%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU067+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:55:11 PM UTC 2026
% Result : Theorem 244.84s 33.54s
% Output : CNFRefutation 245.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 39
% Syntax : Number of formulae : 8098 ( 176 unt; 0 def)
% Number of atoms : 41060 (8669 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 55387 (22425 ~;32804 |; 121 &)
% ( 18 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 9 con; 0-3 aty)
% Number of variables : 31767 ( 2 sgn31736 !; 31 ?;31378 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f5,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f7,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f8,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f9,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f10,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f11,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f14,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f15,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f16,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f17,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f18,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f19,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f20,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f21,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f22,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f23,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f24,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f25,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f26,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f27,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f30,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f31,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
fof(f32,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_image(X1,relation_dom(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_relat_1) ).
fof(f33,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> relation_image(X1,relation_inverse_image(X1,X0)) = set_intersection2(X0,relation_image(X1,relation_dom(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> relation_image(X1,relation_inverse_image(X1,X0)) = set_intersection2(X0,relation_image(X1,relation_dom(X1))) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,axiom,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f36,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f37,axiom,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(f38,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f39,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f41,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f42,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f43,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f44,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f45,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f19]) ).
fof(f46,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f30]) ).
fof(f47,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& relation_image(X1,relation_inverse_image(X1,X0)) != set_intersection2(X0,relation_image(X1,relation_dom(X1))) ),
inference(ennf_transformation,[],[f34]) ).
fof(f48,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& relation_image(X1,relation_inverse_image(X1,X0)) != set_intersection2(X0,relation_image(X1,relation_dom(X1))) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(ennf_transformation,[],[f35]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f53,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_image(X1,X0),relation_image(X1,relation_dom(X1))) ),
inference(ennf_transformation,[],[f32]) ).
fof(f55,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f56,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f58,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f17]) ).
fof(f59,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f61,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f62,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f63,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f65,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f66,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f68,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f69,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f70,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f42]) ).
fof(f71,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f72,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f40]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f77,plain,
( function(sK1)
& relation(sK1)
& relation_image(sK1,relation_inverse_image(sK1,sK0)) != set_intersection2(sK0,relation_image(sK1,relation_dom(sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f48]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(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_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f83,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
( function(sK3)
& empty(sK3)
& relation(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f24]) ).
fof(f85,plain,
( function(sK4)
& relation(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f20]) ).
fof(f86,plain,
( relation(sK5)
& ~ empty(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X0,sK5)],[f25]) ).
fof(f87,plain,
( relation(sK6)
& empty(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f21]) ).
fof(f88,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f89,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ) ) )
& ( ( ( in(sK7(X0,X1,X2),X2)
| ( in(apply(X0,sK7(X0,X1,X2)),X1)
& in(sK7(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK7(X0,X1,X2),X2)
| ~ in(apply(X0,sK7(X0,X1,X2)),X1)
| ~ in(sK7(X0,X1,X2),relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f90]) ).
fof(f92,plain,
~ empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f27]) ).
fof(f93,plain,
empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f23]) ).
fof(f94,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f95,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK10(X0,X1),X0)
& ~ in(sK10(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f98,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) )
& ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f99,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(rectify,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( apply(X0,sK13(X0,X1,X6)) = X6
& in(sK13(X0,X1,X6),X1)
& in(sK13(X0,X1,X6),relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ( ( in(sK11(X0,X1,X2),X2)
| ( sK11(X0,X1,X2) = apply(X0,sK12(X0,X1,X2))
& in(sK12(X0,X1,X2),X1)
& in(sK12(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK11(X0,X1,X2),X2)
| ! [X4] :
( apply(X0,X4) != sK11(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X3,sK11(X0,X1,X2)),skolemize(X5,sK12(X0,X1,X2)),skolemize(X8,sK13(X0,X1,X6))],[f99]) ).
fof(f101,plain,
! [X0] :
( empty(sK14(X0))
& element(sK14(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X1,sK14(X0))],[f26]) ).
fof(f102,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK15(X0))
& element(sK15(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15(X0))],[f76]) ).
fof(f103,plain,
! [X0] : element(sK16(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X1,sK16(X0))],[f11]) ).
fof(f104,plain,
function(sK1),
inference(cnf_transformation,[],[f77]) ).
fof(f105,plain,
relation(sK1),
inference(cnf_transformation,[],[f77]) ).
fof(f106,plain,
relation_image(sK1,relation_inverse_image(sK1,sK0)) != set_intersection2(sK0,relation_image(sK1,relation_dom(sK1))),
inference(cnf_transformation,[],[f77]) ).
fof(f107,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f108,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f45]) ).
fof(f109,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f110,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f111,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f81]) ).
fof(f112,plain,
! [X2,X0,X1] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f81]) ).
fof(f113,plain,
! [X2,X0,X1] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f81]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f81]) ).
fof(f117,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f83]) ).
fof(f118,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f119,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f37]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f121,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f122,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_image(X1,X0),relation_image(X1,relation_dom(X1))) ),
inference(cnf_transformation,[],[f54]) ).
fof(f123,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f124,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_dom(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f125,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f126,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f127,plain,
function(sK3),
inference(cnf_transformation,[],[f84]) ).
fof(f128,plain,
empty(sK3),
inference(cnf_transformation,[],[f84]) ).
fof(f129,plain,
relation(sK3),
inference(cnf_transformation,[],[f84]) ).
fof(f130,plain,
function(sK4),
inference(cnf_transformation,[],[f85]) ).
fof(f131,plain,
relation(sK4),
inference(cnf_transformation,[],[f85]) ).
fof(f132,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f133,plain,
relation(sK5),
inference(cnf_transformation,[],[f86]) ).
fof(f134,plain,
~ empty(sK5),
inference(cnf_transformation,[],[f86]) ).
fof(f135,plain,
relation(sK6),
inference(cnf_transformation,[],[f87]) ).
fof(f136,plain,
empty(sK6),
inference(cnf_transformation,[],[f87]) ).
fof(f137,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f138,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(apply(X0,X4),X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f139,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,relation_dom(X0)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f140,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK7(X0,X1,X2),X2)
| in(apply(X0,sK7(X0,X1,X2)),X1)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f91]) ).
fof(f142,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,X2),relation_dom(X0))
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f91]) ).
fof(f143,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,X2),X2)
| ~ in(apply(X0,sK7(X0,X1,X2)),X1)
| ~ in(sK7(X0,X1,X2),relation_dom(X0))
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f91]) ).
fof(f144,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f92]) ).
fof(f145,plain,
empty(sK9),
inference(cnf_transformation,[],[f93]) ).
fof(f146,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f147,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f148,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f149,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f150,plain,
! [X0,X1] :
( in(sK10(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f151,plain,
! [X0,X1] :
( ~ in(sK10(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f152,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f153,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f154,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f155,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f46]) ).
fof(f156,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f70]) ).
fof(f157,plain,
relation(empty_set),
inference(cnf_transformation,[],[f16]) ).
fof(f159,plain,
empty(empty_set),
inference(cnf_transformation,[],[f15]) ).
fof(f160,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| apply(X0,sK13(X0,X1,X6)) = X6 ),
inference(cnf_transformation,[],[f100]) ).
fof(f161,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK13(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f162,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK13(X0,X1,X6),relation_dom(X0)) ),
inference(cnf_transformation,[],[f100]) ).
fof(f163,plain,
! [X2,X0,X1,X6,X7] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK11(X0,X1,X2),X2)
| sK11(X0,X1,X2) = apply(X0,sK12(X0,X1,X2))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f100]) ).
fof(f165,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK11(X0,X1,X2),X2)
| in(sK12(X0,X1,X2),X1)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f100]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK11(X0,X1,X2),X2)
| in(sK12(X0,X1,X2),relation_dom(X0))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f100]) ).
fof(f167,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK11(X0,X1,X2),X2)
| apply(X0,X4) != sK11(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f100]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f170,plain,
! [X0] : empty(sK14(X0)),
inference(cnf_transformation,[],[f101]) ).
fof(f171,plain,
! [X0] : element(sK14(X0),powerset(X0)),
inference(cnf_transformation,[],[f101]) ).
fof(f172,plain,
! [X0] :
( empty(X0)
| ~ empty(sK15(X0)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f173,plain,
! [X0] :
( empty(X0)
| element(sK15(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f174,plain,
! [X0] : element(sK16(X0),X0),
inference(cnf_transformation,[],[f103]) ).
fof(f175,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f176,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f111]) ).
fof(f177,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f110]) ).
fof(f178,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f109]) ).
fof(f181,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f140]) ).
fof(f182,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0)) ),
inference(equality_resolution,[],[f139]) ).
fof(f183,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1) ),
inference(equality_resolution,[],[f138]) ).
fof(f184,plain,
! [X2,X0,X1,X7] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(apply(X0,X7),X2) ),
inference(equality_resolution,[],[f163]) ).
fof(f185,plain,
! [X0,X1,X7] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(apply(X0,X7),relation_image(X0,X1)) ),
inference(equality_resolution,[],[f184]) ).
fof(f186,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK13(X0,X1,X6),relation_dom(X0)) ),
inference(equality_resolution,[],[f162]) ).
fof(f187,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK13(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f161]) ).
fof(f188,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| apply(X0,sK13(X0,X1,X6)) = X6 ),
inference(equality_resolution,[],[f160]) ).
tcf(c_49,negated_conjecture,
set_intersection2(sK0,relation_image(sK1,relation_dom(sK1))) != relation_image(sK1,relation_inverse_image(sK1,sK0)),
inference(cnf_transformation,[],[f106]) ).
tcf(c_50,negated_conjecture,
relation(sK1),
inference(cnf_transformation,[],[f105]) ).
tcf(c_51,negated_conjecture,
function(sK1),
inference(cnf_transformation,[],[f104]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_53,plain,
! [X0: $i] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f108]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X1,X2))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f118]) ).
tcf(c_64,plain,
! [X0: $i] : set_intersection2(X0,empty_set) = empty_set,
inference(cnf_transformation,[],[f119]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(X0,X1),relation_image(X0,relation_dom(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(X0,relation_inverse_image(X0,X1)),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_69,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_70,plain,
! [X0: $i] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_71,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_72,plain,
relation(sK3),
inference(cnf_transformation,[],[f129]) ).
tcf(c_73,plain,
empty(sK3),
inference(cnf_transformation,[],[f128]) ).
tcf(c_74,plain,
function(sK3),
inference(cnf_transformation,[],[f127]) ).
tcf(c_75,plain,
relation(sK4),
inference(cnf_transformation,[],[f131]) ).
tcf(c_76,plain,
function(sK4),
inference(cnf_transformation,[],[f130]) ).
tcf(c_77,plain,
! [X0: $i] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_78,plain,
~ empty(sK5),
inference(cnf_transformation,[],[f134]) ).
tcf(c_79,plain,
relation(sK5),
inference(cnf_transformation,[],[f133]) ).
tcf(c_80,plain,
empty(sK6),
inference(cnf_transformation,[],[f136]) ).
tcf(c_81,plain,
relation(sK6),
inference(cnf_transformation,[],[f135]) ).
tcf(c_82,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,X2),X2)
| ~ in(sK7(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,X2),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| in(apply(X0,sK7(X0,X1,X2)),X1)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_inverse_image(X0,X2))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X2) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_89,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f144]) ).
tcf(c_90,plain,
empty(sK9),
inference(cnf_transformation,[],[f145]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK10(X0,X1),X1) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_100,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f155]) ).
tcf(c_101,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_103,plain,
relation(empty_set),
inference(cnf_transformation,[],[f157]) ).
tcf(c_104,plain,
empty(empty_set),
inference(cnf_transformation,[],[f159]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK11(X0,X1,X2),X2)
| ( sK11(X0,X1,X2) != apply(X0,X3) ) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),X2)
| in(sK12(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,X2),X1)
| in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK12(X0,X1,X2)) = sK11(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,X2,X0),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,X2,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK13(X1,X2,X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_115,plain,
! [X0: $i] : element(sK14(X0),powerset(X0)),
inference(cnf_transformation,[],[f171]) ).
tcf(c_116,plain,
! [X0: $i] : empty(sK14(X0)),
inference(cnf_transformation,[],[f170]) ).
tcf(c_117,plain,
! [X0: $i] :
( empty(X0)
| element(sK15(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_118,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK15(X0)) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_119,plain,
! [X0: $i] : element(sK16(X0),X0),
inference(cnf_transformation,[],[f174]) ).
tcf(c_120,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f175]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_98]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_113,c_156]) ).
tcf(c_321,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_114,c_156]) ).
tcf(c_5257,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_104,c_77]) ).
tcf(c_5303,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_101]) ).
tcf(c_5308,plain,
! [X0: $i] : sK14(X0) = empty_set,
inference(superposition,[status(thm)],[c_116,c_101]) ).
tcf(c_5321,plain,
! [X0: $i] : element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[c_115,c_5308]) ).
tcf(c_5369,plain,
! [X0: $i] :
( empty(X0)
| subset(sK15(X0),X0) ),
inference(superposition,[status(thm)],[c_117,c_99]) ).
tcf(c_5371,plain,
! [X0: $i] : subset(empty_set,X0),
inference(superposition,[status(thm)],[c_5321,c_99]) ).
tcf(c_5383,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_104,c_5303]) ).
tcf(c_5402,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X0,X1),X2)
| in(sK10(set_intersection2(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_95,c_58]) ).
tcf(c_5460,plain,
! [X0: $i] :
( empty(X0)
| in(sK16(X0),X0) ),
inference(superposition,[status(thm)],[c_119,c_92]) ).
tcf(c_5490,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| in(sK16(set_intersection2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_5460,c_58]) ).
tcf(c_5609,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_5371,c_60]) ).
tcf(c_5904,plain,
! [X0: $i] :
( ( relation_image(X0,relation_inverse_image(X0,empty_set)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_5609]) ).
tcf(c_6041,plain,
( empty(sK5)
| ~ empty(sK15(sK5)) ),
inference(instantiation,[status(thm)],[c_118]) ).
tcf(c_6042,plain,
( empty(sK8)
| ~ empty(sK15(sK8)) ),
inference(instantiation,[status(thm)],[c_118]) ).
tcf(c_6280,plain,
( ( relation_image(empty_set,relation_inverse_image(empty_set,empty_set)) = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5257,c_5904]) ).
tcf(c_6285,plain,
relation_image(empty_set,relation_inverse_image(empty_set,empty_set)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_6280,c_103]) ).
tcf(c_6327,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,X0),X0)
| ( set_intersection2(X0,X1) = X0 ) ),
inference(equality_factoring,[status(thm)],[c_55]) ).
tcf(c_6674,plain,
! [X0: $i,X1: $i] :
( in(sK13(empty_set,X1,X0),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,relation_image(empty_set,X1)) ),
inference(superposition,[status(thm)],[c_5383,c_110]) ).
tcf(c_6683,plain,
! [X0: $i,X1: $i] :
( in(sK13(empty_set,X1,X0),empty_set)
| ~ in(X0,relation_image(empty_set,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6674,c_5257,c_103]) ).
tcf(c_7570,plain,
! [X0: $i] :
( empty(sK15(sK5))
| in(X0,sK15(sK5))
| ~ element(X0,sK15(sK5)) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_7704,plain,
! [X0: $i] :
( empty(sK15(sK8))
| in(X0,sK15(sK8))
| ~ element(X0,sK15(sK8)) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_7992,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_84,c_91]) ).
tcf(c_8192,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_106,c_91]) ).
tcf(c_8395,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,X2),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_85,c_86]) ).
tcf(c_15228,plain,
( empty(sK15(sK5))
| in(sK16(sK15(sK5)),sK15(sK5))
| ~ element(sK16(sK15(sK5)),sK15(sK5)) ),
inference(instantiation,[status(thm)],[c_7570]) ).
tcf(c_15229,plain,
element(sK16(sK15(sK5)),sK15(sK5)),
inference(instantiation,[status(thm)],[c_119]) ).
tcf(c_15434,plain,
( empty(sK15(sK8))
| in(sK16(sK15(sK8)),sK15(sK8))
| ~ element(sK16(sK15(sK8)),sK15(sK8)) ),
inference(instantiation,[status(thm)],[c_7704]) ).
tcf(c_15435,plain,
element(sK16(sK15(sK8)),sK15(sK8)),
inference(instantiation,[status(thm)],[c_119]) ).
tcf(c_16798,plain,
! [X0: $i,X1: $i] : subset(set_intersection2(X0,X1),X0),
inference(superposition,[status(thm)],[c_5402,c_94]) ).
tcf(c_16889,plain,
! [X0: $i,X1: $i] : subset(set_intersection2(X0,X1),X1),
inference(superposition,[status(thm)],[c_63,c_16798]) ).
tcf(c_16951,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = X0 )
| ~ subset(X0,set_intersection2(X1,X0)) ),
inference(superposition,[status(thm)],[c_16889,c_60]) ).
tcf(c_21733,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ in(sK2(X0,X1,X0),X1)
| ~ in(sK2(X0,X1,X0),X0) ),
inference(superposition,[status(thm)],[c_6327,c_54]) ).
tcf(c_22817,plain,
! [X0: $i,X1: $i] :
( ~ empty(empty_set)
| ~ in(X0,relation_image(empty_set,X1)) ),
inference(superposition,[status(thm)],[c_6683,c_91]) ).
tcf(c_22820,plain,
! [X0: $i,X1: $i] : ~ in(X0,relation_image(empty_set,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_22817,c_104]) ).
tcf(c_22869,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(superposition,[status(thm)],[c_6285,c_22820]) ).
tcf(c_34538,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = X0 )
| ~ subset(X0,X1)
| ~ subset(X0,X0) ),
inference(superposition,[status(thm)],[c_65,c_16951]) ).
tcf(c_34554,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = X0 )
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34538,c_100]) ).
tcf(c_34569,plain,
! [X0: $i] :
( empty(X0)
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_5369,c_34554]) ).
tcf(c_35696,plain,
set_intersection2(sK5,sK15(sK5)) = sK15(sK5),
inference(superposition,[status(thm)],[c_34569,c_78]) ).
tcf(c_35697,plain,
set_intersection2(sK8,sK15(sK8)) = sK15(sK8),
inference(superposition,[status(thm)],[c_34569,c_89]) ).
tcf(c_36303,plain,
( in(sK16(sK15(sK5)),sK5)
| empty(set_intersection2(sK5,sK15(sK5))) ),
inference(superposition,[status(thm)],[c_35696,c_5490]) ).
tcf(c_36351,plain,
( empty(sK15(sK5))
| in(sK16(sK15(sK5)),sK5) ),
inference(light_normalisation,[status(thm)],[c_36303,c_35696]) ).
tcf(c_36564,plain,
( in(sK16(sK15(sK8)),sK8)
| empty(set_intersection2(sK8,sK15(sK8))) ),
inference(superposition,[status(thm)],[c_35697,c_5490]) ).
tcf(c_36612,plain,
( empty(sK15(sK8))
| in(sK16(sK15(sK8)),sK8) ),
inference(light_normalisation,[status(thm)],[c_36564,c_35697]) ).
tcf(c_368429,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_52]) ).
tcf(c_368448,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,X0),X0)
| ( set_intersection2(X0,X1) = X0 ) ),
inference(equality_factoring,[status(thm)],[c_55]) ).
tcf(c_368460,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,X1),X1)
| ( set_intersection2(X0,X1) = X1 ) ),
inference(equality_factoring,[status(thm)],[c_56]) ).
tcf(c_368471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X0) ),
inference(superposition,[status(thm)],[c_57,c_54]) ).
tcf(c_368481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_55,c_58]) ).
tcf(c_368482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| in(sK2(X0,set_intersection2(X1,X2),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_56,c_58]) ).
tcf(c_368483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_56,c_58]) ).
tcf(c_368484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_55,c_58]) ).
tcf(c_368503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(X0,X1),X2,X3),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_55,c_59]) ).
tcf(c_368504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| in(sK2(X0,set_intersection2(X1,X2),X3),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_56,c_59]) ).
tcf(c_368505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_56,c_59]) ).
tcf(c_368506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_55,c_59]) ).
tcf(c_368527,plain,
! [X0: $i] :
( ( X0 = sK6 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_80,c_52]) ).
tcf(c_368535,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_63,c_57]) ).
tcf(c_368543,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_64,c_58]) ).
tcf(c_368545,plain,
! [X0: $i] : set_intersection2(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_64,c_63]) ).
tcf(c_368555,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_intersection2(X2,X1))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_63,c_65]) ).
tcf(c_368558,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_65,c_60]) ).
tcf(c_368566,plain,
! [X0: $i] :
( ( X0 = sK9 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_90,c_52]) ).
tcf(c_368576,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_66]) ).
tcf(c_368586,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,relation_dom(X0)) = relation_image(X0,X1) )
| ~ relation(X0)
| ~ subset(relation_image(X0,relation_dom(X0)),relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_67,c_60]) ).
tcf(c_368596,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,relation_inverse_image(X1,X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_inverse_image(X1,X0))) ),
inference(superposition,[status(thm)],[c_68,c_60]) ).
tcf(c_368606,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_52]) ).
tcf(c_368626,plain,
! [X0: $i] :
( function(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_77]) ).
tcf(c_368628,plain,
function(sK6),
inference(superposition,[status(thm)],[c_80,c_77]) ).
tcf(c_368629,plain,
function(sK9),
inference(superposition,[status(thm)],[c_90,c_77]) ).
tcf(c_368630,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_104,c_77]) ).
tcf(c_368640,plain,
relation(sK9),
inference(superposition,[status(thm)],[c_90,c_82]) ).
tcf(c_368654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| ~ in(sK7(X0,set_intersection2(X1,X2),X3),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,set_intersection2(X1,X2),X3)),X2)
| ~ in(apply(X0,sK7(X0,set_intersection2(X1,X2),X3)),X1) ),
inference(superposition,[status(thm)],[c_57,c_83]) ).
tcf(c_368672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK7(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_84,c_59]) ).
tcf(c_368673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK7(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_84,c_58]) ).
tcf(c_368674,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,relation_dom(X0)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_factoring,[status(thm)],[c_84]) ).
tcf(c_368700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| in(apply(X0,sK7(X0,X1,set_intersection2(X2,X3))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_59]) ).
tcf(c_368701,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| in(apply(X0,sK7(X0,X1,set_intersection2(X2,X3))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_58]) ).
tcf(c_368702,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),X3)),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_59]) ).
tcf(c_368703,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),X3)),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_58]) ).
tcf(c_368735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_inverse_image(X0,set_intersection2(X2,X3)))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X3)
| ~ in(apply(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_57,c_86]) ).
tcf(c_368736,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,X2),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_85,c_86]) ).
tcf(c_368757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,X3),X3)
| in(sK2(relation_inverse_image(X0,X1),X2,X3),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_87]) ).
tcf(c_368758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),X3),X3)
| in(sK2(X1,relation_inverse_image(X0,X2),X3),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_87]) ).
tcf(c_368759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X0,X1)),X3)
| in(sK2(X2,X3,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_87]) ).
tcf(c_368760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X0,X1)),X2)
| in(sK2(X2,X3,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_87]) ).
tcf(c_368761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),X3),X3)
| in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),X3)),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_87]) ).
tcf(c_368762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| in(apply(X0,sK7(X0,X2,relation_inverse_image(X1,X3))),X2)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_87]) ).
tcf(c_368763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_84,c_87]) ).
tcf(c_368813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,X3),X3)
| in(apply(X0,sK2(relation_inverse_image(X0,X1),X2,X3)),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_88]) ).
tcf(c_368814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),X3),X3)
| in(apply(X0,sK2(X1,relation_inverse_image(X0,X2),X3)),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_88]) ).
tcf(c_368815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X0,X1)),X3)
| in(apply(X0,sK2(X2,X3,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_88]) ).
tcf(c_368816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X0,X1)),X2)
| in(apply(X0,sK2(X2,X3,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_88]) ).
tcf(c_368817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),X3),X3)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X2),X3))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_88]) ).
tcf(c_368818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X0,X2,relation_inverse_image(X1,X3))),X3)
| in(apply(X0,sK7(X0,X2,relation_inverse_image(X1,X3))),X2)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_88]) ).
tcf(c_368819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X0))
| in(apply(X1,sK7(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_84,c_88]) ).
tcf(c_368865,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_91]) ).
tcf(c_368866,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,X2),X2)
| ( set_intersection2(X1,X0) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_91]) ).
tcf(c_368867,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| ( set_intersection2(X1,X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_56,c_91]) ).
tcf(c_368868,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X1)
| ( set_intersection2(X1,X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_55,c_91]) ).
tcf(c_368869,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_57,c_91]) ).
tcf(c_368870,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_84,c_91]) ).
tcf(c_368871,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_91]) ).
tcf(c_368872,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X2,X1)),X2)
| ( relation_inverse_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_91]) ).
tcf(c_368873,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,X1),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_84,c_91]) ).
tcf(c_368909,plain,
! [X0: $i] : relation(sK14(X0)),
inference(superposition,[status(thm)],[c_116,c_82]) ).
tcf(c_368910,plain,
! [X0: $i] : function(sK14(X0)),
inference(superposition,[status(thm)],[c_116,c_77]) ).
tcf(c_368911,plain,
! [X0: $i,X1: $i] :
( ( sK14(X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_116,c_52]) ).
tcf(c_368924,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_55,c_93]) ).
tcf(c_368925,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_56,c_93]) ).
tcf(c_368926,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_56,c_93]) ).
tcf(c_368927,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_55,c_93]) ).
tcf(c_368928,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_intersection2(X1,X2))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_93]) ).
tcf(c_368929,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| element(sK7(X0,X1,X2),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_84,c_93]) ).
tcf(c_368930,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| element(apply(X0,sK7(X0,X1,X2)),X1)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_93]) ).
tcf(c_368931,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,X2),X2)
| in(apply(X0,sK7(X0,X1,X2)),X1)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_93]) ).
tcf(c_368932,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,X2),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_84,c_93]) ).
tcf(c_368972,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_intersection2(X1,X2))
| ~ in(sK10(X0,set_intersection2(X1,X2)),X2)
| ~ in(sK10(X0,set_intersection2(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_57,c_94]) ).
tcf(c_368976,plain,
! [X0: $i] :
( empty(X0)
| in(sK16(X0),X0) ),
inference(superposition,[status(thm)],[c_119,c_92]) ).
tcf(c_368983,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| element(sK10(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_95,c_93]) ).
tcf(c_368984,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95,c_91]) ).
tcf(c_368985,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X0,X1),X2)
| in(sK10(set_intersection2(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_95,c_59]) ).
tcf(c_368986,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X0,X1),X2)
| in(sK10(set_intersection2(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_95,c_58]) ).
tcf(c_368987,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X0,X1),X2)
| in(apply(X0,sK10(relation_inverse_image(X0,X1),X2)),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_95,c_88]) ).
tcf(c_368988,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X0,X1),X2)
| in(sK10(relation_inverse_image(X0,X1),X2),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_95,c_87]) ).
tcf(c_369012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X2,X3),X3)
| in(sK2(X0,X2,X3),X1)
| ( set_intersection2(X0,X2) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_55,c_96]) ).
tcf(c_369013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X0,X3),X3)
| in(sK2(X2,X0,X3),X1)
| ( set_intersection2(X2,X0) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_96]) ).
tcf(c_369014,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X3)
| in(sK2(X2,X3,X0),X1)
| ( set_intersection2(X2,X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_96]) ).
tcf(c_369015,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X2)
| in(sK2(X2,X3,X0),X1)
| ( set_intersection2(X2,X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_55,c_96]) ).
tcf(c_369016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0)
| ~ subset(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_57,c_96]) ).
tcf(c_369017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,X3),X3)
| in(sK7(X0,X2,X3),X1)
| ( relation_inverse_image(X0,X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_84,c_96]) ).
tcf(c_369018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X0,X3),X3)
| in(apply(X2,sK7(X2,X0,X3)),X1)
| ( relation_inverse_image(X2,X0) = X3 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_85,c_96]) ).
tcf(c_369019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X3,X0),X1)
| in(apply(X2,sK7(X2,X3,X0)),X3)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_85,c_96]) ).
tcf(c_369020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X3,X0),X1)
| in(sK7(X2,X3,X0),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_96]) ).
tcf(c_369021,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK10(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_95,c_96]) ).
tcf(c_369076,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ in(X0,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_55,c_97]) ).
tcf(c_369077,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,X2),X2)
| ( set_intersection2(X1,X0) = X2 )
| ~ in(X0,sK2(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_56,c_97]) ).
tcf(c_369078,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| ( set_intersection2(X1,X2) = X0 )
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_56,c_97]) ).
tcf(c_369079,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X1)
| ( set_intersection2(X1,X2) = X0 )
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_55,c_97]) ).
tcf(c_369080,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(X2,X0)
| ~ in(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_57,c_97]) ).
tcf(c_369081,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK7(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_84,c_97]) ).
tcf(c_369082,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X0,X2),X2)
| ( relation_inverse_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK7(X1,X0,X2))) ),
inference(superposition,[status(thm)],[c_85,c_97]) ).
tcf(c_369083,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,sK7(X1,X2,X0)),X2)
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK7(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_85,c_97]) ).
tcf(c_369084,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X2,X0),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK7(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_84,c_97]) ).
tcf(c_369085,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,sK10(X0,X1)) ),
inference(superposition,[status(thm)],[c_95,c_97]) ).
tcf(c_369131,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(sK14(X0),powerset(X0)) ),
inference(superposition,[status(thm)],[c_115,c_92]) ).
tcf(c_369132,plain,
! [X0: $i] : in(sK14(X0),powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_369131,c_120]) ).
tcf(c_369137,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_98,c_92]) ).
tcf(c_369138,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_369137,c_120]) ).
tcf(c_369150,plain,
! [X0: $i] : subset(sK14(X0),X0),
inference(superposition,[status(thm)],[c_115,c_99]) ).
tcf(c_369151,plain,
! [X0: $i] : subset(sK16(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_119,c_99]) ).
tcf(c_369156,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_101]) ).
tcf(c_369157,plain,
empty_set = sK3,
inference(superposition,[status(thm)],[c_73,c_101]) ).
tcf(c_369158,plain,
empty_set = sK6,
inference(superposition,[status(thm)],[c_80,c_101]) ).
tcf(c_369159,plain,
empty_set = sK9,
inference(superposition,[status(thm)],[c_90,c_101]) ).
tcf(c_369161,plain,
! [X0: $i] : sK14(X0) = empty_set,
inference(superposition,[status(thm)],[c_116,c_101]) ).
tcf(c_369173,plain,
! [X0: $i] : element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[c_115,c_369161]) ).
tcf(c_369177,plain,
! [X0: $i] : subset(empty_set,X0),
inference(light_normalisation,[status(thm)],[c_369150,c_369161]) ).
tcf(c_369178,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_369177,c_60]) ).
tcf(c_369205,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X1,X2,X0),relation_dom(X1))
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK11(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_106,c_97]) ).
tcf(c_369206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X2,X3,X0),X1)
| in(sK12(X2,X3,X0),relation_dom(X2))
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_106,c_96]) ).
tcf(c_369207,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK11(X0,X1,X2),X2)
| in(sK12(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_106,c_93]) ).
tcf(c_369208,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,X1),relation_dom(X0))
| ( relation_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_106,c_91]) ).
tcf(c_369209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK12(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_106,c_59]) ).
tcf(c_369210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK12(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_106,c_58]) ).
tcf(c_369211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X0))
| in(apply(X1,sK11(X0,X3,relation_inverse_image(X1,X2))),X2)
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_106,c_88]) ).
tcf(c_369212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X0))
| in(sK11(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_106,c_87]) ).
tcf(c_369213,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK12(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_106,c_97]) ).
tcf(c_369214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X2,X3),X1)
| in(sK11(X0,X2,X3),X3)
| ( relation_image(X0,X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_106,c_96]) ).
tcf(c_369215,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),X2)
| element(sK12(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_106,c_93]) ).
tcf(c_369216,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_106,c_91]) ).
tcf(c_369298,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X1,X0,X2),X2)
| ( relation_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK12(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_107,c_97]) ).
tcf(c_369299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X2,X0,X3),X1)
| in(sK11(X2,X0,X3),X3)
| ( relation_image(X2,X0) = X3 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_96]) ).
tcf(c_369300,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK12(X0,X1,X2),X1)
| in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_93]) ).
tcf(c_369301,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_91]) ).
tcf(c_369302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X1,X2),X3),X2)
| in(sK11(X0,set_intersection2(X1,X2),X3),X3)
| ( relation_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_59]) ).
tcf(c_369303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X1,X2),X3),X1)
| in(sK11(X0,set_intersection2(X1,X2),X3),X3)
| ( relation_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_58]) ).
tcf(c_369304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),X3),X3)
| in(apply(X1,sK12(X0,relation_inverse_image(X1,X2),X3)),X2)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_88]) ).
tcf(c_369305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),X3),X3)
| in(sK12(X0,relation_inverse_image(X1,X2),X3),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_87]) ).
tcf(c_369306,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X1,X2,X0),X2)
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK11(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_107,c_97]) ).
tcf(c_369307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X2,X3,X0),X3)
| in(sK11(X2,X3,X0),X1)
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_96]) ).
tcf(c_369308,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK11(X0,X1,X2),X2)
| in(sK12(X0,X1,X2),X1)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_93]) ).
tcf(c_369309,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,X1),X2)
| ( relation_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_91]) ).
tcf(c_369310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X1,set_intersection2(X2,X3)),X1)
| in(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_59]) ).
tcf(c_369311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X1,set_intersection2(X2,X3)),X1)
| in(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_58]) ).
tcf(c_369312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_inverse_image(X1,X2)),X3)
| in(apply(X1,sK11(X0,X3,relation_inverse_image(X1,X2))),X2)
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_88]) ).
tcf(c_369313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_inverse_image(X1,X2)),X3)
| in(sK11(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_87]) ).
tcf(c_369435,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = X0 )
| ( apply(X1,sK12(X1,X2,X0)) = sK11(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK11(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_108,c_97]) ).
tcf(c_369436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X2,X3,X0),X1)
| ( relation_image(X2,X3) = X0 )
| ( apply(X2,sK12(X2,X3,X0)) = sK11(X2,X3,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_108,c_96]) ).
tcf(c_369437,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK12(X0,X1,X2)) = sK11(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_93]) ).
tcf(c_369438,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = X1 )
| ( apply(X0,sK12(X0,X2,X1)) = sK11(X0,X2,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_91]) ).
tcf(c_369439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,X3))) = sK11(X0,X1,set_intersection2(X2,X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_59]) ).
tcf(c_369440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,X3))) = sK11(X0,X1,set_intersection2(X2,X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_58]) ).
tcf(c_369441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK11(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_inverse_image(X1,X3) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,relation_inverse_image(X1,X3))) = sK11(X0,X2,relation_inverse_image(X1,X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_88]) ).
tcf(c_369442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| ( relation_inverse_image(X1,X3) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,relation_inverse_image(X1,X3))) = sK11(X0,X2,relation_inverse_image(X1,X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_87]) ).
tcf(c_369498,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X2,X1)
| ~ in(X2,relation_dom(X0))
| ~ in(relation_image(X0,X1),apply(X0,X2)) ),
inference(superposition,[status(thm)],[c_109,c_97]) ).
tcf(c_369499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,X3),X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,X1)
| ~ in(X3,relation_dom(X0))
| ~ subset(relation_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_109,c_96]) ).
tcf(c_369500,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(X1,X0),relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_109,c_93]) ).
tcf(c_369501,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X2,X1)
| ~ in(X2,relation_dom(X0))
| ~ empty(relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_109,c_91]) ).
tcf(c_369502,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,relation_image(X0,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),X2),X2)
| ~ in(sK7(X0,relation_image(X0,X1),X2),X1)
| ~ in(sK7(X0,relation_image(X0,X1),X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_109,c_83]) ).
tcf(c_369503,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_inverse_image(X1,relation_image(X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_109,c_86]) ).
tcf(c_369555,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_image(X0,X1))
| ~ in(relation_dom(X0),sK13(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_110,c_97]) ).
tcf(c_369556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X1,X2,X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_110,c_96]) ).
tcf(c_369557,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK13(X1,X2,X0),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_110,c_93]) ).
tcf(c_369558,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_110,c_91]) ).
tcf(c_369576,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(empty_set,powerset(X0)) ),
inference(superposition,[status(thm)],[c_369173,c_92]) ).
tcf(c_369578,plain,
! [X0: $i] : in(empty_set,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_369576,c_120]) ).
tcf(c_369579,plain,
! [X0: $i] : ~ in(powerset(X0),empty_set),
inference(superposition,[status(thm)],[c_369578,c_97]) ).
tcf(c_369580,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X1)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_369578,c_96]) ).
tcf(c_369593,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X0))
| ~ in(X0,sK13(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_111,c_97]) ).
tcf(c_369594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X1,X2,X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_111,c_96]) ).
tcf(c_369595,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK13(X1,X2,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_111,c_93]) ).
tcf(c_369596,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_111,c_91]) ).
tcf(c_369597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X1,set_intersection2(X2,X3),X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_111,c_59]) ).
tcf(c_369598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X1,set_intersection2(X2,X3),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_111,c_58]) ).
tcf(c_369599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK13(X1,relation_inverse_image(X2,X3),X0)),X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_111,c_88]) ).
tcf(c_369600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X1,relation_inverse_image(X2,X3),X0),relation_dom(X2))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_111,c_87]) ).
tcf(c_369659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_image(X0,X1),X2,X3),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = X3 )
| ( apply(X0,sK13(X0,X1,sK2(relation_image(X0,X1),X2,X3))) = sK2(relation_image(X0,X1),X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_112]) ).
tcf(c_369660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,relation_image(X0,X1),X3),X3)
| ( set_intersection2(X2,relation_image(X0,X1)) = X3 )
| ( apply(X0,sK13(X0,X1,sK2(X2,relation_image(X0,X1),X3))) = sK2(X2,relation_image(X0,X1),X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_112]) ).
tcf(c_369661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_image(X0,X1)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK13(X0,X1,sK2(X2,X3,relation_image(X0,X1)))) = sK2(X2,X3,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_112]) ).
tcf(c_369662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_image(X0,X1)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK13(X0,X1,sK2(X2,X3,relation_image(X0,X1)))) = sK2(X2,X3,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_112]) ).
tcf(c_369663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_image(X1,X2),X3),X3)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = X3 )
| ( apply(X1,sK13(X1,X2,apply(X0,sK7(X0,relation_image(X1,X2),X3)))) = apply(X0,sK7(X0,relation_image(X1,X2),X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_112]) ).
tcf(c_369664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X3,relation_image(X1,X2))),X3)
| ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK7(X0,X3,relation_image(X1,X2)))) = sK7(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_112]) ).
tcf(c_369665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,relation_image(X1,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK7(X0,X3,relation_image(X1,X2)))) = sK7(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_84,c_112]) ).
tcf(c_369666,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_image(X0,X1),X2)
| ( apply(X0,sK13(X0,X1,sK10(relation_image(X0,X1),X2))) = sK10(relation_image(X0,X1),X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_95,c_112]) ).
tcf(c_369667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X0,sK12(X0,X3,relation_image(X1,X2))) = sK11(X0,X3,relation_image(X1,X2)) )
| ( apply(X1,sK13(X1,X2,sK11(X0,X3,relation_image(X1,X2)))) = sK11(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_112]) ).
tcf(c_369668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_image(X1,X2)),X3)
| ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK11(X0,X3,relation_image(X1,X2)))) = sK11(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_112]) ).
tcf(c_369669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_image(X1,X2)),relation_dom(X0))
| ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK11(X0,X3,relation_image(X1,X2)))) = sK11(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_106,c_112]) ).
tcf(c_369670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,relation_image(X1,X2),X3),X3)
| ( relation_image(X0,relation_image(X1,X2)) = X3 )
| ( apply(X1,sK13(X1,X2,sK12(X0,relation_image(X1,X2),X3))) = sK12(X0,relation_image(X1,X2),X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_112]) ).
tcf(c_369671,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK13(X1,X2,apply(X1,X0))) = apply(X1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_109,c_112]) ).
tcf(c_369672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),X0))) = sK13(X1,relation_image(X2,X3),X0) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_111,c_112]) ).
tcf(c_369761,plain,
! [X0: $i] :
( empty(X0)
| empty(powerset(X0))
| in(sK15(X0),powerset(X0)) ),
inference(superposition,[status(thm)],[c_117,c_92]) ).
tcf(c_369762,plain,
! [X0: $i] :
( empty(X0)
| subset(sK15(X0),X0) ),
inference(superposition,[status(thm)],[c_117,c_99]) ).
tcf(c_369765,plain,
! [X0: $i] :
( empty(X0)
| in(sK15(X0),powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_369761,c_120]) ).
tcf(c_369769,plain,
! [X0: $i] :
( ( sK16(powerset(X0)) = X0 )
| ~ subset(X0,sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_369151,c_60]) ).
tcf(c_369782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X2,X3),X3)
| ( set_intersection2(X0,X2) = X3 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_55,c_320]) ).
tcf(c_369783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X0,X3),X3)
| ( set_intersection2(X2,X0) = X3 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_320]) ).
tcf(c_369784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X3)
| ( set_intersection2(X2,X3) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_320]) ).
tcf(c_369785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X2)
| ( set_intersection2(X2,X3) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_55,c_320]) ).
tcf(c_369786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X2)
| ~ in(X3,X1)
| ~ in(X3,X0)
| ~ subset(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_57,c_320]) ).
tcf(c_369787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,X3),X3)
| ( relation_inverse_image(X0,X2) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_84,c_320]) ).
tcf(c_369788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X0,X3),X3)
| ( relation_inverse_image(X2,X0) = X3 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_85,c_320]) ).
tcf(c_369789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK7(X2,X3,X0)),X3)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_85,c_320]) ).
tcf(c_369790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X3,X0),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_320]) ).
tcf(c_369791,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_95,c_320]) ).
tcf(c_369792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X2,X3) = X0 )
| ( apply(X2,sK12(X2,X3,X0)) = sK11(X2,X3,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_108,c_320]) ).
tcf(c_369793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X2,X3,X0),X3)
| ( relation_image(X2,X3) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_320]) ).
tcf(c_369794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X2,X3,X0),relation_dom(X2))
| ( relation_image(X2,X3) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_106,c_320]) ).
tcf(c_369795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X2,X3),X3)
| ( relation_image(X0,X2) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_106,c_320]) ).
tcf(c_369796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X2,X0,X3),X3)
| ( relation_image(X2,X0) = X3 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_320]) ).
tcf(c_369797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,X1)
| ~ in(X3,relation_dom(X0))
| ~ subset(relation_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_109,c_320]) ).
tcf(c_369798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_110,c_320]) ).
tcf(c_369799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_111,c_320]) ).
tcf(c_369800,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_369578,c_320]) ).
tcf(c_369926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X2,X3),X1)
| in(sK2(X0,X2,X3),X3)
| ( set_intersection2(X0,X2) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_55,c_321]) ).
tcf(c_369927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X0,X3),X1)
| in(sK2(X2,X0,X3),X3)
| ( set_intersection2(X2,X0) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_321]) ).
tcf(c_369928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,X0),X1)
| in(sK2(X2,X3,X0),X3)
| ( set_intersection2(X2,X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_321]) ).
tcf(c_369929,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,X0),X1)
| in(sK2(X2,X3,X0),X2)
| ( set_intersection2(X2,X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_55,c_321]) ).
tcf(c_369930,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0)
| ~ subset(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_57,c_321]) ).
tcf(c_369931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X2,X3),X1)
| in(sK7(X0,X2,X3),X3)
| ( relation_inverse_image(X0,X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_84,c_321]) ).
tcf(c_369932,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X0,X3),X3)
| element(apply(X2,sK7(X2,X0,X3)),X1)
| ( relation_inverse_image(X2,X0) = X3 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_85,c_321]) ).
tcf(c_369933,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X2,X3,X0),X1)
| in(apply(X2,sK7(X2,X3,X0)),X3)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_85,c_321]) ).
tcf(c_369934,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X2,X3,X0),X1)
| in(sK7(X2,X3,X0),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_321]) ).
tcf(c_369935,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| element(sK10(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_95,c_321]) ).
tcf(c_369936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X2,X3,X0),X1)
| ( relation_image(X2,X3) = X0 )
| ( apply(X2,sK12(X2,X3,X0)) = sK11(X2,X3,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_108,c_321]) ).
tcf(c_369937,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X2,X3,X0),X1)
| in(sK12(X2,X3,X0),X3)
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_321]) ).
tcf(c_369938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X2,X3,X0),X1)
| in(sK12(X2,X3,X0),relation_dom(X2))
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_106,c_321]) ).
tcf(c_369939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X2,X3),X1)
| in(sK11(X0,X2,X3),X3)
| ( relation_image(X0,X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_106,c_321]) ).
tcf(c_369940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X2,X0,X3),X1)
| in(sK11(X2,X0,X3),X3)
| ( relation_image(X2,X0) = X3 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_321]) ).
tcf(c_369941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X0,X3),X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,X1)
| ~ in(X3,relation_dom(X0))
| ~ subset(relation_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_109,c_321]) ).
tcf(c_369942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK13(X1,X2,X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_110,c_321]) ).
tcf(c_369943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK13(X1,X2,X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_111,c_321]) ).
tcf(c_369944,plain,
! [X0: $i,X1: $i] :
( element(empty_set,X1)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_369578,c_321]) ).
tcf(c_370073,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ in(sK2(X0,X1,X0),X1)
| ~ in(sK2(X0,X1,X0),X0) ),
inference(superposition,[status(thm)],[c_368448,c_54]) ).
tcf(c_370074,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X2,X0),X1)
| ( set_intersection2(X0,X2) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368448,c_321]) ).
tcf(c_370075,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X2) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368448,c_320]) ).
tcf(c_370076,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ in(X0,sK2(X0,X1,X0)) ),
inference(superposition,[status(thm)],[c_368448,c_97]) ).
tcf(c_370077,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,X0),X1)
| ( set_intersection2(X0,X2) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368448,c_96]) ).
tcf(c_370078,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,X0),X0)
| ( set_intersection2(X0,X1) = X0 ) ),
inference(superposition,[status(thm)],[c_368448,c_93]) ).
tcf(c_370079,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368448,c_91]) ).
tcf(c_370080,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_368448,c_59]) ).
tcf(c_370081,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_368448,c_58]) ).
tcf(c_370082,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,X1),X2,relation_inverse_image(X0,X1))),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368448,c_88]) ).
tcf(c_370083,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368448,c_87]) ).
tcf(c_370084,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_image(X0,X1),X2) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(relation_image(X0,X1),X2,relation_image(X0,X1)))) = sK2(relation_image(X0,X1),X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368448,c_112]) ).
tcf(c_370142,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X2,X0,X0),X1)
| ( set_intersection2(X2,X0) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368460,c_321]) ).
tcf(c_370143,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,X0) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368460,c_320]) ).
tcf(c_370144,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = X0 )
| ~ in(X0,sK2(X1,X0,X0)) ),
inference(superposition,[status(thm)],[c_368460,c_97]) ).
tcf(c_370145,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X0,X0),X1)
| ( set_intersection2(X2,X0) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368460,c_96]) ).
tcf(c_370146,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,X1),X1)
| ( set_intersection2(X0,X1) = X1 ) ),
inference(superposition,[status(thm)],[c_368460,c_93]) ).
tcf(c_370147,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368460,c_91]) ).
tcf(c_370148,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368460,c_59]) ).
tcf(c_370149,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368460,c_58]) ).
tcf(c_370150,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK2(X1,relation_inverse_image(X0,X2),relation_inverse_image(X0,X2))),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368460,c_88]) ).
tcf(c_370151,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),relation_inverse_image(X0,X2)),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368460,c_87]) ).
tcf(c_370152,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,relation_image(X0,X1)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,relation_image(X0,X1),relation_image(X0,X1)))) = sK2(X2,relation_image(X0,X1),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368460,c_112]) ).
tcf(c_370216,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_55,c_368471]) ).
tcf(c_370217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X0) ),
inference(superposition,[status(thm)],[c_57,c_368471]) ).
tcf(c_370218,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X0) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X0) ),
inference(superposition,[status(thm)],[c_368460,c_368471]) ).
tcf(c_370219,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X0),X1) = X2 )
| ~ in(sK2(X0,X1,X2),X0)
| ~ in(sK2(set_intersection2(X0,X0),X1,X2),X2)
| ~ in(sK2(set_intersection2(X0,X0),X1,X2),X1)
| ~ in(sK2(set_intersection2(X0,X0),X1,X2),X0) ),
inference(superposition,[status(thm)],[c_53,c_368471]) ).
tcf(c_370220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_63,c_368471]) ).
tcf(c_370222,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 )
| ~ in(sK2(empty_set,X1,X2),X0)
| ~ in(sK2(set_intersection2(X0,empty_set),X1,X2),empty_set)
| ~ in(sK2(set_intersection2(X0,empty_set),X1,X2),X2)
| ~ in(sK2(set_intersection2(X0,empty_set),X1,X2),X1) ),
inference(superposition,[status(thm)],[c_64,c_368471]) ).
tcf(c_370223,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 )
| ~ in(sK2(empty_set,X1,X2),empty_set)
| ~ in(sK2(set_intersection2(empty_set,X0),X1,X2),X2)
| ~ in(sK2(set_intersection2(empty_set,X0),X1,X2),X1)
| ~ in(sK2(set_intersection2(empty_set,X0),X1,X2),X0) ),
inference(superposition,[status(thm)],[c_368545,c_368471]) ).
tcf(c_370227,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(empty_set,X0) = X1 )
| ~ in(sK2(empty_set,X0,X1),empty_set)
| ~ in(sK2(empty_set,X0,X1),X2)
| ~ in(sK2(empty_set,X0,X1),X1)
| ~ in(sK2(empty_set,X0,X1),X0) ),
inference(light_normalisation,[status(thm)],[c_370223,c_368545]) ).
tcf(c_370228,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = empty_set )
| ~ in(sK2(empty_set,X0,X1),empty_set)
| ~ in(sK2(empty_set,X0,X1),X2)
| ~ in(sK2(empty_set,X0,X1),X1)
| ~ in(sK2(empty_set,X0,X1),X0) ),
inference(light_normalisation,[status(thm)],[c_370227,c_368545]) ).
tcf(c_370260,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(set_intersection2(X0,X0),X1,X2),X0)
| ( set_intersection2(set_intersection2(X0,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_53,c_368481]) ).
tcf(c_370261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_63,c_368481]) ).
tcf(c_370263,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| in(sK2(set_intersection2(X0,empty_set),X1,X2),X0)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_368481]) ).
tcf(c_370264,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| in(sK2(set_intersection2(empty_set,X0),X1,X2),empty_set)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_368481]) ).
tcf(c_370265,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X0)
| in(sK2(set_intersection2(X0,X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_53,c_368481]) ).
tcf(c_370266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_63,c_368481]) ).
tcf(c_370268,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X0)
| in(sK2(set_intersection2(X0,empty_set),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_368481]) ).
tcf(c_370269,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),empty_set)
| in(sK2(set_intersection2(empty_set,X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_368481]) ).
tcf(c_370271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X2,X3),X4,X0),X1)
| in(sK2(set_intersection2(X2,X3),X4,X0),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368481,c_321]) ).
tcf(c_370272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,X0),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368481,c_320]) ).
tcf(c_370273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ in(X0,sK2(set_intersection2(X1,X2),X3,X0)) ),
inference(superposition,[status(thm)],[c_368481,c_97]) ).
tcf(c_370274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,X0),X2)
| in(sK2(set_intersection2(X2,X3),X4,X0),X1)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368481,c_96]) ).
tcf(c_370275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_368481,c_93]) ).
tcf(c_370276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368481,c_91]) ).
tcf(c_370277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X4)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368481,c_59]) ).
tcf(c_370278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X3)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368481,c_58]) ).
tcf(c_370279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),X1)
| in(apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368481,c_88]) ).
tcf(c_370280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),X1)
| in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368481,c_87]) ).
tcf(c_370281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)))) = sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368481,c_112]) ).
tcf(c_370283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X0,X2),X3,X4),X1)
| in(sK2(set_intersection2(X0,X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368481,c_321]) ).
tcf(c_370284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368481,c_320]) ).
tcf(c_370285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(X0,sK2(set_intersection2(X0,X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_368481,c_97]) ).
tcf(c_370286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X2),X3,X4),X4)
| in(sK2(set_intersection2(X0,X2),X3,X4),X1)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368481,c_96]) ).
tcf(c_370287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X0)
| in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_368481,c_93]) ).
tcf(c_370288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368481,c_91]) ).
tcf(c_370289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_368481,c_59]) ).
tcf(c_370290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_368481,c_58]) ).
tcf(c_370291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368481,c_88]) ).
tcf(c_370292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368481,c_87]) ).
tcf(c_370293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = X4 )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),X3,X4))) = sK2(set_intersection2(relation_image(X0,X1),X2),X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368481,c_112]) ).
tcf(c_370295,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 ) ),
inference(equality_factoring,[status(thm)],[c_368481]) ).
tcf(c_370310,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X0,X1),X2)
| in(sK2(empty_set,X0,X1),X1)
| ( set_intersection2(empty_set,X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_370268,c_64]) ).
tcf(c_370311,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X0),X2)
| in(sK2(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_370310,c_368545]) ).
tcf(c_370492,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,set_intersection2(X1,X1),X2),X1)
| ( set_intersection2(X0,set_intersection2(X1,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_53,c_368482]) ).
tcf(c_370493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,X1),X3),X3)
| in(sK2(X0,set_intersection2(X1,X2),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_63,c_368482]) ).
