0 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(iPr_def_11,sK2(iPr_def_10,sK18,X0)) ),
inference(light_normalisation,[status(thm)],[c_87038,c_3424]) ).
tcf(c_87172,plain,
! [X0: $i] :
( subset(sK2(iPr_def_10,sK18,X0),iPr_def_11)
| subset(sK2(iPr_def_10,sK18,X0),iPr_def_10)
| in(sK2(iPr_def_10,sK18,X0),X0)
| ( X0 = iPr_def_11 )
| ~ epsilon_transitive(iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_87037,c_3424]) ).
tcf(c_88118,plain,
( ~ in(sK18,sK18)
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( sK5(iPr_def_11) = sK18 )
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_86128,c_7136,c_86128]) ).
tcf(c_88119,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(renaming,[status(thm)],[c_88118]) ).
tcf(c_88127,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88119,c_3592]) ).
tcf(c_88146,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK3(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(sK18,sK18)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_88127,c_49877]) ).
tcf(c_88148,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(X0)
| ~ in(sK18,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_88127,c_359]) ).
tcf(c_88149,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18)
| ~ subset(sK4(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_88127,c_358]) ).
tcf(c_88150,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(sK18,sK18)
| ~ in(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_88127,c_77]) ).
tcf(c_88151,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| subset(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_88127,c_65]) ).
tcf(c_88153,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ empty(sK4(iPr_def_11))
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_88127,c_137]) ).
tcf(c_88154,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| element(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ in(sK18,sK18) ),
inference(superposition,[status(thm)],[c_88127,c_127]) ).
tcf(c_88155,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X0)
| in(sK4(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(sK18,sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_88127,c_45801]) ).
tcf(c_88228,plain,
( ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_86137,c_41868,c_43439]) ).
tcf(c_88229,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) ) ),
inference(renaming,[status(thm)],[c_88228]) ).
tcf(c_88239,plain,
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| in(sK3(iPr_def_11),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ( sK3(iPr_def_11) = sK5(iPr_def_11) )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(sK3(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_88229,c_7260]) ).
tcf(c_88240,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ empty(X0)
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_88229,c_359]) ).
tcf(c_88241,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),X0)
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ subset(sK3(iPr_def_11),X0) ),
inference(superposition,[status(thm)],[c_88229,c_358]) ).
tcf(c_88242,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_88229,c_77]) ).
tcf(c_88243,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| subset(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_88229,c_65]) ).
tcf(c_88244,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ in(sK3(iPr_def_11),sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_88229,c_49]) ).
tcf(c_88245,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ empty(sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_88229,c_137]) ).
tcf(c_88246,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK3(iPr_def_11),iPr_def_10)
| element(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) ) ),
inference(superposition,[status(thm)],[c_88229,c_127]) ).
tcf(c_88314,plain,
( subset(sK4(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86190,c_65]) ).
tcf(c_88329,plain,
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK5(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_88314,c_13657]) ).
tcf(c_88330,plain,
! [X0: $i] :
( subset(X0,iPr_def_10)
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_88314,c_128]) ).
tcf(c_88331,plain,
( subset(sK4(iPr_def_11),iPr_def_11)
| ~ epsilon_transitive(iPr_def_10) ),
inference(superposition,[status(thm)],[c_88314,c_3868]) ).
tcf(c_88351,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3564,c_86189]) ).
tcf(c_88352,plain,
( subset(empty_set,sK18)
| in(sK4(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3420,c_86189]) ).
tcf(c_88353,plain,
( epsilon_transitive(powerset(sK4(iPr_def_11)))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK1(powerset(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3566,c_86189]) ).
tcf(c_88354,plain,
( epsilon_connected(powerset(sK4(iPr_def_11)))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK3(powerset(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3567,c_86189]) ).
tcf(c_88355,plain,
( epsilon_connected(powerset(sK4(iPr_def_11)))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(powerset(sK4(iPr_def_11))),sK18) ),
inference(superposition,[status(thm)],[c_3568,c_86189]) ).
tcf(c_88356,plain,
( epsilon_connected(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK3(sK4(iPr_def_11)),sK18)
| ~ epsilon_transitive(sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3807,c_86189]) ).
tcf(c_88357,plain,
( epsilon_connected(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(sK4(iPr_def_11)),sK18)
| ~ epsilon_transitive(sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3808,c_86189]) ).
tcf(c_88358,plain,
( empty(sK4(iPr_def_11))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK5(sK4(iPr_def_11)),sK18)
| ~ epsilon_transitive(sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3899,c_86189]) ).
tcf(c_88359,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,X1,sK4(iPr_def_11)),sK18)
| in(sK2(X0,X1,sK4(iPr_def_11)),X1)
| in(sK2(X0,X1,sK4(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ epsilon_transitive(sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4330,c_86189]) ).
tcf(c_88360,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK4(iPr_def_11),X1),sK18)
| in(sK2(X0,sK4(iPr_def_11),X1),X1)
| in(sK2(X0,sK4(iPr_def_11),X1),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = X1 )
| ~ epsilon_transitive(sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_4342,c_86189]) ).
tcf(c_88361,plain,
( epsilon_connected(powerset(empty_set))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK3(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4620,c_86189]) ).
tcf(c_88362,plain,
( epsilon_connected(powerset(empty_set))
| in(sK4(iPr_def_11),iPr_def_10)
| subset(sK4(powerset(empty_set)),sK18) ),
inference(superposition,[status(thm)],[c_4637,c_86189]) ).
tcf(c_88363,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(powerset(sK4(iPr_def_11))))),sK18) ),
inference(superposition,[status(thm)],[c_5196,c_86189]) ).
tcf(c_88364,plain,
( in(sK4(iPr_def_11),iPr_def_10)
| subset(sK5(powerset(sK5(powerset(sK5(powerset(sK4(iPr_def_11))))))),sK18) ),
inference(superposition,[status(thm)],[c_5252,c_86189]) ).
tcf(c_88365,plain,
( subset(sK5(iPr_def_11),sK18)
| in(sK4(iPr_def_11),iPr_def_10)
| ~ epsilon_transitive(sK4(iPr_def_11))
| ~ subset(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_23188,c_86189]) ).
tcf(c_88368,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| subset(sK2(X0,sK4(iPr_def_11),sK18),sK18)
| in(sK2(X0,sK4(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53096,c_86189]) ).
tcf(c_88369,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| subset(sK2(sK4(iPr_def_11),X0,sK18),sK18)
| in(sK2(sK4(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_53129,c_86189]) ).
tcf(c_88444,plain,
! [X0: $i,X1: $i] :
( empty(sK18)
| in(sK2(X0,sK5(sK18),X1),X1)
| in(sK2(X0,sK5(sK18),X1),X0)
| in(sK2(X0,sK5(sK18),X1),sK5(sK18))
| ( set_union2(X0,sK5(sK18)) = X1 )
| ( sK2(X0,sK5(sK18),X1) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ in(sK2(X0,sK5(sK18),X1),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_4343]) ).