tcf(c_370495,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X2)
| in(sK2(X0,set_intersection2(X1,empty_set),X2),X1)
| ( set_intersection2(X0,set_intersection2(X1,empty_set)) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_368482]) ).
tcf(c_370496,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X2)
| in(sK2(X0,set_intersection2(empty_set,X1),X2),empty_set)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_368482]) ).
tcf(c_370497,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,set_intersection2(X1,X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_53,c_368482]) ).
tcf(c_370498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,X1),X3),X1)
| in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_63,c_368482]) ).
tcf(c_370500,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X1)
| in(sK2(X0,set_intersection2(X1,empty_set),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,empty_set)) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_368482]) ).
tcf(c_370501,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),empty_set)
| in(sK2(X0,set_intersection2(empty_set,X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_368482]) ).
tcf(c_370502,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X0),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X0 )
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),X0)
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_368482,c_54]) ).
tcf(c_370503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(X3,X4),X0),X1)
| in(sK2(X2,set_intersection2(X3,X4),X0),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368482,c_321]) ).
tcf(c_370504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),X0),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368482,c_320]) ).
tcf(c_370505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X3),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ~ in(X0,sK2(X1,set_intersection2(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_368482,c_97]) ).
tcf(c_370506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),X0),X3)
| in(sK2(X2,set_intersection2(X3,X4),X0),X1)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368482,c_96]) ).
tcf(c_370507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,set_intersection2(X1,X2),X3),X3)
| in(sK2(X0,set_intersection2(X1,X2),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_368482,c_93]) ).
tcf(c_370508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X3),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368482,c_91]) ).
tcf(c_370509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X4)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368482,c_59]) ).
tcf(c_370510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X3)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368482,c_58]) ).
tcf(c_370511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X2)
| in(apply(X0,sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368482,c_88]) ).
tcf(c_370512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X2)
| in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368482,c_87]) ).
tcf(c_370513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)))) = sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368482,c_112]) ).
tcf(c_370514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X2)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_368482,c_368471]) ).
tcf(c_370516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(X0,X3),X4),X1)
| in(sK2(X2,set_intersection2(X0,X3),X4),X4)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368482,c_321]) ).
tcf(c_370517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X0,X3),X4),X4)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368482,c_320]) ).
tcf(c_370518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X0,X2),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ~ in(X0,sK2(X1,set_intersection2(X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_368482,c_97]) ).
tcf(c_370519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X0,X3),X4),X4)
| in(sK2(X2,set_intersection2(X0,X3),X4),X1)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368482,c_96]) ).
tcf(c_370520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,set_intersection2(X1,X2),X3),X1)
| in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_368482,c_93]) ).
tcf(c_370521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X0,X2),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368482,c_91]) ).
tcf(c_370522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X4)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X2)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X3)) = X4 ) ),
inference(superposition,[status(thm)],[c_368482,c_59]) ).
tcf(c_370523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X4)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X1)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X3)) = X4 ) ),
inference(superposition,[status(thm)],[c_368482,c_58]) ).
tcf(c_370524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),X4),X4)
| in(apply(X0,sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),X4)),X2)
| ( set_intersection2(X1,set_intersection2(relation_inverse_image(X0,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368482,c_88]) ).
tcf(c_370525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),X4),X4)
| in(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),X4),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(relation_inverse_image(X0,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368482,c_87]) ).
tcf(c_370526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(relation_image(X0,X1),X3),X4),X4)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X1),X3)) = X4 )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(relation_image(X0,X1),X3),X4))) = sK2(X2,set_intersection2(relation_image(X0,X1),X3),X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368482,c_112]) ).
tcf(c_370528,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X1),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X1 ) ),
inference(equality_factoring,[status(thm)],[c_368482]) ).
tcf(c_370744,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(sK16(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368976,c_321]) ).
tcf(c_370745,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368976,c_320]) ).
tcf(c_370746,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK16(X0)) ),
inference(superposition,[status(thm)],[c_368976,c_97]) ).
tcf(c_370747,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK16(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368976,c_96]) ).
tcf(c_370750,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| in(sK16(set_intersection2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_368976,c_59]) ).
tcf(c_370751,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| in(sK16(set_intersection2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_368976,c_58]) ).
tcf(c_370752,plain,
! [X0: $i,X1: $i] :
( empty(relation_inverse_image(X0,X1))
| in(apply(X0,sK16(relation_inverse_image(X0,X1))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368976,c_88]) ).
tcf(c_370753,plain,
! [X0: $i,X1: $i] :
( empty(relation_inverse_image(X0,X1))
| in(sK16(relation_inverse_image(X0,X1)),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368976,c_87]) ).
tcf(c_370754,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK13(X0,X1,sK16(relation_image(X0,X1)))) = sK16(relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368976,c_112]) ).
tcf(c_370809,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368984,c_60]) ).
tcf(c_370819,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X0)
| in(sK2(X1,X2,set_intersection2(X0,X0)),X2)
| ( set_intersection2(X0,X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_53,c_368483]) ).
tcf(c_370820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X3,X2)),X2)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_63,c_368483]) ).
tcf(c_370822,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X2)
| in(sK2(X0,X1,set_intersection2(X2,empty_set)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_64,c_368483]) ).
tcf(c_370823,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),empty_set)
| in(sK2(X0,X1,set_intersection2(empty_set,X2)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_368545,c_368483]) ).
tcf(c_370824,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| in(sK2(X1,X2,set_intersection2(X0,X0)),X0)
| ( set_intersection2(X0,X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_53,c_368483]) ).
tcf(c_370825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X3,X2)),X1)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_63,c_368483]) ).
tcf(c_370827,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X1)
| in(sK2(X0,X1,set_intersection2(X2,empty_set)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_64,c_368483]) ).
tcf(c_370828,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X1)
| in(sK2(X0,X1,set_intersection2(empty_set,X2)),empty_set)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_368545,c_368483]) ).
tcf(c_370830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,set_intersection2(X0,X2)),X1)
| in(sK2(X3,X4,set_intersection2(X0,X2)),X4)
| ( set_intersection2(X0,X2) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368483,c_321]) ).
tcf(c_370831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X0,X2)),X4)
| ( set_intersection2(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368483,c_320]) ).
tcf(c_370832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,set_intersection2(X0,X3)),X2)
| ( set_intersection2(X0,X3) = set_intersection2(X1,X2) )
| ~ in(X0,sK2(X1,X2,set_intersection2(X0,X3))) ),
inference(superposition,[status(thm)],[c_368483,c_97]) ).
tcf(c_370833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X0,X2)),X4)
| in(sK2(X3,X4,set_intersection2(X0,X2)),X1)
| ( set_intersection2(X0,X2) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368483,c_96]) ).
tcf(c_370834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368483,c_93]) ).
tcf(c_370835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),X3)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368483,c_91]) ).
tcf(c_370836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(set_intersection2(X0,X1),X2)),X4)
| in(sK2(X3,X4,set_intersection2(set_intersection2(X0,X1),X2)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368483,c_59]) ).
tcf(c_370837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(set_intersection2(X0,X1),X2)),X4)
| in(sK2(X3,X4,set_intersection2(set_intersection2(X0,X1),X2)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368483,c_58]) ).
tcf(c_370838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(relation_inverse_image(X0,X1),X2)),X4)
| in(apply(X0,sK2(X3,X4,set_intersection2(relation_inverse_image(X0,X1),X2))),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368483,c_88]) ).
tcf(c_370839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(relation_inverse_image(X0,X1),X2)),X4)
| in(sK2(X3,X4,set_intersection2(relation_inverse_image(X0,X1),X2)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368483,c_87]) ).
tcf(c_370840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,set_intersection2(relation_image(X0,X1),X4)),X3)
| ( set_intersection2(relation_image(X0,X1),X4) = set_intersection2(X2,X3) )
| ( apply(X0,sK13(X0,X1,sK2(X2,X3,set_intersection2(relation_image(X0,X1),X4)))) = sK2(X2,X3,set_intersection2(relation_image(X0,X1),X4)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368483,c_112]) ).
tcf(c_370842,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_intersection2(X1,X2)),X1)
| ( set_intersection2(X0,X0) = set_intersection2(X1,X2) )
| ~ in(sK2(X0,X0,set_intersection2(X1,X2)),X0)
| ~ in(sK2(X0,X0,set_intersection2(X1,X2)),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_368483,c_54]) ).
tcf(c_370843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,X0,set_intersection2(X3,X4)),X1)
| in(sK2(X2,X0,set_intersection2(X3,X4)),X3)
| ( set_intersection2(X2,X0) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368483,c_321]) ).
tcf(c_370844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X0,set_intersection2(X3,X4)),X3)
| ( set_intersection2(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368483,c_320]) ).
tcf(c_370845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X0,set_intersection2(X2,X3)),X2)
| ( set_intersection2(X1,X0) = set_intersection2(X2,X3) )
| ~ in(X0,sK2(X1,X0,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_368483,c_97]) ).
tcf(c_370846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X0,set_intersection2(X3,X4)),X3)
| in(sK2(X2,X0,set_intersection2(X3,X4)),X1)
| ( set_intersection2(X2,X0) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368483,c_96]) ).
tcf(c_370847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,set_intersection2(X2,X3)),X1)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368483,c_93]) ).
tcf(c_370848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X0,set_intersection2(X2,X3)),X2)
| ( set_intersection2(X1,X0) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368483,c_91]) ).
tcf(c_370849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X3)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368483,c_59]) ).
tcf(c_370851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),set_intersection2(X3,X4)),X3)
| in(apply(X0,sK2(X1,relation_inverse_image(X0,X2),set_intersection2(X3,X4))),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368483,c_88]) ).
tcf(c_370852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),set_intersection2(X3,X4)),X3)
| in(sK2(X1,relation_inverse_image(X0,X2),set_intersection2(X3,X4)),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368483,c_87]) ).
tcf(c_370853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_image(X0,X1),set_intersection2(X3,X4)),X3)
| ( set_intersection2(X2,relation_image(X0,X1)) = set_intersection2(X3,X4) )
| ( apply(X0,sK13(X0,X1,sK2(X2,relation_image(X0,X1),set_intersection2(X3,X4)))) = sK2(X2,relation_image(X0,X1),set_intersection2(X3,X4)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368483,c_112]) ).
tcf(c_370854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X0,set_intersection2(X2,X3)),X2)
| ( set_intersection2(set_intersection2(X0,X1),X0) = set_intersection2(X2,X3) )
| ~ in(sK2(set_intersection2(X0,X1),X0,set_intersection2(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X0,set_intersection2(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),X0,set_intersection2(X2,X3)),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_368483,c_368471]) ).
tcf(c_370855,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_intersection2(X1,X2)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X1,X2) ) ),
inference(equality_factoring,[status(thm)],[c_368483]) ).
tcf(c_370930,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_intersection2(X1,X2)),X1)
| ( set_intersection2(X1,X2) = X0 )
| ~ in(sK2(X0,X0,set_intersection2(X1,X2)),X0)
| ~ in(sK2(X0,X0,set_intersection2(X1,X2)),set_intersection2(X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_370842,c_53]) ).
tcf(c_371085,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X0)
| in(sK2(X1,X2,set_intersection2(X0,X0)),X1)
| ( set_intersection2(X0,X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_53,c_368484]) ).
tcf(c_371086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X3,X2)),X2)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_63,c_368484]) ).
tcf(c_371088,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X2)
| in(sK2(X0,X1,set_intersection2(X2,empty_set)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_64,c_368484]) ).
tcf(c_371089,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),empty_set)
| in(sK2(X0,X1,set_intersection2(empty_set,X2)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_368545,c_368484]) ).
tcf(c_371090,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X1)
| in(sK2(X1,X2,set_intersection2(X0,X0)),X0)
| ( set_intersection2(X0,X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_53,c_368484]) ).
tcf(c_371091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X3,X2)),X0)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_63,c_368484]) ).
tcf(c_371093,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X0)
| in(sK2(X0,X1,set_intersection2(X2,empty_set)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_64,c_368484]) ).
tcf(c_371094,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X0)
| in(sK2(X0,X1,set_intersection2(empty_set,X2)),empty_set)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_368545,c_368484]) ).
tcf(c_371096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,set_intersection2(X0,X2)),X1)
| in(sK2(X3,X4,set_intersection2(X0,X2)),X3)
| ( set_intersection2(X0,X2) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368484,c_321]) ).
tcf(c_371097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X0,X2)),X3)
| ( set_intersection2(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368484,c_320]) ).
tcf(c_371098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,set_intersection2(X0,X3)),X1)
| ( set_intersection2(X0,X3) = set_intersection2(X1,X2) )
| ~ in(X0,sK2(X1,X2,set_intersection2(X0,X3))) ),
inference(superposition,[status(thm)],[c_368484,c_97]) ).
tcf(c_371099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X0,X2)),X3)
| in(sK2(X3,X4,set_intersection2(X0,X2)),X1)
| ( set_intersection2(X0,X2) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368484,c_96]) ).
tcf(c_371100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368484,c_93]) ).
tcf(c_371101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368484,c_91]) ).
tcf(c_371102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(set_intersection2(X0,X1),X2)),X3)
| in(sK2(X3,X4,set_intersection2(set_intersection2(X0,X1),X2)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368484,c_59]) ).
tcf(c_371103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(set_intersection2(X0,X1),X2)),X3)
| in(sK2(X3,X4,set_intersection2(set_intersection2(X0,X1),X2)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368484,c_58]) ).
tcf(c_371104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(relation_inverse_image(X0,X1),X2)),X3)
| in(apply(X0,sK2(X3,X4,set_intersection2(relation_inverse_image(X0,X1),X2))),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368484,c_88]) ).
tcf(c_371105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(relation_inverse_image(X0,X1),X2)),X3)
| in(sK2(X3,X4,set_intersection2(relation_inverse_image(X0,X1),X2)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368484,c_87]) ).
tcf(c_371106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,set_intersection2(relation_image(X0,X1),X4)),X2)
| ( set_intersection2(relation_image(X0,X1),X4) = set_intersection2(X2,X3) )
| ( apply(X0,sK13(X0,X1,sK2(X2,X3,set_intersection2(relation_image(X0,X1),X4)))) = sK2(X2,X3,set_intersection2(relation_image(X0,X1),X4)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368484,c_112]) ).
tcf(c_371107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X3)),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X3) )
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X3)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X3)),set_intersection2(X0,X3)) ),
inference(superposition,[status(thm)],[c_368484,c_368471]) ).
tcf(c_371108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ~ in(sK2(X0,X1,set_intersection2(X2,X3)),X1)
| ~ in(sK2(X0,X1,set_intersection2(X2,X3)),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_368484,c_54]) ).
tcf(c_371109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X2,set_intersection2(X3,X4)),X1)
| in(sK2(X0,X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(X0,X2) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368484,c_321]) ).
tcf(c_371110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368484,c_320]) ).
tcf(c_371111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ~ in(X0,sK2(X0,X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_368484,c_97]) ).
tcf(c_371112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X2,set_intersection2(X3,X4)),X3)
| in(sK2(X0,X2,set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,X2) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368484,c_96]) ).
tcf(c_371113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,set_intersection2(X2,X3)),X0)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368484,c_93]) ).
tcf(c_371114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368484,c_91]) ).
tcf(c_371115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X3)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368484,c_59]) ).
tcf(c_371117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,set_intersection2(X3,X4)),X3)
| in(apply(X0,sK2(relation_inverse_image(X0,X1),X2,set_intersection2(X3,X4))),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368484,c_88]) ).
tcf(c_371118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,set_intersection2(X3,X4)),X3)
| in(sK2(relation_inverse_image(X0,X1),X2,set_intersection2(X3,X4)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368484,c_87]) ).
tcf(c_371119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X0,X1),X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ( apply(X0,sK13(X0,X1,sK2(relation_image(X0,X1),X2,set_intersection2(X3,X4)))) = sK2(relation_image(X0,X1),X2,set_intersection2(X3,X4)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368484,c_112]) ).
tcf(c_371120,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_intersection2(X0,X2)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X0,X2) ) ),
inference(equality_factoring,[status(thm)],[c_368484]) ).
tcf(c_371385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| in(sK2(set_intersection2(X0,X1),X2,X3),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_63,c_368503]) ).
tcf(c_371387,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| in(sK2(set_intersection2(X0,empty_set),X1,X2),empty_set)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_368503]) ).
tcf(c_371388,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| in(sK2(set_intersection2(empty_set,X0),X1,X2),X0)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_368503]) ).
tcf(c_371390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X1)
| in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_63,c_368503]) ).
tcf(c_371392,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),empty_set)
| in(sK2(set_intersection2(X0,empty_set),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_368503]) ).
tcf(c_371393,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X0)
| in(sK2(set_intersection2(empty_set,X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_368503]) ).
tcf(c_371395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X2,X3),X4,X0),X1)
| in(sK2(set_intersection2(X2,X3),X4,X0),X3)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368503,c_321]) ).
tcf(c_371396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,X0),X3)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368503,c_320]) ).
tcf(c_371397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X0),X2)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ in(X0,sK2(set_intersection2(X1,X2),X3,X0)) ),
inference(superposition,[status(thm)],[c_368503,c_97]) ).
tcf(c_371398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,X0),X3)
| in(sK2(set_intersection2(X2,X3),X4,X0),X1)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368503,c_96]) ).
tcf(c_371399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(X0,X1),X2,X3),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_368503,c_93]) ).
tcf(c_371400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X0),X2)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368503,c_91]) ).
tcf(c_371401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X4)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368503,c_59]) ).
tcf(c_371403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),X2)
| in(apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368503,c_88]) ).
tcf(c_371404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),X2)
| in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368503,c_87]) ).
tcf(c_371405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)),X3)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)))) = sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368503,c_112]) ).
tcf(c_371407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X2,X0),X3,X4),X1)
| in(sK2(set_intersection2(X2,X0),X3,X4),X4)
| ( set_intersection2(set_intersection2(X2,X0),X3) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368503,c_321]) ).
tcf(c_371408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X0),X3,X4),X4)
| ( set_intersection2(set_intersection2(X2,X0),X3) = X4 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368503,c_320]) ).
tcf(c_371409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| ( set_intersection2(set_intersection2(X1,X0),X2) = X3 )
| ~ in(X0,sK2(set_intersection2(X1,X0),X2,X3)) ),
inference(superposition,[status(thm)],[c_368503,c_97]) ).
tcf(c_371410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X0),X3,X4),X4)
| in(sK2(set_intersection2(X2,X0),X3,X4),X1)
| ( set_intersection2(set_intersection2(X2,X0),X3) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368503,c_96]) ).
tcf(c_371411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X1)
| in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_368503,c_93]) ).
tcf(c_371412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| ( set_intersection2(set_intersection2(X1,X0),X2) = X3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368503,c_91]) ).
tcf(c_371413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,set_intersection2(X1,X2)),X3,X4),X4)
| in(sK2(set_intersection2(X0,set_intersection2(X1,X2)),X3,X4),X2)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_368503,c_59]) ).
tcf(c_371414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,set_intersection2(X1,X2)),X3,X4),X4)
| in(sK2(set_intersection2(X0,set_intersection2(X1,X2)),X3,X4),X1)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_368503,c_58]) ).
tcf(c_371415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3,X4),X4)
| in(apply(X0,sK2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3,X4)),X2)
| ( set_intersection2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368503,c_88]) ).
tcf(c_371416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3,X4),X4)
| in(sK2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3,X4),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368503,c_87]) ).
tcf(c_371417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,relation_image(X0,X1)),X3,X4),X4)
| ( set_intersection2(set_intersection2(X2,relation_image(X0,X1)),X3) = X4 )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,relation_image(X0,X1)),X3,X4))) = sK2(set_intersection2(X2,relation_image(X0,X1)),X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368503,c_112]) ).
tcf(c_371419,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X1),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X1 ) ),
inference(equality_factoring,[status(thm)],[c_368503]) ).
tcf(c_371431,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X0,X1),empty_set)
| in(sK2(empty_set,X0,X1),X1)
| ( set_intersection2(empty_set,X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_371392,c_64]) ).
tcf(c_371432,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,X0),empty_set)
| in(sK2(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_371431,c_368545]) ).
tcf(c_371664,plain,
! [X0: $i] :
( empty(X0)
| ( sK15(X0) = X0 )
| ~ subset(X0,sK15(X0)) ),
inference(superposition,[status(thm)],[c_369762,c_60]) ).
tcf(c_371676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,X1),X3),X3)
| in(sK2(X0,set_intersection2(X1,X2),X3),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_63,c_368504]) ).
tcf(c_371678,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X2)
| in(sK2(X0,set_intersection2(X1,empty_set),X2),empty_set)
| ( set_intersection2(X0,set_intersection2(X1,empty_set)) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_368504]) ).
tcf(c_371679,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X2)
| in(sK2(X0,set_intersection2(empty_set,X1),X2),X1)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_368504]) ).
tcf(c_371681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,X1),X3),X2)
| in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_63,c_368504]) ).
tcf(c_371683,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),empty_set)
| in(sK2(X0,set_intersection2(X1,empty_set),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,empty_set)) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_368504]) ).
tcf(c_371684,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X1)
| in(sK2(X0,set_intersection2(empty_set,X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_368504]) ).
tcf(c_371685,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X0),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X0 )
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),X0)
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_368504,c_54]) ).
tcf(c_371686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(X3,X4),X0),X1)
| in(sK2(X2,set_intersection2(X3,X4),X0),X4)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368504,c_321]) ).
tcf(c_371687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),X0),X4)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368504,c_320]) ).
tcf(c_371688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X3),X0),X3)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ~ in(X0,sK2(X1,set_intersection2(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_368504,c_97]) ).
tcf(c_371689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),X0),X4)
| in(sK2(X2,set_intersection2(X3,X4),X0),X1)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368504,c_96]) ).
tcf(c_371690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,set_intersection2(X1,X2),X3),X3)
| in(sK2(X0,set_intersection2(X1,X2),X3),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_368504,c_93]) ).
tcf(c_371691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X3),X0),X3)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368504,c_91]) ).
tcf(c_371692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X4)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368504,c_59]) ).
tcf(c_371694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X3)
| in(apply(X0,sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368504,c_88]) ).
tcf(c_371695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X3)
| in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368504,c_87]) ).
tcf(c_371696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)),X4)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)))) = sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368504,c_112]) ).
tcf(c_371697,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X3)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_368504,c_368471]) ).
tcf(c_371699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(X3,X0),X4),X1)
| in(sK2(X2,set_intersection2(X3,X0),X4),X4)
| ( set_intersection2(X2,set_intersection2(X3,X0)) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368504,c_321]) ).
tcf(c_371700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X0),X4),X4)
| ( set_intersection2(X2,set_intersection2(X3,X0)) = X4 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368504,c_320]) ).
tcf(c_371701,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X0),X3),X3)
| ( set_intersection2(X1,set_intersection2(X2,X0)) = X3 )
| ~ in(X0,sK2(X1,set_intersection2(X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_368504,c_97]) ).
tcf(c_371702,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X0),X4),X4)
| in(sK2(X2,set_intersection2(X3,X0),X4),X1)
| ( set_intersection2(X2,set_intersection2(X3,X0)) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368504,c_96]) ).
tcf(c_371703,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,set_intersection2(X1,X2),X3),X2)
| in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_368504,c_93]) ).
tcf(c_371704,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X0),X3),X3)
| ( set_intersection2(X1,set_intersection2(X2,X0)) = X3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368504,c_91]) ).
tcf(c_371705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X3)),X4),X4)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X3)),X4),X3)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X3))) = X4 ) ),
inference(superposition,[status(thm)],[c_368504,c_59]) ).
tcf(c_371706,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X3)),X4),X4)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X3)),X4),X2)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X3))) = X4 ) ),
inference(superposition,[status(thm)],[c_368504,c_58]) ).
tcf(c_371707,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,relation_inverse_image(X0,X3)),X4),X4)
| in(apply(X0,sK2(X1,set_intersection2(X2,relation_inverse_image(X0,X3)),X4)),X3)
| ( set_intersection2(X1,set_intersection2(X2,relation_inverse_image(X0,X3))) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368504,c_88]) ).
tcf(c_371708,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,relation_inverse_image(X0,X3)),X4),X4)
| in(sK2(X1,set_intersection2(X2,relation_inverse_image(X0,X3)),X4),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,relation_inverse_image(X0,X3))) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368504,c_87]) ).
tcf(c_371709,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,relation_image(X0,X1)),X4),X4)
| ( set_intersection2(X2,set_intersection2(X3,relation_image(X0,X1))) = X4 )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,relation_image(X0,X1)),X4))) = sK2(X2,set_intersection2(X3,relation_image(X0,X1)),X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368504,c_112]) ).
tcf(c_371711,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X2 ) ),
inference(equality_factoring,[status(thm)],[c_368504]) ).
tcf(c_371938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X3,X2)),X3)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_63,c_368505]) ).
tcf(c_371940,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),empty_set)
| in(sK2(X0,X1,set_intersection2(X2,empty_set)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_64,c_368505]) ).
tcf(c_371941,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X2)
| in(sK2(X0,X1,set_intersection2(empty_set,X2)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_368545,c_368505]) ).
tcf(c_371943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X3,X2)),X1)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_63,c_368505]) ).
tcf(c_371945,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X1)
| in(sK2(X0,X1,set_intersection2(X2,empty_set)),empty_set)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_64,c_368505]) ).
tcf(c_371946,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X1)
| in(sK2(X0,X1,set_intersection2(empty_set,X2)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_368545,c_368505]) ).
tcf(c_371948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,set_intersection2(X2,X0)),X1)
| in(sK2(X3,X4,set_intersection2(X2,X0)),X4)
| ( set_intersection2(X2,X0) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368505,c_321]) ).
tcf(c_371949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X2,X0)),X4)
| ( set_intersection2(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368505,c_320]) ).
tcf(c_371950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,set_intersection2(X3,X0)),X2)
| ( set_intersection2(X1,X2) = set_intersection2(X3,X0) )
| ~ in(X0,sK2(X1,X2,set_intersection2(X3,X0))) ),
inference(superposition,[status(thm)],[c_368505,c_97]) ).
tcf(c_371951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X2,X0)),X4)
| in(sK2(X3,X4,set_intersection2(X2,X0)),X1)
| ( set_intersection2(X2,X0) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368505,c_96]) ).
tcf(c_371952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368505,c_93]) ).
tcf(c_371953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X1,X0)),X3)
| ( set_intersection2(X1,X0) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368505,c_91]) ).
tcf(c_371954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X0,set_intersection2(X1,X2))),X4)
| in(sK2(X3,X4,set_intersection2(X0,set_intersection2(X1,X2))),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368505,c_59]) ).
tcf(c_371955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X0,set_intersection2(X1,X2))),X4)
| in(sK2(X3,X4,set_intersection2(X0,set_intersection2(X1,X2))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368505,c_58]) ).
tcf(c_371956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X1,relation_inverse_image(X0,X2))),X4)
| in(apply(X0,sK2(X3,X4,set_intersection2(X1,relation_inverse_image(X0,X2)))),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368505,c_88]) ).
tcf(c_371957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X1,relation_inverse_image(X0,X2))),X4)
| in(sK2(X3,X4,set_intersection2(X1,relation_inverse_image(X0,X2))),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368505,c_87]) ).
tcf(c_371958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,set_intersection2(X4,relation_image(X0,X1))),X3)
| ( set_intersection2(X4,relation_image(X0,X1)) = set_intersection2(X2,X3) )
| ( apply(X0,sK13(X0,X1,sK2(X2,X3,set_intersection2(X4,relation_image(X0,X1))))) = sK2(X2,X3,set_intersection2(X4,relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368505,c_112]) ).
tcf(c_371960,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_intersection2(X1,X2)),X2)
| ( set_intersection2(X0,X0) = set_intersection2(X1,X2) )
| ~ in(sK2(X0,X0,set_intersection2(X1,X2)),X0)
| ~ in(sK2(X0,X0,set_intersection2(X1,X2)),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_368505,c_54]) ).
tcf(c_371961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,X0,set_intersection2(X3,X4)),X1)
| in(sK2(X2,X0,set_intersection2(X3,X4)),X4)
| ( set_intersection2(X2,X0) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368505,c_321]) ).
tcf(c_371962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X0,set_intersection2(X3,X4)),X4)
| ( set_intersection2(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368505,c_320]) ).
tcf(c_371963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X0,set_intersection2(X2,X3)),X3)
| ( set_intersection2(X1,X0) = set_intersection2(X2,X3) )
| ~ in(X0,sK2(X1,X0,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_368505,c_97]) ).
tcf(c_371964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X0,set_intersection2(X3,X4)),X4)
| in(sK2(X2,X0,set_intersection2(X3,X4)),X1)
| ( set_intersection2(X2,X0) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368505,c_96]) ).
tcf(c_371965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,set_intersection2(X2,X3)),X1)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368505,c_93]) ).
tcf(c_371966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X0,set_intersection2(X2,X3)),X3)
| ( set_intersection2(X1,X0) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368505,c_91]) ).
tcf(c_371969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),set_intersection2(X3,X4)),X4)
| in(apply(X0,sK2(X1,relation_inverse_image(X0,X2),set_intersection2(X3,X4))),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368505,c_88]) ).
tcf(c_371970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),set_intersection2(X3,X4)),X4)
| in(sK2(X1,relation_inverse_image(X0,X2),set_intersection2(X3,X4)),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368505,c_87]) ).
tcf(c_371971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_image(X0,X1),set_intersection2(X3,X4)),X4)
| ( set_intersection2(X2,relation_image(X0,X1)) = set_intersection2(X3,X4) )
| ( apply(X0,sK13(X0,X1,sK2(X2,relation_image(X0,X1),set_intersection2(X3,X4)))) = sK2(X2,relation_image(X0,X1),set_intersection2(X3,X4)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368505,c_112]) ).
tcf(c_371972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X0,set_intersection2(X2,X3)),X3)
| ( set_intersection2(set_intersection2(X0,X1),X0) = set_intersection2(X2,X3) )
| ~ in(sK2(set_intersection2(X0,X1),X0,set_intersection2(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X0,set_intersection2(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),X0,set_intersection2(X2,X3)),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_368505,c_368471]) ).
tcf(c_371973,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X1) ) ),
inference(equality_factoring,[status(thm)],[c_368505]) ).
tcf(c_372043,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,set_intersection2(X1,X2)),X2)
| ( set_intersection2(X1,X2) = X0 )
| ~ in(sK2(X0,X0,set_intersection2(X1,X2)),X0)
| ~ in(sK2(X0,X0,set_intersection2(X1,X2)),set_intersection2(X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_371960,c_53]) ).
tcf(c_372171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X3,X2)),X3)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_63,c_368506]) ).
tcf(c_372173,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),empty_set)
| in(sK2(X0,X1,set_intersection2(X2,empty_set)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_64,c_368506]) ).
tcf(c_372174,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X2)
| in(sK2(X0,X1,set_intersection2(empty_set,X2)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_368545,c_368506]) ).
tcf(c_372176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X3,X2)),X0)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_63,c_368506]) ).
tcf(c_372178,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X0)
| in(sK2(X0,X1,set_intersection2(X2,empty_set)),empty_set)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_64,c_368506]) ).
tcf(c_372179,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X0)
| in(sK2(X0,X1,set_intersection2(empty_set,X2)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_368545,c_368506]) ).
tcf(c_372180,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X0)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X0) )
| ~ in(sK2(X0,X1,set_intersection2(X2,X0)),X1)
| ~ in(sK2(X0,X1,set_intersection2(X2,X0)),set_intersection2(X2,X0)) ),
inference(superposition,[status(thm)],[c_368506,c_54]) ).
tcf(c_372181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,set_intersection2(X2,X0)),X1)
| in(sK2(X3,X4,set_intersection2(X2,X0)),X3)
| ( set_intersection2(X2,X0) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368506,c_321]) ).
tcf(c_372182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X2,X0)),X3)
| ( set_intersection2(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368506,c_320]) ).
tcf(c_372183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,set_intersection2(X3,X0)),X1)
| ( set_intersection2(X1,X2) = set_intersection2(X3,X0) )
| ~ in(X0,sK2(X1,X2,set_intersection2(X3,X0))) ),
inference(superposition,[status(thm)],[c_368506,c_97]) ).
tcf(c_372184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X2,X0)),X3)
| in(sK2(X3,X4,set_intersection2(X2,X0)),X1)
| ( set_intersection2(X2,X0) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368506,c_96]) ).
tcf(c_372185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368506,c_93]) ).
tcf(c_372186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X1,X0)),X2)
| ( set_intersection2(X1,X0) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368506,c_91]) ).
tcf(c_372187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X0,set_intersection2(X1,X2))),X3)
| in(sK2(X3,X4,set_intersection2(X0,set_intersection2(X1,X2))),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368506,c_59]) ).
tcf(c_372188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X0,set_intersection2(X1,X2))),X3)
| in(sK2(X3,X4,set_intersection2(X0,set_intersection2(X1,X2))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_368506,c_58]) ).
tcf(c_372189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X1,relation_inverse_image(X0,X2))),X3)
| in(apply(X0,sK2(X3,X4,set_intersection2(X1,relation_inverse_image(X0,X2)))),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368506,c_88]) ).
tcf(c_372190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X1,relation_inverse_image(X0,X2))),X3)
| in(sK2(X3,X4,set_intersection2(X1,relation_inverse_image(X0,X2))),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368506,c_87]) ).
tcf(c_372191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,set_intersection2(X4,relation_image(X0,X1))),X2)
| ( set_intersection2(X4,relation_image(X0,X1)) = set_intersection2(X2,X3) )
| ( apply(X0,sK13(X0,X1,sK2(X2,X3,set_intersection2(X4,relation_image(X0,X1))))) = sK2(X2,X3,set_intersection2(X4,relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368506,c_112]) ).
tcf(c_372192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X0)),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X0) )
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X0)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X0)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X0)),set_intersection2(X3,X0)) ),
inference(superposition,[status(thm)],[c_368506,c_368471]) ).
tcf(c_372193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ~ in(sK2(X0,X1,set_intersection2(X2,X3)),X1)
| ~ in(sK2(X0,X1,set_intersection2(X2,X3)),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_368506,c_54]) ).
tcf(c_372194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X2,set_intersection2(X3,X4)),X1)
| in(sK2(X0,X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(X0,X2) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368506,c_321]) ).
tcf(c_372195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368506,c_320]) ).
tcf(c_372196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ~ in(X0,sK2(X0,X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_368506,c_97]) ).
tcf(c_372197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X2,set_intersection2(X3,X4)),X4)
| in(sK2(X0,X2,set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,X2) = set_intersection2(X3,X4) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368506,c_96]) ).
tcf(c_372198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,set_intersection2(X2,X3)),X0)
| in(sK2(X0,X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368506,c_93]) ).
tcf(c_372199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368506,c_91]) ).
tcf(c_372202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,set_intersection2(X3,X4)),X4)
| in(apply(X0,sK2(relation_inverse_image(X0,X1),X2,set_intersection2(X3,X4))),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368506,c_88]) ).
tcf(c_372203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,set_intersection2(X3,X4)),X4)
| in(sK2(relation_inverse_image(X0,X1),X2,set_intersection2(X3,X4)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368506,c_87]) ).
tcf(c_372204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X0,X1),X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(relation_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ( apply(X0,sK13(X0,X1,sK2(relation_image(X0,X1),X2,set_intersection2(X3,X4)))) = sK2(relation_image(X0,X1),X2,set_intersection2(X3,X4)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368506,c_112]) ).
tcf(c_372205,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X1,X2) ) ),
inference(equality_factoring,[status(thm)],[c_368506]) ).
tcf(c_372426,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_368543,c_22869]) ).
tcf(c_372428,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X0,X1),X1)
| ( set_intersection2(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_55,c_372426]) ).
tcf(c_372429,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,empty_set,X1),X1)
| ( set_intersection2(X0,empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_56,c_372426]) ).
tcf(c_372430,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,empty_set),X1)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_56,c_372426]) ).
tcf(c_372431,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,empty_set),X0)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_55,c_372426]) ).
tcf(c_372432,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,empty_set,X1),X1)
| ( relation_inverse_image(X0,empty_set) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_372426]) ).
tcf(c_372433,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK7(X0,X1,empty_set)),X1)
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_372426]) ).
tcf(c_372434,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_84,c_372426]) ).
tcf(c_372436,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = empty_set )
| ( apply(X0,sK12(X0,X1,empty_set)) = sK11(X0,X1,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_372426]) ).
tcf(c_372437,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,empty_set),X1)
| ( relation_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_372426]) ).
tcf(c_372438,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,empty_set),relation_dom(X0))
| ( relation_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_106,c_372426]) ).
tcf(c_372439,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,empty_set,X1),X1)
| ( relation_image(X0,empty_set) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_372426]) ).
tcf(c_372440,plain,
! [X0: $i,X1: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_111,c_372426]) ).
tcf(c_372442,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_368506,c_372426]) ).
tcf(c_372443,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_368484,c_372426]) ).
tcf(c_372444,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_intersection2(X2,empty_set)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_368506,c_372426]) ).
tcf(c_372445,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_intersection2(X2,empty_set)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_368505,c_372426]) ).
tcf(c_372446,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_intersection2(empty_set,X2)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_368484,c_372426]) ).
tcf(c_372447,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,set_intersection2(empty_set,X2)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_368483,c_372426]) ).
tcf(c_372448,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = empty_set ) ),
inference(superposition,[status(thm)],[c_368503,c_372426]) ).
tcf(c_372449,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = empty_set ) ),
inference(superposition,[status(thm)],[c_368481,c_372426]) ).
tcf(c_372450,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,empty_set),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368503,c_372426]) ).
tcf(c_372451,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(empty_set,X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368481,c_372426]) ).
tcf(c_372453,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,empty_set,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_368505,c_372426]) ).
tcf(c_372454,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,empty_set,set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(superposition,[status(thm)],[c_368483,c_372426]) ).
tcf(c_372455,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_368504,c_372426]) ).
tcf(c_372456,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_368482,c_372426]) ).
tcf(c_372457,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,empty_set),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,empty_set)) = X2 ) ),
inference(superposition,[status(thm)],[c_368504,c_372426]) ).
tcf(c_372458,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(empty_set,X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_368482,c_372426]) ).
tcf(c_372467,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_372429,c_64]) ).
tcf(c_372470,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_372428,c_368545]) ).
tcf(c_372550,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_368984,c_368558]) ).
tcf(c_372552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ~ subset(set_intersection2(X2,X3),X1)
| ~ subset(set_intersection2(X2,X3),X0)
| ~ subset(set_intersection2(X0,X1),X3)
| ~ subset(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_65,c_368558]) ).
tcf(c_372553,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X0) = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_368558]) ).
tcf(c_372554,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X0) = X2 )
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_63,c_368558]) ).
tcf(c_372556,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,empty_set) = X0 )
| ~ subset(empty_set,X0)
| ~ subset(X0,empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_368558]) ).
tcf(c_372557,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(empty_set,X1) = X0 )
| ~ subset(empty_set,X0)
| ~ subset(X0,empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368545,c_368558]) ).
tcf(c_372559,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(empty_set,X1) = X0 )
| ~ subset(X0,empty_set)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_372557,c_369177]) ).
tcf(c_372563,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,empty_set) = X0 )
| ~ subset(X0,empty_set)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_372556,c_369177]) ).
tcf(c_372584,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(sK15(X0),X1)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_369765,c_321]) ).
tcf(c_372586,plain,
! [X0: $i] :
( empty(X0)
| ~ in(powerset(X0),sK15(X0)) ),
inference(superposition,[status(thm)],[c_369765,c_97]) ).
tcf(c_372587,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK15(X0),X1)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_369765,c_96]) ).
tcf(c_372616,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,relation_dom(X0)) = relation_image(X0,X1) )
| ~ relation(X0)
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_368984,c_368586]) ).
tcf(c_372630,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,relation_inverse_image(X0,X1)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368984,c_368596]) ).
tcf(c_372631,plain,
! [X0: $i] :
( ( relation_image(X0,relation_inverse_image(X0,empty_set)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369177,c_368596]) ).
tcf(c_372645,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| subset(sK10(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_368983,c_99]) ).
tcf(c_372654,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_368606]) ).
tcf(c_372655,plain,
! [X0: $i] :
( ( relation_dom(empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_104,c_368606]) ).
tcf(c_372675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,set_intersection2(set_intersection2(X1,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X4)
| ~ in(sK7(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,set_intersection2(set_intersection2(X1,X2),X3),X4)),X3)
| ~ in(apply(X0,sK7(X0,set_intersection2(set_intersection2(X1,X2),X3),X4)),X2)
| ~ in(apply(X0,sK7(X0,set_intersection2(set_intersection2(X1,X2),X3),X4)),X1) ),
inference(superposition,[status(thm)],[c_57,c_368654]) ).
tcf(c_372676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,set_intersection2(relation_image(X0,X1),X2)) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,set_intersection2(relation_image(X0,X1),X2),X3),X3)
| ~ in(sK7(X0,set_intersection2(relation_image(X0,X1),X2),X3),X1)
| ~ in(sK7(X0,set_intersection2(relation_image(X0,X1),X2),X3),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,set_intersection2(relation_image(X0,X1),X2),X3)),X2) ),
inference(superposition,[status(thm)],[c_109,c_368654]) ).
tcf(c_372677,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,set_intersection2(X1,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,X1,X2)),X1)
| ~ in(sK7(X0,set_intersection2(X1,X1),X2),X2)
| ~ in(sK7(X0,set_intersection2(X1,X1),X2),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,set_intersection2(X1,X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_53,c_368654]) ).
tcf(c_372678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| ~ in(sK7(X0,set_intersection2(X1,X2),X3),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,set_intersection2(X2,X1),X3)),X1)
| ~ in(apply(X0,sK7(X0,set_intersection2(X1,X2),X3)),X2) ),
inference(superposition,[status(thm)],[c_63,c_368654]) ).
tcf(c_372680,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,set_intersection2(X1,empty_set)) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,empty_set,X2)),X1)
| ~ in(sK7(X0,set_intersection2(X1,empty_set),X2),X2)
| ~ in(sK7(X0,set_intersection2(X1,empty_set),X2),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,set_intersection2(X1,empty_set),X2)),empty_set) ),
inference(superposition,[status(thm)],[c_64,c_368654]) ).
tcf(c_372681,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,set_intersection2(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,empty_set,X2)),empty_set)
| ~ in(sK7(X0,set_intersection2(empty_set,X1),X2),X2)
| ~ in(sK7(X0,set_intersection2(empty_set,X1),X2),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,set_intersection2(empty_set,X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_368545,c_368654]) ).
tcf(c_372730,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,set_intersection2(X2,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_368672]) ).
tcf(c_372731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X3,X2)),X3)
| in(sK7(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_368672]) ).
tcf(c_372734,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),X2)
| in(sK7(X0,X1,set_intersection2(empty_set,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_368672]) ).
tcf(c_372735,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),relation_dom(X0))
| in(sK7(X0,X1,set_intersection2(X2,X2)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_368672]) ).
tcf(c_372736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK7(X0,X1,set_intersection2(X3,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_368672]) ).
tcf(c_372738,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(X0))
| in(sK7(X0,X1,set_intersection2(X2,empty_set)),empty_set)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_368672]) ).
tcf(c_372739,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(X0))
| in(sK7(X0,X1,set_intersection2(empty_set,X2)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_368672]) ).
tcf(c_372740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,X3,set_intersection2(X4,X0)),X1)
| in(sK7(X2,X3,set_intersection2(X4,X0)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368672,c_321]) ).
tcf(c_372741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X3,set_intersection2(X4,X0)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X4,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368672,c_320]) ).
tcf(c_372742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X2,set_intersection2(X3,X0)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = set_intersection2(X3,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK7(X1,X2,set_intersection2(X3,X0))) ),
inference(superposition,[status(thm)],[c_368672,c_97]) ).
tcf(c_372743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X3,set_intersection2(X4,X0)),X1)
| in(sK7(X2,X3,set_intersection2(X4,X0)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368672,c_96]) ).
tcf(c_372744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK7(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_93]) ).
tcf(c_372745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,set_intersection2(X3,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_91]) ).
tcf(c_372746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(X1,set_intersection2(X2,X3))),X3)
| in(sK7(X0,X4,set_intersection2(X1,set_intersection2(X2,X3))),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_59]) ).
tcf(c_372747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(X1,set_intersection2(X2,X3))),X2)
| in(sK7(X0,X4,set_intersection2(X1,set_intersection2(X2,X3))),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_58]) ).
tcf(c_372748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3))),relation_dom(X0))
| in(apply(X1,sK7(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3)))),X3)
| ( set_intersection2(X2,relation_inverse_image(X1,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_88]) ).
tcf(c_372749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3))),relation_dom(X1))
| in(sK7(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3))),relation_dom(X0))
| ( set_intersection2(X2,relation_inverse_image(X1,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_87]) ).
tcf(c_372750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,set_intersection2(X4,relation_image(X1,X2))),relation_dom(X0))
| ( set_intersection2(X4,relation_image(X1,X2)) = relation_inverse_image(X0,X3) )
| ( apply(X1,sK13(X1,X2,sK7(X0,X3,set_intersection2(X4,relation_image(X1,X2))))) = sK7(X0,X3,set_intersection2(X4,relation_image(X1,X2))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_112]) ).
tcf(c_372751,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,set_intersection2(X2,empty_set)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_372426]) ).
tcf(c_372752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X2,set_intersection2(X3,X4)),X1)
| in(sK7(X0,X2,set_intersection2(X3,X4)),X4)
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368672,c_321]) ).
tcf(c_372753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X2,set_intersection2(X3,X4)),X4)
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368672,c_320]) ).
tcf(c_372754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK7(X0,X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_368672,c_97]) ).
tcf(c_372755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X2,set_intersection2(X3,X4)),X4)
| in(sK7(X0,X2,set_intersection2(X3,X4)),X1)
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368672,c_96]) ).
tcf(c_372756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| element(sK7(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_93]) ).
tcf(c_372757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368672,c_91]) ).
tcf(c_372758,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,set_intersection2(X1,relation_dom(X0))),relation_dom(X0))
| ( set_intersection2(X1,relation_dom(X0)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_factoring,[status(thm)],[c_368672]) ).
tcf(c_372783,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_372738,c_372426]) ).
tcf(c_372979,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(powerset(X0),X1) = X2 )
| ~ subset(sK2(powerset(X0),X1,X2),X0)
| ~ in(sK2(powerset(X0),X1,X2),X2)
| ~ in(sK2(powerset(X0),X1,X2),X1) ),
inference(superposition,[status(thm)],[c_369138,c_54]) ).
tcf(c_372980,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ subset(X2,X0)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_369138,c_321]) ).
tcf(c_372981,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ subset(X2,X0)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_369138,c_320]) ).
tcf(c_372982,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_369138,c_97]) ).
tcf(c_372983,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ subset(X2,X0)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_369138,c_96]) ).
tcf(c_372985,plain,
! [X0: $i,X1: $i] :
( ~ empty(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369138,c_91]) ).
tcf(c_372986,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,powerset(X1)) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,powerset(X1),X2),X2)
| ~ in(sK7(X0,powerset(X1),X2),relation_dom(X0))
| ~ subset(apply(X0,sK7(X0,powerset(X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_369138,c_83]) ).
tcf(c_372987,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_inverse_image(X0,powerset(X2)))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ subset(apply(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_369138,c_86]) ).
tcf(c_372988,plain,
! [X0: $i,X1: $i] :
( subset(X0,powerset(X1))
| ~ subset(sK10(X0,powerset(X1)),X1) ),
inference(superposition,[status(thm)],[c_369138,c_94]) ).
tcf(c_372989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(powerset(X0),X1),X2) = X3 )
| ~ subset(sK2(set_intersection2(powerset(X0),X1),X2,X3),X0)
| ~ in(sK2(set_intersection2(powerset(X0),X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(powerset(X0),X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(powerset(X0),X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_369138,c_368471]) ).
tcf(c_372990,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,set_intersection2(powerset(X1),X2)) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,set_intersection2(powerset(X1),X2),X3),X3)
| ~ in(sK7(X0,set_intersection2(powerset(X1),X2),X3),relation_dom(X0))
| ~ subset(apply(X0,sK7(X0,set_intersection2(powerset(X1),X2),X3)),X1)
| ~ in(apply(X0,sK7(X0,set_intersection2(powerset(X1),X2),X3)),X2) ),
inference(superposition,[status(thm)],[c_369138,c_368654]) ).
tcf(c_373107,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_369156]) ).
tcf(c_373108,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_104,c_369156]) ).
tcf(c_373122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X3,X2)),X2)
| in(sK7(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_368673]) ).
tcf(c_373127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK7(X0,X1,set_intersection2(X3,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_368673]) ).
tcf(c_373129,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(X0))
| in(sK7(X0,X1,set_intersection2(X2,empty_set)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_368673]) ).
tcf(c_373130,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(X0))
| in(sK7(X0,X1,set_intersection2(empty_set,X2)),empty_set)
| ( relation_inverse_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_368673]) ).
tcf(c_373131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,X3,set_intersection2(X0,X4)),X1)
| in(sK7(X2,X3,set_intersection2(X0,X4)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368673,c_321]) ).
tcf(c_373132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X3,set_intersection2(X0,X4)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368673,c_320]) ).
tcf(c_373133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X2,set_intersection2(X0,X3)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = set_intersection2(X0,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK7(X1,X2,set_intersection2(X0,X3))) ),
inference(superposition,[status(thm)],[c_368673,c_97]) ).
tcf(c_373134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X3,set_intersection2(X0,X4)),X1)
| in(sK7(X2,X3,set_intersection2(X0,X4)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368673,c_96]) ).
tcf(c_373135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK7(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_93]) ).
tcf(c_373136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,set_intersection2(X1,X3)),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = set_intersection2(X1,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_91]) ).
tcf(c_373137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(set_intersection2(X1,X2),X3)),X2)
| in(sK7(X0,X4,set_intersection2(set_intersection2(X1,X2),X3)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_59]) ).
tcf(c_373138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(set_intersection2(X1,X2),X3)),X1)
| in(sK7(X0,X4,set_intersection2(set_intersection2(X1,X2),X3)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_58]) ).
tcf(c_373139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3)),relation_dom(X0))
| in(apply(X1,sK7(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3))),X2)
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_88]) ).
tcf(c_373140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3)),relation_dom(X1))
| in(sK7(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_87]) ).
tcf(c_373141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,set_intersection2(relation_image(X1,X2),X4)),relation_dom(X0))
| ( set_intersection2(relation_image(X1,X2),X4) = relation_inverse_image(X0,X3) )
| ( apply(X1,sK13(X1,X2,sK7(X0,X3,set_intersection2(relation_image(X1,X2),X4)))) = sK7(X0,X3,set_intersection2(relation_image(X1,X2),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_112]) ).
tcf(c_373142,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,set_intersection2(empty_set,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_372426]) ).
tcf(c_373143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X2,set_intersection2(X3,X4)),X1)
| in(sK7(X0,X2,set_intersection2(X3,X4)),X3)
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368673,c_321]) ).
tcf(c_373144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X2,set_intersection2(X3,X4)),X3)
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368673,c_320]) ).
tcf(c_373145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK7(X0,X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_368673,c_97]) ).
tcf(c_373146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X2,set_intersection2(X3,X4)),X3)
| in(sK7(X0,X2,set_intersection2(X3,X4)),X1)
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368673,c_96]) ).
tcf(c_373147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| element(sK7(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_93]) ).
tcf(c_373148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368673,c_91]) ).
tcf(c_373149,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,set_intersection2(relation_dom(X0),X1)),relation_dom(X0))
| ( set_intersection2(relation_dom(X0),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_factoring,[status(thm)],[c_368673]) ).
tcf(c_373169,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_373130,c_372426]) ).
tcf(c_373335,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X2,relation_dom(X0)),X1)
| ( relation_inverse_image(X0,X2) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368674,c_321]) ).
tcf(c_373336,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X2) = relation_dom(X0) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368674,c_320]) ).
tcf(c_373337,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,X1) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK7(X0,X1,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_368674,c_97]) ).
tcf(c_373338,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,relation_dom(X0)),X1)
| ( relation_inverse_image(X0,X2) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368674,c_96]) ).
tcf(c_373339,plain,
! [X0: $i,X1: $i] :
( element(sK7(X0,X1,relation_dom(X0)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368674,c_93]) ).
tcf(c_373340,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,X1) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368674,c_91]) ).
tcf(c_373383,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| in(apply(X0,sK7(X0,X1,set_intersection2(X2,X2))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_368700]) ).
tcf(c_373384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X3,X2)),X3)
| in(apply(X0,sK7(X0,X1,set_intersection2(X2,X3))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_368700]) ).
tcf(c_373387,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),X2)
| in(apply(X0,sK7(X0,X1,set_intersection2(empty_set,X2))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_368700]) ).
tcf(c_373388,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,X2)),X1)
| in(sK7(X0,X1,set_intersection2(X2,X2)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_368700]) ).
tcf(c_373389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| in(apply(X0,sK7(X0,X1,set_intersection2(X3,X2))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_368700]) ).
tcf(c_373391,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,set_intersection2(X2,empty_set)),empty_set)
| in(apply(X0,sK7(X0,X1,empty_set)),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_368700]) ).
tcf(c_373392,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,empty_set)),X1)
| in(sK7(X0,X1,set_intersection2(empty_set,X2)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_368700]) ).
tcf(c_373393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,X3,set_intersection2(X4,X0)),X1)
| in(apply(X2,sK7(X2,X3,set_intersection2(X4,X0))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368700,c_321]) ).
tcf(c_373394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,X3,set_intersection2(X4,X0))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X4,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368700,c_320]) ).
tcf(c_373395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,X2,set_intersection2(X3,X0))),X2)
| ( relation_inverse_image(X1,X2) = set_intersection2(X3,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK7(X1,X2,set_intersection2(X3,X0))) ),
inference(superposition,[status(thm)],[c_368700,c_97]) ).
tcf(c_373396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X3,set_intersection2(X4,X0)),X1)
| in(apply(X2,sK7(X2,X3,set_intersection2(X4,X0))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368700,c_96]) ).
tcf(c_373397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| in(apply(X0,sK7(X0,X1,set_intersection2(X2,X3))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_93]) ).
tcf(c_373398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X2,set_intersection2(X3,X1))),X2)
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_91]) ).
tcf(c_373399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(X1,set_intersection2(X2,X3))),X3)
| in(apply(X0,sK7(X0,X4,set_intersection2(X1,set_intersection2(X2,X3)))),X4)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_59]) ).
tcf(c_373400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(X1,set_intersection2(X2,X3))),X2)
| in(apply(X0,sK7(X0,X4,set_intersection2(X1,set_intersection2(X2,X3)))),X4)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_58]) ).
tcf(c_373401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3)))),X3)
| in(apply(X0,sK7(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3)))),X4)
| ( set_intersection2(X2,relation_inverse_image(X1,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_88]) ).
tcf(c_373402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3))),relation_dom(X1))
| in(apply(X0,sK7(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3)))),X4)
| ( set_intersection2(X2,relation_inverse_image(X1,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_87]) ).
tcf(c_373403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X3,set_intersection2(X4,relation_image(X1,X2)))),X3)
| ( set_intersection2(X4,relation_image(X1,X2)) = relation_inverse_image(X0,X3) )
| ( apply(X1,sK13(X1,X2,sK7(X0,X3,set_intersection2(X4,relation_image(X1,X2))))) = sK7(X0,X3,set_intersection2(X4,relation_image(X1,X2))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_112]) ).
tcf(c_373404,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,set_intersection2(X2,empty_set))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_372426]) ).
tcf(c_373405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X0,set_intersection2(X3,X4)),X4)
| element(apply(X2,sK7(X2,X0,set_intersection2(X3,X4))),X1)
| ( relation_inverse_image(X2,X0) = set_intersection2(X3,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368700,c_321]) ).
tcf(c_373406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X0,set_intersection2(X3,X4)),X4)
| ( relation_inverse_image(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368700,c_320]) ).
tcf(c_373407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X0,set_intersection2(X2,X3)),X3)
| ( relation_inverse_image(X1,X0) = set_intersection2(X2,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK7(X1,X0,set_intersection2(X2,X3)))) ),
inference(superposition,[status(thm)],[c_368700,c_97]) ).
tcf(c_373408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X0,set_intersection2(X3,X4)),X4)
| in(apply(X2,sK7(X2,X0,set_intersection2(X3,X4))),X1)
| ( relation_inverse_image(X2,X0) = set_intersection2(X3,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368700,c_96]) ).
tcf(c_373409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| element(apply(X0,sK7(X0,X1,set_intersection2(X2,X3))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_93]) ).
tcf(c_373410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_91]) ).
tcf(c_373411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X4)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),set_intersection2(X3,X4))),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_59]) ).
tcf(c_373412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X4)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),set_intersection2(X3,X4))),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_58]) ).
tcf(c_373413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ~ in(sK7(X0,X1,set_intersection2(X2,X3)),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_368700,c_83]) ).
tcf(c_373414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK7(X0,X1,set_intersection2(X2,X3)),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,set_intersection2(X2,X3)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368700,c_86]) ).
tcf(c_373415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4)),X4)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4)))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_88]) ).
tcf(c_373416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4)),X4)
| in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_87]) ).
tcf(c_373417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_image(X1,X2),set_intersection2(X3,X4)),X4)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X2,apply(X0,sK7(X0,relation_image(X1,X2),set_intersection2(X3,X4))))) = apply(X0,sK7(X0,relation_image(X1,X2),set_intersection2(X3,X4))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_112]) ).
tcf(c_373418,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,set_intersection2(X1,X2)),X2)
| ( set_intersection2(X1,X2) = relation_inverse_image(X0,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_372426]) ).
tcf(c_373448,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,empty_set)),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_373391,c_372426]) ).
tcf(c_373732,plain,
! [X0: $i,X1: $i] :
( in(sK13(empty_set,X1,X0),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,relation_image(empty_set,X1)) ),
inference(superposition,[status(thm)],[c_373108,c_110]) ).
tcf(c_373733,plain,
! [X0: $i] :
( in(sK7(empty_set,X0,empty_set),empty_set)
| ( relation_inverse_image(empty_set,X0) = relation_dom(empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_368674]) ).
tcf(c_373734,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,set_intersection2(X0,X1)),empty_set)
| in(sK7(empty_set,X2,set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_368673]) ).
tcf(c_373735,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,set_intersection2(X0,X1)),empty_set)
| in(sK7(empty_set,X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_368672]) ).
tcf(c_373736,plain,
! [X0: $i] :
( ( relation_image(empty_set,relation_dom(empty_set)) = relation_image(empty_set,X0) )
| ~ relation(empty_set)
| ~ subset(relation_image(empty_set,empty_set),relation_image(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_373108,c_368586]) ).
tcf(c_373738,plain,
! [X0: $i,X1: $i] :
( in(sK12(empty_set,X0,X1),empty_set)
| in(sK11(empty_set,X0,X1),X1)
| ( relation_image(empty_set,X0) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_106]) ).
tcf(c_373739,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X0,X1),empty_set)
| in(sK7(empty_set,X0,X1),X1)
| ( relation_inverse_image(empty_set,X0) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_84]) ).
tcf(c_373743,plain,
! [X0: $i] :
( subset(relation_image(empty_set,X0),relation_image(empty_set,empty_set))
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_67]) ).
tcf(c_373744,plain,
! [X0: $i] : subset(relation_image(empty_set,X0),relation_image(empty_set,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_373743,c_103]) ).
tcf(c_373745,plain,
! [X0: $i,X1: $i] : ~ in(X0,relation_image(empty_set,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_373732,c_372426,c_368630,c_103]) ).
tcf(c_373746,plain,
! [X0: $i] :
( in(sK7(empty_set,X0,empty_set),empty_set)
| ( relation_inverse_image(empty_set,X0) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_373733,c_373108]) ).
tcf(c_373747,plain,
! [X0: $i] : relation_inverse_image(empty_set,X0) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_373746,c_372426,c_368630,c_103]) ).
tcf(c_373748,plain,
! [X0: $i] :
( ( relation_image(empty_set,X0) = relation_image(empty_set,empty_set) )
| ~ relation(empty_set)
| ~ subset(relation_image(empty_set,empty_set),relation_image(empty_set,X0)) ),
inference(light_normalisation,[status(thm)],[c_373736,c_373108]) ).
tcf(c_373749,plain,
! [X0: $i] :
( ( relation_image(empty_set,X0) = relation_image(empty_set,empty_set) )
| ~ subset(relation_image(empty_set,empty_set),relation_image(empty_set,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_373748,c_103]) ).
tcf(c_373752,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X0,X1),X1)
| ( relation_inverse_image(empty_set,X0) = X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_373739,c_372426,c_368630,c_103]) ).
tcf(c_373755,plain,
! [X0: $i,X1: $i] :
( in(sK11(empty_set,X0,X1),X1)
| ( relation_image(empty_set,X0) = X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_373738,c_372426,c_368630,c_103]) ).
tcf(c_373758,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_373735,c_372426,c_368630,c_103]) ).
tcf(c_373761,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_373734,c_372426,c_368630,c_103]) ).
tcf(c_373784,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_image(empty_set,X0),X1,X2),X2)
| ( set_intersection2(relation_image(empty_set,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_55,c_373745]) ).
tcf(c_373785,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,relation_image(empty_set,X1),X2),X2)
| ( set_intersection2(X0,relation_image(empty_set,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_56,c_373745]) ).
tcf(c_373786,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,relation_image(empty_set,X2)),X1)
| ( set_intersection2(X0,X1) = relation_image(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_56,c_373745]) ).
tcf(c_373787,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,relation_image(empty_set,X2)),X0)
| ( set_intersection2(X0,X1) = relation_image(empty_set,X2) ) ),
inference(superposition,[status(thm)],[c_55,c_373745]) ).
tcf(c_373788,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_image(empty_set,X1),X2),X2)
| ( relation_inverse_image(X0,relation_image(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_373745]) ).
tcf(c_373789,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,relation_image(empty_set,X2))),X1)
| ( relation_inverse_image(X0,X1) = relation_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_373745]) ).
tcf(c_373790,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,relation_image(empty_set,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_84,c_373745]) ).
tcf(c_373791,plain,
! [X0: $i,X1: $i] : subset(relation_image(empty_set,X0),X1),
inference(superposition,[status(thm)],[c_95,c_373745]) ).
tcf(c_373792,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_image(empty_set,X2) )
| ( apply(X0,sK12(X0,X1,relation_image(empty_set,X2))) = sK11(X0,X1,relation_image(empty_set,X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_373745]) ).
tcf(c_373793,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,relation_image(empty_set,X2)),X1)
| ( relation_image(X0,X1) = relation_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_373745]) ).
tcf(c_373794,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,relation_image(empty_set,X2)),relation_dom(X0))
| ( relation_image(X0,X1) = relation_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_106,c_373745]) ).
tcf(c_373795,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,relation_image(empty_set,X1),X2),X2)
| ( relation_image(X0,relation_image(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_373745]) ).
tcf(c_373796,plain,
! [X0: $i,X1: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,X1)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_109,c_373745]) ).
tcf(c_373797,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_image(empty_set,X2))) ),
inference(superposition,[status(thm)],[c_111,c_373745]) ).
tcf(c_373798,plain,
! [X0: $i] : empty(relation_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_368976,c_373745]) ).
tcf(c_373799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_image(empty_set,X0),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(relation_image(empty_set,X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368506,c_373745]) ).
tcf(c_373800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_image(empty_set,X0),X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(relation_image(empty_set,X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368484,c_373745]) ).
tcf(c_373801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,relation_image(empty_set,X1))),X2)
| ( set_intersection2(X0,relation_image(empty_set,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368506,c_373745]) ).
tcf(c_373802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,relation_image(empty_set,X1))),X3)
| ( set_intersection2(X0,relation_image(empty_set,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368505,c_373745]) ).
tcf(c_373803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(relation_image(empty_set,X0),X1)),X2)
| ( set_intersection2(relation_image(empty_set,X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368484,c_373745]) ).
tcf(c_373804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(relation_image(empty_set,X0),X1)),X3)
| ( set_intersection2(relation_image(empty_set,X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368483,c_373745]) ).
tcf(c_373805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,relation_image(empty_set,X3)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_image(empty_set,X3) ) ),
inference(superposition,[status(thm)],[c_368503,c_373745]) ).
tcf(c_373806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,relation_image(empty_set,X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_image(empty_set,X3) ) ),
inference(superposition,[status(thm)],[c_368481,c_373745]) ).
tcf(c_373807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,relation_image(empty_set,X1)),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,relation_image(empty_set,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_368503,c_373745]) ).
tcf(c_373808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_image(empty_set,X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_image(empty_set,X0),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_368481,c_373745]) ).
tcf(c_373809,plain,
! [X0: $i,X1: $i] : set_intersection2(relation_image(empty_set,X0),X1) = relation_image(empty_set,X0),
inference(superposition,[status(thm)],[c_368448,c_373745]) ).
tcf(c_373810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,relation_image(empty_set,X1),set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,relation_image(empty_set,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368505,c_373745]) ).
tcf(c_373811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,relation_image(empty_set,X1),set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,relation_image(empty_set,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368483,c_373745]) ).
tcf(c_373812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),relation_image(empty_set,X3)),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_image(empty_set,X3) ) ),
inference(superposition,[status(thm)],[c_368504,c_373745]) ).
tcf(c_373813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),relation_image(empty_set,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_image(empty_set,X3) ) ),
inference(superposition,[status(thm)],[c_368482,c_373745]) ).
tcf(c_373814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,relation_image(empty_set,X2)),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,relation_image(empty_set,X2))) = X3 ) ),
inference(superposition,[status(thm)],[c_368504,c_373745]) ).
tcf(c_373815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(relation_image(empty_set,X1),X2),X3),X3)
| ( set_intersection2(X0,set_intersection2(relation_image(empty_set,X1),X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_368482,c_373745]) ).
tcf(c_373816,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,relation_image(empty_set,X1)) = relation_image(empty_set,X1),
inference(superposition,[status(thm)],[c_368460,c_373745]) ).
tcf(c_373817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X3,set_intersection2(X1,relation_image(empty_set,X2)))),X3)
| ( set_intersection2(X1,relation_image(empty_set,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_373745]) ).
tcf(c_373818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X1,relation_image(empty_set,X2))),relation_dom(X0))
| ( set_intersection2(X1,relation_image(empty_set,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_373745]) ).
tcf(c_373819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(relation_image(empty_set,X1),X2)),relation_dom(X0))
| ( set_intersection2(relation_image(empty_set,X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_373745]) ).
tcf(c_373820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_image(empty_set,X1),set_intersection2(X2,X3)),X3)
| ( relation_inverse_image(X0,relation_image(empty_set,X1)) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_373745]) ).
tcf(c_373824,plain,
! [X0: $i,X1: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set)
| ~ in(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_373796,c_373108]) ).
tcf(c_374120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X3,X2)),X2)
| in(apply(X0,sK7(X0,X1,set_intersection2(X2,X3))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_368701]) ).
tcf(c_374125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| in(apply(X0,sK7(X0,X1,set_intersection2(X3,X2))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_368701]) ).
tcf(c_374127,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,empty_set)),X1)
| in(sK7(X0,X1,set_intersection2(X2,empty_set)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_368701]) ).
tcf(c_374128,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,set_intersection2(empty_set,X2)),empty_set)
| in(apply(X0,sK7(X0,X1,empty_set)),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_368701]) ).
tcf(c_374129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,X3,set_intersection2(X0,X4)),X1)
| in(apply(X2,sK7(X2,X3,set_intersection2(X0,X4))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368701,c_321]) ).
tcf(c_374130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,X3,set_intersection2(X0,X4))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368701,c_320]) ).
tcf(c_374131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,X2,set_intersection2(X0,X3))),X2)
| ( relation_inverse_image(X1,X2) = set_intersection2(X0,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK7(X1,X2,set_intersection2(X0,X3))) ),
inference(superposition,[status(thm)],[c_368701,c_97]) ).
tcf(c_374132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X3,set_intersection2(X0,X4)),X1)
| in(apply(X2,sK7(X2,X3,set_intersection2(X0,X4))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368701,c_96]) ).
tcf(c_374133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| in(apply(X0,sK7(X0,X1,set_intersection2(X2,X3))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_93]) ).
tcf(c_374134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X2,set_intersection2(X1,X3))),X2)
| ( relation_inverse_image(X0,X2) = set_intersection2(X1,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_91]) ).
tcf(c_374135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(set_intersection2(X1,X2),X3)),X2)
| in(apply(X0,sK7(X0,X4,set_intersection2(set_intersection2(X1,X2),X3))),X4)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_59]) ).
tcf(c_374136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(set_intersection2(X1,X2),X3)),X1)
| in(apply(X0,sK7(X0,X4,set_intersection2(set_intersection2(X1,X2),X3))),X4)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_58]) ).
tcf(c_374137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3))),X2)
| in(apply(X0,sK7(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3))),X4)
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_88]) ).
tcf(c_374138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3)),relation_dom(X1))
| in(apply(X0,sK7(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3))),X4)
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_87]) ).
tcf(c_374139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X3,set_intersection2(relation_image(X1,X2),X4))),X3)
| ( set_intersection2(relation_image(X1,X2),X4) = relation_inverse_image(X0,X3) )
| ( apply(X1,sK13(X1,X2,sK7(X0,X3,set_intersection2(relation_image(X1,X2),X4)))) = sK7(X0,X3,set_intersection2(relation_image(X1,X2),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_112]) ).
tcf(c_374140,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,set_intersection2(empty_set,X2))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_372426]) ).
tcf(c_374141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X3,set_intersection2(relation_image(empty_set,X1),X2))),X3)
| ( set_intersection2(relation_image(empty_set,X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_373745]) ).
tcf(c_374142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X0,set_intersection2(X3,X4)),X3)
| element(apply(X2,sK7(X2,X0,set_intersection2(X3,X4))),X1)
| ( relation_inverse_image(X2,X0) = set_intersection2(X3,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368701,c_321]) ).
tcf(c_374143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X0,set_intersection2(X3,X4)),X3)
| ( relation_inverse_image(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368701,c_320]) ).
tcf(c_374144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X0,set_intersection2(X2,X3)),X2)
| ( relation_inverse_image(X1,X0) = set_intersection2(X2,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK7(X1,X0,set_intersection2(X2,X3)))) ),
inference(superposition,[status(thm)],[c_368701,c_97]) ).
tcf(c_374145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X0,set_intersection2(X3,X4)),X3)
| in(apply(X2,sK7(X2,X0,set_intersection2(X3,X4))),X1)
| ( relation_inverse_image(X2,X0) = set_intersection2(X3,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368701,c_96]) ).
tcf(c_374146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| element(apply(X0,sK7(X0,X1,set_intersection2(X2,X3))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_93]) ).
tcf(c_374147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_91]) ).
tcf(c_374148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),set_intersection2(X3,X4))),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_59]) ).
tcf(c_374149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),set_intersection2(X3,X4))),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_58]) ).
tcf(c_374150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ~ in(sK7(X0,X1,set_intersection2(X2,X3)),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_368701,c_83]) ).
tcf(c_374151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK7(X0,X1,set_intersection2(X2,X3)),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,set_intersection2(X2,X3)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368701,c_86]) ).
tcf(c_374152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4)),X3)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4)))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_88]) ).
tcf(c_374153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4)),X3)
| in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_87]) ).
tcf(c_374154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_image(X1,X2),set_intersection2(X3,X4)),X3)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X2,apply(X0,sK7(X0,relation_image(X1,X2),set_intersection2(X3,X4))))) = apply(X0,sK7(X0,relation_image(X1,X2),set_intersection2(X3,X4))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_112]) ).
tcf(c_374155,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,set_intersection2(X1,X2)),X1)
| ( set_intersection2(X1,X2) = relation_inverse_image(X0,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_372426]) ).
tcf(c_374156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_image(empty_set,X1),set_intersection2(X2,X3)),X2)
| ( relation_inverse_image(X0,relation_image(empty_set,X1)) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_373745]) ).
tcf(c_374189,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,empty_set)),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_374128,c_372426]) ).
tcf(c_374521,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| in(apply(X0,sK7(X0,set_intersection2(X1,X1),X2)),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_368702]) ).
tcf(c_374522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X2,X1),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),X3)),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_368702]) ).
tcf(c_374524,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,X2),X2)
| in(apply(X0,sK7(X0,set_intersection2(X1,empty_set),X2)),empty_set)
| ( relation_inverse_image(X0,set_intersection2(X1,empty_set)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_368702]) ).
tcf(c_374525,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,X2),X2)
| in(apply(X0,sK7(X0,set_intersection2(empty_set,X1),X2)),X1)
| ( relation_inverse_image(X0,set_intersection2(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_368702]) ).
tcf(c_374526,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,X2)),X1)
| in(sK7(X0,set_intersection2(X1,X1),X2),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_368702]) ).
tcf(c_374527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X2,X1),X3)),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_368702]) ).
tcf(c_374530,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,empty_set,X2)),X1)
| in(sK7(X0,set_intersection2(empty_set,X1),X2),X2)
| ( relation_inverse_image(X0,set_intersection2(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_368702]) ).
tcf(c_374531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,set_intersection2(X3,X4),X0),X1)
| in(apply(X2,sK7(X2,set_intersection2(X3,X4),X0)),X4)
| ( relation_inverse_image(X2,set_intersection2(X3,X4)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368702,c_321]) ).
tcf(c_374532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,set_intersection2(X3,X4),X0)),X4)
| ( relation_inverse_image(X2,set_intersection2(X3,X4)) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368702,c_320]) ).
tcf(c_374533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,set_intersection2(X2,X3),X0)),X3)
| ( relation_inverse_image(X1,set_intersection2(X2,X3)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK7(X1,set_intersection2(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_368702,c_97]) ).
tcf(c_374534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,set_intersection2(X3,X4),X0),X1)
| in(apply(X2,sK7(X2,set_intersection2(X3,X4),X0)),X4)
| ( relation_inverse_image(X2,set_intersection2(X3,X4)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368702,c_96]) ).
tcf(c_374535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,set_intersection2(X1,X2),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),X3)),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_93]) ).
tcf(c_374536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X2,X3),X1)),X3)
| ( relation_inverse_image(X0,set_intersection2(X2,X3)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_91]) ).
tcf(c_374539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4))),X4)
| in(apply(X0,sK7(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4))),X3)
| ( relation_inverse_image(X0,set_intersection2(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_88]) ).
tcf(c_374540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| in(apply(X0,sK7(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4))),X3)
| ( relation_inverse_image(X0,set_intersection2(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_87]) ).
tcf(c_374541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X3,X4),relation_image(X1,X2))),X4)
| ( relation_inverse_image(X0,set_intersection2(X3,X4)) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK7(X0,set_intersection2(X3,X4),relation_image(X1,X2)))) = sK7(X0,set_intersection2(X3,X4),relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_112]) ).
tcf(c_374542,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X1,X2),empty_set)),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_372426]) ).
tcf(c_374543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X1,X2),relation_image(empty_set,X3))),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = relation_image(empty_set,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_373745]) ).
tcf(c_374544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,set_intersection2(X3,X0),X4),X4)
| element(apply(X2,sK7(X2,set_intersection2(X3,X0),X4)),X1)
| ( relation_inverse_image(X2,set_intersection2(X3,X0)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368702,c_321]) ).
tcf(c_374545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,set_intersection2(X3,X0),X4),X4)
| ( relation_inverse_image(X2,set_intersection2(X3,X0)) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368702,c_320]) ).
tcf(c_374546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,set_intersection2(X2,X0),X3),X3)
| ( relation_inverse_image(X1,set_intersection2(X2,X0)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK7(X1,set_intersection2(X2,X0),X3))) ),
inference(superposition,[status(thm)],[c_368702,c_97]) ).
tcf(c_374547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,set_intersection2(X3,X0),X4),X4)
| in(apply(X2,sK7(X2,set_intersection2(X3,X0),X4)),X1)
| ( relation_inverse_image(X2,set_intersection2(X3,X0)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368702,c_96]) ).
tcf(c_374548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| element(apply(X0,sK7(X0,set_intersection2(X1,X2),X3)),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_93]) ).
tcf(c_374549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X2,X1),X3),X3)
| ( relation_inverse_image(X0,set_intersection2(X2,X1)) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_91]) ).
tcf(c_374550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X1,set_intersection2(X2,X3)),X4),X4)
| in(apply(X0,sK7(X0,set_intersection2(X1,set_intersection2(X2,X3)),X4)),X3)
| ( relation_inverse_image(X0,set_intersection2(X1,set_intersection2(X2,X3))) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_59]) ).
tcf(c_374551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X1,set_intersection2(X2,X3)),X4),X4)
| in(apply(X0,sK7(X0,set_intersection2(X1,set_intersection2(X2,X3)),X4)),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,set_intersection2(X2,X3))) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_58]) ).
tcf(c_374552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| in(sK7(X0,set_intersection2(X1,X2),X3),relation_inverse_image(X0,X2))
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,set_intersection2(X1,X2),X3),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368702,c_86]) ).
tcf(c_374553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X2,relation_inverse_image(X1,X3)),X4),X4)
| in(apply(X1,apply(X0,sK7(X0,set_intersection2(X2,relation_inverse_image(X1,X3)),X4))),X3)
| ( relation_inverse_image(X0,set_intersection2(X2,relation_inverse_image(X1,X3))) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_88]) ).
tcf(c_374554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X2,relation_inverse_image(X1,X3)),X4),X4)
| in(apply(X0,sK7(X0,set_intersection2(X2,relation_inverse_image(X1,X3)),X4)),relation_dom(X1))
| ( relation_inverse_image(X0,set_intersection2(X2,relation_inverse_image(X1,X3))) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_87]) ).
tcf(c_374555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X3,relation_image(X1,X2)),X4),X4)
| ( relation_inverse_image(X0,set_intersection2(X3,relation_image(X1,X2))) = X4 )
| ( apply(X1,sK13(X1,X2,apply(X0,sK7(X0,set_intersection2(X3,relation_image(X1,X2)),X4)))) = apply(X0,sK7(X0,set_intersection2(X3,relation_image(X1,X2)),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_112]) ).
tcf(c_374556,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,set_intersection2(X1,empty_set),X2),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,empty_set)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_372426]) ).
tcf(c_374557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,relation_image(empty_set,X2)),X3),X3)
| ( relation_inverse_image(X0,set_intersection2(X1,relation_image(empty_set,X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_373745]) ).
tcf(c_374606,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,X2),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,empty_set)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_374524,c_372426]) ).
tcf(c_374796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X2,X1),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),X3)),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_368703]) ).
tcf(c_374798,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,X2),X2)
| in(apply(X0,sK7(X0,set_intersection2(X1,empty_set),X2)),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,empty_set)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_368703]) ).
tcf(c_374799,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,X2),X2)
| in(apply(X0,sK7(X0,set_intersection2(empty_set,X1),X2)),empty_set)
| ( relation_inverse_image(X0,set_intersection2(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_368703]) ).
tcf(c_374801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X2,X1),X3)),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_368703]) ).
tcf(c_374805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,set_intersection2(X3,X4),X0),X1)
| in(apply(X2,sK7(X2,set_intersection2(X3,X4),X0)),X3)
| ( relation_inverse_image(X2,set_intersection2(X3,X4)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368703,c_321]) ).
tcf(c_374806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,set_intersection2(X3,X4),X0)),X3)
| ( relation_inverse_image(X2,set_intersection2(X3,X4)) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368703,c_320]) ).
tcf(c_374807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,set_intersection2(X2,X3),X0)),X2)
| ( relation_inverse_image(X1,set_intersection2(X2,X3)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK7(X1,set_intersection2(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_368703,c_97]) ).
tcf(c_374808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,set_intersection2(X3,X4),X0),X1)
| in(apply(X2,sK7(X2,set_intersection2(X3,X4),X0)),X3)
| ( relation_inverse_image(X2,set_intersection2(X3,X4)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368703,c_96]) ).
tcf(c_374809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,set_intersection2(X1,X2),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),X3)),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_93]) ).
tcf(c_374810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X2,X3),X1)),X2)
| ( relation_inverse_image(X0,set_intersection2(X2,X3)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_91]) ).
tcf(c_374813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4))),X4)
| in(apply(X0,sK7(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4))),X2)
| ( relation_inverse_image(X0,set_intersection2(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_88]) ).
tcf(c_374814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| in(apply(X0,sK7(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4))),X2)
| ( relation_inverse_image(X0,set_intersection2(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_87]) ).
tcf(c_374815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X3,X4),relation_image(X1,X2))),X3)
| ( relation_inverse_image(X0,set_intersection2(X3,X4)) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK7(X0,set_intersection2(X3,X4),relation_image(X1,X2)))) = sK7(X0,set_intersection2(X3,X4),relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_112]) ).
tcf(c_374816,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X1,X2),empty_set)),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_372426]) ).
tcf(c_374817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X1,X2),relation_image(empty_set,X3))),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = relation_image(empty_set,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_373745]) ).
tcf(c_374818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,set_intersection2(X0,X3),X4),X4)
| element(apply(X2,sK7(X2,set_intersection2(X0,X3),X4)),X1)
| ( relation_inverse_image(X2,set_intersection2(X0,X3)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368703,c_321]) ).
tcf(c_374819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,set_intersection2(X0,X3),X4),X4)
| ( relation_inverse_image(X2,set_intersection2(X0,X3)) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368703,c_320]) ).
tcf(c_374820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,set_intersection2(X0,X2),X3),X3)
| ( relation_inverse_image(X1,set_intersection2(X0,X2)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK7(X1,set_intersection2(X0,X2),X3))) ),
inference(superposition,[status(thm)],[c_368703,c_97]) ).
tcf(c_374821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,set_intersection2(X0,X3),X4),X4)
| in(apply(X2,sK7(X2,set_intersection2(X0,X3),X4)),X1)
| ( relation_inverse_image(X2,set_intersection2(X0,X3)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368703,c_96]) ).
tcf(c_374822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| element(apply(X0,sK7(X0,set_intersection2(X1,X2),X3)),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_93]) ).
tcf(c_374823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_91]) ).
tcf(c_374824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X4)
| in(apply(X0,sK7(X0,set_intersection2(set_intersection2(X1,X2),X3),X4)),X2)
| ( relation_inverse_image(X0,set_intersection2(set_intersection2(X1,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_59]) ).
tcf(c_374825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X4)
| in(apply(X0,sK7(X0,set_intersection2(set_intersection2(X1,X2),X3),X4)),X1)
| ( relation_inverse_image(X0,set_intersection2(set_intersection2(X1,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_58]) ).
tcf(c_374826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| in(sK7(X0,set_intersection2(X1,X2),X3),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,set_intersection2(X1,X2),X3),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368703,c_86]) ).
tcf(c_374827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(relation_inverse_image(X1,X2),X3),X4),X4)
| in(apply(X1,apply(X0,sK7(X0,set_intersection2(relation_inverse_image(X1,X2),X3),X4))),X2)
| ( relation_inverse_image(X0,set_intersection2(relation_inverse_image(X1,X2),X3)) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_88]) ).
tcf(c_374828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(relation_inverse_image(X1,X2),X3),X4),X4)
| in(apply(X0,sK7(X0,set_intersection2(relation_inverse_image(X1,X2),X3),X4)),relation_dom(X1))
| ( relation_inverse_image(X0,set_intersection2(relation_inverse_image(X1,X2),X3)) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_87]) ).
tcf(c_374829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(relation_image(X1,X2),X3),X4),X4)
| ( relation_inverse_image(X0,set_intersection2(relation_image(X1,X2),X3)) = X4 )
| ( apply(X1,sK13(X1,X2,apply(X0,sK7(X0,set_intersection2(relation_image(X1,X2),X3),X4)))) = apply(X0,sK7(X0,set_intersection2(relation_image(X1,X2),X3),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_112]) ).
tcf(c_374830,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,set_intersection2(empty_set,X1),X2),X2)
| ( relation_inverse_image(X0,set_intersection2(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_372426]) ).
tcf(c_374831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(relation_image(empty_set,X1),X2),X3),X3)
| ( relation_inverse_image(X0,set_intersection2(relation_image(empty_set,X1),X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_373745]) ).
tcf(c_374865,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,X2),X2)
| ( relation_inverse_image(X0,set_intersection2(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_374799,c_372426]) ).
tcf(c_375095,plain,
! [X0: $i] : relation_dom(relation_image(empty_set,X0)) = empty_set,
inference(superposition,[status(thm)],[c_373798,c_369156]) ).
tcf(c_375096,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_image(empty_set,X1)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_373798,c_368606]) ).
tcf(c_375097,plain,
! [X0: $i] : relation_image(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_373798,c_101]) ).
tcf(c_375098,plain,
! [X0: $i] : relation(relation_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_373798,c_82]) ).
tcf(c_375099,plain,
! [X0: $i] : function(relation_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_373798,c_77]) ).
tcf(c_375100,plain,
! [X0: $i,X1: $i] :
( ( relation_image(empty_set,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_373798,c_52]) ).
tcf(c_375132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_inverse_image(X0,set_intersection2(X3,X2)))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X3)
| ~ in(apply(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_63,c_368735]) ).
tcf(c_375134,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_inverse_image(X0,empty_set))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),empty_set)
| ~ in(apply(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_64,c_368735]) ).
tcf(c_375136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3,X4),X4)
| ~ in(sK2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3,X4),X3)
| ~ in(sK2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3,X4),relation_dom(X0))
| ~ in(apply(X0,sK2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3,X4)),X2)
| ~ in(apply(X0,sK2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3,X4)),X1) ),
inference(superposition,[status(thm)],[c_368735,c_54]) ).
tcf(c_375137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(X4,X3)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X2)
| ~ in(apply(X0,X4),X1)
| ~ subset(relation_inverse_image(X0,set_intersection2(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_368735,c_321]) ).
tcf(c_375138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ empty(X3)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X2)
| ~ in(apply(X0,X4),X1)
| ~ subset(relation_inverse_image(X0,set_intersection2(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_368735,c_320]) ).
tcf(c_375139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X2)
| ~ in(apply(X0,X3),X1)
| ~ in(relation_inverse_image(X0,set_intersection2(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_368735,c_97]) ).
tcf(c_375140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X4,X3)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X2)
| ~ in(apply(X0,X4),X1)
| ~ subset(relation_inverse_image(X0,set_intersection2(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_368735,c_96]) ).
tcf(c_375141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X1,relation_inverse_image(X0,set_intersection2(X2,X3)))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X3)
| ~ in(apply(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_368735,c_93]) ).
tcf(c_375142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X2)
| ~ in(apply(X0,X3),X1)
| ~ empty(relation_inverse_image(X0,set_intersection2(X1,X2))) ),
inference(superposition,[status(thm)],[c_368735,c_91]) ).
tcf(c_375143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X1,relation_inverse_image(X0,set_intersection2(X2,X3))) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK7(X1,relation_inverse_image(X0,set_intersection2(X2,X3)),X4),X4)
| ~ in(sK7(X1,relation_inverse_image(X0,set_intersection2(X2,X3)),X4),relation_dom(X1))
| ~ in(apply(X1,sK7(X1,relation_inverse_image(X0,set_intersection2(X2,X3)),X4)),relation_dom(X0))
| ~ in(apply(X0,apply(X1,sK7(X1,relation_inverse_image(X0,set_intersection2(X2,X3)),X4))),X3)
| ~ in(apply(X0,apply(X1,sK7(X1,relation_inverse_image(X0,set_intersection2(X2,X3)),X4))),X2) ),
inference(superposition,[status(thm)],[c_368735,c_83]) ).
tcf(c_375144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,relation_inverse_image(X1,relation_inverse_image(X0,set_intersection2(X3,X4))))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X2,relation_dom(X1))
| ~ in(apply(X1,X2),relation_dom(X0))
| ~ in(apply(X0,apply(X1,X2)),X4)
| ~ in(apply(X0,apply(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_368735,c_86]) ).
tcf(c_375145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,X1),set_intersection2(X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X3)
| ~ in(apply(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_368735,c_88]) ).
tcf(c_375147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X1,relation_inverse_image(X0,set_intersection2(X2,X3)))
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK10(X1,relation_inverse_image(X0,set_intersection2(X2,X3))),relation_dom(X0))
| ~ in(apply(X0,sK10(X1,relation_inverse_image(X0,set_intersection2(X2,X3)))),X3)
| ~ in(apply(X0,sK10(X1,relation_inverse_image(X0,set_intersection2(X2,X3)))),X2) ),
inference(superposition,[status(thm)],[c_368735,c_94]) ).
tcf(c_375148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4,X5),X5)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4,X5),X4)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4,X5),X3)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4,X5),relation_dom(X0))
| ~ in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4,X5)),X2)
| ~ in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4,X5)),X1) ),
inference(superposition,[status(thm)],[c_368735,c_368471]) ).
tcf(c_375149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_inverse_image(X1,set_intersection2(relation_inverse_image(X0,set_intersection2(X2,X3)),X4)) = X5 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK7(X1,set_intersection2(relation_inverse_image(X0,set_intersection2(X2,X3)),X4),X5),X5)
| ~ in(sK7(X1,set_intersection2(relation_inverse_image(X0,set_intersection2(X2,X3)),X4),X5),relation_dom(X1))
| ~ in(apply(X1,sK7(X1,set_intersection2(relation_inverse_image(X0,set_intersection2(X2,X3)),X4),X5)),X4)
| ~ in(apply(X1,sK7(X1,set_intersection2(relation_inverse_image(X0,set_intersection2(X2,X3)),X4),X5)),relation_dom(X0))
| ~ in(apply(X0,apply(X1,sK7(X1,set_intersection2(relation_inverse_image(X0,set_intersection2(X2,X3)),X4),X5))),X3)
| ~ in(apply(X0,apply(X1,sK7(X1,set_intersection2(relation_inverse_image(X0,set_intersection2(X2,X3)),X4),X5))),X2) ),
inference(superposition,[status(thm)],[c_368735,c_368654]) ).
tcf(c_375319,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,X2),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_368736,c_84,c_8395]) ).
tcf(c_375331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X2,X3,X0),X1)
| in(sK7(X2,X3,X0),relation_inverse_image(X2,X3))
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_375319,c_321]) ).
tcf(c_375332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X3,X0),relation_inverse_image(X2,X3))
| ( relation_inverse_image(X2,X3) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_375319,c_320]) ).
tcf(c_375333,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X2,X0),relation_inverse_image(X1,X2))
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK7(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_375319,c_97]) ).
tcf(c_375334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X3,X0),X1)
| in(sK7(X2,X3,X0),relation_inverse_image(X2,X3))
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_375319,c_96]) ).
tcf(c_375335,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,X2),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375319,c_93]) ).
tcf(c_375336,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,X1),relation_inverse_image(X0,X2))
| ( relation_inverse_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375319,c_91]) ).
tcf(c_375337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK7(X0,X1,set_intersection2(X2,X3)),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375319,c_59]) ).
tcf(c_375338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK7(X0,X1,set_intersection2(X2,X3)),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375319,c_58]) ).
tcf(c_375339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_inverse_image(X0,X2))
| in(apply(X1,sK7(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375319,c_88]) ).
tcf(c_375340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_inverse_image(X0,X2))
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375319,c_87]) ).
tcf(c_375341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,relation_image(X1,X2)),relation_inverse_image(X0,X3))
| ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK7(X0,X3,relation_image(X1,X2)))) = sK7(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375319,c_112]) ).
tcf(c_375342,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,empty_set),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375319,c_372426]) ).
tcf(c_375343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X1,X3),X2)
| in(sK7(X0,X1,X3),X3)
| ( relation_inverse_image(X0,X1) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_inverse_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_375319,c_321]) ).
tcf(c_375344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,X3),X3)
| ( relation_inverse_image(X0,X1) = X3 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_inverse_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_375319,c_320]) ).
tcf(c_375345,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_inverse_image(X0,X1),sK7(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_375319,c_97]) ).
tcf(c_375346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,X3),X3)
| in(sK7(X0,X1,X3),X2)
| ( relation_inverse_image(X0,X1) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_inverse_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_375319,c_96]) ).
tcf(c_375347,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| element(sK7(X0,X1,X2),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375319,c_93]) ).
tcf(c_375348,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_inverse_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_375319,c_91]) ).
tcf(c_375549,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_inverse_image(empty_set,X0),X1,X2),empty_set)
| in(sK2(relation_inverse_image(empty_set,X0),X1,X2),X2)
| ( set_intersection2(relation_inverse_image(empty_set,X0),X1) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_368757]) ).
tcf(c_375551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(relation_inverse_image(X2,X3),X4,X0),X1)
| in(sK2(relation_inverse_image(X2,X3),X4,X0),relation_dom(X2))
| ( set_intersection2(relation_inverse_image(X2,X3),X4) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368757,c_321]) ).
tcf(c_375552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X2,X3),X4,X0),relation_dom(X2))
| ( set_intersection2(relation_inverse_image(X2,X3),X4) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368757,c_320]) ).
tcf(c_375553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X1,X2),X3,X0),relation_dom(X1))
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(relation_inverse_image(X1,X2),X3,X0)) ),
inference(superposition,[status(thm)],[c_368757,c_97]) ).
tcf(c_375554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X2,X3),X4,X0),X1)
| in(sK2(relation_inverse_image(X2,X3),X4,X0),relation_dom(X2))
| ( set_intersection2(relation_inverse_image(X2,X3),X4) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368757,c_96]) ).
tcf(c_375555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(relation_inverse_image(X0,X1),X2,X3),X3)
| in(sK2(relation_inverse_image(X0,X1),X2,X3),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368757,c_93]) ).
tcf(c_375556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X2),X3,X1),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X2),X3) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368757,c_91]) ).
tcf(c_375559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X2),X3,relation_inverse_image(X1,X4)),relation_dom(X0))
| in(apply(X1,sK2(relation_inverse_image(X0,X2),X3,relation_inverse_image(X1,X4))),X4)
| ( set_intersection2(relation_inverse_image(X0,X2),X3) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368757,c_88]) ).
tcf(c_375560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X2),X3,relation_inverse_image(X1,X4)),relation_dom(X1))
| in(sK2(relation_inverse_image(X0,X2),X3,relation_inverse_image(X1,X4)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X2),X3) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368757,c_87]) ).
tcf(c_375561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X3),X4,relation_image(X1,X2)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X3),X4) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK2(relation_inverse_image(X0,X3),X4,relation_image(X1,X2)))) = sK2(relation_inverse_image(X0,X3),X4,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368757,c_112]) ).
tcf(c_375562,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,empty_set),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368757,c_372426]) ).
tcf(c_375563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(relation_inverse_image(X0,X2),X3,X4),X1)
| in(sK2(relation_inverse_image(X0,X2),X3,X4),X4)
| ( set_intersection2(relation_inverse_image(X0,X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368757,c_321]) ).
tcf(c_375564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X2),X3,X4),X4)
| ( set_intersection2(relation_inverse_image(X0,X2),X3) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368757,c_320]) ).
tcf(c_375565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,X3),X3)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK2(relation_inverse_image(X0,X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_368757,c_97]) ).
tcf(c_375566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X2),X3,X4),X4)
| in(sK2(relation_inverse_image(X0,X2),X3,X4),X1)
| ( set_intersection2(relation_inverse_image(X0,X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368757,c_96]) ).
tcf(c_375567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,X3),X3)
| element(sK2(relation_inverse_image(X0,X1),X2,X3),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368757,c_93]) ).
tcf(c_375568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,X3),X3)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368757,c_91]) ).
tcf(c_375569,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,relation_dom(X0)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_factoring,[status(thm)],[c_368757]) ).
tcf(c_375601,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X0,X1),empty_set)
| in(sK2(empty_set,X0,X1),X1)
| ( set_intersection2(empty_set,X0) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_375549,c_373747]) ).
tcf(c_375602,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,X0),empty_set)
| in(sK2(empty_set,X1,X0),X0)
| ( X0 = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_375601,c_368545]) ).
tcf(c_375731,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,relation_inverse_image(empty_set,X1),X2),empty_set)
| in(sK2(X0,relation_inverse_image(empty_set,X1),X2),X2)
| ( set_intersection2(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_368758]) ).
tcf(c_375732,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,relation_inverse_image(X1,X2),X0),relation_dom(X1))
| ( set_intersection2(X0,relation_inverse_image(X1,X2)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,relation_inverse_image(X1,X2),X0),X0)
| ~ in(sK2(X0,relation_inverse_image(X1,X2),X0),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_368758,c_54]) ).
tcf(c_375733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,relation_inverse_image(X2,X4),X0),X1)
| in(sK2(X3,relation_inverse_image(X2,X4),X0),relation_dom(X2))
| ( set_intersection2(X3,relation_inverse_image(X2,X4)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368758,c_321]) ).
tcf(c_375734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_inverse_image(X2,X4),X0),relation_dom(X2))
| ( set_intersection2(X3,relation_inverse_image(X2,X4)) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368758,c_320]) ).
tcf(c_375735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,relation_inverse_image(X2,X3),X0),relation_dom(X2))
| ( set_intersection2(X1,relation_inverse_image(X2,X3)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,sK2(X1,relation_inverse_image(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_368758,c_97]) ).
tcf(c_375736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_inverse_image(X2,X4),X0),X1)
| in(sK2(X3,relation_inverse_image(X2,X4),X0),relation_dom(X2))
| ( set_intersection2(X3,relation_inverse_image(X2,X4)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368758,c_96]) ).
tcf(c_375737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X1,relation_inverse_image(X0,X2),X3),X3)
| in(sK2(X1,relation_inverse_image(X0,X2),X3),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368758,c_93]) ).
tcf(c_375738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,relation_inverse_image(X0,X3),X1),relation_dom(X0))
| ( set_intersection2(X2,relation_inverse_image(X0,X3)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368758,c_91]) ).
tcf(c_375741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_inverse_image(X0,X3),relation_inverse_image(X1,X4)),relation_dom(X0))
| in(apply(X1,sK2(X2,relation_inverse_image(X0,X3),relation_inverse_image(X1,X4))),X4)
| ( set_intersection2(X2,relation_inverse_image(X0,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368758,c_88]) ).
tcf(c_375742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_inverse_image(X0,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| in(sK2(X2,relation_inverse_image(X0,X3),relation_inverse_image(X1,X4)),relation_dom(X0))
| ( set_intersection2(X2,relation_inverse_image(X0,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368758,c_87]) ).
tcf(c_375743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_inverse_image(X0,X4),relation_image(X1,X2)),relation_dom(X0))
| ( set_intersection2(X3,relation_inverse_image(X0,X4)) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK2(X3,relation_inverse_image(X0,X4),relation_image(X1,X2)))) = sK2(X3,relation_inverse_image(X0,X4),relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368758,c_112]) ).
tcf(c_375744,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),empty_set),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368758,c_372426]) ).
tcf(c_375745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),X0),relation_dom(X2))
| ( set_intersection2(set_intersection2(X0,X1),relation_inverse_image(X2,X3)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),X0),X0)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),X0),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368758,c_368471]) ).
tcf(c_375747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,relation_inverse_image(X0,X3),X4),X1)
| in(sK2(X2,relation_inverse_image(X0,X3),X4),X4)
| ( set_intersection2(X2,relation_inverse_image(X0,X3)) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368758,c_321]) ).
tcf(c_375748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_inverse_image(X0,X3),X4),X4)
| ( set_intersection2(X2,relation_inverse_image(X0,X3)) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368758,c_320]) ).
tcf(c_375749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),X3),X3)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK2(X1,relation_inverse_image(X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_368758,c_97]) ).
tcf(c_375750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_inverse_image(X0,X3),X4),X4)
| in(sK2(X2,relation_inverse_image(X0,X3),X4),X1)
| ( set_intersection2(X2,relation_inverse_image(X0,X3)) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368758,c_96]) ).
tcf(c_375751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),X3),X3)
| element(sK2(X1,relation_inverse_image(X0,X2),X3),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368758,c_93]) ).
tcf(c_375752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),X3),X3)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368758,c_91]) ).
tcf(c_375754,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),relation_dom(X0)),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_factoring,[status(thm)],[c_368758]) ).
tcf(c_375786,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,relation_inverse_image(empty_set,X1),X2),X2)
| ( set_intersection2(X0,relation_inverse_image(empty_set,X1)) = X2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_375731,c_372426,c_368630,c_103]) ).
tcf(c_375973,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,relation_inverse_image(empty_set,X2)),empty_set)
| in(sK2(X0,X1,relation_inverse_image(empty_set,X2)),X1)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_368759]) ).
tcf(c_375974,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,relation_inverse_image(X1,X2)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = set_intersection2(X0,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,X0,relation_inverse_image(X1,X2)),X0)
| ~ in(sK2(X0,X0,relation_inverse_image(X1,X2)),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_368759,c_54]) ).
tcf(c_375975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X0,relation_inverse_image(X2,X3)),X1)
| in(sK2(X4,X0,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368759,c_321]) ).
tcf(c_375976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X4,X0,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X4,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368759,c_320]) ).
tcf(c_375977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X0,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X1,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,sK2(X1,X0,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_368759,c_97]) ).
tcf(c_375978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X4,X0,relation_inverse_image(X2,X3)),X1)
| in(sK2(X4,X0,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368759,c_96]) ).
tcf(c_375979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,relation_inverse_image(X0,X1)),X3)
| in(sK2(X2,X3,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368759,c_93]) ).
tcf(c_375980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,X1,relation_inverse_image(X0,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368759,c_91]) ).
tcf(c_375983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_inverse_image(X1,X3),relation_inverse_image(X0,X4)),relation_dom(X0))
| in(apply(X1,sK2(X2,relation_inverse_image(X1,X3),relation_inverse_image(X0,X4))),X3)
| ( set_intersection2(X2,relation_inverse_image(X1,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368759,c_88]) ).
tcf(c_375984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_inverse_image(X1,X3),relation_inverse_image(X0,X4)),relation_dom(X1))
| in(sK2(X2,relation_inverse_image(X1,X3),relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(X2,relation_inverse_image(X1,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368759,c_87]) ).
tcf(c_375985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_image(X1,X2),relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(X3,relation_image(X1,X2)) = relation_inverse_image(X0,X4) )
| ( apply(X1,sK13(X1,X2,sK2(X3,relation_image(X1,X2),relation_inverse_image(X0,X4)))) = sK2(X3,relation_image(X1,X2),relation_inverse_image(X0,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368759,c_112]) ).
tcf(c_375986,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,empty_set,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368759,c_372426]) ).
tcf(c_375987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X0,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( set_intersection2(set_intersection2(X0,X1),X0) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,relation_inverse_image(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X0,relation_inverse_image(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),X0,relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368759,c_368471]) ).
tcf(c_375989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,relation_inverse_image(X0,X2)),X1)
| in(sK2(X3,X4,relation_inverse_image(X0,X2)),X4)
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368759,c_321]) ).
tcf(c_375990,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,X2)),X4)
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368759,c_320]) ).
tcf(c_375991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,X3)),X2)
| ( relation_inverse_image(X0,X3) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK2(X1,X2,relation_inverse_image(X0,X3))) ),
inference(superposition,[status(thm)],[c_368759,c_97]) ).
tcf(c_375992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,X2)),X4)
| in(sK2(X3,X4,relation_inverse_image(X0,X2)),X1)
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368759,c_96]) ).
tcf(c_375993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X0,X1)),X3)
| element(sK2(X2,X3,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368759,c_93]) ).
tcf(c_375994,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X0,X1)),X3)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368759,c_91]) ).
tcf(c_375996,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,relation_dom(X0),relation_inverse_image(X0,X2)),relation_dom(X0))
| ( set_intersection2(X1,relation_dom(X0)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_factoring,[status(thm)],[c_368759]) ).
tcf(c_376028,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,relation_inverse_image(empty_set,X2)),X1)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_375973,c_372426,c_368630,c_103]) ).
tcf(c_376075,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,relation_inverse_image(X1,X2)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,X0,relation_inverse_image(X1,X2)),X0)
| ~ in(sK2(X0,X0,relation_inverse_image(X1,X2)),relation_inverse_image(X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_375974,c_53]) ).
tcf(c_376151,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,relation_inverse_image(empty_set,X2)),empty_set)
| in(sK2(X0,X1,relation_inverse_image(empty_set,X2)),X0)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_368760]) ).
tcf(c_376152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X1) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,relation_inverse_image(X2,X3)),X1)
| ~ in(sK2(X0,X1,relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368760,c_54]) ).
tcf(c_376153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X4,relation_inverse_image(X2,X3)),X1)
| in(sK2(X0,X4,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368760,c_321]) ).
tcf(c_376154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X4,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368760,c_320]) ).
tcf(c_376155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X1) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,sK2(X0,X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_368760,c_97]) ).
tcf(c_376156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X4,relation_inverse_image(X2,X3)),X1)
| in(sK2(X0,X4,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368760,c_96]) ).
tcf(c_376157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,relation_inverse_image(X0,X1)),X2)
| in(sK2(X2,X3,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368760,c_93]) ).
tcf(c_376158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X3,relation_inverse_image(X0,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = set_intersection2(X1,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368760,c_91]) ).
tcf(c_376161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X1,X2),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| in(apply(X1,sK2(relation_inverse_image(X1,X2),X3,relation_inverse_image(X0,X4))),X2)
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368760,c_88]) ).
tcf(c_376162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X1,X2),X3,relation_inverse_image(X0,X4)),relation_dom(X1))
| in(sK2(relation_inverse_image(X1,X2),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368760,c_87]) ).
tcf(c_376163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X1,X2),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(relation_image(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ( apply(X1,sK13(X1,X2,sK2(relation_image(X1,X2),X3,relation_inverse_image(X0,X4)))) = sK2(relation_image(X1,X2),X3,relation_inverse_image(X0,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368760,c_112]) ).
tcf(c_376164,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368760,c_372426]) ).
tcf(c_376166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,relation_inverse_image(X0,X2)),X1)
| in(sK2(X3,X4,relation_inverse_image(X0,X2)),X3)
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368760,c_321]) ).
tcf(c_376167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,X2)),X3)
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368760,c_320]) ).
tcf(c_376168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,X3)),X1)
| ( relation_inverse_image(X0,X3) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK2(X1,X2,relation_inverse_image(X0,X3))) ),
inference(superposition,[status(thm)],[c_368760,c_97]) ).
tcf(c_376169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,X2)),X3)
| in(sK2(X3,X4,relation_inverse_image(X0,X2)),X1)
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368760,c_96]) ).
tcf(c_376170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X0,X1)),X2)
| element(sK2(X2,X3,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368760,c_93]) ).
tcf(c_376171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X0,X1)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368760,c_91]) ).
tcf(c_376172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X0,X3)),set_intersection2(relation_dom(X0),X1))
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X0,X3)),X2)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X0,X3)),X1)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X0,X3)),relation_inverse_image(X0,X3)) ),
inference(superposition,[status(thm)],[c_368760,c_368471]) ).