tcf(c_88445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,X3),X2)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X0,sK2(X1,X2,X3),X4),X4)
| in(sK2(X0,sK2(X1,X2,X3),X4),X0)
| in(sK2(X0,sK2(X1,X2,X3),X4),sK2(X1,X2,X3))
| ( set_union2(X1,X2) = X3 )
| ( set_union2(X0,sK2(X1,X2,X3)) = X4 )
| ( sK2(X0,sK2(X1,X2,X3),X4) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X3)
| ~ in(sK2(X0,sK2(X1,X2,X3),X4),X3) ),
inference(superposition,[status(thm)],[c_4329,c_4343]) ).
tcf(c_88446,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X0,X1),X2)
| in(sK2(X2,X0,X1),X1)
| in(sK2(X2,X0,X1),X0)
| ( set_union2(X2,X0) = X1 )
| ( sK2(X2,X0,X1) = X0 )
| ~ epsilon_connected(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4329,c_4343]) ).
tcf(c_88447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,X3),X3)
| in(sK2(X1,X2,X3),X1)
| in(sK2(X0,sK2(X1,X2,X3),X4),X4)
| in(sK2(X0,sK2(X1,X2,X3),X4),X0)
| in(sK2(X0,sK2(X1,X2,X3),X4),sK2(X1,X2,X3))
| ( set_union2(X1,X2) = X3 )
| ( set_union2(X0,sK2(X1,X2,X3)) = X4 )
| ( sK2(X0,sK2(X1,X2,X3),X4) = sK2(X1,X2,X3) )
| ~ epsilon_connected(X2)
| ~ in(sK2(X0,sK2(X1,X2,X3),X4),X2) ),
inference(superposition,[status(thm)],[c_4341,c_4343]) ).
tcf(c_88448,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,X2),X2)
| in(sK2(X1,X0,X2),X1)
| in(sK2(X1,X0,X2),X0)
| ( set_union2(X1,X0) = X2 )
| ( sK2(X1,X0,X2) = X0 )
| ~ epsilon_connected(X0)
| ~ in(X0,X0) ),
inference(superposition,[status(thm)],[c_4341,c_4343]) ).
tcf(c_88449,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| in(sK2(X0,sK5(iPr_def_11),X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ( sK2(X0,sK5(iPr_def_11),X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK2(X0,sK5(iPr_def_11),X1),sK18) ),
inference(superposition,[status(thm)],[c_7234,c_4343]) ).
tcf(c_88451,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK5(iPr_def_11),X2)
| in(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| in(sK2(X0,sK5(iPr_def_11),X1),sK5(iPr_def_11))
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ( sK2(X0,sK5(iPr_def_11),X1) = sK5(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK2(X0,sK5(iPr_def_11),X1),sK18) ),
inference(superposition,[status(thm)],[c_13652,c_4343]) ).
tcf(c_88452,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| in(sK2(X0,sK5(iPr_def_11),X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = sK18 )
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ( sK2(X0,sK5(iPr_def_11),X1) = sK5(iPr_def_11) )
| ~ in(sK2(X0,sK5(iPr_def_11),X1),sK18) ),
inference(superposition,[status(thm)],[c_7241,c_4343]) ).
tcf(c_88453,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ( sK2(X0,sK5(iPr_def_11),X1) = sK5(iPr_def_11) )
| ~ empty(sK5(iPr_def_11))
| ~ in(sK2(X0,sK5(iPr_def_11),X1),sK18) ),
inference(superposition,[status(thm)],[c_7246,c_4343]) ).
tcf(c_88454,plain,
! [X0: $i,X1: $i] :
( element(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| in(sK2(X0,sK5(iPr_def_11),X1),sK5(iPr_def_11))
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ( sK2(X0,sK5(iPr_def_11),X1) = sK5(iPr_def_11) )
| ~ in(sK2(X0,sK5(iPr_def_11),X1),sK18) ),
inference(superposition,[status(thm)],[c_7238,c_4343]) ).
tcf(c_88455,plain,
! [X0: $i,X1: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| in(sK2(X0,sK5(iPr_def_11),X1),sK5(iPr_def_11))
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ( sK2(X0,sK5(iPr_def_11),X1) = sK5(iPr_def_11) )
| ~ in(sK2(X0,sK5(iPr_def_11),X1),sK18) ),
inference(superposition,[status(thm)],[c_7155,c_4343]) ).
tcf(c_88456,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK5(iPr_def_11))
| in(sK5(iPr_def_11),X2)
| in(sK2(X0,sK5(iPr_def_11),X1),X1)
| in(sK2(X0,sK5(iPr_def_11),X1),X0)
| in(sK2(X0,sK5(iPr_def_11),X1),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X2 )
| ( set_union2(X0,sK5(iPr_def_11)) = X1 )
| ( sK2(X0,sK5(iPr_def_11),X1) = sK5(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK2(X0,sK5(iPr_def_11),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_7234,c_4343]) ).
tcf(c_88457,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK2(X0,sK1(iPr_def_11),X1),X1)
| in(sK2(X0,sK1(iPr_def_11),X1),X0)
| in(sK2(X0,sK1(iPr_def_11),X1),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,sK1(iPr_def_11)) = X1 )
| ( sK2(X0,sK1(iPr_def_11),X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK2(X0,sK1(iPr_def_11),X1),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_4343]) ).
tcf(c_88458,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_transitive(iPr_def_11)
| in(X2,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X2)
| in(sK2(X0,sK1(iPr_def_11),X1),X1)
| in(sK2(X0,sK1(iPr_def_11),X1),X0)
| in(sK2(X0,sK1(iPr_def_11),X1),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X2 )
| ( set_union2(X0,sK1(iPr_def_11)) = X1 )
| ( sK2(X0,sK1(iPr_def_11),X1) = sK1(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK2(X0,sK1(iPr_def_11),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_4343]) ).
tcf(c_88459,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK2(X0,sK3(iPr_def_11),X1),X1)
| in(sK2(X0,sK3(iPr_def_11),X1),X0)
| in(sK2(X0,sK3(iPr_def_11),X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,sK3(iPr_def_11)) = X1 )
| ( sK2(X0,sK3(iPr_def_11),X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,iPr_def_10)
| ~ in(sK2(X0,sK3(iPr_def_11),X1),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_4343]) ).
tcf(c_88460,plain,
! [X0: $i,X1: $i,X2: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X2)
| in(sK2(X0,sK3(iPr_def_11),X1),X1)
| in(sK2(X0,sK3(iPr_def_11),X1),X0)
| in(sK2(X0,sK3(iPr_def_11),X1),sK3(iPr_def_11))
| ( set_union2(X0,sK3(iPr_def_11)) = X1 )
| ( sK2(X0,sK3(iPr_def_11),X1) = sK3(iPr_def_11) )
| ~ subset(iPr_def_10,X2)
| ~ in(sK2(X0,sK3(iPr_def_11),X1),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_4343]) ).