tcf(c_376173,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_dom(X0),X1,relation_inverse_image(X0,X2)),relation_dom(X0))
| ( set_intersection2(relation_dom(X0),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_factoring,[status(thm)],[c_368760]) ).
tcf(c_376205,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,relation_inverse_image(empty_set,X2)),X0)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_376151,c_372426,c_368630,c_103]) ).
tcf(c_376395,plain,
! [X0: $i] :
( ( relation_image(empty_set,relation_inverse_image(empty_set,X0)) = X0 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(X0,relation_image(empty_set,empty_set)) ),
inference(superposition,[status(thm)],[c_373747,c_368596]) ).
tcf(c_376397,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X0)
| in(sK2(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(empty_set))
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_368760]) ).
tcf(c_376399,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X1)
| in(sK2(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(empty_set))
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_368759]) ).
tcf(c_376400,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),relation_dom(empty_set))
| in(sK2(relation_inverse_image(empty_set,X0),X1,X2),X2)
| ( set_intersection2(relation_inverse_image(empty_set,X0),X1) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_368757]) ).
tcf(c_376401,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| in(sK2(relation_inverse_image(empty_set,X0),X1,X2),relation_dom(empty_set))
| ( set_intersection2(relation_inverse_image(empty_set,X0),X1) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_368757]) ).
tcf(c_376403,plain,
! [X0: $i] :
( subset(relation_image(empty_set,empty_set),X0)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_68]) ).
tcf(c_376405,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X2)
| in(sK2(X0,relation_inverse_image(empty_set,X1),X2),relation_dom(empty_set))
| ( set_intersection2(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_368758]) ).
tcf(c_376408,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,relation_dom(empty_set))
| ~ in(apply(empty_set,X0),X2)
| ~ in(apply(empty_set,X0),X1) ),
inference(superposition,[status(thm)],[c_373747,c_368735]) ).
tcf(c_376409,plain,
! [X0: $i] : subset(relation_image(empty_set,empty_set),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_376403,c_368630,c_103]) ).
tcf(c_376410,plain,
! [X0: $i] :
( ( relation_image(empty_set,empty_set) = X0 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(X0,relation_image(empty_set,empty_set)) ),
inference(light_normalisation,[status(thm)],[c_376395,c_373747]) ).
tcf(c_376411,plain,
! [X0: $i] :
( ( relation_image(empty_set,empty_set) = X0 )
| ~ subset(X0,relation_image(empty_set,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_376410,c_368630,c_103]) ).
tcf(c_376415,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X2)
| in(sK2(X0,relation_inverse_image(empty_set,X1),X2),empty_set)
| ( set_intersection2(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_376405,c_373108]) ).
tcf(c_376416,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X2)
| ( set_intersection2(X0,relation_inverse_image(empty_set,X1)) = X2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_376415,c_372426,c_368630,c_103]) ).
tcf(c_376425,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X1)
| in(sK2(X0,X1,relation_inverse_image(empty_set,X2)),empty_set)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_376399,c_373108]) ).
tcf(c_376426,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X1)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_376425,c_372426,c_368630,c_103]) ).
tcf(c_376429,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X0)
| in(sK2(X0,X1,relation_inverse_image(empty_set,X2)),empty_set)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_376397,c_373108]) ).
tcf(c_376430,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X0)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_376429,c_372426,c_368630,c_103]) ).
tcf(c_376464,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,X2),X2)
| in(apply(X0,sK7(X0,relation_inverse_image(empty_set,X1),X2)),relation_dom(empty_set))
| ( relation_inverse_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_368761]) ).
tcf(c_376465,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_inverse_image(empty_set,X1),X2),X2)
| in(apply(X0,sK7(X0,empty_set,X2)),relation_dom(empty_set))
| ( relation_inverse_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_368761]) ).
tcf(c_376466,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_inverse_image(empty_set,X1),X2),X2)
| in(apply(X0,sK7(X0,relation_inverse_image(empty_set,X1),X2)),empty_set)
| ( relation_inverse_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373108,c_368761]) ).
tcf(c_376467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,relation_inverse_image(X3,X4),X0),X1)
| in(apply(X2,sK7(X2,relation_inverse_image(X3,X4),X0)),relation_dom(X3))
| ( relation_inverse_image(X2,relation_inverse_image(X3,X4)) = X0 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368761,c_321]) ).
tcf(c_376468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,relation_inverse_image(X3,X4),X0)),relation_dom(X3))
| ( relation_inverse_image(X2,relation_inverse_image(X3,X4)) = X0 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368761,c_320]) ).
tcf(c_376469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,relation_inverse_image(X2,X3),X0)),relation_dom(X2))
| ( relation_inverse_image(X1,relation_inverse_image(X2,X3)) = X0 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,sK7(X1,relation_inverse_image(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_368761,c_97]) ).
tcf(c_376470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,relation_inverse_image(X3,X4),X0),X1)
| in(apply(X2,sK7(X2,relation_inverse_image(X3,X4),X0)),relation_dom(X3))
| ( relation_inverse_image(X2,relation_inverse_image(X3,X4)) = X0 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368761,c_96]) ).
tcf(c_376471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,relation_inverse_image(X1,X2),X3),X3)
| in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),X3)),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368761,c_93]) ).
tcf(c_376472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,relation_inverse_image(X1,X3),X2)),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X3)) = X2 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368761,c_91]) ).
tcf(c_376475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4))),X4)
| in(apply(X0,sK7(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X3)) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368761,c_88]) ).
tcf(c_376476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4)),relation_dom(X2))
| in(apply(X0,sK7(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X3)) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368761,c_87]) ).
tcf(c_376477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,relation_inverse_image(X1,X4),relation_image(X2,X3))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X4)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X0,relation_inverse_image(X1,X4),relation_image(X2,X3)))) = sK7(X0,relation_inverse_image(X1,X4),relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368761,c_112]) ).
tcf(c_376478,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),empty_set)),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = empty_set )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368761,c_372426]) ).
tcf(c_376479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,relation_inverse_image(X0,X3),X4),X4)
| element(apply(X2,sK7(X2,relation_inverse_image(X0,X3),X4)),X1)
| ( relation_inverse_image(X2,relation_inverse_image(X0,X3)) = X4 )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368761,c_321]) ).
tcf(c_376480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,relation_inverse_image(X0,X3),X4),X4)
| ( relation_inverse_image(X2,relation_inverse_image(X0,X3)) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368761,c_320]) ).
tcf(c_376481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,relation_inverse_image(X0,X2),X3),X3)
| ( relation_inverse_image(X1,relation_inverse_image(X0,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(relation_dom(X0),apply(X1,sK7(X1,relation_inverse_image(X0,X2),X3))) ),
inference(superposition,[status(thm)],[c_368761,c_97]) ).
tcf(c_376482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,relation_inverse_image(X0,X3),X4),X4)
| in(apply(X2,sK7(X2,relation_inverse_image(X0,X3),X4)),X1)
| ( relation_inverse_image(X2,relation_inverse_image(X0,X3)) = X4 )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368761,c_96]) ).
tcf(c_376483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),X3),X3)
| element(apply(X0,sK7(X0,relation_inverse_image(X1,X2),X3)),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368761,c_93]) ).
tcf(c_376484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,relation_inverse_image(X0,X2),X3),X3)
| ( relation_inverse_image(X1,relation_inverse_image(X0,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368761,c_91]) ).
tcf(c_376485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),X3),X3)
| in(sK7(X0,relation_inverse_image(X1,X2),X3),relation_inverse_image(X0,relation_dom(X1)))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK7(X0,relation_inverse_image(X1,X2),X3),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368761,c_86]) ).
tcf(c_376514,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,empty_set,X2)),empty_set)
| in(sK7(X0,relation_inverse_image(empty_set,X1),X2),X2)
| ( relation_inverse_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_376465,c_373108]) ).
tcf(c_376515,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_inverse_image(empty_set,X1),X2),X2)
| ( relation_inverse_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_376514,c_372426,c_368630,c_103]) ).
tcf(c_376520,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,X2),X2)
| in(apply(X0,sK7(X0,relation_inverse_image(empty_set,X1),X2)),empty_set)
| ( relation_inverse_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_376464,c_373108]) ).
tcf(c_376521,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,X2),X2)
| ( relation_inverse_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_376520,c_372426,c_368630,c_103]) ).
tcf(c_376677,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(empty_set))
| in(apply(X0,sK7(X0,X1,relation_inverse_image(empty_set,X2))),X1)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_368762]) ).
tcf(c_376678,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,relation_inverse_image(empty_set,X2)),empty_set)
| in(apply(X0,sK7(X0,X1,relation_inverse_image(empty_set,X2))),X1)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373108,c_368762]) ).
tcf(c_376679,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,empty_set)),X1)
| in(sK7(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(empty_set))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_368762]) ).
tcf(c_376680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,X4,relation_inverse_image(X0,X3)),X1)
| in(apply(X2,sK7(X2,X4,relation_inverse_image(X0,X3))),X4)
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368762,c_321]) ).
tcf(c_376681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,X4,relation_inverse_image(X0,X3))),X4)
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X2,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368762,c_320]) ).
tcf(c_376682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,X2,relation_inverse_image(X0,X3))),X2)
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK7(X1,X2,relation_inverse_image(X0,X3))) ),
inference(superposition,[status(thm)],[c_368762,c_97]) ).
tcf(c_376683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X4,relation_inverse_image(X0,X3)),X1)
| in(apply(X2,sK7(X2,X4,relation_inverse_image(X0,X3))),X4)
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368762,c_96]) ).
tcf(c_376684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| in(apply(X0,sK7(X0,X2,relation_inverse_image(X1,X3))),X2)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368762,c_93]) ).
tcf(c_376685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,X3,relation_inverse_image(X0,X2))),X3)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368762,c_91]) ).
tcf(c_376686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X0,relation_inverse_image(X3,X4)),relation_dom(X3))
| element(apply(X2,sK7(X2,X0,relation_inverse_image(X3,X4))),X1)
| ( relation_inverse_image(X2,X0) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368762,c_321]) ).
tcf(c_376687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X0,relation_inverse_image(X3,X4)),relation_dom(X3))
| ( relation_inverse_image(X2,X0) = relation_inverse_image(X3,X4) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368762,c_320]) ).
tcf(c_376688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X0,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X1,X0) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK7(X1,X0,relation_inverse_image(X2,X3)))) ),
inference(superposition,[status(thm)],[c_368762,c_97]) ).
tcf(c_376689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X0,relation_inverse_image(X3,X4)),relation_dom(X3))
| in(apply(X2,sK7(X2,X0,relation_inverse_image(X3,X4))),X1)
| ( relation_inverse_image(X2,X0) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368762,c_96]) ).
tcf(c_376690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| element(apply(X0,sK7(X0,X2,relation_inverse_image(X1,X3))),X2)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368762,c_93]) ).
tcf(c_376691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368762,c_91]) ).
tcf(c_376694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X0))
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368762,c_83]) ).
tcf(c_376695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2))
| in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368762,c_86]) ).
tcf(c_376696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| in(apply(X2,apply(X0,sK7(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4)))),X3)
| ( relation_inverse_image(X0,relation_inverse_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368762,c_88]) ).
tcf(c_376697,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| in(apply(X0,sK7(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4))),relation_dom(X2))
| ( relation_inverse_image(X0,relation_inverse_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368762,c_87]) ).
tcf(c_376698,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_image(X2,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| ( relation_inverse_image(X0,relation_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ( apply(X2,sK13(X2,X3,apply(X0,sK7(X0,relation_image(X2,X3),relation_inverse_image(X1,X4))))) = apply(X0,sK7(X0,relation_image(X2,X3),relation_inverse_image(X1,X4))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368762,c_112]) ).
tcf(c_376699,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,relation_inverse_image(X1,X2)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = relation_inverse_image(X0,empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368762,c_372426]) ).
tcf(c_376728,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,relation_inverse_image(empty_set,X2)),empty_set)
| in(apply(X0,sK7(X0,X1,empty_set)),X1)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_376679,c_373108]) ).
tcf(c_376729,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,empty_set)),X1)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_376728,c_372426,c_368630,c_103]) ).
tcf(c_376734,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),empty_set)
| in(apply(X0,sK7(X0,X1,relation_inverse_image(empty_set,X2))),X1)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_376677,c_373108]) ).
tcf(c_376735,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,relation_inverse_image(empty_set,X2))),X1)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_376734,c_372426,c_368630,c_103]) ).
tcf(c_376894,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(empty_set))
| in(sK7(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_368763]) ).
tcf(c_376895,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,relation_inverse_image(empty_set,X2)),empty_set)
| in(sK7(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373108,c_368763]) ).
tcf(c_376896,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(X0))
| in(sK7(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(empty_set))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_368763]) ).
tcf(c_376897,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,relation_inverse_image(X0,X1)),empty_set)
| in(sK7(empty_set,X2,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373108,c_368763]) ).
tcf(c_376898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,X4,relation_inverse_image(X0,X3)),X1)
| in(sK7(X2,X4,relation_inverse_image(X0,X3)),relation_dom(X2))
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368763,c_321]) ).
tcf(c_376899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X4,relation_inverse_image(X0,X3)),relation_dom(X2))
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X2,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368763,c_320]) ).
tcf(c_376900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X2,relation_inverse_image(X0,X3)),relation_dom(X1))
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK7(X1,X2,relation_inverse_image(X0,X3))) ),
inference(superposition,[status(thm)],[c_368763,c_97]) ).
tcf(c_376901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X4,relation_inverse_image(X0,X3)),X1)
| in(sK7(X2,X4,relation_inverse_image(X0,X3)),relation_dom(X2))
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368763,c_96]) ).
tcf(c_376902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368763,c_93]) ).
tcf(c_376903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X3,relation_inverse_image(X0,X2)),relation_dom(X1))
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368763,c_91]) ).
tcf(c_376904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X3,relation_inverse_image(X2,X4)),X1)
| in(sK7(X0,X3,relation_inverse_image(X2,X4)),relation_dom(X2))
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368763,c_321]) ).
tcf(c_376905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,relation_inverse_image(X2,X4)),relation_dom(X2))
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X2,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368763,c_320]) ).
tcf(c_376906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK7(X0,X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_368763,c_97]) ).
tcf(c_376907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,relation_inverse_image(X2,X4)),X1)
| in(sK7(X0,X3,relation_inverse_image(X2,X4)),relation_dom(X2))
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368763,c_96]) ).
tcf(c_376908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X0))
| in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368763,c_93]) ).
tcf(c_376909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368763,c_91]) ).
tcf(c_376910,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,relation_inverse_image(X0,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_factoring,[status(thm)],[c_368763]) ).
tcf(c_376930,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(X0))
| in(sK7(X0,X1,relation_inverse_image(empty_set,X2)),empty_set)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_376896,c_373108]) ).
tcf(c_376931,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_376930,c_372426,c_368630,c_103]) ).
tcf(c_376936,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),empty_set)
| in(sK7(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_376894,c_373108]) ).
tcf(c_376937,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_376936,c_372426,c_368630,c_103]) ).
tcf(c_376958,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_376897,c_372426,c_368630,c_103]) ).
tcf(c_377175,plain,
! [X0: $i] :
( ( relation_image(empty_set,relation_dom(empty_set)) = relation_image(empty_set,X0) )
| ~ relation(empty_set)
| ~ subset(relation_image(empty_set,relation_dom(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_375097,c_368586]) ).
tcf(c_377176,plain,
( subset(empty_set,relation_image(empty_set,relation_dom(empty_set)))
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_375097,c_67]) ).
tcf(c_377177,plain,
! [X0: $i] :
( ( relation_image(empty_set,relation_dom(empty_set)) = relation_image(empty_set,X0) )
| ~ relation(empty_set)
| ~ subset(empty_set,relation_image(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_375097,c_368586]) ).
tcf(c_377178,plain,
! [X0: $i] :
( subset(relation_image(empty_set,X0),empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_375097,c_67]) ).
tcf(c_377179,plain,
! [X0: $i] :
( ( relation_image(empty_set,relation_inverse_image(empty_set,X0)) = X0 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_375097,c_368596]) ).
tcf(c_377182,plain,
! [X0: $i,X1: $i] :
( in(apply(empty_set,X0),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,X1)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_375097,c_109]) ).
tcf(c_377183,plain,
( subset(empty_set,empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_377178,c_375097]) ).
tcf(c_377184,plain,
( subset(empty_set,relation_image(empty_set,empty_set))
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_377176,c_373108]) ).
tcf(c_377185,plain,
! [X0: $i] :
( ( relation_image(empty_set,empty_set) = X0 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_377179,c_373747]) ).
tcf(c_377186,plain,
! [X0: $i] :
( ( relation_image(empty_set,empty_set) = X0 )
| ~ subset(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_377185,c_368630,c_103]) ).
tcf(c_377189,plain,
( ( relation_image(empty_set,empty_set) = empty_set )
| ~ relation(empty_set)
| ~ subset(empty_set,empty_set) ),
inference(light_normalisation,[status(thm)],[c_377177,c_373108,c_375097]) ).
tcf(c_377190,plain,
( ( relation_image(empty_set,empty_set) = empty_set )
| ~ relation(empty_set)
| ~ subset(relation_image(empty_set,empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_377175,c_373108,c_375097]) ).
tcf(c_377191,plain,
! [X0: $i,X1: $i] :
( in(apply(empty_set,X0),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set)
| ~ in(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_377182,c_373108]) ).
tcf(c_377192,plain,
subset(empty_set,relation_image(empty_set,empty_set)),
inference(light_normalisation,[status(thm)],[c_373744,c_375097]) ).
tcf(c_377193,plain,
subset(empty_set,empty_set),
inference(demodulation,[status(thm)],[c_377192,c_375097]) ).
tcf(c_377204,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| in(apply(empty_set,sK2(relation_inverse_image(empty_set,X0),X1,X2)),X0)
| ( set_intersection2(relation_inverse_image(empty_set,X0),X1) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_368813]) ).
tcf(c_377205,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,sK2(empty_set,X1,X2)),X0)
| in(sK2(relation_inverse_image(empty_set,X0),X1,X2),X2)
| ( set_intersection2(relation_inverse_image(empty_set,X0),X1) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_368813]) ).
tcf(c_377207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(relation_inverse_image(X2,X3),X4,X0),X1)
| in(apply(X2,sK2(relation_inverse_image(X2,X3),X4,X0)),X3)
| ( set_intersection2(relation_inverse_image(X2,X3),X4) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368813,c_321]) ).
tcf(c_377208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK2(relation_inverse_image(X2,X3),X4,X0)),X3)
| ( set_intersection2(relation_inverse_image(X2,X3),X4) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368813,c_320]) ).
tcf(c_377209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK2(relation_inverse_image(X1,X2),X3,X0)),X2)
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(relation_inverse_image(X1,X2),X3,X0)) ),
inference(superposition,[status(thm)],[c_368813,c_97]) ).
tcf(c_377210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X2,X3),X4,X0),X1)
| in(apply(X2,sK2(relation_inverse_image(X2,X3),X4,X0)),X3)
| ( set_intersection2(relation_inverse_image(X2,X3),X4) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368813,c_96]) ).
tcf(c_377211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(relation_inverse_image(X0,X1),X2,X3),X3)
| in(apply(X0,sK2(relation_inverse_image(X0,X1),X2,X3)),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_93]) ).
tcf(c_377212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,X2),X3,X1)),X2)
| ( set_intersection2(relation_inverse_image(X0,X2),X3) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_91]) ).
tcf(c_377215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(relation_inverse_image(X0,X2),X3,relation_inverse_image(X1,X4))),X4)
| in(apply(X0,sK2(relation_inverse_image(X0,X2),X3,relation_inverse_image(X1,X4))),X2)
| ( set_intersection2(relation_inverse_image(X0,X2),X3) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_88]) ).
tcf(c_377216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X2),X3,relation_inverse_image(X1,X4)),relation_dom(X1))
| in(apply(X0,sK2(relation_inverse_image(X0,X2),X3,relation_inverse_image(X1,X4))),X2)
| ( set_intersection2(relation_inverse_image(X0,X2),X3) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_87]) ).
tcf(c_377217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,X3),X4,relation_image(X1,X2))),X3)
| ( set_intersection2(relation_inverse_image(X0,X3),X4) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK2(relation_inverse_image(X0,X3),X4,relation_image(X1,X2)))) = sK2(relation_inverse_image(X0,X3),X4,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_112]) ).
tcf(c_377218,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,X1),X2,empty_set)),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_372426]) ).
tcf(c_377219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X2,X0),X3,X4),X4)
| element(apply(X2,sK2(relation_inverse_image(X2,X0),X3,X4)),X1)
| ( set_intersection2(relation_inverse_image(X2,X0),X3) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368813,c_321]) ).
tcf(c_377220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X2,X0),X3,X4),X4)
| ( set_intersection2(relation_inverse_image(X2,X0),X3) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368813,c_320]) ).
tcf(c_377221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X1,X0),X2,X3),X3)
| ( set_intersection2(relation_inverse_image(X1,X0),X2) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK2(relation_inverse_image(X1,X0),X2,X3))) ),
inference(superposition,[status(thm)],[c_368813,c_97]) ).
tcf(c_377222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X2,X0),X3,X4),X4)
| in(apply(X2,sK2(relation_inverse_image(X2,X0),X3,X4)),X1)
| ( set_intersection2(relation_inverse_image(X2,X0),X3) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368813,c_96]) ).
tcf(c_377223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,X3),X3)
| element(apply(X0,sK2(relation_inverse_image(X0,X1),X2,X3)),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_93]) ).
tcf(c_377224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,X3),X3)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_91]) ).
tcf(c_377225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3,X4),X4)
| in(apply(X0,sK2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3,X4)),X2)
| ( set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_59]) ).
tcf(c_377226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3,X4),X4)
| in(apply(X0,sK2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3,X4)),X1)
| ( set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_58]) ).
tcf(c_377227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,X3),X3)
| in(sK2(relation_inverse_image(X0,X1),X2,X3),relation_inverse_image(X0,X1))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(relation_inverse_image(X0,X1),X2,X3),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368813,c_86]) ).
tcf(c_377228,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3,X4),X4)
| in(apply(X1,apply(X0,sK2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3,X4))),X2)
| ( set_intersection2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_88]) ).
tcf(c_377229,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3,X4),X4)
| in(apply(X0,sK2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3,X4)),relation_dom(X1))
| ( set_intersection2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_87]) ).
tcf(c_377230,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,relation_image(X1,X2)),X3,X4),X4)
| ( set_intersection2(relation_inverse_image(X0,relation_image(X1,X2)),X3) = X4 )
| ( apply(X1,sK13(X1,X2,apply(X0,sK2(relation_inverse_image(X0,relation_image(X1,X2)),X3,X4)))) = apply(X0,sK2(relation_inverse_image(X0,relation_image(X1,X2)),X3,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_112]) ).
tcf(c_377231,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_inverse_image(X0,empty_set),X1,X2),X2)
| ( set_intersection2(relation_inverse_image(X0,empty_set),X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_372426]) ).
tcf(c_377256,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X0,X1),X1)
| in(apply(empty_set,sK2(empty_set,X0,X1)),X2)
| ( set_intersection2(empty_set,X0) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_377205,c_373747]) ).
tcf(c_377257,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X0),X0)
| in(apply(empty_set,sK2(empty_set,X1,X0)),X2)
| ( X0 = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_377256,c_368545]) ).
tcf(c_377258,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X0),X0)
| in(apply(empty_set,sK2(empty_set,X1,X0)),X2)
| ( X0 = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_377257,c_368630,c_103]) ).
tcf(c_377435,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X2)
| in(apply(empty_set,sK2(X0,relation_inverse_image(empty_set,X1),X2)),X1)
| ( set_intersection2(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_368814]) ).
tcf(c_377437,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,sK2(X0,relation_inverse_image(X1,X2),X0)),X2)
| ( set_intersection2(X0,relation_inverse_image(X1,X2)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,relation_inverse_image(X1,X2),X0),X0)
| ~ in(sK2(X0,relation_inverse_image(X1,X2),X0),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_368814,c_54]) ).
tcf(c_377438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,relation_inverse_image(X2,X4),X0),X1)
| in(apply(X2,sK2(X3,relation_inverse_image(X2,X4),X0)),X4)
| ( set_intersection2(X3,relation_inverse_image(X2,X4)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368814,c_321]) ).
tcf(c_377439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK2(X3,relation_inverse_image(X2,X4),X0)),X4)
| ( set_intersection2(X3,relation_inverse_image(X2,X4)) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368814,c_320]) ).
tcf(c_377440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK2(X1,relation_inverse_image(X2,X3),X0)),X3)
| ( set_intersection2(X1,relation_inverse_image(X2,X3)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,sK2(X1,relation_inverse_image(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_368814,c_97]) ).
tcf(c_377441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_inverse_image(X2,X4),X0),X1)
| in(apply(X2,sK2(X3,relation_inverse_image(X2,X4),X0)),X4)
| ( set_intersection2(X3,relation_inverse_image(X2,X4)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368814,c_96]) ).
tcf(c_377442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X1,relation_inverse_image(X0,X2),X3),X3)
| in(apply(X0,sK2(X1,relation_inverse_image(X0,X2),X3)),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_93]) ).
tcf(c_377443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(X2,relation_inverse_image(X0,X3),X1)),X3)
| ( set_intersection2(X2,relation_inverse_image(X0,X3)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_91]) ).
tcf(c_377446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(X2,relation_inverse_image(X0,X3),relation_inverse_image(X1,X4))),X4)
| in(apply(X0,sK2(X2,relation_inverse_image(X0,X3),relation_inverse_image(X1,X4))),X3)
| ( set_intersection2(X2,relation_inverse_image(X0,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_88]) ).
tcf(c_377447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_inverse_image(X0,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| in(apply(X0,sK2(X2,relation_inverse_image(X0,X3),relation_inverse_image(X1,X4))),X3)
| ( set_intersection2(X2,relation_inverse_image(X0,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_87]) ).
tcf(c_377448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(X3,relation_inverse_image(X0,X4),relation_image(X1,X2))),X4)
| ( set_intersection2(X3,relation_inverse_image(X0,X4)) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK2(X3,relation_inverse_image(X0,X4),relation_image(X1,X2)))) = sK2(X3,relation_inverse_image(X0,X4),relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_112]) ).
tcf(c_377449,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK2(X1,relation_inverse_image(X0,X2),empty_set)),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_372426]) ).
tcf(c_377450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),X0)),X3)
| ( set_intersection2(set_intersection2(X0,X1),relation_inverse_image(X2,X3)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),X0),X0)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),X0),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368814,c_368471]) ).
tcf(c_377451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_inverse_image(X2,X0),X4),X4)
| element(apply(X2,sK2(X3,relation_inverse_image(X2,X0),X4)),X1)
| ( set_intersection2(X3,relation_inverse_image(X2,X0)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368814,c_321]) ).
tcf(c_377452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_inverse_image(X2,X0),X4),X4)
| ( set_intersection2(X3,relation_inverse_image(X2,X0)) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368814,c_320]) ).
tcf(c_377453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,relation_inverse_image(X1,X0),X3),X3)
| ( set_intersection2(X2,relation_inverse_image(X1,X0)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK2(X2,relation_inverse_image(X1,X0),X3))) ),
inference(superposition,[status(thm)],[c_368814,c_97]) ).
tcf(c_377454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_inverse_image(X2,X0),X4),X4)
| in(apply(X2,sK2(X3,relation_inverse_image(X2,X0),X4)),X1)
| ( set_intersection2(X3,relation_inverse_image(X2,X0)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368814,c_96]) ).
tcf(c_377455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),X3),X3)
| element(apply(X0,sK2(X1,relation_inverse_image(X0,X2),X3)),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_93]) ).
tcf(c_377456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,relation_inverse_image(X0,X1),X3),X3)
| ( set_intersection2(X2,relation_inverse_image(X0,X1)) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_91]) ).
tcf(c_377457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,relation_inverse_image(X0,set_intersection2(X2,X3)),X4),X4)
| in(apply(X0,sK2(X1,relation_inverse_image(X0,set_intersection2(X2,X3)),X4)),X3)
| ( set_intersection2(X1,relation_inverse_image(X0,set_intersection2(X2,X3))) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_59]) ).
tcf(c_377458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,relation_inverse_image(X0,set_intersection2(X2,X3)),X4),X4)
| in(apply(X0,sK2(X1,relation_inverse_image(X0,set_intersection2(X2,X3)),X4)),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,set_intersection2(X2,X3))) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_58]) ).
tcf(c_377459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,relation_inverse_image(X1,X2),X3),X3)
| in(sK2(X0,relation_inverse_image(X1,X2),X3),relation_inverse_image(X1,X2))
| ( set_intersection2(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,relation_inverse_image(X1,X2),X3),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_368814,c_86]) ).
tcf(c_377460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_inverse_image(X0,relation_inverse_image(X1,X3)),X4),X4)
| in(apply(X1,apply(X0,sK2(X2,relation_inverse_image(X0,relation_inverse_image(X1,X3)),X4))),X3)
| ( set_intersection2(X2,relation_inverse_image(X0,relation_inverse_image(X1,X3))) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_88]) ).
tcf(c_377461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_inverse_image(X0,relation_inverse_image(X1,X3)),X4),X4)
| in(apply(X0,sK2(X2,relation_inverse_image(X0,relation_inverse_image(X1,X3)),X4)),relation_dom(X1))
| ( set_intersection2(X2,relation_inverse_image(X0,relation_inverse_image(X1,X3))) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_87]) ).
tcf(c_377462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_inverse_image(X0,relation_image(X1,X2)),X4),X4)
| ( set_intersection2(X3,relation_inverse_image(X0,relation_image(X1,X2))) = X4 )
| ( apply(X1,sK13(X1,X2,apply(X0,sK2(X3,relation_inverse_image(X0,relation_image(X1,X2)),X4)))) = apply(X0,sK2(X3,relation_inverse_image(X0,relation_image(X1,X2)),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_112]) ).
tcf(c_377463,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,relation_inverse_image(X0,empty_set),X2),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,empty_set)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_372426]) ).
tcf(c_377488,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X2)
| in(apply(empty_set,sK2(X0,relation_inverse_image(empty_set,X1),X2)),X1)
| ( set_intersection2(X0,relation_inverse_image(empty_set,X1)) = X2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_377435,c_368630,c_103]) ).
tcf(c_377703,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X1)
| in(apply(empty_set,sK2(X0,X1,relation_inverse_image(empty_set,X2))),X2)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_368815]) ).
tcf(c_377705,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,sK2(X0,X0,relation_inverse_image(X1,X2))),X2)
| ( relation_inverse_image(X1,X2) = set_intersection2(X0,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,X0,relation_inverse_image(X1,X2)),X0)
| ~ in(sK2(X0,X0,relation_inverse_image(X1,X2)),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_368815,c_54]) ).
tcf(c_377706,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X0,relation_inverse_image(X2,X3)),X1)
| in(apply(X2,sK2(X4,X0,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368815,c_321]) ).
tcf(c_377707,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK2(X4,X0,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X4,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368815,c_320]) ).
tcf(c_377708,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK2(X1,X0,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X1,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,sK2(X1,X0,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_368815,c_97]) ).
tcf(c_377709,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X4,X0,relation_inverse_image(X2,X3)),X1)
| in(apply(X2,sK2(X4,X0,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368815,c_96]) ).
tcf(c_377710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,relation_inverse_image(X0,X1)),X3)
| in(apply(X0,sK2(X2,X3,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_93]) ).
tcf(c_377711,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(X3,X1,relation_inverse_image(X0,X2))),X2)
| ( relation_inverse_image(X0,X2) = set_intersection2(X3,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_91]) ).
tcf(c_377714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(X2,relation_inverse_image(X1,X3),relation_inverse_image(X0,X4))),X3)
| in(apply(X0,sK2(X2,relation_inverse_image(X1,X3),relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(X2,relation_inverse_image(X1,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_88]) ).
tcf(c_377715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_inverse_image(X1,X3),relation_inverse_image(X0,X4)),relation_dom(X1))
| in(apply(X0,sK2(X2,relation_inverse_image(X1,X3),relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(X2,relation_inverse_image(X1,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_87]) ).
tcf(c_377716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(X3,relation_image(X1,X2),relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(X3,relation_image(X1,X2)) = relation_inverse_image(X0,X4) )
| ( apply(X1,sK13(X1,X2,sK2(X3,relation_image(X1,X2),relation_inverse_image(X0,X4)))) = sK2(X3,relation_image(X1,X2),relation_inverse_image(X0,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_112]) ).
tcf(c_377717,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK2(X2,empty_set,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_372426]) ).
tcf(c_377718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK2(set_intersection2(X0,X1),X0,relation_inverse_image(X2,X3))),X3)
| ( set_intersection2(set_intersection2(X0,X1),X0) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,relation_inverse_image(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X0,relation_inverse_image(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),X0,relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368815,c_368471]) ).
tcf(c_377719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X2,X0)),X4)
| element(apply(X2,sK2(X3,X4,relation_inverse_image(X2,X0))),X1)
| ( relation_inverse_image(X2,X0) = set_intersection2(X3,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368815,c_321]) ).
tcf(c_377720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X2,X0)),X4)
| ( relation_inverse_image(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368815,c_320]) ).
tcf(c_377721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X1,X0)),X3)
| ( relation_inverse_image(X1,X0) = set_intersection2(X2,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK2(X2,X3,relation_inverse_image(X1,X0)))) ),
inference(superposition,[status(thm)],[c_368815,c_97]) ).
tcf(c_377722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X2,X0)),X4)
| in(apply(X2,sK2(X3,X4,relation_inverse_image(X2,X0))),X1)
| ( relation_inverse_image(X2,X0) = set_intersection2(X3,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368815,c_96]) ).
tcf(c_377723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X0,X1)),X3)
| element(apply(X0,sK2(X2,X3,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_93]) ).
tcf(c_377724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X0,X1)),X3)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_91]) ).
tcf(c_377725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,set_intersection2(X1,X2))),X4)
| in(apply(X0,sK2(X3,X4,relation_inverse_image(X0,set_intersection2(X1,X2)))),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_59]) ).
tcf(c_377726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,set_intersection2(X1,X2))),X4)
| in(apply(X0,sK2(X3,X4,relation_inverse_image(X0,set_intersection2(X1,X2)))),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_58]) ).
tcf(c_377727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,relation_inverse_image(X2,X3)),X1)
| in(sK2(X0,X1,relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3))
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X1) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2)) ),
inference(superposition,[status(thm)],[c_368815,c_86]) ).
tcf(c_377728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,relation_inverse_image(X1,X2))),X4)
| in(apply(X1,apply(X0,sK2(X3,X4,relation_inverse_image(X0,relation_inverse_image(X1,X2))))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_88]) ).
tcf(c_377729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,relation_inverse_image(X1,X2))),X4)
| in(apply(X0,sK2(X3,X4,relation_inverse_image(X0,relation_inverse_image(X1,X2)))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_87]) ).
tcf(c_377730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,relation_image(X1,X2))),X4)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X2,apply(X0,sK2(X3,X4,relation_inverse_image(X0,relation_image(X1,X2)))))) = apply(X0,sK2(X3,X4,relation_inverse_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_112]) ).
tcf(c_377731,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,empty_set)),X2)
| ( set_intersection2(X1,X2) = relation_inverse_image(X0,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_372426]) ).
tcf(c_377756,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X1)
| in(apply(empty_set,sK2(X0,X1,relation_inverse_image(empty_set,X2))),X2)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_377703,c_368630,c_103]) ).
tcf(c_377826,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,sK2(X0,X0,relation_inverse_image(X1,X2))),X2)
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,X0,relation_inverse_image(X1,X2)),X0)
| ~ in(sK2(X0,X0,relation_inverse_image(X1,X2)),relation_inverse_image(X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_377705,c_53]) ).
tcf(c_378043,plain,
sK16(powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_369151,c_369178]) ).
tcf(c_378055,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X0)
| in(apply(empty_set,sK2(X0,X1,relation_inverse_image(empty_set,X2))),X2)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_368816]) ).
tcf(c_378057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK2(X0,X1,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X1) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,relation_inverse_image(X2,X3)),X1)
| ~ in(sK2(X0,X1,relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368816,c_54]) ).
tcf(c_378058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X4,relation_inverse_image(X2,X3)),X1)
| in(apply(X2,sK2(X0,X4,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368816,c_321]) ).
tcf(c_378059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK2(X0,X4,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368816,c_320]) ).
tcf(c_378060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK2(X0,X1,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X1) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,sK2(X0,X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_368816,c_97]) ).
tcf(c_378061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X4,relation_inverse_image(X2,X3)),X1)
| in(apply(X2,sK2(X0,X4,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368816,c_96]) ).
tcf(c_378062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,relation_inverse_image(X0,X1)),X2)
| in(apply(X0,sK2(X2,X3,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_93]) ).
tcf(c_378063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(X1,X3,relation_inverse_image(X0,X2))),X2)
| ( relation_inverse_image(X0,X2) = set_intersection2(X1,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_91]) ).
tcf(c_378066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(relation_inverse_image(X1,X2),X3,relation_inverse_image(X0,X4))),X2)
| in(apply(X0,sK2(relation_inverse_image(X1,X2),X3,relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_88]) ).
tcf(c_378067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X1,X2),X3,relation_inverse_image(X0,X4)),relation_dom(X1))
| in(apply(X0,sK2(relation_inverse_image(X1,X2),X3,relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_87]) ).
tcf(c_378068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(relation_image(X1,X2),X3,relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(relation_image(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ( apply(X1,sK13(X1,X2,sK2(relation_image(X1,X2),X3,relation_inverse_image(X0,X4)))) = sK2(relation_image(X1,X2),X3,relation_inverse_image(X0,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_112]) ).
tcf(c_378069,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK2(empty_set,X2,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_372426]) ).
tcf(c_378070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X2,X0)),X3)
| element(apply(X2,sK2(X3,X4,relation_inverse_image(X2,X0))),X1)
| ( relation_inverse_image(X2,X0) = set_intersection2(X3,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368816,c_321]) ).
tcf(c_378071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X2,X0)),X3)
| ( relation_inverse_image(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368816,c_320]) ).
tcf(c_378072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X1,X0)),X2)
| ( relation_inverse_image(X1,X0) = set_intersection2(X2,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK2(X2,X3,relation_inverse_image(X1,X0)))) ),
inference(superposition,[status(thm)],[c_368816,c_97]) ).
tcf(c_378073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X2,X0)),X3)
| in(apply(X2,sK2(X3,X4,relation_inverse_image(X2,X0))),X1)
| ( relation_inverse_image(X2,X0) = set_intersection2(X3,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368816,c_96]) ).
tcf(c_378074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X0,X1)),X2)
| element(apply(X0,sK2(X2,X3,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_93]) ).
tcf(c_378075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X0,X1)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_91]) ).
tcf(c_378076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,set_intersection2(X1,X2))),X3)
| in(apply(X0,sK2(X3,X4,relation_inverse_image(X0,set_intersection2(X1,X2)))),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_59]) ).
tcf(c_378077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,set_intersection2(X1,X2))),X3)
| in(apply(X0,sK2(X3,X4,relation_inverse_image(X0,set_intersection2(X1,X2)))),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_58]) ).
tcf(c_378078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,relation_inverse_image(X2,X3)),X0)
| in(sK2(X0,X1,relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3))
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X1) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2)) ),
inference(superposition,[status(thm)],[c_368816,c_86]) ).
tcf(c_378079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,relation_inverse_image(X1,X2))),X3)
| in(apply(X1,apply(X0,sK2(X3,X4,relation_inverse_image(X0,relation_inverse_image(X1,X2))))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_88]) ).
tcf(c_378080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,relation_inverse_image(X1,X2))),X3)
| in(apply(X0,sK2(X3,X4,relation_inverse_image(X0,relation_inverse_image(X1,X2)))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_87]) ).
tcf(c_378081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,relation_image(X1,X2))),X3)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X2,apply(X0,sK2(X3,X4,relation_inverse_image(X0,relation_image(X1,X2)))))) = apply(X0,sK2(X3,X4,relation_inverse_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_112]) ).
tcf(c_378082,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,empty_set)),X1)
| ( set_intersection2(X1,X2) = relation_inverse_image(X0,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_372426]) ).
tcf(c_378107,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,empty_set),X0)
| in(apply(empty_set,sK2(X0,X1,relation_inverse_image(empty_set,X2))),X2)
| ( set_intersection2(X0,X1) = relation_inverse_image(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_378055,c_368630,c_103]) ).
tcf(c_378277,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,X2),X2)
| in(apply(empty_set,apply(X0,sK7(X0,relation_inverse_image(empty_set,X1),X2))),X1)
| ( relation_inverse_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_368817]) ).
tcf(c_378278,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_inverse_image(empty_set,X1),X2),X2)
| in(apply(empty_set,apply(X0,sK7(X0,empty_set,X2))),X1)
| ( relation_inverse_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_368817]) ).
tcf(c_378279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,relation_inverse_image(X3,X4),X0),X1)
| in(apply(X3,apply(X2,sK7(X2,relation_inverse_image(X3,X4),X0))),X4)
| ( relation_inverse_image(X2,relation_inverse_image(X3,X4)) = X0 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368817,c_321]) ).
tcf(c_378280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,apply(X2,sK7(X2,relation_inverse_image(X3,X4),X0))),X4)
| ( relation_inverse_image(X2,relation_inverse_image(X3,X4)) = X0 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368817,c_320]) ).
tcf(c_378281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,apply(X1,sK7(X1,relation_inverse_image(X2,X3),X0))),X3)
| ( relation_inverse_image(X1,relation_inverse_image(X2,X3)) = X0 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,sK7(X1,relation_inverse_image(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_368817,c_97]) ).
tcf(c_378282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,relation_inverse_image(X3,X4),X0),X1)
| in(apply(X3,apply(X2,sK7(X2,relation_inverse_image(X3,X4),X0))),X4)
| ( relation_inverse_image(X2,relation_inverse_image(X3,X4)) = X0 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368817,c_96]) ).
tcf(c_378283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,relation_inverse_image(X1,X2),X3),X3)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X2),X3))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_93]) ).
tcf(c_378284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X3),X2))),X3)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X3)) = X2 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_91]) ).
tcf(c_378287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4))),X4)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4)))),X3)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X3)) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_88]) ).
tcf(c_378288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4)),relation_dom(X2))
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4)))),X3)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X3)) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_87]) ).
tcf(c_378289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X4),relation_image(X2,X3)))),X4)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X4)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X0,relation_inverse_image(X1,X4),relation_image(X2,X3)))) = sK7(X0,relation_inverse_image(X1,X4),relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_112]) ).
tcf(c_378290,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X2),empty_set))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = empty_set )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_372426]) ).
tcf(c_378291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,relation_inverse_image(X3,X0),X4),X4)
| element(apply(X3,apply(X2,sK7(X2,relation_inverse_image(X3,X0),X4))),X1)
| ( relation_inverse_image(X2,relation_inverse_image(X3,X0)) = X4 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368817,c_321]) ).
tcf(c_378292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,relation_inverse_image(X3,X0),X4),X4)
| ( relation_inverse_image(X2,relation_inverse_image(X3,X0)) = X4 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368817,c_320]) ).
tcf(c_378293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,relation_inverse_image(X1,X0),X3),X3)
| ( relation_inverse_image(X2,relation_inverse_image(X1,X0)) = X3 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,apply(X1,apply(X2,sK7(X2,relation_inverse_image(X1,X0),X3)))) ),
inference(superposition,[status(thm)],[c_368817,c_97]) ).
tcf(c_378294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,relation_inverse_image(X3,X0),X4),X4)
| in(apply(X3,apply(X2,sK7(X2,relation_inverse_image(X3,X0),X4))),X1)
| ( relation_inverse_image(X2,relation_inverse_image(X3,X0)) = X4 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368817,c_96]) ).
tcf(c_378295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),X3),X3)
| element(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X2),X3))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_93]) ).
tcf(c_378296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),X3),X3)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_91]) ).
tcf(c_378297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X1,set_intersection2(X2,X3)),X4),X4)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,set_intersection2(X2,X3)),X4))),X3)
| ( relation_inverse_image(X0,relation_inverse_image(X1,set_intersection2(X2,X3))) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_59]) ).
tcf(c_378298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X1,set_intersection2(X2,X3)),X4),X4)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,set_intersection2(X2,X3)),X4))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,set_intersection2(X2,X3))) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_58]) ).
tcf(c_378299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),X3),X3)
| in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),X3)),relation_inverse_image(X1,X2))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),X3)),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_368817,c_86]) ).
tcf(c_378300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X1,relation_inverse_image(X2,X3)),X4),X4)
| in(apply(X2,apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,relation_inverse_image(X2,X3)),X4)))),X3)
| ( relation_inverse_image(X0,relation_inverse_image(X1,relation_inverse_image(X2,X3))) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_88]) ).
tcf(c_378301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X1,relation_inverse_image(X2,X3)),X4),X4)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,relation_inverse_image(X2,X3)),X4))),relation_dom(X2))
| ( relation_inverse_image(X0,relation_inverse_image(X1,relation_inverse_image(X2,X3))) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_87]) ).
tcf(c_378302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X1,relation_image(X2,X3)),X4),X4)
| ( relation_inverse_image(X0,relation_inverse_image(X1,relation_image(X2,X3))) = X4 )
| ( apply(X2,sK13(X2,X3,apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,relation_image(X2,X3)),X4))))) = apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,relation_image(X2,X3)),X4))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_112]) ).
tcf(c_378303,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_inverse_image(X1,empty_set),X2),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,empty_set)) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_372426]) ).
tcf(c_378338,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_inverse_image(empty_set,X1),X2),X2)
| in(apply(empty_set,apply(X0,sK7(X0,empty_set,X2))),X1)
| ( relation_inverse_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_378278,c_368630,c_103]) ).
tcf(c_378344,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,X2),X2)
| in(apply(empty_set,apply(X0,sK7(X0,relation_inverse_image(empty_set,X1),X2))),X1)
| ( relation_inverse_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_378277,c_368630,c_103]) ).
tcf(c_378544,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,sK7(X0,X1,empty_set)),X2)
| in(apply(X0,sK7(X0,X1,relation_inverse_image(empty_set,X2))),X1)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_368818]) ).
tcf(c_378545,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,empty_set)),X1)
| in(apply(empty_set,sK7(X0,X1,relation_inverse_image(empty_set,X2))),X2)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_368818]) ).
tcf(c_378546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(apply(X3,sK7(X2,X4,relation_inverse_image(X3,X0))),X1)
| in(apply(X2,sK7(X2,X4,relation_inverse_image(X3,X0))),X4)
| ( relation_inverse_image(X2,X4) = relation_inverse_image(X3,X0) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368818,c_321]) ).
tcf(c_378547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,X4,relation_inverse_image(X3,X0))),X4)
| ( relation_inverse_image(X2,X4) = relation_inverse_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368818,c_320]) ).
tcf(c_378548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK7(X2,X3,relation_inverse_image(X1,X0))),X3)
| ( relation_inverse_image(X1,X0) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK7(X2,X3,relation_inverse_image(X1,X0)))) ),
inference(superposition,[status(thm)],[c_368818,c_97]) ).
tcf(c_378549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X2,X4,relation_inverse_image(X3,X0))),X1)
| in(apply(X2,sK7(X2,X4,relation_inverse_image(X3,X0))),X4)
| ( relation_inverse_image(X2,X4) = relation_inverse_image(X3,X0) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368818,c_96]) ).
tcf(c_378550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X1,sK7(X0,X2,relation_inverse_image(X1,X3))),X3)
| in(apply(X0,sK7(X0,X2,relation_inverse_image(X1,X3))),X2)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_93]) ).
tcf(c_378551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X3,relation_inverse_image(X1,X2))),X3)
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_91]) ).
tcf(c_378552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3)))),X3)
| in(apply(X0,sK7(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3)))),X4)
| ( relation_inverse_image(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_59]) ).
tcf(c_378553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3)))),X2)
| in(apply(X0,sK7(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3)))),X4)
| ( relation_inverse_image(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_58]) ).
tcf(c_378555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3))
| in(apply(X0,sK7(X0,X1,relation_inverse_image(X2,X3))),X1)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2)) ),
inference(superposition,[status(thm)],[c_368818,c_86]) ).
tcf(c_378556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3)))),X4)
| in(apply(X2,apply(X1,sK7(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3))))),X3)
| ( relation_inverse_image(X1,relation_inverse_image(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_88]) ).
tcf(c_378557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3)))),X4)
| in(apply(X1,sK7(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3)))),relation_dom(X2))
| ( relation_inverse_image(X1,relation_inverse_image(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_87]) ).
tcf(c_378558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X4,relation_inverse_image(X1,relation_image(X2,X3)))),X4)
| ( relation_inverse_image(X1,relation_image(X2,X3)) = relation_inverse_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,apply(X1,sK7(X0,X4,relation_inverse_image(X1,relation_image(X2,X3)))))) = apply(X1,sK7(X0,X4,relation_inverse_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_112]) ).
tcf(c_378559,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X2,relation_inverse_image(X1,empty_set))),X2)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_372426]) ).
tcf(c_378560,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X1,X2),relation_inverse_image(X0,X1))),set_intersection2(X1,X2))
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,set_intersection2(X1,X2),relation_inverse_image(X0,X1)),relation_dom(X0))
| ~ in(sK7(X0,set_intersection2(X1,X2),relation_inverse_image(X0,X1)),relation_inverse_image(X0,X1))
| ~ in(apply(X0,sK7(X0,set_intersection2(X1,X2),relation_inverse_image(X0,X1))),X2) ),
inference(superposition,[status(thm)],[c_368818,c_368654]) ).
tcf(c_378561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(apply(X2,sK7(X2,X0,relation_inverse_image(X3,X4))),X1)
| in(apply(X3,sK7(X2,X0,relation_inverse_image(X3,X4))),X4)
| ( relation_inverse_image(X2,X0) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368818,c_321]) ).
tcf(c_378562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X2,X0,relation_inverse_image(X3,X4))),X4)
| ( relation_inverse_image(X2,X0) = relation_inverse_image(X3,X4) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368818,c_320]) ).
tcf(c_378563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK7(X1,X0,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X1,X0) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK7(X1,X0,relation_inverse_image(X2,X3)))) ),
inference(superposition,[status(thm)],[c_368818,c_97]) ).
tcf(c_378564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X2,X0,relation_inverse_image(X3,X4))),X4)
| in(apply(X2,sK7(X2,X0,relation_inverse_image(X3,X4))),X1)
| ( relation_inverse_image(X2,X0) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368818,c_96]) ).
tcf(c_378565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X0,sK7(X0,X2,relation_inverse_image(X1,X3))),X2)
| in(apply(X1,sK7(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_93]) ).
tcf(c_378566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_91]) ).
tcf(c_378569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK7(X0,X1,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X0))
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368818,c_83]) ).
tcf(c_378570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_inverse_image(X0,X1))
| in(apply(X2,sK7(X0,X1,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368818,c_86]) ).
tcf(c_378571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4))),X4)
| in(apply(X2,apply(X0,sK7(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4)))),X3)
| ( relation_inverse_image(X0,relation_inverse_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_88]) ).
tcf(c_378572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4))),X4)
| in(apply(X0,sK7(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4))),relation_dom(X2))
| ( relation_inverse_image(X0,relation_inverse_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_87]) ).
tcf(c_378573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X0,relation_image(X2,X3),relation_inverse_image(X1,X4))),X4)
| ( relation_inverse_image(X0,relation_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ( apply(X2,sK13(X2,X3,apply(X0,sK7(X0,relation_image(X2,X3),relation_inverse_image(X1,X4))))) = apply(X0,sK7(X0,relation_image(X2,X3),relation_inverse_image(X1,X4))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_112]) ).
tcf(c_378574,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,sK7(X0,empty_set,relation_inverse_image(X1,X2))),X2)
| ( relation_inverse_image(X1,X2) = relation_inverse_image(X0,empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_372426]) ).
tcf(c_378619,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X1,empty_set)),X1)
| in(apply(empty_set,sK7(X0,X1,relation_inverse_image(empty_set,X2))),X2)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_378545,c_368630,c_103]) ).
tcf(c_378877,plain,
( empty(powerset(empty_set))
| ~ in(powerset(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_378043,c_370746]) ).
tcf(c_378878,plain,
( empty(powerset(empty_set))
| in(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_378043,c_368976]) ).
tcf(c_378879,plain,
element(empty_set,powerset(empty_set)),
inference(superposition,[status(thm)],[c_378043,c_119]) ).
tcf(c_378887,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(empty_set,set_intersection2(X1,X2))
| ~ subset(powerset(X0),X2)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_65,c_369580]) ).
tcf(c_378905,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(X0))
| in(apply(empty_set,sK7(X0,X1,relation_inverse_image(empty_set,X2))),X2)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_368819]) ).
tcf(c_378906,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,relation_inverse_image(X0,X1)),empty_set)
| in(apply(X0,sK7(empty_set,X2,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373108,c_368819]) ).
tcf(c_378907,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,sK7(X0,X1,empty_set)),X2)
| in(sK7(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_368819]) ).
tcf(c_378908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X3,relation_inverse_image(X2,X4)),X1)
| in(apply(X2,sK7(X0,X3,relation_inverse_image(X2,X4))),X4)
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368819,c_321]) ).
tcf(c_378909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X0,X3,relation_inverse_image(X2,X4))),X4)
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X2,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368819,c_320]) ).
tcf(c_378910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK7(X0,X1,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK7(X0,X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_368819,c_97]) ).
tcf(c_378911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,relation_inverse_image(X2,X4)),X1)
| in(apply(X2,sK7(X0,X3,relation_inverse_image(X2,X4))),X4)
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368819,c_96]) ).
tcf(c_378912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X0))
| in(apply(X1,sK7(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368819,c_93]) ).
tcf(c_378913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368819,c_91]) ).
tcf(c_378914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X4,relation_inverse_image(X3,X0)),relation_dom(X2))
| element(apply(X3,sK7(X2,X4,relation_inverse_image(X3,X0))),X1)
| ( relation_inverse_image(X2,X4) = relation_inverse_image(X3,X0) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368819,c_321]) ).
tcf(c_378915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X4,relation_inverse_image(X3,X0)),relation_dom(X2))
| ( relation_inverse_image(X2,X4) = relation_inverse_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368819,c_320]) ).
tcf(c_378916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X3,relation_inverse_image(X1,X0)),relation_dom(X2))
| ( relation_inverse_image(X1,X0) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK7(X2,X3,relation_inverse_image(X1,X0)))) ),
inference(superposition,[status(thm)],[c_368819,c_97]) ).
tcf(c_378917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X4,relation_inverse_image(X3,X0)),relation_dom(X2))
| in(apply(X3,sK7(X2,X4,relation_inverse_image(X3,X0))),X1)
| ( relation_inverse_image(X2,X4) = relation_inverse_image(X3,X0) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368819,c_96]) ).
tcf(c_378918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X0))
| element(apply(X1,sK7(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368819,c_93]) ).
tcf(c_378919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X3) = relation_inverse_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368819,c_91]) ).
tcf(c_378920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3))),relation_dom(X0))
| in(apply(X1,sK7(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3)))),X3)
| ( relation_inverse_image(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368819,c_59]) ).
tcf(c_378921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3))),relation_dom(X0))
| in(apply(X1,sK7(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3)))),X2)
| ( relation_inverse_image(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368819,c_58]) ).
tcf(c_378923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X0))
| in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2)) ),
inference(superposition,[status(thm)],[c_368819,c_86]) ).
tcf(c_378924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3))),relation_dom(X0))
| in(apply(X2,apply(X1,sK7(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3))))),X3)
| ( relation_inverse_image(X1,relation_inverse_image(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368819,c_88]) ).
tcf(c_378925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3))),relation_dom(X0))
| in(apply(X1,sK7(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3)))),relation_dom(X2))
| ( relation_inverse_image(X1,relation_inverse_image(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368819,c_87]) ).
tcf(c_378926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,relation_inverse_image(X1,relation_image(X2,X3))),relation_dom(X0))
| ( relation_inverse_image(X1,relation_image(X2,X3)) = relation_inverse_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,apply(X1,sK7(X0,X4,relation_inverse_image(X1,relation_image(X2,X3)))))) = apply(X1,sK7(X0,X4,relation_inverse_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368819,c_112]) ).
tcf(c_378927,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,empty_set)),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368819,c_372426]) ).
tcf(c_378958,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,empty_set),relation_dom(X0))
| in(apply(empty_set,sK7(X0,X1,relation_inverse_image(empty_set,X2))),X2)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_378905,c_368630,c_103]) ).
tcf(c_378972,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(empty_set,X2,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_378906,c_372426,c_368630,c_103]) ).
tcf(c_379141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,X0),X1)
| ( set_intersection2(X2,X3) = X0 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368865,c_321]) ).
tcf(c_379142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,X3) = X0 )
| ~ empty(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368865,c_320]) ).
tcf(c_379143,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X2) = X0 )
| ~ empty(X1)
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_368865,c_97]) ).
tcf(c_379144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X1)
| ( set_intersection2(X2,X3) = X0 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368865,c_96]) ).
tcf(c_379145,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368865,c_93]) ).
tcf(c_379146,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X2) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368865,c_91]) ).
tcf(c_379151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X2) = set_intersection2(X1,X3) )
| ( apply(X0,sK13(X0,X2,sK2(X1,X3,relation_image(X0,X2)))) = sK2(X1,X3,relation_image(X0,X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368865,c_112]) ).
tcf(c_379152,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368865,c_372426]) ).
tcf(c_379153,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ empty(set_intersection2(X0,X1))
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_368865,c_368471]) ).
tcf(c_379201,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ empty(X1)
| ~ in(sK2(X0,X1,X0),X1)
| ~ in(sK2(X0,X1,X0),X0) ),
inference(superposition,[status(thm)],[c_368866,c_54]) ).
tcf(c_379202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X3,X2,X0),X1)
| ( set_intersection2(X3,X2) = X0 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368866,c_321]) ).
tcf(c_379203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,X2) = X0 )
| ~ empty(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368866,c_320]) ).
tcf(c_379204,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X2) = X0 )
| ~ empty(X2)
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_368866,c_97]) ).
tcf(c_379205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,X2,X0),X1)
| ( set_intersection2(X3,X2) = X0 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368866,c_96]) ).
tcf(c_379206,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X0,X2),X2)
| ( set_intersection2(X1,X0) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368866,c_93]) ).
tcf(c_379207,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368866,c_91]) ).
tcf(c_379212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X2) = set_intersection2(X3,X1) )
| ( apply(X0,sK13(X0,X2,sK2(X3,X1,relation_image(X0,X2)))) = sK2(X3,X1,relation_image(X0,X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368866,c_112]) ).
tcf(c_379213,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368866,c_372426]) ).
tcf(c_379214,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ empty(X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_368866,c_368471]) ).
tcf(c_379280,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(powerset(X2),X1)
| ~ subset(powerset(X2),X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369800]) ).
tcf(c_379290,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(empty_set,set_intersection2(X1,X2))
| ~ subset(powerset(X0),X2)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_65,c_369944]) ).
tcf(c_379300,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X0) = X1 )
| ~ empty(X1)
| ~ in(sK2(X0,X0,X1),X1)
| ~ in(sK2(X0,X0,X1),X0) ),
inference(superposition,[status(thm)],[c_368867,c_54]) ).
tcf(c_379301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X3,X0,X2),X1)
| ( set_intersection2(X3,X0) = X2 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368867,c_321]) ).
tcf(c_379302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,X0) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368867,c_320]) ).
tcf(c_379303,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X0) = X2 )
| ~ empty(X2)
| ~ in(X0,sK2(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_368867,c_97]) ).
tcf(c_379304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,X0,X2),X1)
| ( set_intersection2(X3,X0) = X2 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368867,c_96]) ).
tcf(c_379305,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X2,X0),X2)
| ( set_intersection2(X1,X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368867,c_93]) ).
tcf(c_379306,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,X1) = X0 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368867,c_91]) ).
tcf(c_379311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,relation_image(X0,X2)) = X1 )
| ( apply(X0,sK13(X0,X2,sK2(X3,relation_image(X0,X2),X1))) = sK2(X3,relation_image(X0,X2),X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368867,c_112]) ).
tcf(c_379312,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368867,c_372426]) ).
tcf(c_379313,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X0) = X2 )
| ~ empty(X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X1)
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X0) ),
inference(superposition,[status(thm)],[c_368867,c_368471]) ).
tcf(c_379337,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ in(sK2(X0,X0,X1),X1)
| ~ in(sK2(X0,X0,X1),X0) ),
inference(light_normalisation,[status(thm)],[c_379300,c_53]) ).
tcf(c_379421,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ empty(X2)
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1) ),
inference(superposition,[status(thm)],[c_368868,c_54]) ).
tcf(c_379422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X3,X2),X1)
| ( set_intersection2(X0,X3) = X2 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368868,c_321]) ).
tcf(c_379423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X3) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368868,c_320]) ).
tcf(c_379424,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ empty(X2)
| ~ in(X0,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_368868,c_97]) ).
tcf(c_379425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X3,X2),X1)
| ( set_intersection2(X0,X3) = X2 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368868,c_96]) ).
tcf(c_379426,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X2,X0),X1)
| ( set_intersection2(X1,X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368868,c_93]) ).
tcf(c_379427,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X2) = X0 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368868,c_91]) ).
tcf(c_379432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_image(X0,X2),X3) = X1 )
| ( apply(X0,sK13(X0,X2,sK2(relation_image(X0,X2),X3,X1))) = sK2(relation_image(X0,X2),X3,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368868,c_112]) ).
tcf(c_379433,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(empty_set,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368868,c_372426]) ).
tcf(c_379482,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ empty(relation_dom(X0))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_368870,c_77,c_71,c_7992]) ).
tcf(c_379483,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(renaming,[status(thm)],[c_379482]) ).
tcf(c_379492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X2,X3,X0),X1)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_379483,c_321]) ).
tcf(c_379493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X2,X3) = X0 )
| ~ empty(X1)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_379483,c_320]) ).
tcf(c_379494,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X1,X2) = X0 )
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ in(X0,sK7(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_379483,c_97]) ).
tcf(c_379495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X3,X0),X1)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_379483,c_96]) ).
tcf(c_379496,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_93]) ).
tcf(c_379497,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_91]) ).
tcf(c_379498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_59]) ).
tcf(c_379499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_58]) ).
tcf(c_379500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_88]) ).
tcf(c_379501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| ( relation_inverse_image(X0,X2) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_87]) ).
tcf(c_379502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK7(X0,X3,relation_image(X1,X2)))) = sK7(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_112]) ).
tcf(c_379503,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,X1) = empty_set )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_372426]) ).
tcf(c_379596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X2,X3,X0),X1)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368871,c_321]) ).
tcf(c_379597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X2,X3) = X0 )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368871,c_320]) ).
tcf(c_379598,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X1,X2) = X0 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK7(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_368871,c_97]) ).
tcf(c_379599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X3,X0),X1)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368871,c_96]) ).
tcf(c_379600,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368871,c_93]) ).
tcf(c_379601,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368871,c_91]) ).
tcf(c_379606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X2) = relation_image(X1,X3) )
| ( apply(X1,sK13(X1,X3,sK7(X0,X2,relation_image(X1,X3)))) = sK7(X0,X2,relation_image(X1,X3)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368871,c_112]) ).
tcf(c_379607,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,X1) = empty_set )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368871,c_372426]) ).
tcf(c_379662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X2,sK7(X2,X0,X3)),X1)
| ( relation_inverse_image(X2,X0) = X3 )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368872,c_321]) ).
tcf(c_379663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X2,X0) = X3 )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368872,c_320]) ).
tcf(c_379664,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X1,X0) = X2 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK7(X1,X0,X2))) ),
inference(superposition,[status(thm)],[c_368872,c_97]) ).
tcf(c_379665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK7(X2,X0,X3)),X1)
| ( relation_inverse_image(X2,X0) = X3 )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368872,c_96]) ).
tcf(c_379666,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(X0,sK7(X0,X2,X1)),X2)
| ( relation_inverse_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368872,c_93]) ).
tcf(c_379667,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X2) = X1 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368872,c_91]) ).
tcf(c_379670,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,X2),X2)
| ~ in(sK7(X0,X1,X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368872,c_83]) ).
tcf(c_379671,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368872,c_86]) ).
tcf(c_379674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,relation_image(X1,X3)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X0,sK7(X0,relation_image(X1,X3),X2)))) = apply(X0,sK7(X0,relation_image(X1,X3),X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368872,c_112]) ).
tcf(c_379675,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,empty_set) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368872,c_372426]) ).
tcf(c_379815,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(X0),X1) = relation_dom(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_370079]) ).
tcf(c_379829,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X1,X0),empty_set)
| ( relation_inverse_image(empty_set,X1) = X0 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_373108,c_368873]) ).
tcf(c_379830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X3,X2),X1)
| ( relation_inverse_image(X0,X3) = X2 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368873,c_321]) ).
tcf(c_379831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X3) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368873,c_320]) ).
tcf(c_379832,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK7(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_368873,c_97]) ).
tcf(c_379833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,X2),X1)
| ( relation_inverse_image(X0,X3) = X2 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368873,c_96]) ).
tcf(c_379834,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X2,X1),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368873,c_93]) ).
tcf(c_379835,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368873,c_91]) ).
tcf(c_379841,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(empty_set,X1) = X0 )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_379829,c_372426,c_368630,c_103]) ).
tcf(c_379905,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(powerset(X0),X1,X2),X0)
| in(sK2(powerset(X0),X1,X2),X2)
| ( set_intersection2(powerset(X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368924,c_99]) ).
tcf(c_379907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,X0),X2)
| element(sK2(X2,X3,X0),X1)
| ( set_intersection2(X2,X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368924,c_321]) ).
tcf(c_379908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,X0),X2)
| ( set_intersection2(X2,X3) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368924,c_320]) ).
tcf(c_379909,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X2,X0),X1)
| ( set_intersection2(X1,X2) = X0 )
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_368924,c_97]) ).
tcf(c_379910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,X0),X2)
| in(sK2(X2,X3,X0),X1)
| ( set_intersection2(X2,X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368924,c_96]) ).
tcf(c_379911,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| element(sK2(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368924,c_93]) ).
tcf(c_379917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,relation_image(X0,X1)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK13(X0,X1,sK2(X2,X3,relation_image(X0,X1)))) = sK2(X2,X3,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368924,c_112]) ).
tcf(c_379918,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,empty_set),X0)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_368924,c_372426]) ).
tcf(c_379919,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_368924,c_368471]) ).
tcf(c_380111,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,powerset(X1),X2),X1)
| in(sK2(X0,powerset(X1),X2),X2)
| ( set_intersection2(X0,powerset(X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_368925,c_99]) ).
tcf(c_380113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,X0),X3)
| element(sK2(X2,X3,X0),X1)
| ( set_intersection2(X2,X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368925,c_321]) ).
tcf(c_380114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,X0),X3)
| ( set_intersection2(X2,X3) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368925,c_320]) ).
tcf(c_380115,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X2,X0),X2)
| ( set_intersection2(X1,X2) = X0 )
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_368925,c_97]) ).
tcf(c_380116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,X0),X3)
| in(sK2(X2,X3,X0),X1)
| ( set_intersection2(X2,X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368925,c_96]) ).
tcf(c_380117,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| element(sK2(X0,X1,X2),X1)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368925,c_93]) ).
tcf(c_380123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,relation_image(X0,X1)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK13(X0,X1,sK2(X2,X3,relation_image(X0,X1)))) = sK2(X2,X3,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368925,c_112]) ).
tcf(c_380124,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X1,empty_set),X1)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_368925,c_372426]) ).
tcf(c_380125,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_368925,c_368471]) ).
tcf(c_380163,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(X0)) = relation_dom(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_370147]) ).
tcf(c_380182,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_370745]) ).
tcf(c_380183,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ~ relation(X0)
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_67,c_370745]) ).
tcf(c_380184,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,relation_inverse_image(X0,X1)))
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_370745]) ).
tcf(c_380186,plain,
! [X0: $i] :
( empty(sK16(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_369151,c_370745]) ).
tcf(c_380239,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,powerset(X2)),X2)
| in(sK2(X0,X1,powerset(X2)),X1)
| ( set_intersection2(X0,X1) = powerset(X2) ) ),
inference(superposition,[status(thm)],[c_368926,c_99]) ).
tcf(c_380240,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X0,X1),X1)
| ( set_intersection2(X0,X0) = X1 )
| ~ in(sK2(X0,X0,X1),X1)
| ~ in(sK2(X0,X0,X1),X0) ),
inference(superposition,[status(thm)],[c_368926,c_54]) ).
tcf(c_380241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X0,X3),X3)
| element(sK2(X2,X0,X3),X1)
| ( set_intersection2(X2,X0) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368926,c_321]) ).
tcf(c_380242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X0,X3),X3)
| ( set_intersection2(X2,X0) = X3 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368926,c_320]) ).
tcf(c_380243,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,X0,X2),X2)
| ( set_intersection2(X1,X0) = X2 )
| ~ in(X0,sK2(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_368926,c_97]) ).
tcf(c_380244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X0,X3),X3)
| in(sK2(X2,X0,X3),X1)
| ( set_intersection2(X2,X0) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368926,c_96]) ).
tcf(c_380251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,relation_image(X0,X1),X3),X3)
| ( set_intersection2(X2,relation_image(X0,X1)) = X3 )
| ( apply(X0,sK13(X0,X1,sK2(X2,relation_image(X0,X1),X3))) = sK2(X2,relation_image(X0,X1),X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368926,c_112]) ).
tcf(c_380252,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,empty_set,X1),X1)
| ( set_intersection2(X0,empty_set) = X1 ) ),
inference(superposition,[status(thm)],[c_368926,c_372426]) ).
tcf(c_380253,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(X0,X1),X0,X2),X2)
| ( set_intersection2(set_intersection2(X0,X1),X0) = X2 )
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X1)
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X0) ),
inference(superposition,[status(thm)],[c_368926,c_368471]) ).
tcf(c_380254,plain,
! [X0: $i,X1: $i] :
( element(sK2(X1,empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_380252,c_64]) ).
tcf(c_380275,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,X0,X1),X1)
| ( X0 = X1 )
| ~ in(sK2(X0,X0,X1),X1)
| ~ in(sK2(X0,X0,X1),X0) ),
inference(light_normalisation,[status(thm)],[c_380240,c_53]) ).
tcf(c_380315,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,powerset(X2)),X2)
| in(sK2(X0,X1,powerset(X2)),X0)
| ( set_intersection2(X0,X1) = powerset(X2) ) ),
inference(superposition,[status(thm)],[c_368927,c_99]) ).
tcf(c_380316,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1) ),
inference(superposition,[status(thm)],[c_368927,c_54]) ).
tcf(c_380317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X2,X3),X3)
| element(sK2(X0,X2,X3),X1)
| ( set_intersection2(X0,X2) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368927,c_321]) ).
tcf(c_380318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X2,X3),X3)
| ( set_intersection2(X0,X2) = X3 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368927,c_320]) ).
tcf(c_380319,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ in(X0,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_368927,c_97]) ).
tcf(c_380320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X2,X3),X3)
| in(sK2(X0,X2,X3),X1)
| ( set_intersection2(X0,X2) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368927,c_96]) ).
tcf(c_380327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(relation_image(X0,X1),X2,X3),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = X3 )
| ( apply(X0,sK13(X0,X1,sK2(relation_image(X0,X1),X2,X3))) = sK2(relation_image(X0,X1),X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368927,c_112]) ).
tcf(c_380328,plain,
! [X0: $i,X1: $i] :
( element(sK2(empty_set,X0,X1),X1)
| ( set_intersection2(empty_set,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_368927,c_372426]) ).
tcf(c_380329,plain,
! [X0: $i,X1: $i] :
( element(sK2(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_380328,c_368545]) ).
tcf(c_380372,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_63,c_368928]) ).
tcf(c_380411,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,sK16(powerset(X0))) = sK16(powerset(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_370147]) ).
tcf(c_380412,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK16(powerset(X0)),X1) = sK16(powerset(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_370079]) ).
tcf(c_380413,plain,
! [X0: $i] :
( ( relation_dom(sK16(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_369156]) ).
tcf(c_380414,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK16(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_368606]) ).
tcf(c_380415,plain,
! [X0: $i] :
( ( sK16(powerset(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_101]) ).
tcf(c_380416,plain,
! [X0: $i] :
( relation(sK16(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_82]) ).
tcf(c_380417,plain,
! [X0: $i] :
( function(sK16(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_77]) ).
tcf(c_380418,plain,
! [X0: $i,X1: $i] :
( ( sK16(powerset(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_52]) ).
tcf(c_380453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X2,X3,X0),X1)
| element(sK7(X2,X3,X0),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368929,c_321]) ).
tcf(c_380454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X2,X3,X0),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368929,c_320]) ).
tcf(c_380455,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X1,X2,X0),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK7(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_368929,c_97]) ).
tcf(c_380456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X3,X0),X1)
| element(sK7(X2,X3,X0),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368929,c_96]) ).
tcf(c_380457,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,X2),X2)
| element(sK7(X0,X1,X2),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368929,c_93]) ).
tcf(c_380463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X3,relation_image(X1,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK7(X0,X3,relation_image(X1,X2)))) = sK7(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368929,c_112]) ).
tcf(c_380464,plain,
! [X0: $i,X1: $i] :
( element(sK7(X0,X1,empty_set),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368929,c_372426]) ).
tcf(c_380515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X2,X3,X0),X1)
| element(apply(X2,sK7(X2,X3,X0)),X3)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368930,c_321]) ).
tcf(c_380516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X2,sK7(X2,X3,X0)),X3)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368930,c_320]) ).
tcf(c_380517,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(X1,sK7(X1,X2,X0)),X2)
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK7(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_368930,c_97]) ).
tcf(c_380518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X3,X0),X1)
| element(apply(X2,sK7(X2,X3,X0)),X3)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368930,c_96]) ).
tcf(c_380519,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,X2),X2)
| element(apply(X0,sK7(X0,X1,X2)),X1)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368930,c_93]) ).
tcf(c_380525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X0,sK7(X0,X3,relation_image(X1,X2))),X3)
| ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK7(X0,X3,relation_image(X1,X2)))) = sK7(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368930,c_112]) ).
tcf(c_380526,plain,
! [X0: $i,X1: $i] :
( element(apply(X0,sK7(X0,X1,empty_set)),X1)
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368930,c_372426]) ).
tcf(c_380528,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,powerset(X1),X2),X2)
| subset(apply(X0,sK7(X0,powerset(X1),X2)),X1)
| ( relation_inverse_image(X0,powerset(X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368930,c_99]) ).
tcf(c_380584,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK7(X0,X1,powerset(X2)),X2)
| in(apply(X0,sK7(X0,X1,powerset(X2))),X1)
| ( relation_inverse_image(X0,X1) = powerset(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368931,c_99]) ).
tcf(c_380585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X2,X0,X3),X3)
| element(apply(X2,sK7(X2,X0,X3)),X1)
| ( relation_inverse_image(X2,X0) = X3 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368931,c_321]) ).
tcf(c_380586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X2,X0,X3),X3)
| ( relation_inverse_image(X2,X0) = X3 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368931,c_320]) ).
tcf(c_380587,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X1,X0,X2),X2)
| ( relation_inverse_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK7(X1,X0,X2))) ),
inference(superposition,[status(thm)],[c_368931,c_97]) ).
tcf(c_380588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X2,X0,X3),X3)
| in(apply(X2,sK7(X2,X0,X3)),X1)
| ( relation_inverse_image(X2,X0) = X3 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368931,c_96]) ).
tcf(c_380593,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,X2),X2)
| ~ in(sK7(X0,X1,X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368931,c_83]) ).
tcf(c_380597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,relation_image(X1,X2),X3),X3)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = X3 )
| ( apply(X1,sK13(X1,X2,apply(X0,sK7(X0,relation_image(X1,X2),X3)))) = apply(X0,sK7(X0,relation_image(X1,X2),X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368931,c_112]) ).
tcf(c_380598,plain,
! [X0: $i,X1: $i] :
( element(sK7(X0,empty_set,X1),X1)
| ( relation_inverse_image(X0,empty_set) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368931,c_372426]) ).
tcf(c_380682,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(powerset(X2),X1)
| ~ in(powerset(X2),X0)
| ~ subset(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_57,c_372982]) ).
tcf(c_380683,plain,
! [X0: $i,X1: $i] :
( ~ subset(powerset(X1),X0)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_369138,c_372982]) ).
tcf(c_380684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(powerset(X3),relation_dom(X0))
| ~ in(apply(X0,powerset(X3)),X2)
| ~ in(apply(X0,powerset(X3)),X1)
| ~ subset(relation_inverse_image(X0,set_intersection2(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_368735,c_372982]) ).
tcf(c_380707,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X0,X1),empty_set)
| element(sK7(empty_set,X0,X1),X1)
| ( relation_inverse_image(empty_set,X0) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_368932]) ).
tcf(c_380709,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK7(X0,X1,powerset(X2)),X2)
| in(sK7(X0,X1,powerset(X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = powerset(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368932,c_99]) ).
tcf(c_380710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X2,X3),X3)
| element(sK7(X0,X2,X3),X1)
| ( relation_inverse_image(X0,X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368932,c_321]) ).
tcf(c_380711,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X2,X3),X3)
| ( relation_inverse_image(X0,X2) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368932,c_320]) ).
tcf(c_380712,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK7(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_368932,c_97]) ).
tcf(c_380713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X2,X3),X3)
| in(sK7(X0,X2,X3),X1)
| ( relation_inverse_image(X0,X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368932,c_96]) ).
tcf(c_380715,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368932,c_91]) ).
tcf(c_380721,plain,
! [X0: $i,X1: $i] :
( in(sK7(empty_set,X1,X0),empty_set)
| element(sK7(empty_set,X1,X0),X0)
| ( X0 = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_380707,c_373747]) ).
tcf(c_380722,plain,
! [X0: $i,X1: $i] :
( element(sK7(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_380721,c_372426,c_368630,c_103]) ).
tcf(c_380781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,set_intersection2(set_intersection2(X1,X2),X3))
| ~ in(sK10(X0,set_intersection2(set_intersection2(X1,X2),X3)),X3)
| ~ in(sK10(X0,set_intersection2(set_intersection2(X1,X2),X3)),X2)
| ~ in(sK10(X0,set_intersection2(set_intersection2(X1,X2),X3)),X1) ),
inference(superposition,[status(thm)],[c_57,c_368972]) ).
tcf(c_380782,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_intersection2(X0,X1))
| ~ in(sK10(X0,set_intersection2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_95,c_368972]) ).
tcf(c_380783,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_intersection2(powerset(X1),X2))
| ~ subset(sK10(X0,set_intersection2(powerset(X1),X2)),X1)
| ~ in(sK10(X0,set_intersection2(powerset(X1),X2)),X2) ),
inference(superposition,[status(thm)],[c_369138,c_368972]) ).
tcf(c_380784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(X1,set_intersection2(relation_inverse_image(X0,set_intersection2(X2,X3)),X4))
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK10(X1,set_intersection2(relation_inverse_image(X0,set_intersection2(X2,X3)),X4)),X4)
| ~ in(sK10(X1,set_intersection2(relation_inverse_image(X0,set_intersection2(X2,X3)),X4)),relation_dom(X0))
| ~ in(apply(X0,sK10(X1,set_intersection2(relation_inverse_image(X0,set_intersection2(X2,X3)),X4))),X3)
| ~ in(apply(X0,sK10(X1,set_intersection2(relation_inverse_image(X0,set_intersection2(X2,X3)),X4))),X2) ),
inference(superposition,[status(thm)],[c_368735,c_368972]) ).
tcf(c_380785,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_intersection2(X1,X1))
| ~ in(sK10(X0,X1),X1)
| ~ in(sK10(X0,set_intersection2(X1,X1)),X1) ),
inference(superposition,[status(thm)],[c_53,c_368972]) ).
tcf(c_380786,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_intersection2(X1,X2))
| ~ in(sK10(X0,set_intersection2(X2,X1)),X1)
| ~ in(sK10(X0,set_intersection2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_63,c_368972]) ).
tcf(c_380788,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_intersection2(X1,empty_set))
| ~ in(sK10(X0,empty_set),X1)
| ~ in(sK10(X0,set_intersection2(X1,empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_64,c_368972]) ).
tcf(c_380789,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_intersection2(empty_set,X1))
| ~ in(sK10(X0,empty_set),empty_set)
| ~ in(sK10(X0,set_intersection2(empty_set,X1)),X1) ),
inference(superposition,[status(thm)],[c_368545,c_368972]) ).
tcf(c_380835,plain,
! [X0: $i,X1: $i] :
( subset(set_intersection2(X0,X0),X1)
| in(sK10(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_53,c_368985]) ).
tcf(c_380836,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X1,X0),X2)
| in(sK10(set_intersection2(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_63,c_368985]) ).
tcf(c_380838,plain,
! [X0: $i,X1: $i] :
( in(sK10(empty_set,X1),empty_set)
| subset(set_intersection2(X0,empty_set),X1) ),
inference(superposition,[status(thm)],[c_64,c_368985]) ).
tcf(c_380839,plain,
! [X0: $i,X1: $i] :
( subset(set_intersection2(empty_set,X1),X0)
| in(sK10(empty_set,X0),X1) ),
inference(superposition,[status(thm)],[c_368545,c_368985]) ).
tcf(c_380840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X2,X0),X3)
| element(sK10(set_intersection2(X2,X0),X3),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368985,c_321]) ).
tcf(c_380841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X2,X0),X3)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368985,c_320]) ).
tcf(c_380842,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X1,X0),X2)
| ~ in(X0,sK10(set_intersection2(X1,X0),X2)) ),
inference(superposition,[status(thm)],[c_368985,c_97]) ).
tcf(c_380843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X2,X0),X3)
| in(sK10(set_intersection2(X2,X0),X3),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368985,c_96]) ).
tcf(c_380844,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X0,X1),X2)
| element(sK10(set_intersection2(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_368985,c_93]) ).
tcf(c_380845,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X1,X0),X2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368985,c_91]) ).
tcf(c_380846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X0,set_intersection2(X1,X2)),X3)
| in(sK10(set_intersection2(X0,set_intersection2(X1,X2)),X3),X2) ),
inference(superposition,[status(thm)],[c_368985,c_59]) ).
tcf(c_380847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X0,set_intersection2(X1,X2)),X3)
| in(sK10(set_intersection2(X0,set_intersection2(X1,X2)),X3),X1) ),
inference(superposition,[status(thm)],[c_368985,c_58]) ).
tcf(c_380848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X1,relation_inverse_image(X0,X2)),X3)
| in(apply(X0,sK10(set_intersection2(X1,relation_inverse_image(X0,X2)),X3)),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368985,c_88]) ).
tcf(c_380849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X1,relation_inverse_image(X0,X2)),X3)
| in(sK10(set_intersection2(X1,relation_inverse_image(X0,X2)),X3),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368985,c_87]) ).
tcf(c_380850,plain,
! [X0: $i,X1: $i] : subset(set_intersection2(X0,X1),X1),
inference(superposition,[status(thm)],[c_368985,c_94]) ).
tcf(c_380851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X2,relation_image(X0,X1)),X3)
| ( apply(X0,sK13(X0,X1,sK10(set_intersection2(X2,relation_image(X0,X1)),X3))) = sK10(set_intersection2(X2,relation_image(X0,X1)),X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368985,c_112]) ).
tcf(c_380852,plain,
! [X0: $i,X1: $i] : subset(set_intersection2(X0,empty_set),X1),
inference(superposition,[status(thm)],[c_368985,c_372426]) ).
tcf(c_380853,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X0,X1),set_intersection2(X1,X2))
| ~ in(sK10(set_intersection2(X0,X1),set_intersection2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_368985,c_368972]) ).
tcf(c_380859,plain,
! [X0: $i] :
( subset(empty_set,X0)
| in(sK10(empty_set,X0),empty_set) ),
inference(light_normalisation,[status(thm)],[c_380838,c_64]) ).
tcf(c_380919,plain,
! [X0: $i,X1: $i] : subset(set_intersection2(X0,X1),X0),
inference(superposition,[status(thm)],[c_63,c_380850]) ).
tcf(c_380923,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380850,c_370745]) ).
tcf(c_380924,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = X0 )
| ~ subset(X0,set_intersection2(X1,X0)) ),
inference(superposition,[status(thm)],[c_380850,c_60]) ).
tcf(c_380925,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = X0 )
| ~ subset(X0,X1)
| ~ subset(X0,X0) ),
inference(superposition,[status(thm)],[c_380850,c_368558]) ).
tcf(c_380931,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = X0 )
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_380925,c_100]) ).
tcf(c_381102,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380919,c_370745]) ).
tcf(c_381103,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_380919,c_60]) ).
tcf(c_381104,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,X1)
| ~ subset(X0,X0) ),
inference(superposition,[status(thm)],[c_380919,c_368558]) ).
tcf(c_381110,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_381104,c_100]) ).
tcf(c_381118,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X1,X0),X2)
| in(sK10(set_intersection2(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_63,c_368986]) ).
tcf(c_381120,plain,
! [X0: $i,X1: $i] :
( subset(set_intersection2(X1,empty_set),X0)
| in(sK10(empty_set,X0),X1) ),
inference(superposition,[status(thm)],[c_64,c_368986]) ).
tcf(c_381121,plain,
! [X0: $i,X1: $i] :
( in(sK10(empty_set,X1),empty_set)
| subset(set_intersection2(empty_set,X0),X1) ),
inference(superposition,[status(thm)],[c_368545,c_368986]) ).
tcf(c_381122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X0,X2),X3)
| element(sK10(set_intersection2(X0,X2),X3),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368986,c_321]) ).
tcf(c_381123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X0,X2),X3)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368986,c_320]) ).
tcf(c_381124,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X0,X1),X2)
| ~ in(X0,sK10(set_intersection2(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_368986,c_97]) ).
tcf(c_381125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X0,X2),X3)
| in(sK10(set_intersection2(X0,X2),X3),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368986,c_96]) ).
tcf(c_381126,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X0,X1),X2)
| element(sK10(set_intersection2(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_368986,c_93]) ).
tcf(c_381127,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X0,X1),X2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368986,c_91]) ).
tcf(c_381128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(set_intersection2(X0,X1),X2),X3)
| in(sK10(set_intersection2(set_intersection2(X0,X1),X2),X3),X1) ),
inference(superposition,[status(thm)],[c_368986,c_59]) ).
tcf(c_381129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(set_intersection2(X0,X1),X2),X3)
| in(sK10(set_intersection2(set_intersection2(X0,X1),X2),X3),X0) ),
inference(superposition,[status(thm)],[c_368986,c_58]) ).
tcf(c_381130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(relation_inverse_image(X0,X1),X2),X3)
| in(apply(X0,sK10(set_intersection2(relation_inverse_image(X0,X1),X2),X3)),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368986,c_88]) ).
tcf(c_381131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(relation_inverse_image(X0,X1),X2),X3)
| in(sK10(set_intersection2(relation_inverse_image(X0,X1),X2),X3),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368986,c_87]) ).
tcf(c_381133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(relation_image(X0,X1),X2),X3)
| ( apply(X0,sK13(X0,X1,sK10(set_intersection2(relation_image(X0,X1),X2),X3))) = sK10(set_intersection2(relation_image(X0,X1),X2),X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368986,c_112]) ).
tcf(c_381134,plain,
! [X0: $i,X1: $i] : subset(set_intersection2(empty_set,X0),X1),
inference(superposition,[status(thm)],[c_368986,c_372426]) ).
tcf(c_381135,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X0,X1),set_intersection2(X0,X2))
| ~ in(sK10(set_intersection2(X0,X1),set_intersection2(X0,X2)),X2) ),
inference(superposition,[status(thm)],[c_368986,c_368972]) ).
tcf(c_381210,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(empty_set,X1),X0)
| in(apply(empty_set,sK10(empty_set,X0)),X1)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_368987]) ).
tcf(c_381211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X2,X0),X3)
| element(apply(X2,sK10(relation_inverse_image(X2,X0),X3)),X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368987,c_321]) ).
tcf(c_381212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X2,X0),X3)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368987,c_320]) ).
tcf(c_381213,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X1,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK10(relation_inverse_image(X1,X0),X2))) ),
inference(superposition,[status(thm)],[c_368987,c_97]) ).
tcf(c_381214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X2,X0),X3)
| in(apply(X2,sK10(relation_inverse_image(X2,X0),X3)),X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368987,c_96]) ).
tcf(c_381215,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X0,X1),X2)
| element(apply(X0,sK10(relation_inverse_image(X0,X1),X2)),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368987,c_93]) ).
tcf(c_381216,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X0,X1),X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368987,c_91]) ).
tcf(c_381217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X0,set_intersection2(X1,X2)),X3)
| in(apply(X0,sK10(relation_inverse_image(X0,set_intersection2(X1,X2)),X3)),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368987,c_59]) ).
tcf(c_381218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X0,set_intersection2(X1,X2)),X3)
| in(apply(X0,sK10(relation_inverse_image(X0,set_intersection2(X1,X2)),X3)),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368987,c_58]) ).
tcf(c_381219,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X0,X1),X2)
| in(sK10(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1))
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK10(relation_inverse_image(X0,X1),X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368987,c_86]) ).
tcf(c_381220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3)
| in(apply(X1,apply(X0,sK10(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3))),X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368987,c_88]) ).
tcf(c_381221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3)
| in(apply(X0,sK10(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3)),relation_dom(X1))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368987,c_87]) ).
tcf(c_381222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X0,relation_image(X1,X2)),X3)
| ( apply(X1,sK13(X1,X2,apply(X0,sK10(relation_inverse_image(X0,relation_image(X1,X2)),X3)))) = apply(X0,sK10(relation_inverse_image(X0,relation_image(X1,X2)),X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368987,c_112]) ).
tcf(c_381223,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(X0,empty_set),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368987,c_372426]) ).
tcf(c_381236,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(empty_set,X1),X0)
| in(apply(empty_set,sK10(empty_set,X0)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_381210,c_368630,c_103]) ).
tcf(c_381312,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(empty_set,X1),X0)
| in(sK10(empty_set,X0),relation_dom(empty_set))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_368988]) ).
tcf(c_381313,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(empty_set,X0),X1)
| in(sK10(relation_inverse_image(empty_set,X0),X1),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_368988]) ).
tcf(c_381314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X0,X2),X3)
| element(sK10(relation_inverse_image(X0,X2),X3),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368988,c_321]) ).
tcf(c_381315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X0,X2),X3)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368988,c_320]) ).
tcf(c_381316,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X0,X1),X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK10(relation_inverse_image(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_368988,c_97]) ).
tcf(c_381317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X0,X2),X3)
| in(sK10(relation_inverse_image(X0,X2),X3),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368988,c_96]) ).
tcf(c_381318,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X0,X1),X2)
| element(sK10(relation_inverse_image(X0,X1),X2),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368988,c_93]) ).
tcf(c_381319,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X0,X1),X2)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368988,c_91]) ).
tcf(c_381320,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(X0,X1),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368988,c_94]) ).
tcf(c_381321,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X0,X1),set_intersection2(relation_dom(X0),X2))
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK10(relation_inverse_image(X0,X1),set_intersection2(relation_dom(X0),X2)),X2) ),
inference(superposition,[status(thm)],[c_368988,c_368972]) ).
tcf(c_381329,plain,
! [X0: $i,X1: $i] :
( in(sK10(empty_set,X1),empty_set)
| subset(relation_inverse_image(empty_set,X0),X1)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_381312,c_373108]) ).
tcf(c_381330,plain,
! [X0: $i] :
( subset(empty_set,X0)
| in(sK10(empty_set,X0),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_381329,c_373747]) ).
tcf(c_381370,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X2,X0)) = set_intersection2(X2,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_370147]) ).
tcf(c_381371,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,X0),X2) = set_intersection2(X1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_370079]) ).
tcf(c_381372,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_369156]) ).
tcf(c_381373,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X2,X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_368606]) ).
tcf(c_381375,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X1,X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_82]) ).
tcf(c_381376,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X1,X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_77]) ).
tcf(c_381378,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_380923,c_368869]) ).
tcf(c_381424,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X0,X2)) = set_intersection2(X0,X2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_370147]) ).
tcf(c_381425,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_370079]) ).
tcf(c_381426,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X0,X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_369156]) ).
tcf(c_381427,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X0,X2)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_368606]) ).
tcf(c_381429,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X0,X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_82]) ).
tcf(c_381430,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X0,X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_77]) ).
tcf(c_381454,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X0),X2)
| ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,X2)
| ~ in(sK2(X0,X1,X0),X1)
| ~ in(sK2(X0,X1,X0),X0) ),
inference(superposition,[status(thm)],[c_369012,c_54]) ).
tcf(c_381455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X4,X2),X3)
| in(sK2(X0,X4,X2),X1)
| ( set_intersection2(X0,X4) = X2 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_321]) ).
tcf(c_381456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X4,X2),X1)
| ( set_intersection2(X0,X4) = X2 )
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_320]) ).
tcf(c_381457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X0),X3)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X1,X3)
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369012,c_97]) ).
tcf(c_381458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X4,X2),X3)
| in(sK2(X0,X4,X2),X1)
| ( set_intersection2(X0,X4) = X2 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_96]) ).
tcf(c_381465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X4,relation_image(X2,X3)),X1)
| ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK2(X0,X4,relation_image(X2,X3)))) = sK2(X0,X4,relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_112]) ).
tcf(c_381466,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,empty_set),X1)
| ( set_intersection2(X0,X2) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_372426]) ).
tcf(c_381467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ subset(set_intersection2(X0,X1),X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_369012,c_368471]) ).
tcf(c_381469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X3,X4),X2)
| in(sK2(X0,X3,X4),X4)
| ( set_intersection2(X0,X3) = X4 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_321]) ).
tcf(c_381470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| ( set_intersection2(X0,X3) = X4 )
| ~ empty(X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_320]) ).
tcf(c_381471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X3),X3)
| ( set_intersection2(X1,X2) = X3 )
| ~ subset(X1,X0)
| ~ in(X0,sK2(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_369012,c_97]) ).
tcf(c_381472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| in(sK2(X0,X3,X4),X2)
| ( set_intersection2(X0,X3) = X4 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_96]) ).
tcf(c_381475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| in(sK2(X0,X3,X4),X2)
| ( set_intersection2(X0,X3) = X4 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369012,c_59]) ).
tcf(c_381476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| in(sK2(X0,X3,X4),X1)
| ( set_intersection2(X0,X3) = X4 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369012,c_58]) ).
tcf(c_381477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| in(apply(X1,sK2(X0,X3,X4)),X2)
| ( set_intersection2(X0,X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369012,c_88]) ).
tcf(c_381478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| in(sK2(X0,X3,X4),relation_dom(X1))
| ( set_intersection2(X0,X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369012,c_87]) ).
tcf(c_381479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| ( set_intersection2(X0,X3) = X4 )
| ( apply(X1,sK13(X1,X2,sK2(X0,X3,X4))) = sK2(X0,X3,X4) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369012,c_112]) ).
tcf(c_381480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X0,X1,X2),X3)
| in(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ subset(X0,sK10(sK2(X0,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_369012,c_369085]) ).
tcf(c_381481,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_369012,c_372426]) ).
tcf(c_381482,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK2(X0,X1,X2))
| in(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ subset(X0,sK16(sK2(X0,X1,X2))) ),
inference(superposition,[status(thm)],[c_369012,c_370746]) ).
tcf(c_381484,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,X1),X1)
| ( set_intersection2(X0,X2) = X1 )
| ~ subset(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_369012]) ).
tcf(c_381618,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X0),X2)
| ( set_intersection2(X0,X1) = X0 )
| ~ subset(X1,X2)
| ~ in(sK2(X0,X1,X0),X1)
| ~ in(sK2(X0,X1,X0),X0) ),
inference(superposition,[status(thm)],[c_369013,c_54]) ).
tcf(c_381619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X0,X2),X3)
| in(sK2(X4,X0,X2),X1)
| ( set_intersection2(X4,X0) = X2 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_321]) ).
tcf(c_381620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X4,X0,X2),X1)
| ( set_intersection2(X4,X0) = X2 )
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_320]) ).
tcf(c_381621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X0),X3)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X2,X3)
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369013,c_97]) ).
tcf(c_381622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X4,X0,X2),X3)
| in(sK2(X4,X0,X2),X1)
| ( set_intersection2(X4,X0) = X2 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_96]) ).
tcf(c_381629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X4,X0,relation_image(X2,X3)),X1)
| ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ( apply(X2,sK13(X2,X3,sK2(X4,X0,relation_image(X2,X3)))) = sK2(X4,X0,relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_112]) ).
tcf(c_381630,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X0,empty_set),X1)
| ( set_intersection2(X2,X0) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_372426]) ).
tcf(c_381631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ subset(X2,X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_369013,c_368471]) ).
tcf(c_381633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X0,X4),X2)
| in(sK2(X3,X0,X4),X4)
| ( set_intersection2(X3,X0) = X4 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_321]) ).
tcf(c_381634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| ( set_intersection2(X3,X0) = X4 )
| ~ empty(X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_320]) ).
tcf(c_381635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X3),X3)
| ( set_intersection2(X1,X2) = X3 )
| ~ subset(X2,X0)
| ~ in(X0,sK2(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_369013,c_97]) ).
tcf(c_381636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| in(sK2(X3,X0,X4),X2)
| ( set_intersection2(X3,X0) = X4 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_96]) ).
tcf(c_381639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| in(sK2(X3,X0,X4),X2)
| ( set_intersection2(X3,X0) = X4 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369013,c_59]) ).
tcf(c_381640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| in(sK2(X3,X0,X4),X1)
| ( set_intersection2(X3,X0) = X4 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369013,c_58]) ).
tcf(c_381641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| in(apply(X1,sK2(X3,X0,X4)),X2)
| ( set_intersection2(X3,X0) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369013,c_88]) ).
tcf(c_381642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| in(sK2(X3,X0,X4),relation_dom(X1))
| ( set_intersection2(X3,X0) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369013,c_87]) ).
tcf(c_381643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| ( set_intersection2(X3,X0) = X4 )
| ( apply(X1,sK13(X1,X2,sK2(X3,X0,X4))) = sK2(X3,X0,X4) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369013,c_112]) ).
tcf(c_381644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X1,X0,X2),X3)
| in(sK2(X1,X0,X2),X2)
| ( set_intersection2(X1,X0) = X2 )
| ~ subset(X0,sK10(sK2(X1,X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_369013,c_369085]) ).
tcf(c_381645,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,X2),X2)
| ( set_intersection2(X1,X0) = X2 )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_369013,c_372426]) ).
tcf(c_381646,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK2(X1,X0,X2))
| in(sK2(X1,X0,X2),X2)
| ( set_intersection2(X1,X0) = X2 )
| ~ subset(X0,sK16(sK2(X1,X0,X2))) ),
inference(superposition,[status(thm)],[c_369013,c_370746]) ).
tcf(c_381648,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X0,X1),X1)
| ( set_intersection2(X2,X0) = X1 )
| ~ subset(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_369013]) ).
tcf(c_381815,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,X1),X2)
| ( set_intersection2(X0,X0) = X1 )
| ~ subset(X1,X2)
| ~ in(sK2(X0,X0,X1),X1)
| ~ in(sK2(X0,X0,X1),X0) ),
inference(superposition,[status(thm)],[c_369014,c_54]) ).
tcf(c_381816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X2,X0),X3)
| in(sK2(X4,X2,X0),X1)
| ( set_intersection2(X4,X2) = X0 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_321]) ).
tcf(c_381817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X4,X2,X0),X1)
| ( set_intersection2(X4,X2) = X0 )
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_320]) ).
tcf(c_381818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X0,X2),X3)
| ( set_intersection2(X1,X0) = X2 )
| ~ subset(X2,X3)
| ~ in(X0,sK2(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_369014,c_97]) ).
tcf(c_381819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X4,X2,X0),X3)
| in(sK2(X4,X2,X0),X1)
| ( set_intersection2(X4,X2) = X0 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_96]) ).
tcf(c_381826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X4,relation_image(X2,X3),X0),X1)
| ( set_intersection2(X4,relation_image(X2,X3)) = X0 )
| ( apply(X2,sK13(X2,X3,sK2(X4,relation_image(X2,X3),X0))) = sK2(X4,relation_image(X2,X3),X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_112]) ).
tcf(c_381827,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,empty_set,X0),X1)
| ( set_intersection2(X2,empty_set) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_372426]) ).
tcf(c_381828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X0,X2),X3)
| ( set_intersection2(set_intersection2(X0,X1),X0) = X2 )
| ~ subset(X2,X3)
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X1)
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X0) ),
inference(superposition,[status(thm)],[c_369014,c_368471]) ).
tcf(c_381830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,X0),X2)
| in(sK2(X3,X4,X0),X4)
| ( set_intersection2(X3,X4) = X0 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_321]) ).
tcf(c_381831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| ( set_intersection2(X3,X4) = X0 )
| ~ empty(X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_320]) ).
tcf(c_381832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X3),X2)
| ( set_intersection2(X1,X2) = X3 )
| ~ subset(X3,X0)
| ~ in(X0,sK2(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_369014,c_97]) ).
tcf(c_381833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| in(sK2(X3,X4,X0),X2)
| ( set_intersection2(X3,X4) = X0 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_96]) ).
tcf(c_381836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| in(sK2(X3,X4,X0),X2)
| ( set_intersection2(X3,X4) = X0 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369014,c_59]) ).
tcf(c_381837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| in(sK2(X3,X4,X0),X1)
| ( set_intersection2(X3,X4) = X0 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369014,c_58]) ).
tcf(c_381838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| in(apply(X1,sK2(X3,X4,X0)),X2)
| ( set_intersection2(X3,X4) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369014,c_88]) ).
tcf(c_381839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| in(sK2(X3,X4,X0),relation_dom(X1))
| ( set_intersection2(X3,X4) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369014,c_87]) ).
tcf(c_381840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| ( set_intersection2(X3,X4) = X0 )
| ( apply(X1,sK13(X1,X2,sK2(X3,X4,X0))) = sK2(X3,X4,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369014,c_112]) ).
tcf(c_381841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X1,X2,X0),X3)
| in(sK2(X1,X2,X0),X2)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X0,sK10(sK2(X1,X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_369014,c_369085]) ).
tcf(c_381842,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_369014,c_372426]) ).
tcf(c_381843,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),X2)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X0,sK16(sK2(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_369014,c_370746]) ).
tcf(c_381845,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X1,X0),X1)
| ( set_intersection2(X2,X1) = X0 )
| ~ subset(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_369014]) ).
tcf(c_381910,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X0,X1),X2)
| ( X0 = X1 )
| ~ subset(X1,X2)
| ~ in(sK2(X0,X0,X1),X1)
| ~ in(sK2(X0,X0,X1),X0) ),
inference(light_normalisation,[status(thm)],[c_381815,c_53]) ).
tcf(c_382038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,X2),X3)
| ( set_intersection2(X0,X1) = X2 )
| ~ subset(X2,X3)
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1) ),
inference(superposition,[status(thm)],[c_369015,c_54]) ).
tcf(c_382039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,X4,X0),X3)
| in(sK2(X2,X4,X0),X1)
| ( set_intersection2(X2,X4) = X0 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_321]) ).
tcf(c_382040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X4,X0),X1)
| ( set_intersection2(X2,X4) = X0 )
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_320]) ).
tcf(c_382041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,X2),X3)
| ( set_intersection2(X0,X1) = X2 )
| ~ subset(X2,X3)
| ~ in(X0,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_369015,c_97]) ).
tcf(c_382042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X4,X0),X3)
| in(sK2(X2,X4,X0),X1)
| ( set_intersection2(X2,X4) = X0 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_96]) ).
tcf(c_382049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X2,X3),X4,X0),X1)
| ( set_intersection2(relation_image(X2,X3),X4) = X0 )
| ( apply(X2,sK13(X2,X3,sK2(relation_image(X2,X3),X4,X0))) = sK2(relation_image(X2,X3),X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_112]) ).
tcf(c_382050,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,X0),X1)
| ( set_intersection2(empty_set,X2) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_372426]) ).
tcf(c_382052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,X0),X2)
| in(sK2(X3,X4,X0),X3)
| ( set_intersection2(X3,X4) = X0 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_321]) ).
tcf(c_382053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| ( set_intersection2(X3,X4) = X0 )
| ~ empty(X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_320]) ).
tcf(c_382054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X3),X1)
| ( set_intersection2(X1,X2) = X3 )
| ~ subset(X3,X0)
| ~ in(X0,sK2(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_369015,c_97]) ).
tcf(c_382055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| in(sK2(X3,X4,X0),X2)
| ( set_intersection2(X3,X4) = X0 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_96]) ).
tcf(c_382058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| in(sK2(X3,X4,X0),X2)
| ( set_intersection2(X3,X4) = X0 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369015,c_59]) ).
tcf(c_382059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| in(sK2(X3,X4,X0),X1)
| ( set_intersection2(X3,X4) = X0 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369015,c_58]) ).
tcf(c_382060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| in(apply(X1,sK2(X3,X4,X0)),X2)
| ( set_intersection2(X3,X4) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369015,c_88]) ).
tcf(c_382061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| in(sK2(X3,X4,X0),relation_dom(X1))
| ( set_intersection2(X3,X4) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369015,c_87]) ).
tcf(c_382062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| ( set_intersection2(X3,X4) = X0 )
| ( apply(X1,sK13(X1,X2,sK2(X3,X4,X0))) = sK2(X3,X4,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369015,c_112]) ).
tcf(c_382063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X1,X2,X0),X3)
| in(sK2(X1,X2,X0),X1)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X0,sK10(sK2(X1,X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_369015,c_369085]) ).
tcf(c_382064,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X1)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_369015,c_372426]) ).
tcf(c_382065,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK2(X1,X2,X0))
| in(sK2(X1,X2,X0),X1)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X0,sK16(sK2(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_369015,c_370746]) ).
tcf(c_382066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(X3,X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_369015,c_368471]) ).
tcf(c_382067,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X1)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_369015]) ).
tcf(c_382224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X4,set_intersection2(X2,X3))
| ~ in(X4,X1)
| ~ in(X4,X0)
| ~ subset(set_intersection2(X0,X1),X3)
| ~ subset(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_65,c_369016]) ).
tcf(c_382249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X4,X2),X3)
| in(sK7(X0,X4,X2),X1)
| ( relation_inverse_image(X0,X4) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_321]) ).
tcf(c_382250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,X2),X1)
| ( relation_inverse_image(X0,X4) = X2 )
| ~ empty(X3)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_320]) ).
tcf(c_382251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X2,X0),X3)
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ in(X0,sK7(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369017,c_97]) ).
tcf(c_382252,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,X2),X3)
| in(sK7(X0,X4,X2),X1)
| ( relation_inverse_image(X0,X4) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_96]) ).