tcf(c_88461,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK2(X0,sK3(iPr_def_11),X1),X1)
| in(sK2(X0,sK3(iPr_def_11),X1),X0)
| in(sK2(X0,sK3(iPr_def_11),X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( set_union2(X0,sK3(iPr_def_11)) = X1 )
| ( sK2(X0,sK3(iPr_def_11),X1) = sK3(iPr_def_11) )
| ~ in(sK2(X0,sK3(iPr_def_11),X1),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_4343]) ).
tcf(c_88462,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK3(iPr_def_11),X1),X1)
| in(sK2(X0,sK3(iPr_def_11),X1),X0)
| ( set_union2(X0,sK3(iPr_def_11)) = X1 )
| ( sK2(X0,sK3(iPr_def_11),X1) = sK3(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ in(sK2(X0,sK3(iPr_def_11),X1),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_4343]) ).
tcf(c_88463,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK3(iPr_def_11),X1),X1)
| in(sK2(X0,sK3(iPr_def_11),X1),X0)
| in(sK2(X0,sK3(iPr_def_11),X1),sK3(iPr_def_11))
| ( set_union2(X0,sK3(iPr_def_11)) = X1 )
| ( sK2(X0,sK3(iPr_def_11),X1) = sK3(iPr_def_11) )
| ~ in(sK2(X0,sK3(iPr_def_11),X1),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_4343]) ).
tcf(c_88464,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK3(iPr_def_11),X1),X1)
| in(sK2(X0,sK3(iPr_def_11),X1),X0)
| in(sK2(X0,sK3(iPr_def_11),X1),sK3(iPr_def_11))
| ( set_union2(X0,sK3(iPr_def_11)) = X1 )
| ( sK2(X0,sK3(iPr_def_11),X1) = sK3(iPr_def_11) )
| ~ in(sK2(X0,sK3(iPr_def_11),X1),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_4343]) ).
tcf(c_88465,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X2)
| in(sK2(X0,sK3(iPr_def_11),X1),X1)
| in(sK2(X0,sK3(iPr_def_11),X1),X0)
| in(sK2(X0,sK3(iPr_def_11),X1),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X2 )
| ( set_union2(X0,sK3(iPr_def_11)) = X1 )
| ( sK2(X0,sK3(iPr_def_11),X1) = sK3(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X2,sK18)
| ~ in(sK2(X0,sK3(iPr_def_11),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_4343]) ).
tcf(c_88466,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK2(X0,sK4(iPr_def_11),X1),X1)
| in(sK2(X0,sK4(iPr_def_11),X1),X0)
| in(sK2(X0,sK4(iPr_def_11),X1),sK4(iPr_def_11))
| ( set_union2(X0,sK4(iPr_def_11)) = X1 )
| ( sK2(X0,sK4(iPr_def_11),X1) = sK4(iPr_def_11) )
| ~ in(sK2(X0,sK4(iPr_def_11),X1),sK18) ),
inference(superposition,[status(thm)],[c_86122,c_4343]) ).
tcf(c_88712,plain,
! [X0: $i] :
( ~ subset(iPr_def_11,X0)
| in(sK4(iPr_def_11),X0) ),
inference(global_subsumption_just,[status(thm)],[c_86083,c_23190,c_86083]) ).
tcf(c_88713,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),X0)
| ~ subset(iPr_def_11,X0) ),
inference(renaming,[status(thm)],[c_88712]) ).
tcf(c_88718,plain,
! [X0: $i] :
( in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK3(iPr_def_11))
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| in(sK3(iPr_def_11),sK4(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ subset(iPr_def_11,X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_88713,c_49877]) ).
tcf(c_88719,plain,
! [X0: $i] :
( in(sK5(iPr_def_11),iPr_def_10)
| in(X0,sK5(iPr_def_11))
| in(sK5(iPr_def_11),sK4(iPr_def_11))
| in(sK4(iPr_def_11),sK5(iPr_def_11))
| ( sK5(iPr_def_11) = X0 )
| ( sK4(iPr_def_11) = sK5(iPr_def_11) )
| ~ epsilon_connected(X0)
| ~ subset(iPr_def_11,X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_88713,c_7260]) ).
tcf(c_88721,plain,
! [X0: $i,X1: $i] :
( element(sK4(iPr_def_11),X1)
| ~ subset(iPr_def_11,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_88713,c_358]) ).
tcf(c_88722,plain,
! [X0: $i,X1: $i] :
( in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(X1)
| ~ subset(iPr_def_11,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_88713,c_77]) ).
tcf(c_88723,plain,
! [X0: $i] :
( subset(sK4(iPr_def_11),X0)
| ~ epsilon_transitive(X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_88713,c_65]) ).
tcf(c_88724,plain,
! [X0: $i] :
( ~ subset(iPr_def_11,X0)
| ~ in(X0,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_88713,c_49]) ).
tcf(c_88727,plain,
! [X0: $i] :
( ( sK4(iPr_def_11) = X0 )
| ~ subset(iPr_def_11,singleton(X0)) ),
inference(superposition,[status(thm)],[c_88713,c_62]) ).
tcf(c_88728,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ~ in(X2,X1)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ subset(iPr_def_11,set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_88713,c_4213]) ).
tcf(c_88729,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X2)
| ( sK4(iPr_def_11) = X2 )
| ~ in(X2,X0)
| ~ epsilon_connected(set_union2(X0,X1))
| ~ subset(iPr_def_11,set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_88713,c_4212]) ).
tcf(c_88730,plain,
! [X0: $i,X1: $i] :
( in(sK4(iPr_def_11),X1)
| in(sK4(iPr_def_11),X0)
| ~ subset(iPr_def_11,set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_88713,c_71]) ).
tcf(c_88731,plain,
( epsilon_connected(iPr_def_11)
| ~ subset(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_88713,c_76]) ).
tcf(c_88733,plain,
( subset(sK4(iPr_def_11),iPr_def_11)
| ~ subset(iPr_def_11,sK18) ),
inference(superposition,[status(thm)],[c_88713,c_12813]) ).
tcf(c_88737,plain,
( epsilon_transitive(sK4(iPr_def_11))
| ~ subset(iPr_def_11,sK1(sK4(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_88713,c_3523]) ).
tcf(c_88738,plain,
( epsilon_connected(sK4(iPr_def_11))
| ~ subset(iPr_def_11,sK3(sK4(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_88713,c_3524]) ).
tcf(c_88739,plain,
( epsilon_connected(sK4(iPr_def_11))
| ~ subset(iPr_def_11,sK4(sK4(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_88713,c_3525]) ).
tcf(c_88743,plain,
( ( sK4(iPr_def_11) = sK18 )
| ~ subset(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_88713,c_3592]) ).
tcf(c_88747,plain,
( empty(sK4(iPr_def_11))
| ~ subset(iPr_def_11,sK5(sK4(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_88713,c_3900]) ).
tcf(c_88748,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK4(iPr_def_11)),X1)
| in(sK2(X0,X1,sK4(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ subset(iPr_def_11,sK2(X0,X1,sK4(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_88713,c_4331]) ).
tcf(c_88749,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK4(iPr_def_11),X1),X1)
| in(sK2(X0,sK4(iPr_def_11),X1),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = X1 )
| ~ subset(iPr_def_11,sK2(X0,sK4(iPr_def_11),X1)) ),
inference(superposition,[status(thm)],[c_88713,c_4343]) ).
tcf(c_88750,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ~ subset(iPr_def_11,sK18) ),
inference(superposition,[status(thm)],[c_88713,c_10578]) ).
tcf(c_88753,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| in(sK3(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = X0 )
| ~ epsilon_connected(sK3(iPr_def_11))
| ~ in(X0,sK18)
| ~ subset(iPr_def_11,sK3(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_88713,c_9906]) ).
tcf(c_88754,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(X0,sK4(iPr_def_11))
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ epsilon_connected(sK4(iPr_def_11))
| ~ in(X0,sK18)
| ~ subset(iPr_def_11,sK4(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_88713,c_45801]) ).
tcf(c_88755,plain,
! [X0: $i] :
( subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| in(sK2(X0,sK4(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(X0,sK4(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_88713,c_53097]) ).
tcf(c_88756,plain,
! [X0: $i] :
( subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| in(sK2(sK4(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,sK18)) ),
inference(superposition,[status(thm)],[c_88713,c_53130]) ).
tcf(c_88923,plain,
! [X0: $i] :
( ( singleton(X0) = sK4(iPr_def_11) )
| ( sK0(X0,sK4(iPr_def_11)) = X0 )
| ~ subset(iPr_def_11,sK0(X0,sK4(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_60,c_88724]) ).
tcf(c_88925,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK4(iPr_def_11),X0,X1),X1)
| in(sK2(sK4(iPr_def_11),X0,X1),X0)
| ( set_union2(sK4(iPr_def_11),X0) = X1 )
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,X1)) ),
inference(superposition,[status(thm)],[c_4333,c_88724]) ).
tcf(c_88926,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK4(iPr_def_11),X0,X1),X1)
| in(sK2(sK4(iPr_def_11),X0,X1),X0)
| ( set_union2(sK4(iPr_def_11),X0) = X1 )
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,X1)) ),
inference(superposition,[status(thm)],[c_68,c_88724]) ).
tcf(c_88928,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK4(iPr_def_11),X1),X1)
| in(sK2(X0,sK4(iPr_def_11),X1),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = X1 )
| ~ subset(iPr_def_11,sK2(X0,sK4(iPr_def_11),X1)) ),
inference(superposition,[status(thm)],[c_4333,c_88724]) ).
tcf(c_88933,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(sK4(iPr_def_11),X1)),X1)
| ( set_union2(sK4(iPr_def_11),X1) = singleton(X0) )
| ( sK0(X0,set_union2(sK4(iPr_def_11),X1)) = X0 )
| ~ subset(iPr_def_11,sK0(X0,set_union2(sK4(iPr_def_11),X1))) ),
inference(superposition,[status(thm)],[c_4023,c_88724]) ).
tcf(c_88934,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,set_union2(X1,sK4(iPr_def_11))),X1)
| ( set_union2(X1,sK4(iPr_def_11)) = singleton(X0) )
| ( sK0(X0,set_union2(X1,sK4(iPr_def_11))) = X0 )
| ~ subset(iPr_def_11,sK0(X0,set_union2(X1,sK4(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_4023,c_88724]) ).
tcf(c_88935,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(sK4(iPr_def_11),X0))
| in(sK1(set_union2(sK4(iPr_def_11),X0)),X0)
| ~ subset(iPr_def_11,sK1(set_union2(sK4(iPr_def_11),X0))) ),
inference(superposition,[status(thm)],[c_4024,c_88724]) ).
tcf(c_88936,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,sK4(iPr_def_11)))
| in(sK1(set_union2(X0,sK4(iPr_def_11))),X0)
| ~ subset(iPr_def_11,sK1(set_union2(X0,sK4(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_4024,c_88724]) ).
tcf(c_88937,plain,
! [X0: $i] :
( epsilon_connected(set_union2(sK4(iPr_def_11),X0))
| in(sK3(set_union2(sK4(iPr_def_11),X0)),X0)
| ~ subset(iPr_def_11,sK3(set_union2(sK4(iPr_def_11),X0))) ),
inference(superposition,[status(thm)],[c_4027,c_88724]) ).
tcf(c_88938,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,sK4(iPr_def_11)))
| in(sK3(set_union2(X0,sK4(iPr_def_11))),X0)
| ~ subset(iPr_def_11,sK3(set_union2(X0,sK4(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_4027,c_88724]) ).
tcf(c_88939,plain,
! [X0: $i] :
( epsilon_connected(set_union2(sK4(iPr_def_11),X0))
| in(sK4(set_union2(sK4(iPr_def_11),X0)),X0)
| ~ subset(iPr_def_11,sK4(set_union2(sK4(iPr_def_11),X0))) ),
inference(superposition,[status(thm)],[c_4028,c_88724]) ).
tcf(c_88940,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,sK4(iPr_def_11)))
| in(sK4(set_union2(X0,sK4(iPr_def_11))),X0)
| ~ subset(iPr_def_11,sK4(set_union2(X0,sK4(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_4028,c_88724]) ).
tcf(c_88941,plain,
! [X0: $i] :
( empty(set_union2(sK4(iPr_def_11),X0))
| in(sK5(set_union2(sK4(iPr_def_11),X0)),X0)
| ~ subset(iPr_def_11,sK5(set_union2(sK4(iPr_def_11),X0))) ),
inference(superposition,[status(thm)],[c_4029,c_88724]) ).
tcf(c_88942,plain,
! [X0: $i] :
( empty(set_union2(X0,sK4(iPr_def_11)))
| in(sK5(set_union2(X0,sK4(iPr_def_11))),X0)
| ~ subset(iPr_def_11,sK5(set_union2(X0,sK4(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_4029,c_88724]) ).
tcf(c_88943,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),X2)
| in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),X1)
| in(sK2(X0,X1,set_union2(sK4(iPr_def_11),X2)),X0)
| ( set_union2(sK4(iPr_def_11),X2) = set_union2(X0,X1) )
| ~ subset(iPr_def_11,sK2(X0,X1,set_union2(sK4(iPr_def_11),X2))) ),
inference(superposition,[status(thm)],[c_4337,c_88724]) ).
tcf(c_88944,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),X2)
| in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),X1)
| in(sK2(X0,sK4(iPr_def_11),set_union2(X1,X2)),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = set_union2(X1,X2) )
| ~ subset(iPr_def_11,sK2(X0,sK4(iPr_def_11),set_union2(X1,X2))) ),
inference(superposition,[status(thm)],[c_4337,c_88724]) ).