tcf(c_382259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,relation_image(X2,X3)),X1)
| ( relation_inverse_image(X0,X4) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X0,X4,relation_image(X2,X3)))) = sK7(X0,X4,relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_112]) ).
tcf(c_382260,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,empty_set),X1)
| ( relation_inverse_image(X0,X2) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_372426]) ).
tcf(c_382261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X3,X4),X2)
| in(sK7(X0,X3,X4),X4)
| ( relation_inverse_image(X0,X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X1,X2)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_321]) ).
tcf(c_382262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| ( relation_inverse_image(X0,X3) = X4 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X1,X2)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_320]) ).
tcf(c_382263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X2,X3),X3)
| ( relation_inverse_image(X1,X2) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X0)
| ~ in(X0,sK7(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_369017,c_97]) ).
tcf(c_382264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| in(sK7(X0,X3,X4),X2)
| ( relation_inverse_image(X0,X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X1,X2)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_96]) ).
tcf(c_382267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| in(sK7(X0,X3,X4),X2)
| ( relation_inverse_image(X0,X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369017,c_59]) ).
tcf(c_382268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| in(sK7(X0,X3,X4),X1)
| ( relation_inverse_image(X0,X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369017,c_58]) ).
tcf(c_382269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| in(apply(X1,sK7(X0,X3,X4)),X2)
| ( relation_inverse_image(X0,X3) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369017,c_88]) ).
tcf(c_382270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| in(sK7(X0,X3,X4),relation_dom(X1))
| ( relation_inverse_image(X0,X3) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369017,c_87]) ).
tcf(c_382271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| ( relation_inverse_image(X0,X3) = X4 )
| ( apply(X1,sK13(X1,X2,sK7(X0,X3,X4))) = sK7(X0,X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369017,c_112]) ).
tcf(c_382272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK7(X0,X1,X2),X3)
| in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK10(sK7(X0,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_369017,c_369085]) ).
tcf(c_382273,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),empty_set) ),
inference(superposition,[status(thm)],[c_369017,c_372426]) ).
tcf(c_382274,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK7(X0,X1,X2))
| in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK16(sK7(X0,X1,X2))) ),
inference(superposition,[status(thm)],[c_369017,c_370746]) ).
tcf(c_382275,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,X1),X1)
| ( relation_inverse_image(X0,X2) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(equality_factoring,[status(thm)],[c_369017]) ).
tcf(c_382466,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X4,X0,X2),X3)
| in(apply(X4,sK7(X4,X0,X2)),X1)
| ( relation_inverse_image(X4,X0) = X2 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_321]) ).
tcf(c_382467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X4,sK7(X4,X0,X2)),X1)
| ( relation_inverse_image(X4,X0) = X2 )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_320]) ).
tcf(c_382468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,X2,X0)),X3)
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,sK7(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369018,c_97]) ).
tcf(c_382469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X4,X0,X2),X3)
| in(apply(X4,sK7(X4,X0,X2)),X1)
| ( relation_inverse_image(X4,X0) = X2 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_96]) ).
tcf(c_382476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,X0,relation_image(X3,X4))),X1)
| ( relation_inverse_image(X2,X0) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK7(X2,X0,relation_image(X3,X4)))) = sK7(X2,X0,relation_image(X3,X4)) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_112]) ).
tcf(c_382477,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X2,sK7(X2,X0,empty_set)),X1)
| ( relation_inverse_image(X2,X0) = empty_set )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_372426]) ).
tcf(c_382478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| element(apply(X3,sK7(X3,X0,X4)),X2)
| ( relation_inverse_image(X3,X0) = X4 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_321]) ).
tcf(c_382479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| ( relation_inverse_image(X3,X0) = X4 )
| ~ empty(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_320]) ).
tcf(c_382480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X2,X3),X3)
| ( relation_inverse_image(X1,X2) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X0)
| ~ in(X0,apply(X1,sK7(X1,X2,X3))) ),
inference(superposition,[status(thm)],[c_369018,c_97]) ).
tcf(c_382481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| in(apply(X3,sK7(X3,X0,X4)),X2)
| ( relation_inverse_image(X3,X0) = X4 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_96]) ).
tcf(c_382484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| in(apply(X3,sK7(X3,X0,X4)),X2)
| ( relation_inverse_image(X3,X0) = X4 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369018,c_59]) ).
tcf(c_382485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| in(apply(X3,sK7(X3,X0,X4)),X1)
| ( relation_inverse_image(X3,X0) = X4 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369018,c_58]) ).
tcf(c_382487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,X2),X2)
| in(sK7(X0,X1,X2),relation_inverse_image(X0,X3))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X1,X3)
| ~ in(sK7(X0,X1,X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369018,c_86]) ).
tcf(c_382488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| in(apply(X1,apply(X3,sK7(X3,X0,X4))),X2)
| ( relation_inverse_image(X3,X0) = X4 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369018,c_88]) ).
tcf(c_382489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| in(apply(X3,sK7(X3,X0,X4)),relation_dom(X1))
| ( relation_inverse_image(X3,X0) = X4 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369018,c_87]) ).
tcf(c_382490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| ( relation_inverse_image(X3,X0) = X4 )
| ( apply(X1,sK13(X1,X2,apply(X3,sK7(X3,X0,X4)))) = apply(X3,sK7(X3,X0,X4)) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369018,c_112]) ).
tcf(c_382491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X0,X2),X2)
| subset(apply(X1,sK7(X1,X0,X2)),X3)
| ( relation_inverse_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK10(apply(X1,sK7(X1,X0,X2)),X3)) ),
inference(superposition,[status(thm)],[c_369018,c_369085]) ).
tcf(c_382492,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X0,X2),X2)
| ( relation_inverse_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_369018,c_372426]) ).
tcf(c_382493,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X0,X2),X2)
| empty(apply(X1,sK7(X1,X0,X2)))
| ( relation_inverse_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK16(apply(X1,sK7(X1,X0,X2)))) ),
inference(superposition,[status(thm)],[c_369018,c_370746]) ).
tcf(c_382822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X3,X4,X0),X2)
| in(apply(X3,sK7(X3,X4,X0)),X4)
| ( relation_inverse_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_321]) ).
tcf(c_382823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X3,X4,X0)),X4)
| ( relation_inverse_image(X3,X4) = X0 )
| ~ empty(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_320]) ).
tcf(c_382824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,X2,X3)),X2)
| ( relation_inverse_image(X1,X2) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X0)
| ~ in(X0,sK7(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_369019,c_97]) ).
tcf(c_382825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),X2)
| in(apply(X3,sK7(X3,X4,X0)),X4)
| ( relation_inverse_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_96]) ).
tcf(c_382828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),X2)
| in(apply(X3,sK7(X3,X4,X0)),X4)
| ( relation_inverse_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369019,c_59]) ).
tcf(c_382829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),X1)
| in(apply(X3,sK7(X3,X4,X0)),X4)
| ( relation_inverse_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369019,c_58]) ).
tcf(c_382830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X3,X4,X0)),X4)
| in(apply(X1,sK7(X3,X4,X0)),X2)
| ( relation_inverse_image(X3,X4) = X0 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369019,c_88]) ).
tcf(c_382831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),relation_dom(X1))
| in(apply(X3,sK7(X3,X4,X0)),X4)
| ( relation_inverse_image(X3,X4) = X0 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369019,c_87]) ).
tcf(c_382832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X3,X4,X0)),X4)
| ( relation_inverse_image(X3,X4) = X0 )
| ( apply(X1,sK13(X1,X2,sK7(X3,X4,X0))) = sK7(X3,X4,X0) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369019,c_112]) ).
tcf(c_382833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK7(X1,X2,X0),X3)
| in(apply(X1,sK7(X1,X2,X0)),X2)
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK10(sK7(X1,X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_369019,c_369085]) ).
tcf(c_382834,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,sK7(X1,X2,X0)),X2)
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_369019,c_372426]) ).
tcf(c_382835,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK7(X1,X2,X0))
| in(apply(X1,sK7(X1,X2,X0)),X2)
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK16(sK7(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_369019,c_370746]) ).
tcf(c_382836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X4,X2,X0),X1)
| element(apply(X4,sK7(X4,X2,X0)),X3)
| ( relation_inverse_image(X4,X2) = X0 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_321]) ).
tcf(c_382837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X4,X2,X0),X1)
| ( relation_inverse_image(X4,X2) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_320]) ).
tcf(c_382838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X0,X2),X3)
| ( relation_inverse_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,apply(X1,sK7(X1,X0,X2))) ),
inference(superposition,[status(thm)],[c_369019,c_97]) ).
tcf(c_382839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X4,X2,X0),X1)
| in(apply(X4,sK7(X4,X2,X0)),X3)
| ( relation_inverse_image(X4,X2) = X0 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_96]) ).
tcf(c_382844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,X2),X3)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ in(sK7(X0,X1,X2),X2)
| ~ in(sK7(X0,X1,X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369019,c_83]) ).
tcf(c_382845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,X2),X3)
| in(sK7(X0,X1,X2),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ in(sK7(X0,X1,X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369019,c_86]) ).
tcf(c_382848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,relation_image(X3,X4),X0),X1)
| ( relation_inverse_image(X2,relation_image(X3,X4)) = X0 )
| ( apply(X3,sK13(X3,X4,apply(X2,sK7(X2,relation_image(X3,X4),X0)))) = apply(X2,sK7(X2,relation_image(X3,X4),X0)) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_112]) ).
tcf(c_382849,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X2,empty_set,X0),X1)
| ( relation_inverse_image(X2,empty_set) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_372426]) ).
tcf(c_382997,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,X0),empty_set)
| in(sK7(empty_set,X2,X0),X1)
| ( relation_inverse_image(empty_set,X2) = X0 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_373108,c_369020]) ).
tcf(c_382998,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X3,X4,X0),X2)
| in(sK7(X3,X4,X0),relation_dom(X3))
| ( relation_inverse_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369020,c_321]) ).
tcf(c_382999,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),relation_dom(X3))
| ( relation_inverse_image(X3,X4) = X0 )
| ~ empty(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369020,c_320]) ).
tcf(c_383000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X2,X3),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X0)
| ~ in(X0,sK7(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_369020,c_97]) ).
tcf(c_383001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),X2)
| in(sK7(X3,X4,X0),relation_dom(X3))
| ( relation_inverse_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369020,c_96]) ).
tcf(c_383004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),X2)
| in(sK7(X3,X4,X0),relation_dom(X3))
| ( relation_inverse_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369020,c_59]) ).
tcf(c_383005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),X1)
| in(sK7(X3,X4,X0),relation_dom(X3))
| ( relation_inverse_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369020,c_58]) ).
tcf(c_383006,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),relation_dom(X3))
| in(apply(X1,sK7(X3,X4,X0)),X2)
| ( relation_inverse_image(X3,X4) = X0 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369020,c_88]) ).
tcf(c_383007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),relation_dom(X3))
| in(sK7(X3,X4,X0),relation_dom(X1))
| ( relation_inverse_image(X3,X4) = X0 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369020,c_87]) ).
tcf(c_383008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),relation_dom(X3))
| ( relation_inverse_image(X3,X4) = X0 )
| ( apply(X1,sK13(X1,X2,sK7(X3,X4,X0))) = sK7(X3,X4,X0) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369020,c_112]) ).
tcf(c_383009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK7(X1,X2,X0),X3)
| in(sK7(X1,X2,X0),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK10(sK7(X1,X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_369020,c_369085]) ).
tcf(c_383010,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X2,X0),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_369020,c_372426]) ).
tcf(c_383011,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK7(X1,X2,X0))
| in(sK7(X1,X2,X0),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK16(sK7(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_369020,c_370746]) ).
tcf(c_383012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X4,X2),X1)
| in(sK7(X0,X4,X2),X3)
| ( relation_inverse_image(X0,X4) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369020,c_321]) ).
tcf(c_383013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,X2),X3)
| ( relation_inverse_image(X0,X4) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369020,c_320]) ).
tcf(c_383014,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,X2),X3)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ in(relation_dom(X0),sK7(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_369020,c_97]) ).
tcf(c_383017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X3,X0),X1)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369020,c_91]) ).
tcf(c_383018,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X2,X0),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_dom(X1)) ),
inference(equality_factoring,[status(thm)],[c_369020]) ).
tcf(c_383036,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,X0),X1)
| ( relation_inverse_image(empty_set,X2) = X0 )
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_382997,c_372426,c_368630,c_103]) ).
tcf(c_383175,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368545,c_380845]) ).
tcf(c_383176,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,X0))
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380845,c_370745]) ).
tcf(c_383177,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X2) = X0 )
| ~ empty(X2)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_380845,c_60]) ).
tcf(c_383179,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,X1) = X0 )
| ~ empty(X1)
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_380845,c_368558]) ).
tcf(c_383181,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,relation_inverse_image(X0,set_intersection2(X2,X1))) = set_intersection2(X2,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_380845,c_368596]) ).
tcf(c_383205,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,X2))
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381127,c_370745]) ).
tcf(c_383206,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X2) = X0 )
| ~ empty(X1)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_381127,c_60]) ).
tcf(c_383208,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X2) = X0 )
| ~ empty(X1)
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_381127,c_368558]) ).
tcf(c_383210,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,relation_inverse_image(X0,set_intersection2(X1,X2))) = set_intersection2(X1,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_381127,c_368596]) ).
tcf(c_383273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| element(sK10(X0,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369021,c_321]) ).
tcf(c_383274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| ~ empty(X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369021,c_320]) ).
tcf(c_383275,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X1,X2)
| ~ subset(X1,X0)
| ~ in(X0,sK10(X1,X2)) ),
inference(superposition,[status(thm)],[c_369021,c_97]) ).
tcf(c_383276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| in(sK10(X0,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369021,c_96]) ).
tcf(c_383279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| in(sK10(X0,X3),X2)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369021,c_59]) ).
tcf(c_383280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| in(sK10(X0,X3),X1)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369021,c_58]) ).
tcf(c_383281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| in(apply(X1,sK10(X0,X3)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369021,c_88]) ).
tcf(c_383282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| in(sK10(X0,X3),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369021,c_87]) ).
tcf(c_383284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| ( apply(X1,sK13(X1,X2,sK10(X0,X3))) = sK10(X0,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369021,c_112]) ).
tcf(c_383285,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X1)
| subset(sK10(X0,X1),X2)
| ~ subset(X0,sK10(sK10(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_369021,c_369085]) ).
tcf(c_383286,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_369021,c_372426]) ).
tcf(c_383287,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| empty(sK10(X0,X1))
| ~ subset(X0,sK16(sK10(X0,X1))) ),
inference(superposition,[status(thm)],[c_369021,c_370746]) ).
tcf(c_383288,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X1)
| ~ in(sK10(X0,set_intersection2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_369021,c_368972]) ).
tcf(c_383379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X1)
| in(sK2(sK10(X0,X1),X2,X3),X3)
| ( set_intersection2(sK10(X0,X1),X2) = X3 )
| ~ subset(X0,sK2(sK10(X0,X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_369021,c_369076]) ).
tcf(c_383380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,X0),X1)
| in(sK2(sK2(X1,X2,X0),X3,X4),X4)
| ( set_intersection2(X1,X2) = X0 )
| ( set_intersection2(sK2(X1,X2,X0),X3) = X4 )
| ~ subset(X0,sK2(sK2(X1,X2,X0),X3,X4)) ),
inference(superposition,[status(thm)],[c_369015,c_369076]) ).
tcf(c_383381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,X0),X2)
| in(sK2(sK2(X1,X2,X0),X3,X4),X4)
| ( set_intersection2(X1,X2) = X0 )
| ( set_intersection2(sK2(X1,X2,X0),X3) = X4 )
| ~ subset(X0,sK2(sK2(X1,X2,X0),X3,X4)) ),
inference(superposition,[status(thm)],[c_369014,c_369076]) ).
tcf(c_383382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(sK2(X0,X1,X2),X3,X4),X4)
| ( set_intersection2(X0,X1) = X2 )
| ( set_intersection2(sK2(X0,X1,X2),X3) = X4 )
| ~ subset(X0,sK2(sK2(X0,X1,X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_369012,c_369076]) ).
tcf(c_383383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X0,X2),X2)
| in(sK2(sK2(X1,X0,X2),X3,X4),X4)
| ( set_intersection2(X1,X0) = X2 )
| ( set_intersection2(sK2(X1,X0,X2),X3) = X4 )
| ~ subset(X0,sK2(sK2(X1,X0,X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_369013,c_369076]) ).
tcf(c_383384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,X2,X0),relation_dom(X1))
| in(sK2(sK7(X1,X2,X0),X3,X4),X4)
| ( relation_inverse_image(X1,X2) = X0 )
| ( set_intersection2(sK7(X1,X2,X0),X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(sK7(X1,X2,X0),X3,X4)) ),
inference(superposition,[status(thm)],[c_369020,c_369076]) ).
tcf(c_383385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X1,X2,X0)),X2)
| in(sK2(sK7(X1,X2,X0),X3,X4),X4)
| ( relation_inverse_image(X1,X2) = X0 )
| ( set_intersection2(sK7(X1,X2,X0),X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(sK7(X1,X2,X0),X3,X4)) ),
inference(superposition,[status(thm)],[c_369019,c_369076]) ).
tcf(c_383386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,X2),X2)
| in(sK2(sK7(X0,X1,X2),X3,X4),X4)
| ( relation_inverse_image(X0,X1) = X2 )
| ( set_intersection2(sK7(X0,X1,X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(sK7(X0,X1,X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_369017,c_369076]) ).
tcf(c_383387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,X0,X2),X2)
| in(sK2(apply(X1,sK7(X1,X0,X2)),X3,X4),X4)
| ( relation_inverse_image(X1,X0) = X2 )
| ( set_intersection2(apply(X1,sK7(X1,X0,X2)),X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(apply(X1,sK7(X1,X0,X2)),X3,X4)) ),
inference(superposition,[status(thm)],[c_369018,c_369076]) ).
tcf(c_383491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X2)
| in(sK2(X1,sK10(X0,X2),X3),X3)
| ( set_intersection2(X1,sK10(X0,X2)) = X3 )
| ~ subset(X0,sK2(X1,sK10(X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_369021,c_369077]) ).
tcf(c_383492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X0),X2)
| in(sK2(X1,sK2(X2,X3,X0),X4),X4)
| ( set_intersection2(X2,X3) = X0 )
| ( set_intersection2(X1,sK2(X2,X3,X0)) = X4 )
| ~ subset(X0,sK2(X1,sK2(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369015,c_369077]) ).
tcf(c_383493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X0),X3)
| in(sK2(X1,sK2(X2,X3,X0),X4),X4)
| ( set_intersection2(X2,X3) = X0 )
| ( set_intersection2(X1,sK2(X2,X3,X0)) = X4 )
| ~ subset(X0,sK2(X1,sK2(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369014,c_369077]) ).
tcf(c_383494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X2,X3),X3)
| in(sK2(X1,sK2(X0,X2,X3),X4),X4)
| ( set_intersection2(X0,X2) = X3 )
| ( set_intersection2(X1,sK2(X0,X2,X3)) = X4 )
| ~ subset(X0,sK2(X1,sK2(X0,X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_369012,c_369077]) ).
tcf(c_383495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X0,X3),X3)
| in(sK2(X1,sK2(X2,X0,X3),X4),X4)
| ( set_intersection2(X2,X0) = X3 )
| ( set_intersection2(X1,sK2(X2,X0,X3)) = X4 )
| ~ subset(X0,sK2(X1,sK2(X2,X0,X3),X4)) ),
inference(superposition,[status(thm)],[c_369013,c_369077]) ).
tcf(c_383496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X3,X0),relation_dom(X2))
| in(sK2(X1,sK7(X2,X3,X0),X4),X4)
| ( relation_inverse_image(X2,X3) = X0 )
| ( set_intersection2(X1,sK7(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,sK7(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369020,c_369077]) ).
tcf(c_383497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,X3,X0)),X3)
| in(sK2(X1,sK7(X2,X3,X0),X4),X4)
| ( relation_inverse_image(X2,X3) = X0 )
| ( set_intersection2(X1,sK7(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,sK7(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369019,c_369077]) ).
tcf(c_383498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X2,X3),X3)
| in(sK2(X1,sK7(X0,X2,X3),X4),X4)
| ( relation_inverse_image(X0,X2) = X3 )
| ( set_intersection2(X1,sK7(X0,X2,X3)) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(X1,sK7(X0,X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_369017,c_369077]) ).
tcf(c_383499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X0,X3),X3)
| in(sK2(X1,apply(X2,sK7(X2,X0,X3)),X4),X4)
| ( relation_inverse_image(X2,X0) = X3 )
| ( set_intersection2(X1,apply(X2,sK7(X2,X0,X3))) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,apply(X2,sK7(X2,X0,X3)),X4)) ),
inference(superposition,[status(thm)],[c_369018,c_369077]) ).
tcf(c_383558,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(X0,relation_inverse_image(X0,empty_set)),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_383286]) ).
tcf(c_383560,plain,
! [X0: $i] : subset(sK16(powerset(empty_set)),X0),
inference(superposition,[status(thm)],[c_369151,c_383286]) ).
tcf(c_383574,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_373107]) ).
tcf(c_383575,plain,
relation_dom(relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_104,c_373107]) ).
tcf(c_383576,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(X0,X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_373107]) ).
tcf(c_383577,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(set_intersection2(X1,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_373107]) ).
tcf(c_383578,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK16(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_373107]) ).
tcf(c_383594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| in(sK2(X1,X2,sK10(X0,X3)),X2)
| ( set_intersection2(X1,X2) = sK10(X0,X3) )
| ~ subset(X0,sK2(X1,X2,sK10(X0,X3))) ),
inference(superposition,[status(thm)],[c_369021,c_369078]) ).
tcf(c_383595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| in(sK2(X1,X2,sK2(X3,X4,X0)),X2)
| ( set_intersection2(X3,X4) = X0 )
| ( sK2(X3,X4,X0) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369015,c_369078]) ).
tcf(c_383596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| in(sK2(X1,X2,sK2(X3,X4,X0)),X2)
| ( set_intersection2(X3,X4) = X0 )
| ( sK2(X3,X4,X0) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369014,c_369078]) ).
tcf(c_383597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| in(sK2(X1,X2,sK2(X0,X3,X4)),X2)
| ( set_intersection2(X0,X3) = X4 )
| ( sK2(X0,X3,X4) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369012,c_369078]) ).
tcf(c_383598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| in(sK2(X1,X2,sK2(X3,X0,X4)),X2)
| ( set_intersection2(X3,X0) = X4 )
| ( sK2(X3,X0,X4) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369013,c_369078]) ).
tcf(c_383599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),relation_dom(X3))
| in(sK2(X1,X2,sK7(X3,X4,X0)),X2)
| ( relation_inverse_image(X3,X4) = X0 )
| ( sK7(X3,X4,X0) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,sK2(X1,X2,sK7(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369020,c_369078]) ).
tcf(c_383600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X3,X4,X0)),X4)
| in(sK2(X1,X2,sK7(X3,X4,X0)),X2)
| ( relation_inverse_image(X3,X4) = X0 )
| ( sK7(X3,X4,X0) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,sK2(X1,X2,sK7(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369019,c_369078]) ).
tcf(c_383601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| in(sK2(X1,X2,sK7(X0,X3,X4)),X2)
| ( relation_inverse_image(X0,X3) = X4 )
| ( sK7(X0,X3,X4) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(X1,X2,sK7(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369017,c_369078]) ).
tcf(c_383602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| in(sK2(X1,X2,apply(X3,sK7(X3,X0,X4))),X2)
| ( relation_inverse_image(X3,X0) = X4 )
| ( apply(X3,sK7(X3,X0,X4)) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,sK2(X1,X2,apply(X3,sK7(X3,X0,X4)))) ),
inference(superposition,[status(thm)],[c_369018,c_369078]) ).
tcf(c_383693,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| in(sK2(X1,X2,sK10(X0,X3)),X1)
| ( set_intersection2(X1,X2) = sK10(X0,X3) )
| ~ subset(X0,sK2(X1,X2,sK10(X0,X3))) ),
inference(superposition,[status(thm)],[c_369021,c_369079]) ).
tcf(c_383694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| in(sK2(X1,X2,sK2(X3,X4,X0)),X1)
| ( set_intersection2(X3,X4) = X0 )
| ( sK2(X3,X4,X0) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369015,c_369079]) ).
tcf(c_383695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| in(sK2(X1,X2,sK2(X3,X4,X0)),X1)
| ( set_intersection2(X3,X4) = X0 )
| ( sK2(X3,X4,X0) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369014,c_369079]) ).
tcf(c_383696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| in(sK2(X1,X2,sK2(X0,X3,X4)),X1)
| ( set_intersection2(X0,X3) = X4 )
| ( sK2(X0,X3,X4) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369012,c_369079]) ).
tcf(c_383697,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| in(sK2(X1,X2,sK2(X3,X0,X4)),X1)
| ( set_intersection2(X3,X0) = X4 )
| ( sK2(X3,X0,X4) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369013,c_369079]) ).
tcf(c_383698,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),relation_dom(X3))
| in(sK2(X1,X2,sK7(X3,X4,X0)),X1)
| ( relation_inverse_image(X3,X4) = X0 )
| ( sK7(X3,X4,X0) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,sK2(X1,X2,sK7(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369020,c_369079]) ).
tcf(c_383699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X3,X4,X0)),X4)
| in(sK2(X1,X2,sK7(X3,X4,X0)),X1)
| ( relation_inverse_image(X3,X4) = X0 )
| ( sK7(X3,X4,X0) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,sK2(X1,X2,sK7(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369019,c_369079]) ).
tcf(c_383700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| in(sK2(X1,X2,sK7(X0,X3,X4)),X1)
| ( relation_inverse_image(X0,X3) = X4 )
| ( sK7(X0,X3,X4) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(X1,X2,sK7(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369017,c_369079]) ).
tcf(c_383701,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| in(sK2(X1,X2,apply(X3,sK7(X3,X0,X4))),X1)
| ( relation_inverse_image(X3,X0) = X4 )
| ( apply(X3,sK7(X3,X0,X4)) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,sK2(X1,X2,apply(X3,sK7(X3,X0,X4)))) ),
inference(superposition,[status(thm)],[c_369018,c_369079]) ).
tcf(c_383760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(set_intersection2(X2,X3),X1)
| ~ in(set_intersection2(X2,X3),X0)
| ~ in(set_intersection2(X0,X1),X3)
| ~ in(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_57,c_369080]) ).
tcf(c_383762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(set_intersection2(X3,X4),relation_dom(X0))
| ~ in(apply(X0,set_intersection2(X3,X4)),X2)
| ~ in(apply(X0,set_intersection2(X3,X4)),X1)
| ~ in(relation_inverse_image(X0,set_intersection2(X1,X2)),X4)
| ~ in(relation_inverse_image(X0,set_intersection2(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_368735,c_369080]) ).
tcf(c_383785,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(X0),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_379152]) ).
tcf(c_383787,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_379152]) ).
tcf(c_383788,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,X0),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_379152]) ).
tcf(c_383789,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK16(powerset(X0)),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_379152]) ).
tcf(c_383819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X2)
| in(sK7(X1,sK10(X0,X2),X3),X3)
| ( relation_inverse_image(X1,sK10(X0,X2)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK10(X0,X2),X3))) ),
inference(superposition,[status(thm)],[c_369021,c_369082]) ).
tcf(c_383820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X0),X2)
| in(sK7(X1,sK2(X2,X3,X0),X4),X4)
| ( set_intersection2(X2,X3) = X0 )
| ( relation_inverse_image(X1,sK2(X2,X3,X0)) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK2(X2,X3,X0),X4))) ),
inference(superposition,[status(thm)],[c_369015,c_369082]) ).
tcf(c_383821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X0),X3)
| in(sK7(X1,sK2(X2,X3,X0),X4),X4)
| ( set_intersection2(X2,X3) = X0 )
| ( relation_inverse_image(X1,sK2(X2,X3,X0)) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK2(X2,X3,X0),X4))) ),
inference(superposition,[status(thm)],[c_369014,c_369082]) ).
tcf(c_383822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X2,X3),X3)
| in(sK7(X1,sK2(X0,X2,X3),X4),X4)
| ( set_intersection2(X0,X2) = X3 )
| ( relation_inverse_image(X1,sK2(X0,X2,X3)) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK2(X0,X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_369012,c_369082]) ).
tcf(c_383823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X0,X3),X3)
| in(sK7(X1,sK2(X2,X0,X3),X4),X4)
| ( set_intersection2(X2,X0) = X3 )
| ( relation_inverse_image(X1,sK2(X2,X0,X3)) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK2(X2,X0,X3),X4))) ),
inference(superposition,[status(thm)],[c_369013,c_369082]) ).
tcf(c_383824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X3,X0),relation_dom(X2))
| in(sK7(X1,sK7(X2,X3,X0),X4),X4)
| ( relation_inverse_image(X2,X3) = X0 )
| ( relation_inverse_image(X1,sK7(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK7(X2,X3,X0),X4))) ),
inference(superposition,[status(thm)],[c_369020,c_369082]) ).
tcf(c_383825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,X3,X0)),X3)
| in(sK7(X1,sK7(X2,X3,X0),X4),X4)
| ( relation_inverse_image(X2,X3) = X0 )
| ( relation_inverse_image(X1,sK7(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK7(X2,X3,X0),X4))) ),
inference(superposition,[status(thm)],[c_369019,c_369082]) ).
tcf(c_383826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X2,X3),X3)
| in(sK7(X1,sK7(X0,X2,X3),X4),X4)
| ( relation_inverse_image(X0,X2) = X3 )
| ( relation_inverse_image(X1,sK7(X0,X2,X3)) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),apply(X1,sK7(X1,sK7(X0,X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_369017,c_369082]) ).
tcf(c_383827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X0,X3),X3)
| in(sK7(X1,apply(X2,sK7(X2,X0,X3)),X4),X4)
| ( relation_inverse_image(X2,X0) = X3 )
| ( relation_inverse_image(X1,apply(X2,sK7(X2,X0,X3))) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,apply(X2,sK7(X2,X0,X3)),X4))) ),
inference(superposition,[status(thm)],[c_369018,c_369082]) ).
tcf(c_383908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| in(apply(X1,sK7(X1,X2,sK10(X0,X3))),X2)
| ( relation_inverse_image(X1,X2) = sK10(X0,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK10(X0,X3))) ),
inference(superposition,[status(thm)],[c_369021,c_369083]) ).
tcf(c_383909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| in(apply(X1,sK7(X1,X2,sK2(X3,X4,X0))),X2)
| ( set_intersection2(X3,X4) = X0 )
| ( sK2(X3,X4,X0) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369015,c_369083]) ).
tcf(c_383910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| in(apply(X1,sK7(X1,X2,sK2(X3,X4,X0))),X2)
| ( set_intersection2(X3,X4) = X0 )
| ( sK2(X3,X4,X0) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369014,c_369083]) ).
tcf(c_383911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| in(apply(X1,sK7(X1,X2,sK2(X0,X3,X4))),X2)
| ( set_intersection2(X0,X3) = X4 )
| ( sK2(X0,X3,X4) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369012,c_369083]) ).
tcf(c_383912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| in(apply(X1,sK7(X1,X2,sK2(X3,X0,X4))),X2)
| ( set_intersection2(X3,X0) = X4 )
| ( sK2(X3,X0,X4) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369013,c_369083]) ).
tcf(c_383913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),relation_dom(X3))
| in(apply(X1,sK7(X1,X2,sK7(X3,X4,X0))),X2)
| ( relation_inverse_image(X3,X4) = X0 )
| ( sK7(X3,X4,X0) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK7(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369020,c_369083]) ).
tcf(c_383914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X3,X4,X0)),X4)
| in(apply(X1,sK7(X1,X2,sK7(X3,X4,X0))),X2)
| ( relation_inverse_image(X3,X4) = X0 )
| ( sK7(X3,X4,X0) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK7(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369019,c_369083]) ).
tcf(c_383915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| in(apply(X1,sK7(X1,X2,sK7(X0,X3,X4))),X2)
| ( relation_inverse_image(X0,X3) = X4 )
| ( sK7(X0,X3,X4) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK7(X1,X2,sK7(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369017,c_369083]) ).
tcf(c_383916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| in(apply(X1,sK7(X1,X2,apply(X3,sK7(X3,X0,X4)))),X2)
| ( relation_inverse_image(X3,X0) = X4 )
| ( apply(X3,sK7(X3,X0,X4)) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,apply(X3,sK7(X3,X0,X4)))) ),
inference(superposition,[status(thm)],[c_369018,c_369083]) ).
tcf(c_384186,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_379213]) ).
tcf(c_384188,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X0,X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_379213]) ).
tcf(c_384189,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X2,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_379213]) ).
tcf(c_384190,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,sK16(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_379213]) ).
tcf(c_384210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| in(sK7(X1,X2,sK10(X0,X3)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = sK10(X0,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK10(X0,X3))) ),
inference(superposition,[status(thm)],[c_369021,c_369084]) ).
tcf(c_384211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| in(sK7(X1,X2,sK2(X3,X4,X0)),relation_dom(X1))
| ( set_intersection2(X3,X4) = X0 )
| ( sK2(X3,X4,X0) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369015,c_369084]) ).
tcf(c_384212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| in(sK7(X1,X2,sK2(X3,X4,X0)),relation_dom(X1))
| ( set_intersection2(X3,X4) = X0 )
| ( sK2(X3,X4,X0) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369014,c_369084]) ).
tcf(c_384213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| in(sK7(X1,X2,sK2(X0,X3,X4)),relation_dom(X1))
| ( set_intersection2(X0,X3) = X4 )
| ( sK2(X0,X3,X4) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369012,c_369084]) ).
tcf(c_384214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| in(sK7(X1,X2,sK2(X3,X0,X4)),relation_dom(X1))
| ( set_intersection2(X3,X0) = X4 )
| ( sK2(X3,X0,X4) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369013,c_369084]) ).
tcf(c_384215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),relation_dom(X3))
| in(sK7(X1,X2,sK7(X3,X4,X0)),relation_dom(X1))
| ( relation_inverse_image(X3,X4) = X0 )
| ( sK7(X3,X4,X0) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK7(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369020,c_369084]) ).
tcf(c_384216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X3,X4,X0)),X4)
| in(sK7(X1,X2,sK7(X3,X4,X0)),relation_dom(X1))
| ( relation_inverse_image(X3,X4) = X0 )
| ( sK7(X3,X4,X0) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK7(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369019,c_369084]) ).
tcf(c_384217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| in(sK7(X1,X2,sK7(X0,X3,X4)),relation_dom(X1))
| ( relation_inverse_image(X0,X3) = X4 )
| ( sK7(X0,X3,X4) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK7(X1,X2,sK7(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369017,c_369084]) ).
tcf(c_384218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| in(sK7(X1,X2,apply(X3,sK7(X3,X0,X4))),relation_dom(X1))
| ( relation_inverse_image(X3,X0) = X4 )
| ( apply(X3,sK7(X3,X0,X4)) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,apply(X3,sK7(X3,X0,X4)))) ),
inference(superposition,[status(thm)],[c_369018,c_369084]) ).
tcf(c_384325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| in(sK12(X1,X2,sK10(X0,X3)),relation_dom(X1))
| ( relation_image(X1,X2) = sK10(X0,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK10(X0,X3))) ),
inference(superposition,[status(thm)],[c_369021,c_369205]) ).
tcf(c_384326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| in(sK12(X1,X2,sK2(X3,X4,X0)),relation_dom(X1))
| ( set_intersection2(X3,X4) = X0 )
| ( sK2(X3,X4,X0) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369015,c_369205]) ).
tcf(c_384327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| in(sK12(X1,X2,sK2(X3,X4,X0)),relation_dom(X1))
| ( set_intersection2(X3,X4) = X0 )
| ( sK2(X3,X4,X0) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369014,c_369205]) ).
tcf(c_384328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| in(sK12(X1,X2,sK2(X0,X3,X4)),relation_dom(X1))
| ( set_intersection2(X0,X3) = X4 )
| ( sK2(X0,X3,X4) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369012,c_369205]) ).
tcf(c_384329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| in(sK12(X1,X2,sK2(X3,X0,X4)),relation_dom(X1))
| ( set_intersection2(X3,X0) = X4 )
| ( sK2(X3,X0,X4) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369013,c_369205]) ).
tcf(c_384330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),relation_dom(X3))
| in(sK12(X1,X2,sK7(X3,X4,X0)),relation_dom(X1))
| ( relation_inverse_image(X3,X4) = X0 )
| ( sK7(X3,X4,X0) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK7(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369020,c_369205]) ).
tcf(c_384331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X3,X4,X0)),X4)
| in(sK12(X1,X2,sK7(X3,X4,X0)),relation_dom(X1))
| ( relation_inverse_image(X3,X4) = X0 )
| ( sK7(X3,X4,X0) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK7(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369019,c_369205]) ).
tcf(c_384332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| in(sK12(X1,X2,sK7(X0,X3,X4)),relation_dom(X1))
| ( relation_inverse_image(X0,X3) = X4 )
| ( sK7(X0,X3,X4) = relation_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK11(X1,X2,sK7(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369017,c_369205]) ).
tcf(c_384333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| in(sK12(X1,X2,apply(X3,sK7(X3,X0,X4))),relation_dom(X1))
| ( relation_inverse_image(X3,X0) = X4 )
| ( apply(X3,sK7(X3,X0,X4)) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,apply(X3,sK7(X3,X0,X4)))) ),
inference(superposition,[status(thm)],[c_369018,c_369205]) ).
tcf(c_384467,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(empty_set,X2,X0),empty_set)
| in(sK11(empty_set,X2,X0),X1)
| ( relation_image(empty_set,X2) = X0 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_373108,c_369206]) ).
tcf(c_384468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X3,X4,X0),X2)
| in(sK12(X3,X4,X0),relation_dom(X3))
| ( relation_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369206,c_321]) ).
tcf(c_384469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),relation_dom(X3))
| ( relation_image(X3,X4) = X0 )
| ~ empty(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369206,c_320]) ).
tcf(c_384470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,X3),relation_dom(X1))
| ( relation_image(X1,X2) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X0)
| ~ in(X0,sK11(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_369206,c_97]) ).
tcf(c_384471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X4,X0),X2)
| in(sK12(X3,X4,X0),relation_dom(X3))
| ( relation_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369206,c_96]) ).
tcf(c_384474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X4,X0),X2)
| in(sK12(X3,X4,X0),relation_dom(X3))
| ( relation_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369206,c_59]) ).
tcf(c_384475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X4,X0),X1)
| in(sK12(X3,X4,X0),relation_dom(X3))
| ( relation_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369206,c_58]) ).
tcf(c_384476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),relation_dom(X3))
| in(apply(X1,sK11(X3,X4,X0)),X2)
| ( relation_image(X3,X4) = X0 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369206,c_88]) ).
tcf(c_384477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),relation_dom(X3))
| in(sK11(X3,X4,X0),relation_dom(X1))
| ( relation_image(X3,X4) = X0 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369206,c_87]) ).
tcf(c_384478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),relation_dom(X3))
| ( relation_image(X3,X4) = X0 )
| ( apply(X1,sK13(X1,X2,sK11(X3,X4,X0))) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369206,c_112]) ).
tcf(c_384479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK11(X1,X2,X0),X3)
| in(sK12(X1,X2,X0),relation_dom(X1))
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK10(sK11(X1,X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_369206,c_369085]) ).
tcf(c_384480,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X1,X2,X0),relation_dom(X1))
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_369206,c_372426]) ).
tcf(c_384481,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK11(X1,X2,X0))
| in(sK12(X1,X2,X0),relation_dom(X1))
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK16(sK11(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_369206,c_370746]) ).
tcf(c_384482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),relation_dom(X3))
| in(sK2(X1,X2,sK11(X3,X4,X0)),X1)
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,sK2(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369206,c_369079]) ).
tcf(c_384483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),relation_dom(X3))
| in(sK2(X1,X2,sK11(X3,X4,X0)),X2)
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,sK2(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369206,c_369078]) ).
tcf(c_384484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X2,X0),relation_dom(X1))
| in(sK2(sK11(X1,X2,X0),X3,X4),X4)
| ( relation_image(X1,X2) = X0 )
| ( set_intersection2(sK11(X1,X2,X0),X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(sK11(X1,X2,X0),X3,X4)) ),
inference(superposition,[status(thm)],[c_369206,c_369076]) ).
tcf(c_384485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X3,X0),relation_dom(X2))
| in(sK2(X1,sK11(X2,X3,X0),X4),X4)
| ( relation_image(X2,X3) = X0 )
| ( set_intersection2(X1,sK11(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,sK11(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369206,c_369077]) ).
tcf(c_384486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),relation_dom(X3))
| in(sK12(X1,X2,sK11(X3,X4,X0)),relation_dom(X1))
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369206,c_369205]) ).
tcf(c_384487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),relation_dom(X3))
| in(sK7(X1,X2,sK11(X3,X4,X0)),relation_dom(X1))
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369206,c_369084]) ).
tcf(c_384488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),relation_dom(X3))
| in(apply(X1,sK7(X1,X2,sK11(X3,X4,X0))),X2)
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369206,c_369083]) ).
tcf(c_384489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X3,X0),relation_dom(X2))
| in(sK7(X1,sK11(X2,X3,X0),X4),X4)
| ( relation_image(X2,X3) = X0 )
| ( relation_inverse_image(X1,sK11(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK11(X2,X3,X0),X4))) ),
inference(superposition,[status(thm)],[c_369206,c_369082]) ).
tcf(c_384490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X4,X2),X1)
| in(sK11(X0,X4,X2),X3)
| ( relation_image(X0,X4) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369206,c_321]) ).
tcf(c_384491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X4,X2),X3)
| ( relation_image(X0,X4) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369206,c_320]) ).
tcf(c_384492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,X2),X3)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ in(relation_dom(X0),sK12(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_369206,c_97]) ).
tcf(c_384493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,X2),X1)
| in(sK11(X0,X4,X2),X3)
| ( relation_image(X0,X4) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369206,c_96]) ).
tcf(c_384494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X2,X3,X0),X1)
| element(sK12(X2,X3,X0),relation_dom(X2))
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369206,c_93]) ).
tcf(c_384495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X2,X3,X0),X1)
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369206,c_91]) ).
tcf(c_384507,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(empty_set,X2,X0),X1)
| ( relation_image(empty_set,X2) = X0 )
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_384467,c_372426,c_368630,c_103]) ).
tcf(c_384709,plain,
! [X0: $i,X1: $i] :
( in(sK12(empty_set,X0,X1),empty_set)
| element(sK11(empty_set,X0,X1),X1)
| ( relation_image(empty_set,X0) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_369207]) ).
tcf(c_384711,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK11(X0,X1,powerset(X2)),X2)
| in(sK12(X0,X1,powerset(X2)),relation_dom(X0))
| ( relation_image(X0,X1) = powerset(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369207,c_99]) ).
tcf(c_384712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X2,X3),X1)
| element(sK11(X0,X2,X3),X3)
| ( relation_image(X0,X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369207,c_321]) ).
tcf(c_384713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,X2,X3),X3)
| ( relation_image(X0,X2) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369207,c_320]) ).
tcf(c_384714,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK12(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_369207,c_97]) ).
tcf(c_384715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,X2,X3),X3)
| in(sK12(X0,X2,X3),X1)
| ( relation_image(X0,X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369207,c_96]) ).
tcf(c_384716,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK11(X0,X1,X2),X2)
| element(sK12(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369207,c_93]) ).
tcf(c_384717,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369207,c_91]) ).
tcf(c_384723,plain,
! [X0: $i,X1: $i] :
( in(sK12(empty_set,X1,X0),empty_set)
| element(sK11(empty_set,X1,X0),X0)
| ( X0 = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_384709,c_375097]) ).
tcf(c_384724,plain,
! [X0: $i,X1: $i] :
( element(sK11(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_384723,c_372426,c_368630,c_103]) ).
tcf(c_384782,plain,
! [X0: $i,X1: $i] :
( in(sK12(empty_set,X1,X0),empty_set)
| ( relation_image(empty_set,X1) = X0 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_373108,c_369208]) ).
tcf(c_384783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X3,X2),X1)
| ( relation_image(X0,X3) = X2 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369208,c_321]) ).
tcf(c_384784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X3) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369208,c_320]) ).
tcf(c_384785,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = X2 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK12(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_369208,c_97]) ).
tcf(c_384786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,X2),X1)
| ( relation_image(X0,X3) = X2 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369208,c_96]) ).
tcf(c_384787,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK12(X0,X2,X1),relation_dom(X0))
| ( relation_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369208,c_93]) ).
tcf(c_384788,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369208,c_91]) ).
tcf(c_384833,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),X2)
| in(sK12(X0,X1,set_intersection2(X2,X2)),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(X2,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_369209]) ).
tcf(c_384834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X3,X2)),X3)
| in(sK12(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_369209]) ).
tcf(c_384837,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,empty_set),X2)
| in(sK12(X0,X1,set_intersection2(empty_set,X2)),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_369209]) ).
tcf(c_384838,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,X2),relation_dom(X0))
| in(sK11(X0,X1,set_intersection2(X2,X2)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_369209]) ).
tcf(c_384839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK12(X0,X1,set_intersection2(X3,X2)),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_369209]) ).
tcf(c_384841,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),relation_dom(X0))
| in(sK11(X0,X1,set_intersection2(X2,empty_set)),empty_set)
| ( relation_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_369209]) ).
tcf(c_384842,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),relation_dom(X0))
| in(sK11(X0,X1,set_intersection2(empty_set,X2)),X2)
| ( relation_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_369209]) ).
tcf(c_384843,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(empty_set,X2,set_intersection2(X0,X1)),empty_set)
| in(sK11(empty_set,X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = relation_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_369209]) ).
tcf(c_384844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,X3,set_intersection2(X4,X0)),X1)
| in(sK12(X2,X3,set_intersection2(X4,X0)),relation_dom(X2))
| ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369209,c_321]) ).
tcf(c_384845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X3,set_intersection2(X4,X0)),relation_dom(X2))
| ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369209,c_320]) ).
tcf(c_384846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,set_intersection2(X3,X0)),relation_dom(X1))
| ( relation_image(X1,X2) = set_intersection2(X3,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK11(X1,X2,set_intersection2(X3,X0))) ),
inference(superposition,[status(thm)],[c_369209,c_97]) ).
tcf(c_384847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,X3,set_intersection2(X4,X0)),X1)
| in(sK12(X2,X3,set_intersection2(X4,X0)),relation_dom(X2))
| ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369209,c_96]) ).
tcf(c_384848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK12(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369209,c_93]) ).
tcf(c_384849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X2,set_intersection2(X3,X1)),relation_dom(X0))
| ( relation_image(X0,X2) = set_intersection2(X3,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369209,c_91]) ).
tcf(c_384850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X4,set_intersection2(X1,set_intersection2(X2,X3))),X3)
| in(sK12(X0,X4,set_intersection2(X1,set_intersection2(X2,X3))),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369209,c_59]) ).
tcf(c_384851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X4,set_intersection2(X1,set_intersection2(X2,X3))),X2)
| in(sK12(X0,X4,set_intersection2(X1,set_intersection2(X2,X3))),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369209,c_58]) ).
tcf(c_384852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3))),relation_dom(X0))
| in(apply(X1,sK11(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3)))),X3)
| ( set_intersection2(X2,relation_inverse_image(X1,X3)) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369209,c_88]) ).
tcf(c_384853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3))),relation_dom(X0))
| in(sK11(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3))),relation_dom(X1))
| ( set_intersection2(X2,relation_inverse_image(X1,X3)) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369209,c_87]) ).
tcf(c_384854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X3,set_intersection2(X4,relation_image(X1,X2))),relation_dom(X0))
| ( set_intersection2(X4,relation_image(X1,X2)) = relation_image(X0,X3) )
| ( apply(X1,sK13(X1,X2,sK11(X0,X3,set_intersection2(X4,relation_image(X1,X2))))) = sK11(X0,X3,set_intersection2(X4,relation_image(X1,X2))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369209,c_112]) ).
tcf(c_384855,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,set_intersection2(X2,empty_set)),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369209,c_372426]) ).
tcf(c_384856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X2,set_intersection2(X3,X4)),X1)
| in(sK11(X0,X2,set_intersection2(X3,X4)),X4)
| ( relation_image(X0,X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369209,c_321]) ).
tcf(c_384857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X2,set_intersection2(X3,X4)),X4)
| ( relation_image(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369209,c_320]) ).
tcf(c_384858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK12(X0,X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_369209,c_97]) ).
tcf(c_384859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X2,set_intersection2(X3,X4)),X1)
| in(sK11(X0,X2,set_intersection2(X3,X4)),X4)
| ( relation_image(X0,X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369209,c_96]) ).
tcf(c_384860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| element(sK12(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369209,c_93]) ).
tcf(c_384861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369209,c_91]) ).
tcf(c_384881,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_384841,c_372426]) ).
tcf(c_384913,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(empty_set,X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = relation_image(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_384843,c_372426,c_368630,c_103]) ).
tcf(c_385145,plain,
! [X0: $i] :
( ( sK16(powerset(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_380415]) ).
tcf(c_385147,plain,
! [X0: $i,X1: $i] :
( ( sK16(powerset(set_intersection2(X0,X1))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_380415]) ).
tcf(c_385148,plain,
! [X0: $i,X1: $i] :
( ( sK16(powerset(set_intersection2(X1,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_380415]) ).
tcf(c_385149,plain,
! [X0: $i] :
( ( sK16(powerset(sK16(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_380415]) ).
tcf(c_385164,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368984,c_369791]) ).
tcf(c_385166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X2,X3)
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369791]) ).
tcf(c_385167,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_image(X0,X1),X2)
| ~ relation(X0)
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_67,c_369791]) ).
tcf(c_385168,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_image(X0,relation_inverse_image(X0,X1)),X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_369791]) ).
tcf(c_385170,plain,
! [X0: $i,X1: $i] :
( subset(sK16(powerset(X0)),X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_369151,c_369791]) ).
tcf(c_385172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X0,X2),X3)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381127,c_369791]) ).
tcf(c_385173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X2,X0),X3)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380845,c_369791]) ).
tcf(c_385265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X3,X2)),X2)
| in(sK12(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_369210]) ).
tcf(c_385270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK12(X0,X1,set_intersection2(X3,X2)),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_369210]) ).
tcf(c_385272,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),relation_dom(X0))
| in(sK11(X0,X1,set_intersection2(X2,empty_set)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_369210]) ).
tcf(c_385273,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),relation_dom(X0))
| in(sK11(X0,X1,set_intersection2(empty_set,X2)),empty_set)
| ( relation_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_369210]) ).
tcf(c_385274,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(empty_set,X2,set_intersection2(X0,X1)),empty_set)
| in(sK11(empty_set,X2,set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = relation_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_369210]) ).
tcf(c_385275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,X3,set_intersection2(X0,X4)),X1)
| in(sK12(X2,X3,set_intersection2(X0,X4)),relation_dom(X2))
| ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369210,c_321]) ).
tcf(c_385276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X3,set_intersection2(X0,X4)),relation_dom(X2))
| ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369210,c_320]) ).
tcf(c_385277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,set_intersection2(X0,X3)),relation_dom(X1))
| ( relation_image(X1,X2) = set_intersection2(X0,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK11(X1,X2,set_intersection2(X0,X3))) ),
inference(superposition,[status(thm)],[c_369210,c_97]) ).
tcf(c_385278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,X3,set_intersection2(X0,X4)),X1)
| in(sK12(X2,X3,set_intersection2(X0,X4)),relation_dom(X2))
| ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369210,c_96]) ).
tcf(c_385279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK12(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369210,c_93]) ).
tcf(c_385280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X2,set_intersection2(X1,X3)),relation_dom(X0))
| ( relation_image(X0,X2) = set_intersection2(X1,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369210,c_91]) ).
tcf(c_385281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X4,set_intersection2(set_intersection2(X1,X2),X3)),X2)
| in(sK12(X0,X4,set_intersection2(set_intersection2(X1,X2),X3)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369210,c_59]) ).
tcf(c_385282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X4,set_intersection2(set_intersection2(X1,X2),X3)),X1)
| in(sK12(X0,X4,set_intersection2(set_intersection2(X1,X2),X3)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369210,c_58]) ).
tcf(c_385283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3)),relation_dom(X0))
| in(apply(X1,sK11(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3))),X2)
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369210,c_88]) ).
tcf(c_385284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3)),relation_dom(X0))
| in(sK11(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3)),relation_dom(X1))
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369210,c_87]) ).
tcf(c_385285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X3,set_intersection2(relation_image(X1,X2),X4)),relation_dom(X0))
| ( set_intersection2(relation_image(X1,X2),X4) = relation_image(X0,X3) )
| ( apply(X1,sK13(X1,X2,sK11(X0,X3,set_intersection2(relation_image(X1,X2),X4)))) = sK11(X0,X3,set_intersection2(relation_image(X1,X2),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369210,c_112]) ).
tcf(c_385286,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,set_intersection2(empty_set,X2)),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369210,c_372426]) ).
tcf(c_385287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X2,set_intersection2(X3,X4)),X1)
| in(sK11(X0,X2,set_intersection2(X3,X4)),X3)
| ( relation_image(X0,X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369210,c_321]) ).
tcf(c_385288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X2,set_intersection2(X3,X4)),X3)
| ( relation_image(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369210,c_320]) ).
tcf(c_385289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK12(X0,X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_369210,c_97]) ).
tcf(c_385290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X2,set_intersection2(X3,X4)),X1)
| in(sK11(X0,X2,set_intersection2(X3,X4)),X3)
| ( relation_image(X0,X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369210,c_96]) ).
tcf(c_385291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| element(sK12(X0,X1,set_intersection2(X2,X3)),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369210,c_93]) ).
tcf(c_385292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369210,c_91]) ).
tcf(c_385307,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),relation_dom(X0))
| ( relation_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_385273,c_372426]) ).
tcf(c_385329,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(empty_set,X2,set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = relation_image(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_385274,c_372426,c_368630,c_103]) ).
tcf(c_385653,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),relation_dom(X0))
| in(apply(empty_set,sK11(X0,X1,relation_inverse_image(empty_set,X2))),X2)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_369211]) ).
tcf(c_385654,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(empty_set,X2,relation_inverse_image(X0,X1)),empty_set)
| in(apply(X0,sK11(empty_set,X2,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = relation_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373108,c_369211]) ).
tcf(c_385655,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,sK11(X0,X1,empty_set)),X2)
| in(sK12(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(X0))
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_369211]) ).
tcf(c_385656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X4,relation_inverse_image(X2,X3)),X1)
| in(apply(X2,sK11(X0,X4,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = relation_image(X0,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369211,c_321]) ).
tcf(c_385657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK11(X0,X4,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = relation_image(X0,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369211,c_320]) ).
tcf(c_385658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK11(X0,X1,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK12(X0,X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369211,c_97]) ).
tcf(c_385659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_inverse_image(X2,X3)),X1)
| in(apply(X2,sK11(X0,X4,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = relation_image(X0,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369211,c_96]) ).
tcf(c_385660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X0))
| in(apply(X1,sK11(X0,X3,relation_inverse_image(X1,X2))),X2)
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369211,c_93]) ).
tcf(c_385661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK11(X0,X3,relation_inverse_image(X1,X2))),X2)
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369211,c_91]) ).
tcf(c_385662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X4,relation_inverse_image(X3,X0)),relation_dom(X2))
| element(apply(X3,sK11(X2,X4,relation_inverse_image(X3,X0))),X1)
| ( relation_inverse_image(X3,X0) = relation_image(X2,X4) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369211,c_321]) ).
tcf(c_385663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X4,relation_inverse_image(X3,X0)),relation_dom(X2))
| ( relation_inverse_image(X3,X0) = relation_image(X2,X4) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369211,c_320]) ).
tcf(c_385664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X2,X3,relation_inverse_image(X1,X0)),relation_dom(X2))
| ( relation_inverse_image(X1,X0) = relation_image(X2,X3) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK11(X2,X3,relation_inverse_image(X1,X0)))) ),
inference(superposition,[status(thm)],[c_369211,c_97]) ).
tcf(c_385665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X4,relation_inverse_image(X3,X0)),relation_dom(X2))
| in(apply(X3,sK11(X2,X4,relation_inverse_image(X3,X0))),X1)
| ( relation_inverse_image(X3,X0) = relation_image(X2,X4) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369211,c_96]) ).
tcf(c_385666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X0))
| element(apply(X1,sK11(X0,X3,relation_inverse_image(X1,X2))),X2)
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369211,c_93]) ).
tcf(c_385667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X0))
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369211,c_91]) ).
tcf(c_385668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3))),relation_dom(X0))
| in(apply(X1,sK11(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3)))),X3)
| ( relation_inverse_image(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369211,c_59]) ).
tcf(c_385669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3))),relation_dom(X0))
| in(apply(X1,sK11(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3)))),X2)
| ( relation_inverse_image(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369211,c_58]) ).
tcf(c_385670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X0))
| in(sK11(X0,X1,relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3))
| ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2)) ),
inference(superposition,[status(thm)],[c_369211,c_86]) ).
tcf(c_385671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3))),relation_dom(X0))
| in(apply(X2,apply(X1,sK11(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3))))),X3)
| ( relation_inverse_image(X1,relation_inverse_image(X2,X3)) = relation_image(X0,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369211,c_88]) ).
tcf(c_385672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3))),relation_dom(X0))
| in(apply(X1,sK11(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3)))),relation_dom(X2))
| ( relation_inverse_image(X1,relation_inverse_image(X2,X3)) = relation_image(X0,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369211,c_87]) ).
tcf(c_385673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_inverse_image(X1,relation_image(X2,X3))),relation_dom(X0))
| ( relation_inverse_image(X1,relation_image(X2,X3)) = relation_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,apply(X1,sK11(X0,X4,relation_inverse_image(X1,relation_image(X2,X3)))))) = apply(X1,sK11(X0,X4,relation_inverse_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369211,c_112]) ).
tcf(c_385674,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,relation_inverse_image(X1,empty_set)),relation_dom(X0))
| ( relation_image(X0,X2) = relation_inverse_image(X1,empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369211,c_372426]) ).
tcf(c_385703,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,sK11(X0,X1,empty_set)),X2)
| in(sK12(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(X0))
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_385655,c_368630,c_103]) ).
tcf(c_385709,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),relation_dom(X0))
| in(apply(empty_set,sK11(X0,X1,relation_inverse_image(empty_set,X2))),X2)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_385653,c_368630,c_103]) ).
tcf(c_385723,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK11(empty_set,X2,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = relation_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_385654,c_372426,c_368630,c_103]) ).
tcf(c_386024,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),relation_dom(X0))
| in(sK11(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(empty_set))
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_369212]) ).
tcf(c_386025,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(empty_set,X2,relation_inverse_image(X0,X1)),empty_set)
| in(sK11(empty_set,X2,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373108,c_369212]) ).
tcf(c_386026,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,empty_set),relation_dom(empty_set))
| in(sK12(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(X0))
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_369212]) ).
tcf(c_386027,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,relation_inverse_image(empty_set,X2)),empty_set)
| in(sK12(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(X0))
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373108,c_369212]) ).
tcf(c_386028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X4,relation_inverse_image(X2,X3)),X1)
| in(sK11(X0,X4,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = relation_image(X0,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369212,c_321]) ).
tcf(c_386029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X4,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = relation_image(X0,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369212,c_320]) ).
tcf(c_386030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK12(X0,X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369212,c_97]) ).
tcf(c_386031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_inverse_image(X2,X3)),X1)
| in(sK11(X0,X4,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = relation_image(X0,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369212,c_96]) ).
tcf(c_386032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X0))
| in(sK11(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369212,c_93]) ).
tcf(c_386033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369212,c_91]) ).
tcf(c_386034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,X4,relation_inverse_image(X0,X3)),X1)
| in(sK12(X2,X4,relation_inverse_image(X0,X3)),relation_dom(X2))
| ( relation_inverse_image(X0,X3) = relation_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369212,c_321]) ).
tcf(c_386035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X4,relation_inverse_image(X0,X3)),relation_dom(X2))
| ( relation_inverse_image(X0,X3) = relation_image(X2,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369212,c_320]) ).
tcf(c_386036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,relation_inverse_image(X0,X3)),relation_dom(X1))
| ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK11(X1,X2,relation_inverse_image(X0,X3))) ),
inference(superposition,[status(thm)],[c_369212,c_97]) ).
tcf(c_386037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,X4,relation_inverse_image(X0,X3)),X1)
| in(sK12(X2,X4,relation_inverse_image(X0,X3)),relation_dom(X2))
| ( relation_inverse_image(X0,X3) = relation_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369212,c_96]) ).
tcf(c_386038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X1))
| in(sK12(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X0))
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369212,c_93]) ).
tcf(c_386039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X3,relation_inverse_image(X0,X2)),relation_dom(X1))
| ( relation_inverse_image(X0,X2) = relation_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369212,c_91]) ).
tcf(c_386054,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,empty_set),empty_set)
| in(sK12(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(X0))
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_386026,c_373108]) ).
tcf(c_386055,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(X0))
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_386054,c_372426,c_368630,c_103]) ).
tcf(c_386060,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),relation_dom(X0))
| in(sK11(X0,X1,relation_inverse_image(empty_set,X2)),empty_set)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_386024,c_373108]) ).
tcf(c_386061,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),relation_dom(X0))
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_386060,c_372426,c_368630,c_103]) ).
tcf(c_386083,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(empty_set,X2,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_386025,c_372426,c_368630,c_103]) ).
tcf(c_386195,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK16(powerset(X0)),X2)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_385170,c_369791]) ).
tcf(c_386196,plain,
! [X0: $i,X1: $i] :
( empty(sK16(powerset(X0)))
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_385170,c_370745]) ).
tcf(c_386197,plain,
! [X0: $i,X1: $i] :
( ( sK16(powerset(X1)) = X0 )
| ~ empty(X1)
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_385170,c_60]) ).
tcf(c_386200,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,relation_inverse_image(X0,sK16(powerset(X1)))) = sK16(powerset(X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_385170,c_368596]) ).
tcf(c_386237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X3,X4),X2)
| in(sK11(X0,X3,X4),X4)
| ( relation_image(X0,X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X1,X2)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_321]) ).
tcf(c_386238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X3,X4),X4)
| ( relation_image(X0,X3) = X4 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X1,X2)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_320]) ).
tcf(c_386239,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,X2,X3),X3)
| ( relation_image(X1,X2) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X0)
| ~ in(X0,sK12(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_369214,c_97]) ).
tcf(c_386240,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X3,X4),X2)
| in(sK11(X0,X3,X4),X4)
| ( relation_image(X0,X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X1,X2)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_96]) ).
tcf(c_386243,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X3,X4),X2)
| in(sK11(X0,X3,X4),X4)
| ( relation_image(X0,X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369214,c_59]) ).
tcf(c_386244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X3,X4),X1)
| in(sK11(X0,X3,X4),X4)
| ( relation_image(X0,X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369214,c_58]) ).
tcf(c_386245,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X3,X4),X4)
| in(apply(X1,sK12(X0,X3,X4)),X2)
| ( relation_image(X0,X3) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369214,c_88]) ).
tcf(c_386246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X3,X4),X4)
| in(sK12(X0,X3,X4),relation_dom(X1))
| ( relation_image(X0,X3) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369214,c_87]) ).
tcf(c_386247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X3,X4),X4)
| ( relation_image(X0,X3) = X4 )
| ( apply(X1,sK13(X1,X2,sK12(X0,X3,X4))) = sK12(X0,X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369214,c_112]) ).
tcf(c_386248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK12(X0,X1,X2),X3)
| in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK10(sK12(X0,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_369214,c_369085]) ).
tcf(c_386249,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),empty_set) ),
inference(superposition,[status(thm)],[c_369214,c_372426]) ).
tcf(c_386250,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK12(X0,X1,X2))
| in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK16(sK12(X0,X1,X2))) ),
inference(superposition,[status(thm)],[c_369214,c_370746]) ).
tcf(c_386251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X3,X4),X4)
| in(sK2(X1,X2,sK12(X0,X3,X4)),X1)
| ( relation_image(X0,X3) = X4 )
| ( sK12(X0,X3,X4) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(X1,X2,sK12(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369214,c_369079]) ).
tcf(c_386252,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X3,X4),X4)
| in(sK2(X1,X2,sK12(X0,X3,X4)),X2)
| ( relation_image(X0,X3) = X4 )
| ( sK12(X0,X3,X4) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(X1,X2,sK12(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369214,c_369078]) ).
tcf(c_386253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,X2),X2)
| in(sK2(sK12(X0,X1,X2),X3,X4),X4)
| ( relation_image(X0,X1) = X2 )
| ( set_intersection2(sK12(X0,X1,X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(sK12(X0,X1,X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_369214,c_369076]) ).
tcf(c_386254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X2,X3),X3)
| in(sK2(X1,sK12(X0,X2,X3),X4),X4)
| ( relation_image(X0,X2) = X3 )
| ( set_intersection2(X1,sK12(X0,X2,X3)) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(X1,sK12(X0,X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_369214,c_369077]) ).
tcf(c_386255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X3,X4),X4)
| in(sK12(X1,X2,sK12(X0,X3,X4)),relation_dom(X1))
| ( relation_image(X0,X3) = X4 )
| ( sK12(X0,X3,X4) = relation_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK11(X1,X2,sK12(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369214,c_369205]) ).
tcf(c_386256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X3,X4),X4)
| in(sK7(X1,X2,sK12(X0,X3,X4)),relation_dom(X1))
| ( relation_image(X0,X3) = X4 )
| ( sK12(X0,X3,X4) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK7(X1,X2,sK12(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369214,c_369084]) ).
tcf(c_386257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X3,X4),X4)
| in(apply(X1,sK7(X1,X2,sK12(X0,X3,X4))),X2)
| ( relation_image(X0,X3) = X4 )
| ( sK12(X0,X3,X4) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK7(X1,X2,sK12(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369214,c_369083]) ).
tcf(c_386258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X2,X3),X3)
| in(sK7(X1,sK12(X0,X2,X3),X4),X4)
| ( relation_image(X0,X2) = X3 )
| ( relation_inverse_image(X1,sK12(X0,X2,X3)) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),apply(X1,sK7(X1,sK12(X0,X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_369214,c_369082]) ).
tcf(c_386259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X0,X4,X2),X3)
| in(sK12(X0,X4,X2),X1)
| ( relation_image(X0,X4) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_321]) ).
tcf(c_386260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,X2),X1)
| ( relation_image(X0,X4) = X2 )
| ~ empty(X3)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_320]) ).
tcf(c_386261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,X0),X3)
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ in(X0,sK11(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369214,c_97]) ).
tcf(c_386269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_image(X2,X3)),X1)
| ( relation_image(X0,X4) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK11(X0,X4,relation_image(X2,X3)))) = sK11(X0,X4,relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_112]) ).
tcf(c_386270,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,empty_set),X1)
| ( relation_image(X0,X2) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_372426]) ).
tcf(c_386545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X2,X3,X0),X1)
| element(sK12(X2,X3,X0),relation_dom(X2))
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369215,c_321]) ).
tcf(c_386546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X2,X3,X0),relation_dom(X2))
| ( relation_image(X2,X3) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369215,c_320]) ).
tcf(c_386547,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK12(X1,X2,X0),relation_dom(X1))
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK11(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369215,c_97]) ).
tcf(c_386555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X3,relation_image(X1,X2)),relation_dom(X0))
| ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK11(X0,X3,relation_image(X1,X2)))) = sK11(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369215,c_112]) ).
tcf(c_386556,plain,
! [X0: $i,X1: $i] :
( element(sK12(X0,X1,empty_set),relation_dom(X0))
| ( relation_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369215,c_372426]) ).
tcf(c_386592,plain,
! [X0: $i] :
( empty(powerset(empty_set))
| element(empty_set,X0)
| ~ subset(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_378043,c_370744]) ).
tcf(c_386594,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| subset(sK16(X0),X1)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_370744,c_99]) ).
tcf(c_386598,plain,
! [X0: $i] :
( element(empty_set,X0)
| ~ subset(powerset(empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_386592,c_120]) ).
tcf(c_386601,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ empty(relation_dom(X0))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_369216,c_77,c_71,c_8192]) ).
tcf(c_386602,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(renaming,[status(thm)],[c_386601]) ).
tcf(c_386611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X2,X3,X0),X1)
| ( relation_image(X2,X3) = X0 )
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_386602,c_321]) ).
tcf(c_386612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X2,X3) = X0 )
| ~ empty(X1)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_386602,c_320]) ).
tcf(c_386613,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = X0 )
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ in(X0,sK11(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_386602,c_97]) ).
tcf(c_386614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X2,X3,X0),X1)
| ( relation_image(X2,X3) = X0 )
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_386602,c_96]) ).
tcf(c_386615,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_386602,c_93]) ).
tcf(c_386616,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_386602,c_91]) ).
tcf(c_386617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_386602,c_59]) ).
tcf(c_386618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_386602,c_58]) ).
tcf(c_386619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK11(X0,X3,relation_inverse_image(X1,X2))),X2)
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_386602,c_88]) ).
tcf(c_386620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_386602,c_87]) ).
tcf(c_386621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK11(X0,X3,relation_image(X1,X2)))) = sK11(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_386602,c_112]) ).
tcf(c_386622,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = empty_set )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_386602,c_372426]) ).
tcf(c_386690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X2)
| in(sK11(X1,sK10(X0,X2),X3),X3)
| ( relation_image(X1,sK10(X0,X2)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK10(X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_369021,c_369298]) ).
tcf(c_386691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X0),X2)
| in(sK11(X1,sK2(X2,X3,X0),X4),X4)
| ( set_intersection2(X2,X3) = X0 )
| ( relation_image(X1,sK2(X2,X3,X0)) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK2(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369015,c_369298]) ).
tcf(c_386692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X0),X3)
| in(sK11(X1,sK2(X2,X3,X0),X4),X4)
| ( set_intersection2(X2,X3) = X0 )
| ( relation_image(X1,sK2(X2,X3,X0)) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK2(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369014,c_369298]) ).
tcf(c_386693,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X2,X3),X3)
| in(sK11(X1,sK2(X0,X2,X3),X4),X4)
| ( set_intersection2(X0,X2) = X3 )
| ( relation_image(X1,sK2(X0,X2,X3)) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK2(X0,X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_369012,c_369298]) ).
tcf(c_386694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X0,X3),X3)
| in(sK11(X1,sK2(X2,X0,X3),X4),X4)
| ( set_intersection2(X2,X0) = X3 )
| ( relation_image(X1,sK2(X2,X0,X3)) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK2(X2,X0,X3),X4)) ),
inference(superposition,[status(thm)],[c_369013,c_369298]) ).
tcf(c_386695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X3,X0),relation_dom(X2))
| in(sK11(X1,sK11(X2,X3,X0),X4),X4)
| ( relation_image(X2,X3) = X0 )
| ( relation_image(X1,sK11(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK11(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369206,c_369298]) ).
tcf(c_386696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X3,X0),relation_dom(X2))
| in(sK11(X1,sK7(X2,X3,X0),X4),X4)
| ( relation_inverse_image(X2,X3) = X0 )
| ( relation_image(X1,sK7(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK7(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369020,c_369298]) ).
tcf(c_386697,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,X3,X0)),X3)
| in(sK11(X1,sK7(X2,X3,X0),X4),X4)
| ( relation_inverse_image(X2,X3) = X0 )
| ( relation_image(X1,sK7(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK7(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369019,c_369298]) ).
tcf(c_386698,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X2,X3),X3)
| in(sK11(X1,sK7(X0,X2,X3),X4),X4)
| ( relation_inverse_image(X0,X2) = X3 )
| ( relation_image(X1,sK7(X0,X2,X3)) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK12(X1,sK7(X0,X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_369017,c_369298]) ).
tcf(c_386699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X2,X3),X3)
| in(sK11(X1,sK12(X0,X2,X3),X4),X4)
| ( relation_image(X0,X2) = X3 )
| ( relation_image(X1,sK12(X0,X2,X3)) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK12(X1,sK12(X0,X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_369214,c_369298]) ).
tcf(c_386700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X0,X3),X3)
| in(sK11(X1,apply(X2,sK7(X2,X0,X3)),X4),X4)
| ( relation_inverse_image(X2,X0) = X3 )
| ( relation_image(X1,apply(X2,sK7(X2,X0,X3))) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,apply(X2,sK7(X2,X0,X3)),X4)) ),
inference(superposition,[status(thm)],[c_369018,c_369298]) ).
tcf(c_386801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X3,X0,X4),X2)
| in(sK11(X3,X0,X4),X4)
| ( relation_image(X3,X0) = X4 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_321]) ).
tcf(c_386802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X0,X4),X4)
| ( relation_image(X3,X0) = X4 )
| ~ empty(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_320]) ).
tcf(c_386803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,X2,X3),X3)
| ( relation_image(X1,X2) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X0)
| ~ in(X0,sK12(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_369299,c_97]) ).
tcf(c_386804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X0,X4),X2)
| in(sK11(X3,X0,X4),X4)
| ( relation_image(X3,X0) = X4 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_96]) ).
tcf(c_386807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X0,X4),X2)
| in(sK11(X3,X0,X4),X4)
| ( relation_image(X3,X0) = X4 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369299,c_59]) ).
tcf(c_386808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X0,X4),X1)
| in(sK11(X3,X0,X4),X4)
| ( relation_image(X3,X0) = X4 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369299,c_58]) ).
tcf(c_386809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X0,X4),X4)
| in(apply(X1,sK12(X3,X0,X4)),X2)
| ( relation_image(X3,X0) = X4 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369299,c_88]) ).
tcf(c_386810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X0,X4),X4)
| in(sK12(X3,X0,X4),relation_dom(X1))
| ( relation_image(X3,X0) = X4 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369299,c_87]) ).
tcf(c_386811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X0,X4),X4)
| ( relation_image(X3,X0) = X4 )
| ( apply(X1,sK13(X1,X2,sK12(X3,X0,X4))) = sK12(X3,X0,X4) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369299,c_112]) ).
tcf(c_386812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK12(X1,X0,X2),X3)
| in(sK11(X1,X0,X2),X2)
| ( relation_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK10(sK12(X1,X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_369299,c_369085]) ).
tcf(c_386813,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X1,X0,X2),X2)
| ( relation_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_369299,c_372426]) ).
tcf(c_386814,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK12(X1,X0,X2))
| in(sK11(X1,X0,X2),X2)
| ( relation_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK16(sK12(X1,X0,X2))) ),
inference(superposition,[status(thm)],[c_369299,c_370746]) ).
tcf(c_386815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X0,X4),X4)
| in(sK2(X1,X2,sK12(X3,X0,X4)),X1)
| ( relation_image(X3,X0) = X4 )
| ( sK12(X3,X0,X4) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,sK2(X1,X2,sK12(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369299,c_369079]) ).
tcf(c_386816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X0,X4),X4)
| in(sK2(X1,X2,sK12(X3,X0,X4)),X2)
| ( relation_image(X3,X0) = X4 )
| ( sK12(X3,X0,X4) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,sK2(X1,X2,sK12(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369299,c_369078]) ).
tcf(c_386817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X1,X0,X2),X2)
| in(sK2(sK12(X1,X0,X2),X3,X4),X4)
| ( relation_image(X1,X0) = X2 )
| ( set_intersection2(sK12(X1,X0,X2),X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(sK12(X1,X0,X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_369299,c_369076]) ).
tcf(c_386818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,X0,X3),X3)
| in(sK2(X1,sK12(X2,X0,X3),X4),X4)
| ( relation_image(X2,X0) = X3 )
| ( set_intersection2(X1,sK12(X2,X0,X3)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,sK12(X2,X0,X3),X4)) ),
inference(superposition,[status(thm)],[c_369299,c_369077]) ).
tcf(c_386819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,X0,X3),X3)
| in(sK11(X1,sK12(X2,X0,X3),X4),X4)
| ( relation_image(X2,X0) = X3 )
| ( relation_image(X1,sK12(X2,X0,X3)) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK12(X2,X0,X3),X4)) ),
inference(superposition,[status(thm)],[c_369299,c_369298]) ).
tcf(c_386820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X0,X4),X4)
| in(sK12(X1,X2,sK12(X3,X0,X4)),relation_dom(X1))
| ( relation_image(X3,X0) = X4 )
| ( sK12(X3,X0,X4) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK12(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369299,c_369205]) ).
tcf(c_386821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X0,X4),X4)
| in(sK7(X1,X2,sK12(X3,X0,X4)),relation_dom(X1))
| ( relation_image(X3,X0) = X4 )
| ( sK12(X3,X0,X4) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK12(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369299,c_369084]) ).
tcf(c_386822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X0,X4),X4)
| in(apply(X1,sK7(X1,X2,sK12(X3,X0,X4))),X2)
| ( relation_image(X3,X0) = X4 )
| ( sK12(X3,X0,X4) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK12(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369299,c_369083]) ).
tcf(c_386823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,X0,X3),X3)
| in(sK7(X1,sK12(X2,X0,X3),X4),X4)
| ( relation_image(X2,X0) = X3 )
| ( relation_inverse_image(X1,sK12(X2,X0,X3)) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK12(X2,X0,X3),X4))) ),
inference(superposition,[status(thm)],[c_369299,c_369082]) ).
tcf(c_386824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X4,X0,X2),X3)
| in(sK12(X4,X0,X2),X1)
| ( relation_image(X4,X0) = X2 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_321]) ).
tcf(c_386825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X4,X0,X2),X1)
| ( relation_image(X4,X0) = X2 )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_320]) ).
tcf(c_386826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,X0),X3)
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,sK11(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369299,c_97]) ).
tcf(c_386827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X4,X0,X2),X1)
| in(sK11(X4,X0,X2),X3)
| ( relation_image(X4,X0) = X2 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_96]) ).
tcf(c_386828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X2,X0,X3),X3)
| in(sK12(X2,X0,X3),X1)
| ( relation_image(X2,X0) = X3 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_93]) ).
tcf(c_386829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X2,X0,X3),X1)
| ( relation_image(X2,X0) = X3 )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_91]) ).
tcf(c_386830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X0,set_intersection2(X3,X4)),X1)
| in(sK11(X2,X0,set_intersection2(X3,X4)),X4)
| ( relation_image(X2,X0) = set_intersection2(X3,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_59]) ).
tcf(c_386831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X0,set_intersection2(X3,X4)),X1)
| in(sK11(X2,X0,set_intersection2(X3,X4)),X3)
| ( relation_image(X2,X0) = set_intersection2(X3,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_58]) ).
tcf(c_386832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X0,relation_inverse_image(X3,X4)),X1)
| in(apply(X3,sK11(X2,X0,relation_inverse_image(X3,X4))),X4)
| ( relation_inverse_image(X3,X4) = relation_image(X2,X0) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_88]) ).
tcf(c_386833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X0,relation_inverse_image(X3,X4)),X1)
| in(sK11(X2,X0,relation_inverse_image(X3,X4)),relation_dom(X3))
| ( relation_inverse_image(X3,X4) = relation_image(X2,X0) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_87]) ).
tcf(c_386834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X0,relation_image(X3,X4)),X1)
| ( relation_image(X2,X0) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK11(X2,X0,relation_image(X3,X4)))) = sK11(X2,X0,relation_image(X3,X4)) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_112]) ).
tcf(c_386835,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X2,X0,empty_set),X1)
| ( relation_image(X2,X0) = empty_set )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_372426]) ).
tcf(c_387322,plain,
! [X0: $i] :
( empty(powerset(empty_set))
| in(empty_set,X0)
| ~ subset(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_378043,c_370747]) ).
tcf(c_387323,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| element(sK16(X0),X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370747,c_321]) ).
tcf(c_387324,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| ~ empty(X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370747,c_320]) ).
tcf(c_387325,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ~ subset(X1,X0)
| ~ in(X0,sK16(X1)) ),
inference(superposition,[status(thm)],[c_370747,c_97]) ).
tcf(c_387326,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(sK16(X0),X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370747,c_96]) ).
tcf(c_387329,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(sK16(X0),X2)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370747,c_59]) ).
tcf(c_387330,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(sK16(X0),X1)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370747,c_58]) ).
tcf(c_387331,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(apply(X1,sK16(X0)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370747,c_88]) ).
tcf(c_387332,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(sK16(X0),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370747,c_87]) ).
tcf(c_387333,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| ( apply(X1,sK13(X1,X2,sK16(X0))) = sK16(X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370747,c_112]) ).
tcf(c_387334,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| subset(sK16(X0),X1)
| ~ subset(X0,sK10(sK16(X0),X1)) ),
inference(superposition,[status(thm)],[c_370747,c_369085]) ).
tcf(c_387335,plain,
! [X0: $i] :
( empty(X0)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_370747,c_372426]) ).
tcf(c_387336,plain,
! [X0: $i] :
( empty(X0)
| empty(sK16(X0))
| ~ subset(X0,sK16(sK16(X0))) ),
inference(superposition,[status(thm)],[c_370747,c_370746]) ).
tcf(c_387337,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(sK2(X1,X2,sK16(X0)),X1)
| ( set_intersection2(X1,X2) = sK16(X0) )
| ~ subset(X0,sK2(X1,X2,sK16(X0))) ),
inference(superposition,[status(thm)],[c_370747,c_369079]) ).
tcf(c_387338,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(sK2(X1,X2,sK16(X0)),X2)
| ( set_intersection2(X1,X2) = sK16(X0) )
| ~ subset(X0,sK2(X1,X2,sK16(X0))) ),
inference(superposition,[status(thm)],[c_370747,c_369078]) ).
tcf(c_387339,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(sK2(sK16(X0),X1,X2),X2)
| ( set_intersection2(sK16(X0),X1) = X2 )
| ~ subset(X0,sK2(sK16(X0),X1,X2)) ),
inference(superposition,[status(thm)],[c_370747,c_369076]) ).
tcf(c_387340,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(sK2(X1,sK16(X0),X2),X2)
| ( set_intersection2(X1,sK16(X0)) = X2 )
| ~ subset(X0,sK2(X1,sK16(X0),X2)) ),
inference(superposition,[status(thm)],[c_370747,c_369077]) ).
tcf(c_387341,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(sK11(X1,sK16(X0),X2),X2)
| ( relation_image(X1,sK16(X0)) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK16(X0),X2)) ),
inference(superposition,[status(thm)],[c_370747,c_369298]) ).
tcf(c_387342,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(sK12(X1,X2,sK16(X0)),relation_dom(X1))
| ( relation_image(X1,X2) = sK16(X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK16(X0))) ),
inference(superposition,[status(thm)],[c_370747,c_369205]) ).
tcf(c_387343,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(sK7(X1,X2,sK16(X0)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = sK16(X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK16(X0))) ),
inference(superposition,[status(thm)],[c_370747,c_369084]) ).
tcf(c_387344,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(apply(X1,sK7(X1,X2,sK16(X0))),X2)
| ( relation_inverse_image(X1,X2) = sK16(X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK16(X0))) ),
inference(superposition,[status(thm)],[c_370747,c_369083]) ).
tcf(c_387345,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(sK7(X1,sK16(X0),X2),X2)
| ( relation_inverse_image(X1,sK16(X0)) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK16(X0),X2))) ),
inference(superposition,[status(thm)],[c_370747,c_369082]) ).
tcf(c_387354,plain,
! [X0: $i] :
( in(empty_set,X0)
| ~ subset(powerset(empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_387322,c_120]) ).
tcf(c_387499,plain,
! [X0: $i] :
( empty(relation_image(X0,relation_inverse_image(X0,empty_set)))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_387335]) ).
tcf(c_387501,plain,
empty(sK16(powerset(empty_set))),
inference(superposition,[status(thm)],[c_369151,c_387335]) ).
tcf(c_387506,plain,
! [X0: $i] : empty(set_intersection2(empty_set,X0)),
inference(superposition,[status(thm)],[c_380919,c_387335]) ).
tcf(c_387507,plain,
! [X0: $i] : empty(set_intersection2(X0,empty_set)),
inference(superposition,[status(thm)],[c_380850,c_387335]) ).
tcf(c_387525,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK12(X0,powerset(X1),X2),X1)
| in(sK11(X0,powerset(X1),X2),X2)
| ( relation_image(X0,powerset(X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369300,c_99]) ).
tcf(c_387526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X2,X3,X0),X3)
| element(sK11(X2,X3,X0),X1)
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369300,c_321]) ).
tcf(c_387527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X2,X3,X0),X3)
| ( relation_image(X2,X3) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369300,c_320]) ).
tcf(c_387528,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK12(X1,X2,X0),X2)
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK11(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369300,c_97]) ).
tcf(c_387529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X2,X3,X0),X3)
| in(sK11(X2,X3,X0),X1)
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369300,c_96]) ).
tcf(c_387530,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK12(X0,X1,X2),X1)
| element(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369300,c_93]) ).
tcf(c_387531,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK12(X0,X2,X1),X2)
| ( relation_image(X0,X2) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369300,c_91]) ).
tcf(c_387532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X1,set_intersection2(X2,X3)),X1)
| in(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369300,c_59]) ).
tcf(c_387533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X1,set_intersection2(X2,X3)),X1)
| in(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369300,c_58]) ).
tcf(c_387534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X3,relation_inverse_image(X1,X2)),X3)
| in(apply(X1,sK11(X0,X3,relation_inverse_image(X1,X2))),X2)
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369300,c_88]) ).
tcf(c_387535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X3,relation_inverse_image(X1,X2)),X3)
| in(sK11(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369300,c_87]) ).
tcf(c_387536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X3,relation_image(X1,X2)),X3)
| ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK11(X0,X3,relation_image(X1,X2)))) = sK11(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369300,c_112]) ).
tcf(c_387537,plain,
! [X0: $i,X1: $i] :
( element(sK12(X0,X1,empty_set),X1)
| ( relation_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369300,c_372426]) ).
tcf(c_387638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X2,X3,X0),X1)
| ( relation_image(X2,X3) = X0 )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369301,c_321]) ).
tcf(c_387639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X2,X3) = X0 )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369301,c_320]) ).
tcf(c_387640,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = X0 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK11(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369301,c_97]) ).
tcf(c_387641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X2,X3,X0),X1)
| ( relation_image(X2,X3) = X0 )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369301,c_96]) ).
tcf(c_387642,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369301,c_93]) ).
tcf(c_387643,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369301,c_91]) ).
tcf(c_387644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369301,c_59]) ).
tcf(c_387645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369301,c_58]) ).
tcf(c_387646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK11(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_inverse_image(X1,X3) = relation_image(X0,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369301,c_88]) ).
tcf(c_387647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| ( relation_inverse_image(X1,X3) = relation_image(X0,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369301,c_87]) ).
tcf(c_387648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X2) = relation_image(X1,X3) )
| ( apply(X1,sK13(X1,X3,sK11(X0,X2,relation_image(X1,X3)))) = sK11(X0,X2,relation_image(X1,X3)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369301,c_112]) ).
tcf(c_387649,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = empty_set )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369301,c_372426]) ).
tcf(c_387730,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,X2),X1)
| in(sK11(X0,set_intersection2(X1,X1),X2),X2)
| ( relation_image(X0,set_intersection2(X1,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_369302]) ).
tcf(c_387731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X2,X1),X3),X2)
| in(sK11(X0,set_intersection2(X1,X2),X3),X3)
| ( relation_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_369302]) ).
tcf(c_387734,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,empty_set,X2),X1)
| in(sK11(X0,set_intersection2(empty_set,X1),X2),X2)
| ( relation_image(X0,set_intersection2(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_369302]) ).
tcf(c_387735,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),X2)
| in(sK12(X0,set_intersection2(X1,X1),X2),X1)
| ( relation_image(X0,set_intersection2(X1,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_369302]) ).
tcf(c_387736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X1,X2),X3),X2)
| in(sK11(X0,set_intersection2(X2,X1),X3),X3)
| ( relation_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_369302]) ).
tcf(c_387738,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,X2),X2)
| in(sK12(X0,set_intersection2(X1,empty_set),X2),empty_set)
| ( relation_image(X0,set_intersection2(X1,empty_set)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_369302]) ).
tcf(c_387739,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,X2),X2)
| in(sK12(X0,set_intersection2(empty_set,X1),X2),X1)
| ( relation_image(X0,set_intersection2(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_369302]) ).
tcf(c_387740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X2,set_intersection2(X3,X0),X4),X1)
| in(sK11(X2,set_intersection2(X3,X0),X4),X4)
| ( relation_image(X2,set_intersection2(X3,X0)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369302,c_321]) ).
tcf(c_387741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,set_intersection2(X3,X0),X4),X4)
| ( relation_image(X2,set_intersection2(X3,X0)) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369302,c_320]) ).
tcf(c_387742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,set_intersection2(X2,X0),X3),X3)
| ( relation_image(X1,set_intersection2(X2,X0)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK12(X1,set_intersection2(X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_369302,c_97]) ).
tcf(c_387743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,set_intersection2(X3,X0),X4),X1)
| in(sK11(X2,set_intersection2(X3,X0),X4),X4)
| ( relation_image(X2,set_intersection2(X3,X0)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369302,c_96]) ).
tcf(c_387744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,set_intersection2(X1,X2),X3),X2)
| in(sK11(X0,set_intersection2(X1,X2),X3),X3)
| ( relation_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_93]) ).
tcf(c_387745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,set_intersection2(X2,X1),X3),X3)
| ( relation_image(X0,set_intersection2(X2,X1)) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_91]) ).
tcf(c_387746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X1,set_intersection2(X2,X3)),X4),X3)
| in(sK11(X0,set_intersection2(X1,set_intersection2(X2,X3)),X4),X4)
| ( relation_image(X0,set_intersection2(X1,set_intersection2(X2,X3))) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_59]) ).
tcf(c_387747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X1,set_intersection2(X2,X3)),X4),X2)
| in(sK11(X0,set_intersection2(X1,set_intersection2(X2,X3)),X4),X4)
| ( relation_image(X0,set_intersection2(X1,set_intersection2(X2,X3))) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_58]) ).
tcf(c_387748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,set_intersection2(X2,relation_inverse_image(X1,X3)),X4),X4)
| in(apply(X1,sK12(X0,set_intersection2(X2,relation_inverse_image(X1,X3)),X4)),X3)
| ( relation_image(X0,set_intersection2(X2,relation_inverse_image(X1,X3))) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_88]) ).
tcf(c_387749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,set_intersection2(X2,relation_inverse_image(X1,X3)),X4),X4)
| in(sK12(X0,set_intersection2(X2,relation_inverse_image(X1,X3)),X4),relation_dom(X1))
| ( relation_image(X0,set_intersection2(X2,relation_inverse_image(X1,X3))) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_87]) ).
tcf(c_387750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,set_intersection2(X3,relation_image(X1,X2)),X4),X4)
| ( relation_image(X0,set_intersection2(X3,relation_image(X1,X2))) = X4 )
| ( apply(X1,sK13(X1,X2,sK12(X0,set_intersection2(X3,relation_image(X1,X2)),X4))) = sK12(X0,set_intersection2(X3,relation_image(X1,X2)),X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_112]) ).
tcf(c_387751,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,set_intersection2(X1,empty_set),X2),X2)
| ( relation_image(X0,set_intersection2(X1,empty_set)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_372426]) ).
tcf(c_387752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,set_intersection2(X3,X4),X0),X1)
| in(sK12(X2,set_intersection2(X3,X4),X0),X4)
| ( relation_image(X2,set_intersection2(X3,X4)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369302,c_321]) ).
tcf(c_387753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,set_intersection2(X3,X4),X0),X4)
| ( relation_image(X2,set_intersection2(X3,X4)) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369302,c_320]) ).
tcf(c_387754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,set_intersection2(X2,X3),X0),X3)
| ( relation_image(X1,set_intersection2(X2,X3)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK11(X1,set_intersection2(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_369302,c_97]) ).
tcf(c_387755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,set_intersection2(X3,X4),X0),X4)
| in(sK11(X2,set_intersection2(X3,X4),X0),X1)
| ( relation_image(X2,set_intersection2(X3,X4)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369302,c_96]) ).
tcf(c_387756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,set_intersection2(X1,X2),X3),X3)
| in(sK12(X0,set_intersection2(X1,X2),X3),X2)
| ( relation_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_93]) ).
tcf(c_387757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X2,X3),X1),X3)
| ( relation_image(X0,set_intersection2(X2,X3)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_91]) ).
tcf(c_387758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X2)
| in(sK11(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X4)
| ( relation_image(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_59]) ).
tcf(c_387759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X2)
| in(sK11(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X3)
| ( relation_image(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_58]) ).
tcf(c_387760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4)),X3)
| in(apply(X1,sK11(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4))),X4)
| ( relation_image(X0,set_intersection2(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_88]) ).
tcf(c_387761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4)),X3)
| in(sK11(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| ( relation_image(X0,set_intersection2(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_87]) ).
tcf(c_387762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X3,X4),relation_image(X1,X2)),X4)
| ( relation_image(X0,set_intersection2(X3,X4)) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK11(X0,set_intersection2(X3,X4),relation_image(X1,X2)))) = sK11(X0,set_intersection2(X3,X4),relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_112]) ).
tcf(c_387763,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,set_intersection2(X1,X2),empty_set),X2)
| ( relation_image(X0,set_intersection2(X1,X2)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_372426]) ).
tcf(c_387787,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,X2),X2)
| ( relation_image(X0,set_intersection2(X1,empty_set)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_387738,c_372426]) ).
tcf(c_388042,plain,
! [X0: $i] :
( in(sK16(X0),X0)
| empty(set_intersection2(X0,X0)) ),
inference(superposition,[status(thm)],[c_53,c_370750]) ).
tcf(c_388043,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| in(sK16(set_intersection2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_63,c_370750]) ).
tcf(c_388045,plain,
! [X0: $i] :
( in(sK16(empty_set),empty_set)
| empty(set_intersection2(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_64,c_370750]) ).
tcf(c_388046,plain,
! [X0: $i] :
( in(sK16(empty_set),X0)
| empty(set_intersection2(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_368545,c_370750]) ).
tcf(c_388047,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,X0))
| element(sK16(set_intersection2(X2,X0)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370750,c_321]) ).
tcf(c_388048,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,X0))
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370750,c_320]) ).
tcf(c_388049,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ~ in(X0,sK16(set_intersection2(X1,X0))) ),
inference(superposition,[status(thm)],[c_370750,c_97]) ).
tcf(c_388050,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,X0))
| in(sK16(set_intersection2(X2,X0)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370750,c_96]) ).
tcf(c_388051,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| element(sK16(set_intersection2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_370750,c_93]) ).
tcf(c_388053,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,set_intersection2(X1,X2)))
| in(sK16(set_intersection2(X0,set_intersection2(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_370750,c_59]) ).
tcf(c_388054,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,set_intersection2(X1,X2)))
| in(sK16(set_intersection2(X0,set_intersection2(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_370750,c_58]) ).
tcf(c_388055,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X1,relation_inverse_image(X0,X2)))
| in(apply(X0,sK16(set_intersection2(X1,relation_inverse_image(X0,X2)))),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370750,c_88]) ).
tcf(c_388056,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X1,relation_inverse_image(X0,X2)))
| in(sK16(set_intersection2(X1,relation_inverse_image(X0,X2))),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370750,c_87]) ).
tcf(c_388057,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,relation_image(X0,X1)))
| ( apply(X0,sK13(X0,X1,sK16(set_intersection2(X2,relation_image(X0,X1))))) = sK16(set_intersection2(X2,relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370750,c_112]) ).
tcf(c_388059,plain,
! [X0: $i] :
( empty(empty_set)
| in(sK16(empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_388046,c_368545]) ).
tcf(c_388060,plain,
( empty(empty_set)
| in(sK16(empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_388045,c_64]) ).
tcf(c_388289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X2,X1),X3),X1)
| in(sK11(X0,set_intersection2(X1,X2),X3),X3)
| ( relation_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_369303]) ).
tcf(c_388294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X1,X2),X3),X1)
| in(sK11(X0,set_intersection2(X2,X1),X3),X3)
| ( relation_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_369303]) ).
tcf(c_388296,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,X2),X2)
| in(sK12(X0,set_intersection2(X1,empty_set),X2),X1)
| ( relation_image(X0,set_intersection2(X1,empty_set)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_369303]) ).
tcf(c_388297,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,X2),X2)
| in(sK12(X0,set_intersection2(empty_set,X1),X2),empty_set)
| ( relation_image(X0,set_intersection2(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_369303]) ).
tcf(c_388298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X2,set_intersection2(X0,X3),X4),X1)
| in(sK11(X2,set_intersection2(X0,X3),X4),X4)
| ( relation_image(X2,set_intersection2(X0,X3)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369303,c_321]) ).
tcf(c_388299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,set_intersection2(X0,X3),X4),X4)
| ( relation_image(X2,set_intersection2(X0,X3)) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369303,c_320]) ).
tcf(c_388300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,set_intersection2(X0,X2),X3),X3)
| ( relation_image(X1,set_intersection2(X0,X2)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK12(X1,set_intersection2(X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_369303,c_97]) ).
tcf(c_388301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,set_intersection2(X0,X3),X4),X1)
| in(sK11(X2,set_intersection2(X0,X3),X4),X4)
| ( relation_image(X2,set_intersection2(X0,X3)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369303,c_96]) ).
tcf(c_388302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,set_intersection2(X1,X2),X3),X1)
| in(sK11(X0,set_intersection2(X1,X2),X3),X3)
| ( relation_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_93]) ).
tcf(c_388303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,set_intersection2(X1,X2),X3),X3)
| ( relation_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_91]) ).
tcf(c_388304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X2)
| in(sK11(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X4)
| ( relation_image(X0,set_intersection2(set_intersection2(X1,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_59]) ).
tcf(c_388305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X1)
| in(sK11(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X4)
| ( relation_image(X0,set_intersection2(set_intersection2(X1,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_58]) ).
tcf(c_388306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,set_intersection2(relation_inverse_image(X1,X2),X3),X4),X4)
| in(apply(X1,sK12(X0,set_intersection2(relation_inverse_image(X1,X2),X3),X4)),X2)
| ( relation_image(X0,set_intersection2(relation_inverse_image(X1,X2),X3)) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_88]) ).
tcf(c_388307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,set_intersection2(relation_inverse_image(X1,X2),X3),X4),X4)
| in(sK12(X0,set_intersection2(relation_inverse_image(X1,X2),X3),X4),relation_dom(X1))
| ( relation_image(X0,set_intersection2(relation_inverse_image(X1,X2),X3)) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_87]) ).
tcf(c_388308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,set_intersection2(relation_image(X1,X2),X3),X4),X4)
| ( relation_image(X0,set_intersection2(relation_image(X1,X2),X3)) = X4 )
| ( apply(X1,sK13(X1,X2,sK12(X0,set_intersection2(relation_image(X1,X2),X3),X4))) = sK12(X0,set_intersection2(relation_image(X1,X2),X3),X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_112]) ).
tcf(c_388309,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,set_intersection2(empty_set,X1),X2),X2)
| ( relation_image(X0,set_intersection2(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_372426]) ).
tcf(c_388310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,set_intersection2(X3,X4),X0),X1)
| in(sK12(X2,set_intersection2(X3,X4),X0),X3)
| ( relation_image(X2,set_intersection2(X3,X4)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369303,c_321]) ).
tcf(c_388311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,set_intersection2(X3,X4),X0),X3)
| ( relation_image(X2,set_intersection2(X3,X4)) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369303,c_320]) ).
tcf(c_388312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,set_intersection2(X2,X3),X0),X2)
| ( relation_image(X1,set_intersection2(X2,X3)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK11(X1,set_intersection2(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_369303,c_97]) ).
tcf(c_388313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,set_intersection2(X3,X4),X0),X3)
| in(sK11(X2,set_intersection2(X3,X4),X0),X1)
| ( relation_image(X2,set_intersection2(X3,X4)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369303,c_96]) ).
tcf(c_388314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,set_intersection2(X1,X2),X3),X3)
| in(sK12(X0,set_intersection2(X1,X2),X3),X1)
| ( relation_image(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_93]) ).
tcf(c_388315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X2,X3),X1),X2)
| ( relation_image(X0,set_intersection2(X2,X3)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_91]) ).
tcf(c_388316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| in(sK11(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X4)
| ( relation_image(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_59]) ).
tcf(c_388317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| in(sK11(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X3)
| ( relation_image(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_58]) ).
tcf(c_388318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4)),X2)
| in(apply(X1,sK11(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4))),X4)
| ( relation_image(X0,set_intersection2(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_88]) ).
tcf(c_388319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4)),X2)
| in(sK11(X0,set_intersection2(X2,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| ( relation_image(X0,set_intersection2(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_87]) ).
tcf(c_388320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X3,X4),relation_image(X1,X2)),X3)
| ( relation_image(X0,set_intersection2(X3,X4)) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK11(X0,set_intersection2(X3,X4),relation_image(X1,X2)))) = sK11(X0,set_intersection2(X3,X4),relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_112]) ).
tcf(c_388321,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,set_intersection2(X1,X2),empty_set),X1)
| ( relation_image(X0,set_intersection2(X1,X2)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_372426]) ).
tcf(c_388340,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,X2),X2)
| ( relation_image(X0,set_intersection2(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_388297,c_372426]) ).
tcf(c_388565,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,X2),X2)
| in(apply(empty_set,sK12(X0,relation_inverse_image(empty_set,X1),X2)),X1)
| ( relation_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_369304]) ).
tcf(c_388566,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,sK12(X0,empty_set,X2)),X1)
| in(sK11(X0,relation_inverse_image(empty_set,X1),X2),X2)
| ( relation_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_369304]) ).
tcf(c_388567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,relation_inverse_image(X3,X4),X0),X1)
| in(apply(X3,sK12(X2,relation_inverse_image(X3,X4),X0)),X4)
| ( relation_image(X2,relation_inverse_image(X3,X4)) = X0 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369304,c_321]) ).
tcf(c_388568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK12(X2,relation_inverse_image(X3,X4),X0)),X4)
| ( relation_image(X2,relation_inverse_image(X3,X4)) = X0 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369304,c_320]) ).
tcf(c_388569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK12(X1,relation_inverse_image(X2,X3),X0)),X3)
| ( relation_image(X1,relation_inverse_image(X2,X3)) = X0 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,sK11(X1,relation_inverse_image(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_369304,c_97]) ).
tcf(c_388570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,relation_inverse_image(X3,X4),X0),X1)
| in(apply(X3,sK12(X2,relation_inverse_image(X3,X4),X0)),X4)
| ( relation_image(X2,relation_inverse_image(X3,X4)) = X0 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369304,c_96]) ).
tcf(c_388571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,relation_inverse_image(X1,X2),X3),X3)
| in(apply(X1,sK12(X0,relation_inverse_image(X1,X2),X3)),X2)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_93]) ).
tcf(c_388572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK12(X0,relation_inverse_image(X1,X3),X2)),X3)
| ( relation_image(X0,relation_inverse_image(X1,X3)) = X2 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_91]) ).
tcf(c_388573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4)),X4)
| in(apply(X1,sK12(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4))),X2)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_59]) ).
tcf(c_388574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4)),X3)
| in(apply(X1,sK12(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4))),X2)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_58]) ).
tcf(c_388575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK11(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4))),X4)
| in(apply(X1,sK12(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4))),X3)
| ( relation_image(X0,relation_inverse_image(X1,X3)) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_88]) ).
tcf(c_388576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4)),relation_dom(X2))
| in(apply(X1,sK12(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4))),X3)
| ( relation_image(X0,relation_inverse_image(X1,X3)) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_87]) ).
tcf(c_388577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK12(X0,relation_inverse_image(X1,X4),relation_image(X2,X3))),X4)
| ( relation_image(X0,relation_inverse_image(X1,X4)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK11(X0,relation_inverse_image(X1,X4),relation_image(X2,X3)))) = sK11(X0,relation_inverse_image(X1,X4),relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_112]) ).
tcf(c_388578,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,sK12(X0,relation_inverse_image(X1,X2),empty_set)),X2)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = empty_set )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_372426]) ).
tcf(c_388579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,relation_inverse_image(X3,X0),X4),X4)
| element(apply(X3,sK12(X2,relation_inverse_image(X3,X0),X4)),X1)
| ( relation_image(X2,relation_inverse_image(X3,X0)) = X4 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369304,c_321]) ).
tcf(c_388580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,relation_inverse_image(X3,X0),X4),X4)
| ( relation_image(X2,relation_inverse_image(X3,X0)) = X4 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369304,c_320]) ).
tcf(c_388581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X2,relation_inverse_image(X1,X0),X3),X3)
| ( relation_image(X2,relation_inverse_image(X1,X0)) = X3 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK12(X2,relation_inverse_image(X1,X0),X3))) ),
inference(superposition,[status(thm)],[c_369304,c_97]) ).
tcf(c_388582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,relation_inverse_image(X3,X0),X4),X4)
| in(apply(X3,sK12(X2,relation_inverse_image(X3,X0),X4)),X1)
| ( relation_image(X2,relation_inverse_image(X3,X0)) = X4 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369304,c_96]) ).
tcf(c_388583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),X3),X3)
| element(apply(X1,sK12(X0,relation_inverse_image(X1,X2),X3)),X2)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_93]) ).
tcf(c_388584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),X3),X3)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_91]) ).
tcf(c_388585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_inverse_image(X1,set_intersection2(X2,X3)),X4),X4)
| in(apply(X1,sK12(X0,relation_inverse_image(X1,set_intersection2(X2,X3)),X4)),X3)
| ( relation_image(X0,relation_inverse_image(X1,set_intersection2(X2,X3))) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_59]) ).
tcf(c_388586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_inverse_image(X1,set_intersection2(X2,X3)),X4),X4)
| in(apply(X1,sK12(X0,relation_inverse_image(X1,set_intersection2(X2,X3)),X4)),X2)
| ( relation_image(X0,relation_inverse_image(X1,set_intersection2(X2,X3))) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_58]) ).
tcf(c_388587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),X3),X3)
| in(sK12(X0,relation_inverse_image(X1,X2),X3),relation_inverse_image(X1,X2))
| ( relation_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK12(X0,relation_inverse_image(X1,X2),X3),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_369304,c_86]) ).
tcf(c_388588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_inverse_image(X1,relation_inverse_image(X2,X3)),X4),X4)
| in(apply(X2,apply(X1,sK12(X0,relation_inverse_image(X1,relation_inverse_image(X2,X3)),X4))),X3)
| ( relation_image(X0,relation_inverse_image(X1,relation_inverse_image(X2,X3))) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_88]) ).
tcf(c_388589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_inverse_image(X1,relation_inverse_image(X2,X3)),X4),X4)
| in(apply(X1,sK12(X0,relation_inverse_image(X1,relation_inverse_image(X2,X3)),X4)),relation_dom(X2))
| ( relation_image(X0,relation_inverse_image(X1,relation_inverse_image(X2,X3))) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_87]) ).