tcf(c_88945,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_union2(X2,sK4(iPr_def_11))),X2)
| in(sK2(X0,X1,set_union2(X2,sK4(iPr_def_11))),X1)
| in(sK2(X0,X1,set_union2(X2,sK4(iPr_def_11))),X0)
| ( set_union2(X2,sK4(iPr_def_11)) = set_union2(X0,X1) )
| ~ subset(iPr_def_11,sK2(X0,X1,set_union2(X2,sK4(iPr_def_11)))) ),
inference(superposition,[status(thm)],[c_4337,c_88724]) ).
tcf(c_88946,plain,
( empty(sK18)
| in(sK4(iPr_def_11),sK5(sK18))
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ subset(iPr_def_11,sK5(sK18))
| ~ in(sK4(iPr_def_11),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4222,c_88724]) ).
tcf(c_88947,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(sK4(iPr_def_11),X0,X1))
| in(sK2(sK4(iPr_def_11),X0,X1),X2)
| in(sK2(sK4(iPr_def_11),X0,X1),X0)
| ( set_union2(sK4(iPr_def_11),X0) = X1 )
| ( sK2(sK4(iPr_def_11),X0,X1) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,X1)) ),
inference(superposition,[status(thm)],[c_4329,c_88724]) ).
tcf(c_88948,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(X0,sK4(iPr_def_11),X1))
| in(sK2(X0,sK4(iPr_def_11),X1),X2)
| in(sK2(X0,sK4(iPr_def_11),X1),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = X1 )
| ( sK2(X0,sK4(iPr_def_11),X1) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ subset(iPr_def_11,sK2(X0,sK4(iPr_def_11),X1)) ),
inference(superposition,[status(thm)],[c_4329,c_88724]) ).
tcf(c_88949,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK4(iPr_def_11),sK2(X0,X1,X2))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK4(iPr_def_11) )
| ~ epsilon_connected(X2)
| ~ in(sK4(iPr_def_11),X2)
| ~ subset(iPr_def_11,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4329,c_88724]) ).
tcf(c_88950,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK4(iPr_def_11),X0,X1),X0)
| ( set_union2(sK4(iPr_def_11),X0) = X1 )
| ~ empty(X1)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,X1)) ),
inference(superposition,[status(thm)],[c_4332,c_88724]) ).
tcf(c_88951,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK4(iPr_def_11),X0,X1),X1)
| in(sK2(sK4(iPr_def_11),X0,X1),X0)
| ( set_union2(sK4(iPr_def_11),X0) = X1 )
| ~ epsilon_transitive(X1)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,X1)) ),
inference(superposition,[status(thm)],[c_4330,c_88724]) ).
tcf(c_88952,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK4(iPr_def_11),X1),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = X1 )
| ~ empty(X1)
| ~ subset(iPr_def_11,sK2(X0,sK4(iPr_def_11),X1)) ),
inference(superposition,[status(thm)],[c_4332,c_88724]) ).
tcf(c_88953,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK4(iPr_def_11),X1),X1)
| in(sK2(X0,sK4(iPr_def_11),X1),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = X1 )
| ~ epsilon_transitive(X1)
| ~ subset(iPr_def_11,sK2(X0,sK4(iPr_def_11),X1)) ),
inference(superposition,[status(thm)],[c_4330,c_88724]) ).
tcf(c_88954,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK4(iPr_def_11),X0,singleton(X1)),X0)
| ( set_union2(sK4(iPr_def_11),X0) = singleton(X1) )
| ( sK2(sK4(iPr_def_11),X0,singleton(X1)) = X1 )
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,singleton(X1))) ),
inference(superposition,[status(thm)],[c_4334,c_88724]) ).
tcf(c_88955,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK4(iPr_def_11),singleton(X1)),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = singleton(X1) )
| ( sK2(X0,sK4(iPr_def_11),singleton(X1)) = X1 )
| ~ subset(iPr_def_11,sK2(X0,sK4(iPr_def_11),singleton(X1))) ),
inference(superposition,[status(thm)],[c_4334,c_88724]) ).
tcf(c_88956,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK4(iPr_def_11),X0,set_union2(X1,X2)),X2)
| in(sK2(sK4(iPr_def_11),X0,set_union2(X1,X2)),X1)
| in(sK2(sK4(iPr_def_11),X0,set_union2(X1,X2)),X0)
| ( set_union2(sK4(iPr_def_11),X0) = set_union2(X1,X2) )
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,set_union2(X1,X2))) ),
inference(superposition,[status(thm)],[c_4337,c_88724]) ).
tcf(c_88957,plain,
! [X0: $i] :
( in(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_11)
| in(sK2(sK4(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,sK18)) ),
inference(superposition,[status(thm)],[c_4339,c_88724]) ).
tcf(c_88958,plain,
! [X0: $i] :
( subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| element(sK2(sK4(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,sK18)) ),
inference(superposition,[status(thm)],[c_53099,c_88724]) ).
tcf(c_88960,plain,
! [X0: $i] :
( in(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_11)
| in(sK2(X0,sK4(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ~ subset(iPr_def_11,sK2(X0,sK4(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_4339,c_88724]) ).
tcf(c_88961,plain,
! [X0: $i] :
( subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| subset(sK2(X0,sK4(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ subset(iPr_def_11,sK2(X0,sK4(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53129,c_88724]) ).
tcf(c_88962,plain,
! [X0: $i] :
( subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| element(sK2(X0,sK4(iPr_def_11),sK18),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(X0,sK4(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53132,c_88724]) ).
tcf(c_88963,plain,
! [X0: $i] :
( subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ subset(iPr_def_11,sK2(X0,sK4(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53131,c_88724]) ).
tcf(c_88965,plain,
! [X0: $i] :
( in(sK2(sK4(iPr_def_11),X0,iPr_def_10),iPr_def_11)
| in(sK2(sK4(iPr_def_11),X0,iPr_def_10),X0)
| ( set_union2(sK4(iPr_def_11),X0) = iPr_def_10 )
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4340,c_88724]) ).
tcf(c_88966,plain,
! [X0: $i] :
( in(sK2(X0,sK4(iPr_def_11),iPr_def_10),iPr_def_11)
| in(sK2(X0,sK4(iPr_def_11),iPr_def_10),X0)
| ( set_union2(X0,sK4(iPr_def_11)) = iPr_def_10 )
| ~ subset(iPr_def_11,sK2(X0,sK4(iPr_def_11),iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4340,c_88724]) ).
tcf(c_88967,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(sK4(iPr_def_11),X0,X1))
| in(sK2(sK4(iPr_def_11),X0,X1),X2)
| in(sK2(sK4(iPr_def_11),X0,X1),X1)
| ( set_union2(sK4(iPr_def_11),X0) = X1 )
| ( sK2(sK4(iPr_def_11),X0,X1) = X2 )
| ~ epsilon_connected(X0)
| ~ in(X2,X0)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,X1)) ),
inference(superposition,[status(thm)],[c_4341,c_88724]) ).
tcf(c_88968,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(X0,X1,sK4(iPr_def_11)))
| in(sK2(X0,X1,sK4(iPr_def_11)),X2)
| in(sK2(X0,X1,sK4(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ( sK2(X0,X1,sK4(iPr_def_11)) = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ subset(iPr_def_11,sK2(X0,X1,sK4(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_4341,c_88724]) ).
tcf(c_88969,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| in(sK4(iPr_def_11),sK2(X0,X1,X2))
| ( set_union2(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = sK4(iPr_def_11) )
| ~ epsilon_connected(X1)
| ~ in(sK4(iPr_def_11),X1)
| ~ subset(iPr_def_11,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_4341,c_88724]) ).
tcf(c_88970,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK4(iPr_def_11),X0,X1),X0)
| in(sK2(sK4(iPr_def_11),X0,X1),X1)
| ( set_union2(sK4(iPr_def_11),X0) = X1 )
| ~ epsilon_transitive(X0)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,X1)) ),
inference(superposition,[status(thm)],[c_4342,c_88724]) ).
tcf(c_88971,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,X1,sK4(iPr_def_11)),X1)
| in(sK2(X0,X1,sK4(iPr_def_11)),X0)
| ( set_union2(X0,X1) = sK4(iPr_def_11) )
| ~ epsilon_transitive(X1)
| ~ subset(iPr_def_11,sK2(X0,X1,sK4(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_4342,c_88724]) ).
tcf(c_88972,plain,
! [X0: $i] :
( subset(sK2(sK4(iPr_def_11),sK18,X0),iPr_def_10)
| in(sK2(sK4(iPr_def_11),sK18,X0),X0)
| ( set_union2(sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),sK18,X0)) ),
inference(superposition,[status(thm)],[c_85213,c_88724]) ).
tcf(c_88973,plain,
! [X0: $i] :
( subset(sK2(X0,sK18,sK4(iPr_def_11)),iPr_def_10)
| in(sK2(X0,sK18,sK4(iPr_def_11)),X0)
| ( set_union2(X0,sK18) = sK4(iPr_def_11) )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(X0,sK18,sK4(iPr_def_11))) ),
inference(superposition,[status(thm)],[c_85213,c_88724]) ).
tcf(c_88982,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ subset(iPr_def_11,sK1(iPr_def_11))
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_8680,c_88724]) ).
tcf(c_88983,plain,
! [X0: $i] :
( epsilon_transitive(iPr_def_11)
| in(X0,sK1(iPr_def_11))
| in(sK1(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK1(iPr_def_11))
| ( sK1(iPr_def_11) = X0 )
| ( sK1(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ subset(iPr_def_11,sK1(iPr_def_11))
| ~ in(sK4(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8680,c_88724]) ).
tcf(c_88984,plain,
! [X0: $i] :
( in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,iPr_def_10)
| ~ subset(iPr_def_11,sK3(iPr_def_11))
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_48071,c_88724]) ).
tcf(c_88985,plain,
! [X0: $i] :
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ subset(iPr_def_10,X0)
| ~ subset(iPr_def_11,sK3(iPr_def_11))
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_13640,c_88724]) ).
tcf(c_88986,plain,
( epsilon_connected(iPr_def_11)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK18 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ subset(iPr_def_11,sK3(iPr_def_11))
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9904,c_88724]) ).
tcf(c_88987,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ empty(sK3(iPr_def_11))
| ~ subset(iPr_def_11,sK3(iPr_def_11))
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9909,c_88724]) ).
tcf(c_88988,plain,
( epsilon_connected(iPr_def_11)
| element(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ subset(iPr_def_11,sK3(iPr_def_11))
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9901,c_88724]) ).
tcf(c_88989,plain,
( epsilon_connected(iPr_def_11)
| in(sK3(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ subset(iPr_def_11,sK3(iPr_def_11))
| ~ in(sK4(iPr_def_11),sK18) ),
inference(superposition,[status(thm)],[c_9595,c_88724]) ).
tcf(c_88990,plain,
! [X0: $i] :
( in(X0,sK3(iPr_def_11))
| in(sK3(iPr_def_11),X0)
| in(sK4(iPr_def_11),sK3(iPr_def_11))
| ( sK3(iPr_def_11) = X0 )
| ( sK3(iPr_def_11) = sK4(iPr_def_11) )
| ~ epsilon_connected(iPr_def_10)
| ~ in(X0,sK18)
| ~ subset(iPr_def_11,sK3(iPr_def_11))
| ~ in(sK4(iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_48071,c_88724]) ).
tcf(c_88991,plain,
~ subset(iPr_def_11,sK4(iPr_def_11)),
inference(superposition,[status(thm)],[c_88713,c_88724]) ).
tcf(c_88993,plain,
! [X0: $i] :
( in(sK4(iPr_def_11),iPr_def_10)
| in(sK4(iPr_def_11),X0)
| ( sK4(iPr_def_11) = X0 )
| ~ subset(iPr_def_11,X0)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_86122,c_88724]) ).
tcf(c_88994,plain,
( epsilon_connected(iPr_def_11)
| element(sK4(iPr_def_11),iPr_def_10)
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK5(sK18))
| ~ in(sK5(sK18),sK18) ),
inference(superposition,[status(thm)],[c_31298,c_88724]) ).
tcf(c_88996,plain,
! [X0: $i] :
( subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| subset(sK2(sK4(iPr_def_11),X0,sK18),X0)
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ epsilon_transitive(X0)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,sK18)) ),
inference(superposition,[status(thm)],[c_53096,c_88724]) ).
tcf(c_88997,plain,
! [X0: $i] :
( subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ empty(X0)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,sK18)) ),
inference(superposition,[status(thm)],[c_53098,c_88724]) ).
tcf(c_88998,plain,
! [X0: $i,X1: $i] :
( subset(sK2(sK4(iPr_def_11),X0,sK18),iPr_def_10)
| element(sK2(sK4(iPr_def_11),X0,sK18),X1)
| ( set_union2(sK4(iPr_def_11),X0) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),X0,sK18)) ),
inference(superposition,[status(thm)],[c_53094,c_88724]) ).
tcf(c_88999,plain,
! [X0: $i] :
( subset(sK2(sK4(iPr_def_11),singleton(X0),sK18),iPr_def_10)
| ( set_union2(sK4(iPr_def_11),singleton(X0)) = sK18 )
| ( sK2(sK4(iPr_def_11),singleton(X0),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),singleton(X0),sK18)) ),
inference(superposition,[status(thm)],[c_53100,c_88724]) ).
tcf(c_89000,plain,
( subset(sK2(sK4(iPr_def_11),sK18,sK18),iPr_def_10)
| ( set_union2(sK4(iPr_def_11),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),sK18,sK18)) ),
inference(superposition,[status(thm)],[c_63091,c_88724]) ).
tcf(c_89001,plain,
( subset(sK2(sK4(iPr_def_11),sK18,sK18),iPr_def_11)
| ( set_union2(sK4(iPr_def_11),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),sK18,sK18)) ),
inference(superposition,[status(thm)],[c_55425,c_88724]) ).
tcf(c_89002,plain,
( subset(sK2(sK4(iPr_def_11),iPr_def_10,sK18),iPr_def_10)
| ( set_union2(sK4(iPr_def_11),iPr_def_10) = sK18 )
| ( sK2(sK4(iPr_def_11),iPr_def_10,sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53114,c_88724]) ).
tcf(c_89003,plain,
( subset(sK2(sK4(iPr_def_11),iPr_def_10,sK18),iPr_def_10)
| in(sK2(sK4(iPr_def_11),iPr_def_10,sK18),iPr_def_11)
| ( set_union2(sK4(iPr_def_11),iPr_def_10) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),iPr_def_10,sK18)) ),
inference(superposition,[status(thm)],[c_53115,c_88724]) ).
tcf(c_89004,plain,
( subset(sK2(sK4(iPr_def_11),iPr_def_11,sK18),iPr_def_10)
| ( set_union2(sK4(iPr_def_11),iPr_def_11) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK4(iPr_def_11),iPr_def_11,sK18)) ),
inference(superposition,[status(thm)],[c_77034,c_88724]) ).
tcf(c_89005,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,sK4(iPr_def_11),sK18),iPr_def_10)
| element(sK2(X0,sK4(iPr_def_11),sK18),X1)
| ( set_union2(X0,sK4(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(X0,X1)
| ~ subset(iPr_def_11,sK2(X0,sK4(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53127,c_88724]) ).
tcf(c_89006,plain,
! [X0: $i] :
( subset(sK2(singleton(X0),sK4(iPr_def_11),sK18),iPr_def_10)
| ( set_union2(singleton(X0),sK4(iPr_def_11)) = sK18 )
| ( sK2(singleton(X0),sK4(iPr_def_11),sK18) = X0 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(singleton(X0),sK4(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53133,c_88724]) ).
tcf(c_89007,plain,
( subset(sK2(sK18,sK4(iPr_def_11),sK18),iPr_def_10)
| ( set_union2(sK18,sK4(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK18,sK4(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_66184,c_88724]) ).
tcf(c_89008,plain,
( subset(sK2(sK18,sK4(iPr_def_11),sK18),iPr_def_11)
| ( set_union2(sK18,sK4(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(sK18,sK4(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_58667,c_88724]) ).
tcf(c_89009,plain,
( subset(sK2(iPr_def_10,sK4(iPr_def_11),sK18),iPr_def_10)
| ( set_union2(iPr_def_10,sK4(iPr_def_11)) = sK18 )
| ( sK2(iPr_def_10,sK4(iPr_def_11),sK18) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(iPr_def_10,sK4(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53147,c_88724]) ).
tcf(c_89010,plain,
( subset(sK2(iPr_def_10,sK4(iPr_def_11),sK18),iPr_def_10)
| in(sK2(iPr_def_10,sK4(iPr_def_11),sK18),iPr_def_11)
| ( set_union2(iPr_def_10,sK4(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(iPr_def_10,sK4(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_53148,c_88724]) ).
tcf(c_89011,plain,
( subset(sK2(iPr_def_11,sK4(iPr_def_11),sK18),iPr_def_10)
| ( set_union2(iPr_def_11,sK4(iPr_def_11)) = sK18 )
| ~ epsilon_transitive(iPr_def_10)
| ~ subset(iPr_def_11,sK2(iPr_def_11,sK4(iPr_def_11),sK18)) ),
inference(superposition,[status(thm)],[c_77535,c_88724]) ).
tcf(c_89088,plain,
( empty(sK18)
| in(sK4(iPr_def_11),sK5(sK18))
| ( sK4(iPr_def_11) = sK5(sK18) )
| ~ epsilon_connected(iPr_def_11)
| ~ subset(iPr_def_11,sK5(sK18)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88946,c_83428]) ).
tcf(c_89715,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_89088,c_89011,c_89010,c_89009,c_89008,c_89007,c_89006,c_89005,c_89004,c_89003,c_89002,c_89001,c_89000,c_88999,c_88998,c_88997,c_88996,c_88994,c_88993,c_88991,c_88990,c_88989,c_88988,c_88987,c_88986,c_88985,c_88984,c_88983,c_88982,c_88973,c_88972,c_88971,c_88970,c_88969,c_88968,c_88967,c_88966,c_88965,c_88963,c_88962,c_88961,c_88960,c_88958,c_88957,c_88956,c_88955,c_88954,c_88953,c_88952,c_88951,c_88950,c_88949,c_88948,c_88947,c_88946,c_88945,c_88944,c_88943,c_88942,c_88941,c_88940,c_88939,c_88938,c_88937,c_88936,c_88935,c_88934,c_88933,c_88928,c_88926,c_88925,c_88923,c_88756,c_88755,c_88754,c_88753,c_88750,c_88749,c_88748,c_88747,c_88743,c_88739,c_88738,c_88737,c_88733,c_88731,c_88730,c_88729,c_88728,c_88727,c_88724,c_88723,c_88722,c_88721,c_88719,c_88718,c_88713,c_88466,c_88465,c_88464,c_88463,c_88462,c_88461,c_88460,c_88459,c_88458,c_88457,c_88456,c_88455,c_88454,c_88453,c_88452,c_88451,c_88449,c_88448,c_88447,c_88446,c_88445,c_88444,c_88369,c_88368,c_88365,c_88364,c_88363,c_88362,c_88361,c_88360,c_88331,c_88330,c_88329,c_88314,c_88246,c_88245,c_88244,c_88243,c_88242,c_88241,c_88240,c_88239,c_88229,c_88155,c_88154,c_88153,c_88151,c_88150,c_88149,c_88148,c_88146,c_88127,c_88119,c_88359,c_87172,c_87124,c_87118,c_87082,c_87076,c_87052,c_87051,c_87050,c_87049,c_87048,c_87047,c_87046,c_87045,c_87044,c_87043,c_87042,c_87041,c_87040,c_87039,c_87038,c_87037,c_87036,c_87035,c_87034,c_87033,c_87032,c_87031,c_87030,c_87029,c_87026,c_87025,c_87024,c_87023,c_87022,c_87021,c_87020,c_87019,c_87018,c_87017,c_87015,c_87014,c_87013,c_87012,c_87011,c_87010,c_87009,c_87008,c_87006,c_87005,c_87004,c_87003,c_86998,c_86997,c_86996,c_86995,c_86994,c_86992,c_86991,c_86990,c_86989,c_86988,c_86987,c_86986,c_86985,c_86984,c_86983,c_86981,c_86980,c_86979,c_86494,c_86493,c_86490,c_86489,c_86487,c_86460,c_86459,c_86458,c_86457,c_86456,c_86455,c_86454,c_86453,c_86448,c_86447,c_86446,c_86445,c_86444,c_86443,c_86442,c_86441,c_86440,c_86439,c_86438,c_86437,c_86436,c_86431,c_86430,c_86427,c_86426,c_86415,c_86414,c_86412,c_86401,c_86400,c_86241,c_86240,c_86238,c_86237,c_86233,c_86231,c_86227,c_86226,c_86190,c_86185,c_86179,c_86178,c_86167,c_86137,c_86128,c_86098,c_86097,c_86096,c_86095,c_86084,c_86083,c_86054,c_86032,c_86031,c_86030,c_86029,c_86028,c_86027,c_86025,c_86024,c_86023,c_86022,c_86021,c_86020,c_85993,c_85992,c_85991,c_85334,c_85213,c_85101,c_85031,c_85030,c_85029,c_85028,c_85027,c_85026,c_85025,c_85024,c_85023,c_85022,c_85021,c_85020,c_85019,c_85018,c_85017,c_85016,c_85015,c_85014,c_85013,c_85012,c_85011,c_85010,c_85009,c_85008,c_85005,c_85004,c_85003,c_85002,c_85001,c_85000,c_84999,c_84998,c_84997,c_84996,c_84994,c_84993,c_84992,c_84991,c_84990,c_84989,c_84988,c_84987,c_84986,c_84984,c_84983,c_84982,c_84981,c_84979,c_84978,c_84977,c_84976,c_84974,c_84973,c_84972,c_84967,c_84966,c_84964,c_84963,c_84962,c_84961,c_84960,c_84959,c_84958,c_84957,c_84956,c_84955,c_84954,c_84953,c_84952,c_84951,c_84950,c_84949,c_84948,c_84947,c_84946,c_84945,c_84944,c_84943,c_84942,c_84941,c_84940,c_84939,c_84938,c_84937,c_84936,c_84934,c_84933,c_84932,c_84931,c_84930,c_84929,c_84928,c_84927,c_84926,c_84925,c_84924,c_84923,c_84922,c_84921,c_84920,c_84919,c_84918,c_84693,c_84687,c_84686,c_84685,c_84684,c_84683,c_84682,c_84681,c_84680,c_84679,c_84678,c_84677,c_84676,c_84675,c_84674,c_84673,c_84672,c_84671,c_84669,c_84647,c_84449,c_84448,c_84447,c_84445,c_84444,c_84443,c_84442,c_84441,c_84440,c_84438,c_84435,c_84434,c_84431,c_84262,c_84261,c_84260,c_84258,c_84257,c_84256,c_84255,c_84254,c_84253,c_84251,c_84248,c_84247,c_84244,c_84054,c_84053,c_84052,c_84050,c_84049,c_84048,c_84047,c_84046,c_84045,c_84043,c_84042,c_84040,c_84039,c_84036,c_83915,c_83914,c_83913,c_83911,c_83910,c_83909,c_83908,c_83907,c_83906,c_83904,c_83903,c_83901,c_83900,c_83897,c_83766,c_83765,c_83764,c_83762,c_83761,c_83760,c_83759,c_83758,c_83757,c_83755,c_83752,c_83751,c_83750,c_83748,c_83585,c_83584,c_83583,c_83581,c_83580,c_83579,c_83578,c_83577,c_83576,c_83574,c_83571,c_83570,c_83569,c_83567,c_83480,c_83479,c_83478,c_83476,c_83475,c_83474,c_83473,c_83472,c_83470,c_83469,c_83466,c_83465,c_83462,c_83438,c_83435,c_83434,c_83433,c_83432,c_83428,c_83427,c_83426,c_83360,c_83358,c_83356,c_83134,c_83133,c_83132,c_83131,c_83130,c_83129,c_83128,c_83127,c_83126,c_83125,c_83124,c_83123,c_83122,c_83121,c_83120,c_83119,c_83118,c_83117,c_83116,c_83115,c_83114,c_83113,c_83112,c_83111,c_83110,c_83109,c_83108,c_83107,c_83106,c_83105,c_83008,c_83002,c_83001,c_83000,c_82999,c_82998,c_82997,c_82996,c_82101,c_81417,c_81416,c_81413,c_81409,c_81408,c_81407,c_81406,c_81405,c_81404,c_81403,c_81402,c_81401,c_81400,c_81397,c_81396,c_81395,c_81394,c_81393,c_81392,c_81391,c_81390,c_81389,c_81388,c_81387,c_81386,c_81385,c_81384,c_81383,c_81382,c_81381,c_81380,c_81379,c_81376,c_81375,c_81374,c_81372,c_81371,c_81370,c_81369,c_81368,c_81367,c_81366,c_81365,c_81364,c_81363,c_81362,c_81361,c_81360,c_81359,c_81358,c_81357,c_81356,c_81355,c_81354,c_81353,c_81352,c_81351,c_81350,c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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM396+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 03:48:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 40.21/7.88 % SZS status Started for theBenchmark.p
% 40.21/7.88 % SZS status Theorem for theBenchmark.p
% 40.21/7.88
% 40.21/7.88 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 40.21/7.88
% 40.21/7.88 % ------ iProver source info
% 40.21/7.88
% 40.21/7.88 % git: date: 2026-07-19 20:42:38 +0200
% 40.21/7.88 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 40.21/7.88 % git: non_committed_changes: false
% 40.21/7.88
% 40.21/7.88 % ------ Parsing...
% 40.21/7.88 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 40.21/7.88
% 40.21/7.88 % ------ Preprocessing... sup_sim: 0 sf_s rm: 23 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 40.21/7.88
% 40.21/7.88 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 40.21/7.88
% 40.21/7.88 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 40.21/7.88 % ------ Proving...
% 40.21/7.88 % ------ Problem Properties
% 40.21/7.88
% 40.21/7.88 %
% 40.21/7.88 % clauses 63
% 40.21/7.88 % conjectures 0
% 40.21/7.88 % EPR 33
% 40.21/7.88 % Horn 55
% 40.21/7.88 % unary 29
% 40.21/7.88 % binary 21
% 40.21/7.88 % lits 114
% 40.21/7.88 % lits eq 21
% 40.21/7.88 % fd_pure 0
% 40.21/7.88 % fd_pseudo 0
% 40.21/7.88 % fd_cond 1
% 40.21/7.88 % fd_pseudo_cond 7
% 40.21/7.88 % AC symbols 0
% 40.21/7.88
% 40.21/7.88 % ------ Schedule dynamic 5 is on
% 40.21/7.88
% 40.21/7.88 % ------ no conjectures: strip conj schedule
% 40.21/7.88
% 40.21/7.88 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 40.21/7.88
% 40.21/7.88
% 40.21/7.88 % ------
% 40.21/7.88 % Current options:
% 40.21/7.88 % ------
% 40.21/7.88
% 40.21/7.88
% 40.21/7.88 %
% 40.21/7.88
% 40.21/7.88 % ------ Proving...
% 40.21/7.88 %
% 40.21/7.88
% 40.21/7.88 % SZS status Theorem for theBenchmark.p
% 40.21/7.88
% 40.21/7.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 50.54/8.11
% 50.54/8.11
%------------------------------------------------------------------------------