tcf(c_388590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_inverse_image(X1,relation_image(X2,X3)),X4),X4)
| ( relation_image(X0,relation_inverse_image(X1,relation_image(X2,X3))) = X4 )
| ( apply(X2,sK13(X2,X3,apply(X1,sK12(X0,relation_inverse_image(X1,relation_image(X2,X3)),X4)))) = apply(X1,sK12(X0,relation_inverse_image(X1,relation_image(X2,X3)),X4)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_112]) ).
tcf(c_388591,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,relation_inverse_image(X1,empty_set),X2),X2)
| ( relation_image(X0,relation_inverse_image(X1,empty_set)) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_372426]) ).
tcf(c_388626,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,sK12(X0,empty_set,X2)),X1)
| in(sK11(X0,relation_inverse_image(empty_set,X1),X2),X2)
| ( relation_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_388566,c_368630,c_103]) ).
tcf(c_388632,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,X2),X2)
| in(apply(empty_set,sK12(X0,relation_inverse_image(empty_set,X1),X2)),X1)
| ( relation_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_388565,c_368630,c_103]) ).
tcf(c_388854,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,X2),X2)
| in(sK12(X0,relation_inverse_image(empty_set,X1),X2),relation_dom(empty_set))
| ( relation_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_369305]) ).
tcf(c_388855,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,empty_set,X2),relation_dom(empty_set))
| in(sK11(X0,relation_inverse_image(empty_set,X1),X2),X2)
| ( relation_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_369305]) ).
tcf(c_388856,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,relation_inverse_image(empty_set,X1),X2),empty_set)
| in(sK11(X0,relation_inverse_image(empty_set,X1),X2),X2)
| ( relation_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373108,c_369305]) ).
tcf(c_388857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,relation_inverse_image(X3,X4),X0),X1)
| in(sK12(X2,relation_inverse_image(X3,X4),X0),relation_dom(X3))
| ( relation_image(X2,relation_inverse_image(X3,X4)) = X0 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369305,c_321]) ).
tcf(c_388858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,relation_inverse_image(X3,X4),X0),relation_dom(X3))
| ( relation_image(X2,relation_inverse_image(X3,X4)) = X0 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369305,c_320]) ).
tcf(c_388859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,relation_inverse_image(X2,X3),X0),relation_dom(X2))
| ( relation_image(X1,relation_inverse_image(X2,X3)) = X0 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,sK11(X1,relation_inverse_image(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_369305,c_97]) ).
tcf(c_388860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,relation_inverse_image(X3,X4),X0),X1)
| in(sK12(X2,relation_inverse_image(X3,X4),X0),relation_dom(X3))
| ( relation_image(X2,relation_inverse_image(X3,X4)) = X0 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369305,c_96]) ).
tcf(c_388861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,relation_inverse_image(X1,X2),X3),X3)
| in(sK12(X0,relation_inverse_image(X1,X2),X3),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369305,c_93]) ).
tcf(c_388862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,relation_inverse_image(X1,X3),X2),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X3)) = X2 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369305,c_91]) ).
tcf(c_388863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4)),X4)
| in(sK12(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4)),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369305,c_59]) ).
tcf(c_388864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4)),X3)
| in(sK12(X0,relation_inverse_image(X1,X2),set_intersection2(X3,X4)),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369305,c_58]) ).
tcf(c_388865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4)),relation_dom(X1))
| in(apply(X2,sK11(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4))),X4)
| ( relation_image(X0,relation_inverse_image(X1,X3)) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369305,c_88]) ).
tcf(c_388866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4)),relation_dom(X1))
| in(sK11(X0,relation_inverse_image(X1,X3),relation_inverse_image(X2,X4)),relation_dom(X2))
| ( relation_image(X0,relation_inverse_image(X1,X3)) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369305,c_87]) ).
tcf(c_388867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,relation_inverse_image(X1,X4),relation_image(X2,X3)),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X4)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK11(X0,relation_inverse_image(X1,X4),relation_image(X2,X3)))) = sK11(X0,relation_inverse_image(X1,X4),relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369305,c_112]) ).
tcf(c_388868,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,relation_inverse_image(X1,X2),empty_set),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X2)) = empty_set )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369305,c_372426]) ).
tcf(c_388869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X2,relation_inverse_image(X0,X3),X4),X1)
| in(sK11(X2,relation_inverse_image(X0,X3),X4),X4)
| ( relation_image(X2,relation_inverse_image(X0,X3)) = X4 )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369305,c_321]) ).
tcf(c_388870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,relation_inverse_image(X0,X3),X4),X4)
| ( relation_image(X2,relation_inverse_image(X0,X3)) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369305,c_320]) ).
tcf(c_388871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,relation_inverse_image(X0,X2),X3),X3)
| ( relation_image(X1,relation_inverse_image(X0,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK12(X1,relation_inverse_image(X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_369305,c_97]) ).
tcf(c_388872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,relation_inverse_image(X0,X3),X4),X1)
| in(sK11(X2,relation_inverse_image(X0,X3),X4),X4)
| ( relation_image(X2,relation_inverse_image(X0,X3)) = X4 )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369305,c_96]) ).
tcf(c_388873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),X3),X3)
| element(sK12(X0,relation_inverse_image(X1,X2),X3),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369305,c_93]) ).
tcf(c_388874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,relation_inverse_image(X0,X2),X3),X3)
| ( relation_image(X1,relation_inverse_image(X0,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369305,c_91]) ).
tcf(c_388895,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,empty_set,X2),empty_set)
| in(sK11(X0,relation_inverse_image(empty_set,X1),X2),X2)
| ( relation_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_388855,c_373108]) ).
tcf(c_388896,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,relation_inverse_image(empty_set,X1),X2),X2)
| ( relation_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_388895,c_372426,c_368630,c_103]) ).
tcf(c_388901,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,X2),X2)
| in(sK12(X0,relation_inverse_image(empty_set,X1),X2),empty_set)
| ( relation_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_388854,c_373108]) ).
tcf(c_388902,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,X2),X2)
| ( relation_image(X0,relation_inverse_image(empty_set,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_388901,c_372426,c_368630,c_103]) ).
tcf(c_389060,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| in(sK16(set_intersection2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_63,c_370751]) ).
tcf(c_389062,plain,
! [X0: $i] :
( in(sK16(empty_set),X0)
| empty(set_intersection2(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_64,c_370751]) ).
tcf(c_389063,plain,
! [X0: $i] :
( in(sK16(empty_set),empty_set)
| empty(set_intersection2(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_368545,c_370751]) ).
tcf(c_389064,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,X2))
| element(sK16(set_intersection2(X0,X2)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370751,c_321]) ).
tcf(c_389065,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,X2))
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370751,c_320]) ).
tcf(c_389066,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ~ in(X0,sK16(set_intersection2(X0,X1))) ),
inference(superposition,[status(thm)],[c_370751,c_97]) ).
tcf(c_389067,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,X2))
| in(sK16(set_intersection2(X0,X2)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370751,c_96]) ).
tcf(c_389068,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| element(sK16(set_intersection2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_370751,c_93]) ).
tcf(c_389070,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),X2))
| in(sK16(set_intersection2(set_intersection2(X0,X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_370751,c_59]) ).
tcf(c_389071,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),X2))
| in(sK16(set_intersection2(set_intersection2(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_370751,c_58]) ).
tcf(c_389072,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_inverse_image(X0,X1),X2))
| in(apply(X0,sK16(set_intersection2(relation_inverse_image(X0,X1),X2))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370751,c_88]) ).
tcf(c_389073,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_inverse_image(X0,X1),X2))
| in(sK16(set_intersection2(relation_inverse_image(X0,X1),X2)),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370751,c_87]) ).
tcf(c_389074,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_image(X0,X1),X2))
| ( apply(X0,sK13(X0,X1,sK16(set_intersection2(relation_image(X0,X1),X2)))) = sK16(set_intersection2(relation_image(X0,X1),X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370751,c_112]) ).
tcf(c_389132,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( set_intersection2(X0,empty_set) = X0 )
| ~ in(sK2(X0,empty_set,X0),empty_set)
| ~ in(sK2(X0,empty_set,X0),X0) ),
inference(superposition,[status(thm)],[c_372467,c_54]) ).
tcf(c_389133,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X2,empty_set,X0),X1)
| ( X0 = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_372467,c_321]) ).
tcf(c_389134,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_372467,c_320]) ).
tcf(c_389135,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK2(X1,empty_set,X0)) ),
inference(superposition,[status(thm)],[c_372467,c_97]) ).
tcf(c_389136,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,empty_set,X0),X1)
| ( X0 = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_372467,c_96]) ).
tcf(c_389139,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,empty_set,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_372467,c_59]) ).
tcf(c_389140,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,empty_set,set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_372467,c_58]) ).
tcf(c_389141,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK2(X2,empty_set,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372467,c_88]) ).
tcf(c_389142,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,empty_set,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372467,c_87]) ).
tcf(c_389143,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = empty_set )
| ( apply(X0,sK13(X0,X1,sK2(X2,empty_set,relation_image(X0,X1)))) = sK2(X2,empty_set,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372467,c_112]) ).
tcf(c_389145,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( set_intersection2(set_intersection2(X0,X1),empty_set) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),empty_set,X0),empty_set)
| ~ in(sK2(set_intersection2(X0,X1),empty_set,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),empty_set,X0),X0) ),
inference(superposition,[status(thm)],[c_372467,c_368471]) ).
tcf(c_389169,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ in(sK2(X0,empty_set,X0),empty_set)
| ~ in(sK2(X0,empty_set,X0),X0) ),
inference(light_normalisation,[status(thm)],[c_389132,c_64]) ).
tcf(c_389191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| in(sK12(X1,X2,sK10(X0,X3)),X2)
| ( relation_image(X1,X2) = sK10(X0,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK10(X0,X3))) ),
inference(superposition,[status(thm)],[c_369021,c_369306]) ).
tcf(c_389192,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| in(sK12(X1,X2,sK16(X0)),X2)
| ( relation_image(X1,X2) = sK16(X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK16(X0))) ),
inference(superposition,[status(thm)],[c_370747,c_369306]) ).
tcf(c_389193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| in(sK12(X1,X2,sK2(X3,X4,X0)),X2)
| ( set_intersection2(X3,X4) = X0 )
| ( sK2(X3,X4,X0) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369015,c_369306]) ).
tcf(c_389194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| in(sK12(X1,X2,sK2(X3,X4,X0)),X2)
| ( set_intersection2(X3,X4) = X0 )
| ( sK2(X3,X4,X0) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369014,c_369306]) ).
tcf(c_389195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| in(sK12(X1,X2,sK2(X0,X3,X4)),X2)
| ( set_intersection2(X0,X3) = X4 )
| ( sK2(X0,X3,X4) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369012,c_369306]) ).
tcf(c_389196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| in(sK12(X1,X2,sK2(X3,X0,X4)),X2)
| ( set_intersection2(X3,X0) = X4 )
| ( sK2(X3,X0,X4) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369013,c_369306]) ).
tcf(c_389197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X0,X4),X4)
| in(sK12(X1,X2,sK12(X3,X0,X4)),X2)
| ( relation_image(X3,X0) = X4 )
| ( sK12(X3,X0,X4) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK12(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369299,c_369306]) ).
tcf(c_389198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),relation_dom(X3))
| in(sK12(X1,X2,sK11(X3,X4,X0)),X2)
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369206,c_369306]) ).
tcf(c_389199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),relation_dom(X3))
| in(sK12(X1,X2,sK7(X3,X4,X0)),X2)
| ( relation_inverse_image(X3,X4) = X0 )
| ( sK7(X3,X4,X0) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK7(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369020,c_369306]) ).
tcf(c_389200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X3,X4,X0)),X4)
| in(sK12(X1,X2,sK7(X3,X4,X0)),X2)
| ( relation_inverse_image(X3,X4) = X0 )
| ( sK7(X3,X4,X0) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK7(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369019,c_369306]) ).
tcf(c_389201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| in(sK12(X1,X2,sK7(X0,X3,X4)),X2)
| ( relation_inverse_image(X0,X3) = X4 )
| ( sK7(X0,X3,X4) = relation_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK11(X1,X2,sK7(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369017,c_369306]) ).
tcf(c_389202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X3,X4),X4)
| in(sK12(X1,X2,sK12(X0,X3,X4)),X2)
| ( relation_image(X0,X3) = X4 )
| ( sK12(X0,X3,X4) = relation_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK11(X1,X2,sK12(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369214,c_369306]) ).
tcf(c_389203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| in(sK12(X1,X2,apply(X3,sK7(X3,X0,X4))),X2)
| ( relation_inverse_image(X3,X0) = X4 )
| ( apply(X3,sK7(X3,X0,X4)) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,apply(X3,sK7(X3,X0,X4)))) ),
inference(superposition,[status(thm)],[c_369018,c_369306]) ).
tcf(c_389358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X4,X2,X0),X3)
| in(sK11(X4,X2,X0),X1)
| ( relation_image(X4,X2) = X0 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_321]) ).
tcf(c_389359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X4,X2,X0),X1)
| ( relation_image(X4,X2) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_320]) ).
tcf(c_389360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,X0,X2),X3)
| ( relation_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,sK12(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_369307,c_97]) ).
tcf(c_389361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X4,X2,X0),X3)
| in(sK11(X4,X2,X0),X1)
| ( relation_image(X4,X2) = X0 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_96]) ).
tcf(c_389368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,relation_image(X3,X4),X0),X1)
| ( relation_image(X2,relation_image(X3,X4)) = X0 )
| ( apply(X3,sK13(X3,X4,sK12(X2,relation_image(X3,X4),X0))) = sK12(X2,relation_image(X3,X4),X0) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_112]) ).
tcf(c_389369,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X2,empty_set,X0),X1)
| ( relation_image(X2,empty_set) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_372426]) ).
tcf(c_389370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X3,X4,X0),X2)
| in(sK12(X3,X4,X0),X4)
| ( relation_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_321]) ).
tcf(c_389371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| ( relation_image(X3,X4) = X0 )
| ~ empty(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_320]) ).
tcf(c_389372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,X3),X2)
| ( relation_image(X1,X2) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X0)
| ~ in(X0,sK11(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_369307,c_97]) ).
tcf(c_389373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| in(sK11(X3,X4,X0),X2)
| ( relation_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_96]) ).
tcf(c_389376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| in(sK11(X3,X4,X0),X2)
| ( relation_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369307,c_59]) ).
tcf(c_389377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| in(sK11(X3,X4,X0),X1)
| ( relation_image(X3,X4) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369307,c_58]) ).
tcf(c_389378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| in(apply(X1,sK11(X3,X4,X0)),X2)
| ( relation_image(X3,X4) = X0 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369307,c_88]) ).
tcf(c_389379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| in(sK11(X3,X4,X0),relation_dom(X1))
| ( relation_image(X3,X4) = X0 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369307,c_87]) ).
tcf(c_389380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| ( relation_image(X3,X4) = X0 )
| ( apply(X1,sK13(X1,X2,sK11(X3,X4,X0))) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369307,c_112]) ).
tcf(c_389381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK11(X1,X2,X0),X3)
| in(sK12(X1,X2,X0),X2)
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK10(sK11(X1,X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_369307,c_369085]) ).
tcf(c_389382,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X1,X2,X0),X2)
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_369307,c_372426]) ).
tcf(c_389383,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK11(X1,X2,X0))
| in(sK12(X1,X2,X0),X2)
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK16(sK11(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_369307,c_370746]) ).
tcf(c_389384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| in(sK2(X1,X2,sK11(X3,X4,X0)),X1)
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,sK2(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369307,c_369079]) ).
tcf(c_389385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| in(sK2(X1,X2,sK11(X3,X4,X0)),X2)
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,sK2(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369307,c_369078]) ).
tcf(c_389386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X2,X0),X2)
| in(sK2(sK11(X1,X2,X0),X3,X4),X4)
| ( relation_image(X1,X2) = X0 )
| ( set_intersection2(sK11(X1,X2,X0),X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(sK11(X1,X2,X0),X3,X4)) ),
inference(superposition,[status(thm)],[c_369307,c_369076]) ).
tcf(c_389387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X3,X0),X3)
| in(sK2(X1,sK11(X2,X3,X0),X4),X4)
| ( relation_image(X2,X3) = X0 )
| ( set_intersection2(X1,sK11(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,sK11(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369307,c_369077]) ).
tcf(c_389388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X3,X0),X3)
| in(sK11(X1,sK11(X2,X3,X0),X4),X4)
| ( relation_image(X2,X3) = X0 )
| ( relation_image(X1,sK11(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK11(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369307,c_369298]) ).
tcf(c_389389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| in(sK12(X1,X2,sK11(X3,X4,X0)),X2)
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369307,c_369306]) ).
tcf(c_389390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| in(sK12(X1,X2,sK11(X3,X4,X0)),relation_dom(X1))
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369307,c_369205]) ).
tcf(c_389391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| in(sK7(X1,X2,sK11(X3,X4,X0)),relation_dom(X1))
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369307,c_369084]) ).
tcf(c_389392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| in(apply(X1,sK7(X1,X2,sK11(X3,X4,X0))),X2)
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369307,c_369083]) ).
tcf(c_389393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X3,X0),X3)
| in(sK7(X1,sK11(X2,X3,X0),X4),X4)
| ( relation_image(X2,X3) = X0 )
| ( relation_inverse_image(X1,sK11(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK11(X2,X3,X0),X4))) ),
inference(superposition,[status(thm)],[c_369307,c_369082]) ).
tcf(c_389827,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK11(X0,X1,powerset(X2)),X2)
| in(sK12(X0,X1,powerset(X2)),X1)
| ( relation_image(X0,X1) = powerset(X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369308,c_99]) ).
tcf(c_389828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X2,X0,X3),X1)
| element(sK11(X2,X0,X3),X3)
| ( relation_image(X2,X0) = X3 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369308,c_321]) ).
tcf(c_389829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X2,X0,X3),X3)
| ( relation_image(X2,X0) = X3 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369308,c_320]) ).
tcf(c_389830,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK11(X1,X0,X2),X2)
| ( relation_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK12(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_369308,c_97]) ).
tcf(c_389838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,relation_image(X1,X2),X3),X3)
| ( relation_image(X0,relation_image(X1,X2)) = X3 )
| ( apply(X1,sK13(X1,X2,sK12(X0,relation_image(X1,X2),X3))) = sK12(X0,relation_image(X1,X2),X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369308,c_112]) ).
tcf(c_389839,plain,
! [X0: $i,X1: $i] :
( element(sK11(X0,empty_set,X1),X1)
| ( relation_image(X0,empty_set) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369308,c_372426]) ).
tcf(c_389878,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(empty_set,X2,X0),X1)
| ( X0 = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_372470,c_321]) ).
tcf(c_389880,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK2(empty_set,X1,X0)) ),
inference(superposition,[status(thm)],[c_372470,c_97]) ).
tcf(c_389881,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,X0),X1)
| ( X0 = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_372470,c_96]) ).
tcf(c_389884,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_372470,c_59]) ).
tcf(c_389885,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_372470,c_58]) ).
tcf(c_389886,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK2(empty_set,X2,relation_inverse_image(X0,X1))),X1)
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372470,c_88]) ).
tcf(c_389887,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372470,c_87]) ).
tcf(c_389888,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = empty_set )
| ( apply(X0,sK13(X0,X1,sK2(empty_set,X2,relation_image(X0,X1)))) = sK2(empty_set,X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372470,c_112]) ).
tcf(c_389918,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(powerset(X0),X1)
| subset(sK10(powerset(X0),X1),X2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_372645,c_369791]) ).
tcf(c_389919,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| empty(sK10(powerset(X0),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_372645,c_370745]) ).
tcf(c_389920,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( sK10(powerset(X0),X1) = X0 )
| ~ subset(X0,sK10(powerset(X0),X1)) ),
inference(superposition,[status(thm)],[c_372645,c_60]) ).
tcf(c_389921,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| empty(sK10(powerset(empty_set),X0)) ),
inference(superposition,[status(thm)],[c_372645,c_387335]) ).
tcf(c_389922,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X0)
| subset(sK10(powerset(empty_set),X0),X1) ),
inference(superposition,[status(thm)],[c_372645,c_383286]) ).
tcf(c_389923,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| ( sK10(powerset(empty_set),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_372645,c_369178]) ).
tcf(c_389976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X2,X0,X3),X1)
| ( relation_image(X2,X0) = X3 )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369309,c_321]) ).
tcf(c_389977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X2,X0) = X3 )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369309,c_320]) ).
tcf(c_389978,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X0) = X2 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK12(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_369309,c_97]) ).
tcf(c_389981,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = X1 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369309,c_91]) ).
tcf(c_389986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,relation_image(X1,X3)) = X2 )
| ( apply(X1,sK13(X1,X3,sK12(X0,relation_image(X1,X3),X2))) = sK12(X0,relation_image(X1,X3),X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369309,c_112]) ).
tcf(c_389987,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,empty_set) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369309,c_372426]) ).
tcf(c_390031,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,X2),X1)
| in(sK11(X0,X1,set_intersection2(X2,X2)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_369310]) ).
tcf(c_390032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X1,set_intersection2(X3,X2)),X1)
| in(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_369310]) ).
tcf(c_390034,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),X1)
| in(sK11(X0,X1,set_intersection2(X2,empty_set)),empty_set)
| ( relation_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_369310]) ).
tcf(c_390035,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),X1)
| in(sK11(X0,X1,set_intersection2(empty_set,X2)),X2)
| ( relation_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_369310]) ).
tcf(c_390036,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),X2)
| in(sK12(X0,X1,set_intersection2(X2,X2)),X1)
| ( relation_image(X0,X1) = set_intersection2(X2,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_369310]) ).
tcf(c_390037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X1,set_intersection2(X2,X3)),X1)
| in(sK11(X0,X1,set_intersection2(X3,X2)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_369310]) ).
tcf(c_390040,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,empty_set),X2)
| in(sK12(X0,X1,set_intersection2(empty_set,X2)),X1)
| ( relation_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_369310]) ).
tcf(c_390041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X2,X0,set_intersection2(X3,X4)),X1)
| in(sK11(X2,X0,set_intersection2(X3,X4)),X4)
| ( relation_image(X2,X0) = set_intersection2(X3,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369310,c_321]) ).
tcf(c_390042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,X0,set_intersection2(X3,X4)),X4)
| ( relation_image(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369310,c_320]) ).
tcf(c_390043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,X0,set_intersection2(X2,X3)),X3)
| ( relation_image(X1,X0) = set_intersection2(X2,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK12(X1,X0,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_369310,c_97]) ).
tcf(c_390051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_image(X1,X2),set_intersection2(X3,X4)),X4)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X2,sK12(X0,relation_image(X1,X2),set_intersection2(X3,X4)))) = sK12(X0,relation_image(X1,X2),set_intersection2(X3,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_112]) ).
tcf(c_390052,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,set_intersection2(X1,X2)),X2)
| ( set_intersection2(X1,X2) = relation_image(X0,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_372426]) ).
tcf(c_390053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,X3,set_intersection2(X4,X0)),X1)
| in(sK12(X2,X3,set_intersection2(X4,X0)),X3)
| ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369310,c_321]) ).
tcf(c_390054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X3,set_intersection2(X4,X0)),X3)
| ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369310,c_320]) ).
tcf(c_390055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,set_intersection2(X3,X0)),X2)
| ( relation_image(X1,X2) = set_intersection2(X3,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK11(X1,X2,set_intersection2(X3,X0))) ),
inference(superposition,[status(thm)],[c_369310,c_97]) ).
tcf(c_390056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X3,set_intersection2(X4,X0)),X3)
| in(sK11(X2,X3,set_intersection2(X4,X0)),X1)
| ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369310,c_96]) ).
tcf(c_390057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK12(X0,X1,set_intersection2(X2,X3)),X1)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_93]) ).
tcf(c_390058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X2,set_intersection2(X3,X1)),X2)
| ( relation_image(X0,X2) = set_intersection2(X3,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_91]) ).
tcf(c_390059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(X1,set_intersection2(X2,X3))),X4)
| in(sK11(X0,X4,set_intersection2(X1,set_intersection2(X2,X3))),X3)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_59]) ).
tcf(c_390060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(X1,set_intersection2(X2,X3))),X4)
| in(sK11(X0,X4,set_intersection2(X1,set_intersection2(X2,X3))),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_58]) ).
tcf(c_390061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3))),X4)
| in(apply(X1,sK11(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3)))),X3)
| ( set_intersection2(X2,relation_inverse_image(X1,X3)) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_88]) ).
tcf(c_390062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3))),X4)
| in(sK11(X0,X4,set_intersection2(X2,relation_inverse_image(X1,X3))),relation_dom(X1))
| ( set_intersection2(X2,relation_inverse_image(X1,X3)) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_87]) ).
tcf(c_390063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X3,set_intersection2(X4,relation_image(X1,X2))),X3)
| ( set_intersection2(X4,relation_image(X1,X2)) = relation_image(X0,X3) )
| ( apply(X1,sK13(X1,X2,sK11(X0,X3,set_intersection2(X4,relation_image(X1,X2))))) = sK11(X0,X3,set_intersection2(X4,relation_image(X1,X2))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_112]) ).
tcf(c_390064,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,set_intersection2(X2,empty_set)),X1)
| ( relation_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_372426]) ).
tcf(c_390093,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),X1)
| ( relation_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_390034,c_372426]) ).
tcf(c_390279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X1,set_intersection2(X3,X2)),X1)
| in(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_369311]) ).
tcf(c_390281,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),X1)
| in(sK11(X0,X1,set_intersection2(X2,empty_set)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_369311]) ).
tcf(c_390282,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),X1)
| in(sK11(X0,X1,set_intersection2(empty_set,X2)),empty_set)
| ( relation_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_369311]) ).
tcf(c_390284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X1,set_intersection2(X2,X3)),X1)
| in(sK11(X0,X1,set_intersection2(X3,X2)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_369311]) ).
tcf(c_390288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X2,X0,set_intersection2(X3,X4)),X1)
| in(sK11(X2,X0,set_intersection2(X3,X4)),X3)
| ( relation_image(X2,X0) = set_intersection2(X3,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369311,c_321]) ).
tcf(c_390289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,X0,set_intersection2(X3,X4)),X3)
| ( relation_image(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369311,c_320]) ).
tcf(c_390290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,X0,set_intersection2(X2,X3)),X2)
| ( relation_image(X1,X0) = set_intersection2(X2,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK12(X1,X0,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_369311,c_97]) ).
tcf(c_390298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_image(X1,X2),set_intersection2(X3,X4)),X3)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X2,sK12(X0,relation_image(X1,X2),set_intersection2(X3,X4)))) = sK12(X0,relation_image(X1,X2),set_intersection2(X3,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_112]) ).
tcf(c_390299,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,set_intersection2(X1,X2)),X1)
| ( set_intersection2(X1,X2) = relation_image(X0,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_372426]) ).
tcf(c_390300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,X3,set_intersection2(X0,X4)),X1)
| in(sK12(X2,X3,set_intersection2(X0,X4)),X3)
| ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369311,c_321]) ).
tcf(c_390301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X3,set_intersection2(X0,X4)),X3)
| ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369311,c_320]) ).
tcf(c_390302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,set_intersection2(X0,X3)),X2)
| ( relation_image(X1,X2) = set_intersection2(X0,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK11(X1,X2,set_intersection2(X0,X3))) ),
inference(superposition,[status(thm)],[c_369311,c_97]) ).
tcf(c_390303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X3,set_intersection2(X0,X4)),X3)
| in(sK11(X2,X3,set_intersection2(X0,X4)),X1)
| ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369311,c_96]) ).
tcf(c_390304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK12(X0,X1,set_intersection2(X2,X3)),X1)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_93]) ).
tcf(c_390305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X2,set_intersection2(X1,X3)),X2)
| ( relation_image(X0,X2) = set_intersection2(X1,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_91]) ).
tcf(c_390306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(set_intersection2(X1,X2),X3)),X4)
| in(sK11(X0,X4,set_intersection2(set_intersection2(X1,X2),X3)),X2)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_59]) ).
tcf(c_390307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(set_intersection2(X1,X2),X3)),X4)
| in(sK11(X0,X4,set_intersection2(set_intersection2(X1,X2),X3)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_58]) ).
tcf(c_390308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3)),X4)
| in(apply(X1,sK11(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3))),X2)
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_88]) ).
tcf(c_390309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3)),X4)
| in(sK11(X0,X4,set_intersection2(relation_inverse_image(X1,X2),X3)),relation_dom(X1))
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_87]) ).
tcf(c_390310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X3,set_intersection2(relation_image(X1,X2),X4)),X3)
| ( set_intersection2(relation_image(X1,X2),X4) = relation_image(X0,X3) )
| ( apply(X1,sK13(X1,X2,sK11(X0,X3,set_intersection2(relation_image(X1,X2),X4)))) = sK11(X0,X3,set_intersection2(relation_image(X1,X2),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_112]) ).
tcf(c_390311,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,set_intersection2(empty_set,X2)),X1)
| ( relation_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_372426]) ).
tcf(c_390325,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),X1)
| ( relation_image(X0,X1) = set_intersection2(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_390282,c_372426]) ).
tcf(c_390518,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| ( sK16(powerset(sK10(powerset(empty_set),X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_389921,c_380415]) ).
tcf(c_390519,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X1)
| ( set_intersection2(X0,sK10(powerset(empty_set),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_389921,c_379213]) ).
tcf(c_390520,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X0)
| ( set_intersection2(sK10(powerset(empty_set),X0),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_389921,c_379152]) ).
tcf(c_390521,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| ( relation_dom(relation_dom(sK10(powerset(empty_set),X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_389921,c_373107]) ).
tcf(c_390522,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X1)
| ( set_intersection2(X0,sK10(powerset(empty_set),X1)) = sK10(powerset(empty_set),X1) ) ),
inference(superposition,[status(thm)],[c_389921,c_370147]) ).
tcf(c_390523,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X0)
| ( set_intersection2(sK10(powerset(empty_set),X0),X1) = sK10(powerset(empty_set),X0) ) ),
inference(superposition,[status(thm)],[c_389921,c_370079]) ).
tcf(c_390524,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| ( relation_dom(sK10(powerset(empty_set),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_389921,c_369156]) ).
tcf(c_390525,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X1)
| ( relation_dom(sK10(powerset(empty_set),X1)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_389921,c_368606]) ).
tcf(c_390527,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| relation(sK10(powerset(empty_set),X0)) ),
inference(superposition,[status(thm)],[c_389921,c_82]) ).
tcf(c_390528,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| function(sK10(powerset(empty_set),X0)) ),
inference(superposition,[status(thm)],[c_389921,c_77]) ).
tcf(c_390529,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X1)
| ( sK10(powerset(empty_set),X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_389921,c_52]) ).
tcf(c_390634,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),X1)
| in(apply(empty_set,sK11(X0,X1,relation_inverse_image(empty_set,X2))),X2)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_369312]) ).
tcf(c_390635,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,sK11(X0,X1,empty_set)),X2)
| in(sK12(X0,X1,relation_inverse_image(empty_set,X2)),X1)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_369312]) ).
tcf(c_390636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X2,X0,relation_inverse_image(X3,X4)),X1)
| in(apply(X3,sK11(X2,X0,relation_inverse_image(X3,X4))),X4)
| ( relation_inverse_image(X3,X4) = relation_image(X2,X0) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369312,c_321]) ).
tcf(c_390637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK11(X2,X0,relation_inverse_image(X3,X4))),X4)
| ( relation_inverse_image(X3,X4) = relation_image(X2,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369312,c_320]) ).
tcf(c_390638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK11(X1,X0,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = relation_image(X1,X0) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,sK12(X1,X0,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369312,c_97]) ).
tcf(c_390644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK12(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4))),X3)
| in(apply(X1,sK11(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4))),X4)
| ( relation_image(X0,relation_inverse_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_88]) ).
tcf(c_390645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4)),relation_dom(X2))
| in(apply(X1,sK11(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4))),X4)
| ( relation_image(X0,relation_inverse_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_87]) ).
tcf(c_390646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK11(X0,relation_image(X2,X3),relation_inverse_image(X1,X4))),X4)
| ( relation_image(X0,relation_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ( apply(X2,sK13(X2,X3,sK12(X0,relation_image(X2,X3),relation_inverse_image(X1,X4)))) = sK12(X0,relation_image(X2,X3),relation_inverse_image(X1,X4)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_112]) ).
tcf(c_390647,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,sK11(X0,empty_set,relation_inverse_image(X1,X2))),X2)
| ( relation_inverse_image(X1,X2) = relation_image(X0,empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_372426]) ).
tcf(c_390648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X4,relation_inverse_image(X3,X0)),X4)
| element(apply(X3,sK11(X2,X4,relation_inverse_image(X3,X0))),X1)
| ( relation_inverse_image(X3,X0) = relation_image(X2,X4) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369312,c_321]) ).
tcf(c_390649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X4,relation_inverse_image(X3,X0)),X4)
| ( relation_inverse_image(X3,X0) = relation_image(X2,X4) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369312,c_320]) ).
tcf(c_390650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X2,X3,relation_inverse_image(X1,X0)),X3)
| ( relation_inverse_image(X1,X0) = relation_image(X2,X3) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK11(X2,X3,relation_inverse_image(X1,X0)))) ),
inference(superposition,[status(thm)],[c_369312,c_97]) ).
tcf(c_390651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X4,relation_inverse_image(X3,X0)),X4)
| in(apply(X3,sK11(X2,X4,relation_inverse_image(X3,X0))),X1)
| ( relation_inverse_image(X3,X0) = relation_image(X2,X4) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369312,c_96]) ).
tcf(c_390652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_inverse_image(X1,X2)),X3)
| element(apply(X1,sK11(X0,X3,relation_inverse_image(X1,X2))),X2)
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_93]) ).
tcf(c_390653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_inverse_image(X1,X2)),X3)
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_91]) ).
tcf(c_390654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3))),X4)
| in(apply(X1,sK11(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3)))),X3)
| ( relation_inverse_image(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_59]) ).
tcf(c_390655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3))),X4)
| in(apply(X1,sK11(X0,X4,relation_inverse_image(X1,set_intersection2(X2,X3)))),X2)
| ( relation_inverse_image(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_58]) ).
tcf(c_390656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X1,relation_inverse_image(X2,X3)),X1)
| in(sK11(X0,X1,relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3))
| ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2)) ),
inference(superposition,[status(thm)],[c_369312,c_86]) ).
tcf(c_390657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3))),X4)
| in(apply(X2,apply(X1,sK11(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3))))),X3)
| ( relation_inverse_image(X1,relation_inverse_image(X2,X3)) = relation_image(X0,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_88]) ).
tcf(c_390658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3))),X4)
| in(apply(X1,sK11(X0,X4,relation_inverse_image(X1,relation_inverse_image(X2,X3)))),relation_dom(X2))
| ( relation_inverse_image(X1,relation_inverse_image(X2,X3)) = relation_image(X0,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_87]) ).
tcf(c_390659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_inverse_image(X1,relation_image(X2,X3))),X4)
| ( relation_inverse_image(X1,relation_image(X2,X3)) = relation_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,apply(X1,sK11(X0,X4,relation_inverse_image(X1,relation_image(X2,X3)))))) = apply(X1,sK11(X0,X4,relation_inverse_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_112]) ).
tcf(c_390660,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,relation_inverse_image(X1,empty_set)),X2)
| ( relation_image(X0,X2) = relation_inverse_image(X1,empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_372426]) ).
tcf(c_390688,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,sK11(X0,X1,empty_set)),X2)
| in(sK12(X0,X1,relation_inverse_image(empty_set,X2)),X1)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_390635,c_368630,c_103]) ).
tcf(c_390694,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),X1)
| in(apply(empty_set,sK11(X0,X1,relation_inverse_image(empty_set,X2))),X2)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_390634,c_368630,c_103]) ).
tcf(c_390993,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),X1)
| in(sK11(X0,X1,relation_inverse_image(empty_set,X2)),relation_dom(empty_set))
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_369313]) ).
tcf(c_390994,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,empty_set),relation_dom(empty_set))
| in(sK12(X0,X1,relation_inverse_image(empty_set,X2)),X1)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_369313]) ).
tcf(c_390995,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,relation_inverse_image(empty_set,X2)),empty_set)
| in(sK12(X0,X1,relation_inverse_image(empty_set,X2)),X1)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373108,c_369313]) ).
tcf(c_390996,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X2,X0,relation_inverse_image(X3,X4)),X1)
| in(sK11(X2,X0,relation_inverse_image(X3,X4)),relation_dom(X3))
| ( relation_inverse_image(X3,X4) = relation_image(X2,X0) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369313,c_321]) ).
tcf(c_390997,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,X0,relation_inverse_image(X3,X4)),relation_dom(X3))
| ( relation_inverse_image(X3,X4) = relation_image(X2,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369313,c_320]) ).
tcf(c_390998,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,X0,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = relation_image(X1,X0) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,sK12(X1,X0,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369313,c_97]) ).
tcf(c_391004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| in(apply(X2,sK12(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4))),X3)
| ( relation_image(X0,relation_inverse_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369313,c_88]) ).
tcf(c_391005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4)),relation_dom(X2))
| in(sK11(X0,relation_inverse_image(X2,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369313,c_87]) ).
tcf(c_391006,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_image(X2,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| ( relation_image(X0,relation_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ( apply(X2,sK13(X2,X3,sK12(X0,relation_image(X2,X3),relation_inverse_image(X1,X4)))) = sK12(X0,relation_image(X2,X3),relation_inverse_image(X1,X4)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369313,c_112]) ).
tcf(c_391007,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,relation_inverse_image(X1,X2)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = relation_image(X0,empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369313,c_372426]) ).
tcf(c_391008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,X4,relation_inverse_image(X0,X3)),X1)
| in(sK12(X2,X4,relation_inverse_image(X0,X3)),X4)
| ( relation_inverse_image(X0,X3) = relation_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369313,c_321]) ).
tcf(c_391009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X4,relation_inverse_image(X0,X3)),X4)
| ( relation_inverse_image(X0,X3) = relation_image(X2,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369313,c_320]) ).
tcf(c_391010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,relation_inverse_image(X0,X3)),X2)
| ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK11(X1,X2,relation_inverse_image(X0,X3))) ),
inference(superposition,[status(thm)],[c_369313,c_97]) ).
tcf(c_391011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X4,relation_inverse_image(X0,X3)),X4)
| in(sK11(X2,X4,relation_inverse_image(X0,X3)),X1)
| ( relation_inverse_image(X0,X3) = relation_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369313,c_96]) ).
tcf(c_391012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_inverse_image(X1,X2)),X3)
| element(sK11(X0,X3,relation_inverse_image(X1,X2)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369313,c_93]) ).
tcf(c_391013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X3,relation_inverse_image(X0,X2)),X3)
| ( relation_inverse_image(X0,X2) = relation_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369313,c_91]) ).
tcf(c_391027,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,empty_set),empty_set)
| in(sK12(X0,X1,relation_inverse_image(empty_set,X2)),X1)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_390994,c_373108]) ).
tcf(c_391028,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,relation_inverse_image(empty_set,X2)),X1)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_391027,c_372426,c_368630,c_103]) ).
tcf(c_391033,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),X1)
| in(sK11(X0,X1,relation_inverse_image(empty_set,X2)),empty_set)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_390993,c_373108]) ).
tcf(c_391034,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,empty_set),X1)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_391033,c_372426,c_368630,c_103]) ).
tcf(c_391215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| ( relation_image(X1,X2) = sK10(X0,X3) )
| ( apply(X1,sK12(X1,X2,sK10(X0,X3))) = sK11(X1,X2,sK10(X0,X3)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK10(X0,X3))) ),
inference(superposition,[status(thm)],[c_369021,c_369435]) ).
tcf(c_391216,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| ( relation_image(X1,X2) = sK16(X0) )
| ( apply(X1,sK12(X1,X2,sK16(X0))) = sK11(X1,X2,sK16(X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK16(X0))) ),
inference(superposition,[status(thm)],[c_370747,c_369435]) ).
tcf(c_391217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| ( set_intersection2(X3,X4) = X0 )
| ( sK2(X3,X4,X0) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK2(X3,X4,X0))) = sK11(X1,X2,sK2(X3,X4,X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369015,c_369435]) ).
tcf(c_391218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| ( set_intersection2(X3,X4) = X0 )
| ( sK2(X3,X4,X0) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK2(X3,X4,X0))) = sK11(X1,X2,sK2(X3,X4,X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369014,c_369435]) ).
tcf(c_391219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| ( set_intersection2(X0,X3) = X4 )
| ( sK2(X0,X3,X4) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK2(X0,X3,X4))) = sK11(X1,X2,sK2(X0,X3,X4)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369012,c_369435]) ).
tcf(c_391220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| ( set_intersection2(X3,X0) = X4 )
| ( sK2(X3,X0,X4) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK2(X3,X0,X4))) = sK11(X1,X2,sK2(X3,X0,X4)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369013,c_369435]) ).
tcf(c_391221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X0,X4),X4)
| ( relation_image(X3,X0) = X4 )
| ( sK12(X3,X0,X4) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK12(X3,X0,X4))) = sK11(X1,X2,sK12(X3,X0,X4)) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK12(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369299,c_369435]) ).
tcf(c_391222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK11(X3,X4,X0))) = sK11(X1,X2,sK11(X3,X4,X0)) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369307,c_369435]) ).
tcf(c_391223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),relation_dom(X3))
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK11(X3,X4,X0))) = sK11(X1,X2,sK11(X3,X4,X0)) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369206,c_369435]) ).
tcf(c_391224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),relation_dom(X3))
| ( relation_inverse_image(X3,X4) = X0 )
| ( sK7(X3,X4,X0) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK7(X3,X4,X0))) = sK11(X1,X2,sK7(X3,X4,X0)) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK7(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369020,c_369435]) ).
tcf(c_391225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X3,X4,X0)),X4)
| ( relation_inverse_image(X3,X4) = X0 )
| ( sK7(X3,X4,X0) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK7(X3,X4,X0))) = sK11(X1,X2,sK7(X3,X4,X0)) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK7(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369019,c_369435]) ).
tcf(c_391226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| ( relation_inverse_image(X0,X3) = X4 )
| ( sK7(X0,X3,X4) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK7(X0,X3,X4))) = sK11(X1,X2,sK7(X0,X3,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK11(X1,X2,sK7(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369017,c_369435]) ).
tcf(c_391227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X3,X4),X4)
| ( relation_image(X0,X3) = X4 )
| ( sK12(X0,X3,X4) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK12(X0,X3,X4))) = sK11(X1,X2,sK12(X0,X3,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK11(X1,X2,sK12(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369214,c_369435]) ).
tcf(c_391228,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| ( relation_inverse_image(X3,X0) = X4 )
| ( apply(X3,sK7(X3,X0,X4)) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,apply(X3,sK7(X3,X0,X4)))) = sK11(X1,X2,apply(X3,sK7(X3,X0,X4))) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,apply(X3,sK7(X3,X0,X4)))) ),
inference(superposition,[status(thm)],[c_369018,c_369435]) ).
tcf(c_391384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X3,X4,X0),X2)
| ( relation_image(X3,X4) = X0 )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369436,c_321]) ).
tcf(c_391385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X3,X4) = X0 )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ empty(X2)
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369436,c_320]) ).
tcf(c_391386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X1,X2) = X3 )
| ( apply(X1,sK12(X1,X2,X3)) = sK11(X1,X2,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X0)
| ~ in(X0,sK11(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_369436,c_97]) ).
tcf(c_391387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X4,X0),X2)
| ( relation_image(X3,X4) = X0 )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369436,c_96]) ).
tcf(c_391390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X4,X0),X2)
| ( relation_image(X3,X4) = X0 )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369436,c_59]) ).
tcf(c_391391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X4,X0),X1)
| ( relation_image(X3,X4) = X0 )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369436,c_58]) ).
tcf(c_391392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK11(X3,X4,X0)),X2)
| ( relation_image(X3,X4) = X0 )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369436,c_88]) ).
tcf(c_391393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X4,X0),relation_dom(X1))
| ( relation_image(X3,X4) = X0 )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369436,c_87]) ).
tcf(c_391394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X3,X4) = X0 )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ( apply(X1,sK13(X1,X2,sK11(X3,X4,X0))) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369436,c_112]) ).
tcf(c_391395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK11(X1,X2,X0),X3)
| ( relation_image(X1,X2) = X0 )
| ( apply(X1,sK12(X1,X2,X0)) = sK11(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK10(sK11(X1,X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_369436,c_369085]) ).
tcf(c_391396,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = X0 )
| ( apply(X1,sK12(X1,X2,X0)) = sK11(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_369436,c_372426]) ).
tcf(c_391397,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK11(X1,X2,X0))
| ( relation_image(X1,X2) = X0 )
| ( apply(X1,sK12(X1,X2,X0)) = sK11(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK16(sK11(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_369436,c_370746]) ).
tcf(c_391398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,sK11(X3,X4,X0)),X1)
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = set_intersection2(X1,X2) )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,sK2(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369436,c_369079]) ).
tcf(c_391399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,sK11(X3,X4,X0)),X2)
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = set_intersection2(X1,X2) )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,sK2(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369436,c_369078]) ).
tcf(c_391400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(sK11(X1,X2,X0),X3,X4),X4)
| ( relation_image(X1,X2) = X0 )
| ( apply(X1,sK12(X1,X2,X0)) = sK11(X1,X2,X0) )
| ( set_intersection2(sK11(X1,X2,X0),X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(sK11(X1,X2,X0),X3,X4)) ),
inference(superposition,[status(thm)],[c_369436,c_369076]) ).
tcf(c_391401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,sK11(X2,X3,X0),X4),X4)
| ( relation_image(X2,X3) = X0 )
| ( apply(X2,sK12(X2,X3,X0)) = sK11(X2,X3,X0) )
| ( set_intersection2(X1,sK11(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,sK11(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369436,c_369077]) ).
tcf(c_391402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X1,sK11(X2,X3,X0),X4),X4)
| ( relation_image(X2,X3) = X0 )
| ( apply(X2,sK12(X2,X3,X0)) = sK11(X2,X3,X0) )
| ( relation_image(X1,sK11(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK11(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369436,c_369298]) ).
tcf(c_391403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_image(X1,X2) )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ( apply(X1,sK12(X1,X2,sK11(X3,X4,X0))) = sK11(X1,X2,sK11(X3,X4,X0)) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369436,c_369435]) ).
tcf(c_391404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X2,sK11(X3,X4,X0)),X2)
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_image(X1,X2) )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369436,c_369306]) ).
tcf(c_391405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X2,sK11(X3,X4,X0)),relation_dom(X1))
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_image(X1,X2) )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369436,c_369205]) ).
tcf(c_391406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,X2,sK11(X3,X4,X0)),relation_dom(X1))
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_inverse_image(X1,X2) )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369436,c_369084]) ).
tcf(c_391407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X1,X2,sK11(X3,X4,X0))),X2)
| ( relation_image(X3,X4) = X0 )
| ( sK11(X3,X4,X0) = relation_inverse_image(X1,X2) )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK11(X3,X4,X0))) ),
inference(superposition,[status(thm)],[c_369436,c_369083]) ).
tcf(c_391408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,sK11(X2,X3,X0),X4),X4)
| ( relation_image(X2,X3) = X0 )
| ( apply(X2,sK12(X2,X3,X0)) = sK11(X2,X3,X0) )
| ( relation_inverse_image(X1,sK11(X2,X3,X0)) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK11(X2,X3,X0),X4))) ),
inference(superposition,[status(thm)],[c_369436,c_369082]) ).
tcf(c_391692,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK11(X0,X1,powerset(X2)),X2)
| ( relation_image(X0,X1) = powerset(X2) )
| ( apply(X0,sK12(X0,X1,powerset(X2))) = sK11(X0,X1,powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369437,c_99]) ).
tcf(c_391708,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = relation_dom(X1) )
| ( apply(X0,sK12(X0,X2,relation_dom(X1))) = sK11(X0,X2,relation_dom(X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_69,c_369438]) ).
tcf(c_391710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X2) = set_intersection2(X1,X3) )
| ( apply(X0,sK12(X0,X2,set_intersection2(X1,X3))) = sK11(X0,X2,set_intersection2(X1,X3)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_381102,c_369438]) ).
tcf(c_391711,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X2) = set_intersection2(X3,X1) )
| ( apply(X0,sK12(X0,X2,set_intersection2(X3,X1))) = sK11(X0,X2,set_intersection2(X3,X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_380923,c_369438]) ).
tcf(c_391712,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = sK16(powerset(X1)) )
| ( apply(X0,sK12(X0,X2,sK16(powerset(X1)))) = sK11(X0,X2,sK16(powerset(X1))) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_380186,c_369438]) ).
tcf(c_391713,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(powerset(empty_set),X2)
| ( sK10(powerset(empty_set),X2) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,sK10(powerset(empty_set),X2))) = sK11(X0,X1,sK10(powerset(empty_set),X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_389921,c_369438]) ).
tcf(c_391842,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X2) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,X2))) = sK11(X0,X1,set_intersection2(X2,X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_369439]) ).
tcf(c_391843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X3,X2)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,X3))) = sK11(X0,X1,set_intersection2(X2,X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_369439]) ).
tcf(c_391846,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,empty_set),X2)
| ( relation_image(X0,X1) = set_intersection2(empty_set,X2) )
| ( apply(X0,sK12(X0,X1,set_intersection2(empty_set,X2))) = sK11(X0,X1,set_intersection2(empty_set,X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_369439]) ).
tcf(c_391847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,X3,set_intersection2(X4,X0)),X1)
| ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ( apply(X2,sK12(X2,X3,set_intersection2(X4,X0))) = sK11(X2,X3,set_intersection2(X4,X0)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369439,c_321]) ).
tcf(c_391848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ( apply(X2,sK12(X2,X3,set_intersection2(X4,X0))) = sK11(X2,X3,set_intersection2(X4,X0)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369439,c_320]) ).
tcf(c_391849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X1,X2) = set_intersection2(X3,X0) )
| ( apply(X1,sK12(X1,X2,set_intersection2(X3,X0))) = sK11(X1,X2,set_intersection2(X3,X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK11(X1,X2,set_intersection2(X3,X0))) ),
inference(superposition,[status(thm)],[c_369439,c_97]) ).
tcf(c_391850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,X3,set_intersection2(X4,X0)),X1)
| ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ( apply(X2,sK12(X2,X3,set_intersection2(X4,X0))) = sK11(X2,X3,set_intersection2(X4,X0)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369439,c_96]) ).
tcf(c_391851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,X3))) = sK11(X0,X1,set_intersection2(X2,X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369439,c_93]) ).
tcf(c_391853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,set_intersection2(X2,set_intersection2(X3,X4))),X4)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,set_intersection2(X3,X4)))) = sK11(X0,X1,set_intersection2(X2,set_intersection2(X3,X4))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369439,c_59]) ).
tcf(c_391854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,set_intersection2(X2,set_intersection2(X3,X4))),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,set_intersection2(X3,X4)))) = sK11(X0,X1,set_intersection2(X2,set_intersection2(X3,X4))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369439,c_58]) ).
tcf(c_391855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK11(X0,X2,set_intersection2(X3,relation_inverse_image(X1,X4)))),X4)
| ( set_intersection2(X3,relation_inverse_image(X1,X4)) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,set_intersection2(X3,relation_inverse_image(X1,X4)))) = sK11(X0,X2,set_intersection2(X3,relation_inverse_image(X1,X4))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369439,c_88]) ).
tcf(c_391856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X2,set_intersection2(X3,relation_inverse_image(X1,X4))),relation_dom(X1))
| ( set_intersection2(X3,relation_inverse_image(X1,X4)) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,set_intersection2(X3,relation_inverse_image(X1,X4)))) = sK11(X0,X2,set_intersection2(X3,relation_inverse_image(X1,X4))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369439,c_87]) ).
tcf(c_391857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X4,relation_image(X1,X2)) = relation_image(X0,X3) )
| ( apply(X0,sK12(X0,X3,set_intersection2(X4,relation_image(X1,X2)))) = sK11(X0,X3,set_intersection2(X4,relation_image(X1,X2))) )
| ( apply(X1,sK13(X1,X2,sK11(X0,X3,set_intersection2(X4,relation_image(X1,X2))))) = sK11(X0,X3,set_intersection2(X4,relation_image(X1,X2))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369439,c_112]) ).
tcf(c_391858,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = set_intersection2(X2,empty_set) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,empty_set))) = sK11(X0,X1,set_intersection2(X2,empty_set)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369439,c_372426]) ).
tcf(c_392039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X3,X2)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,X3))) = sK11(X0,X1,set_intersection2(X2,X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_63,c_369440]) ).
tcf(c_392043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,X3,set_intersection2(X0,X4)),X1)
| ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ( apply(X2,sK12(X2,X3,set_intersection2(X0,X4))) = sK11(X2,X3,set_intersection2(X0,X4)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369440,c_321]) ).
tcf(c_392044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ( apply(X2,sK12(X2,X3,set_intersection2(X0,X4))) = sK11(X2,X3,set_intersection2(X0,X4)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369440,c_320]) ).
tcf(c_392045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X1,X2) = set_intersection2(X0,X3) )
| ( apply(X1,sK12(X1,X2,set_intersection2(X0,X3))) = sK11(X1,X2,set_intersection2(X0,X3)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK11(X1,X2,set_intersection2(X0,X3))) ),
inference(superposition,[status(thm)],[c_369440,c_97]) ).
tcf(c_392046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,X3,set_intersection2(X0,X4)),X1)
| ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ( apply(X2,sK12(X2,X3,set_intersection2(X0,X4))) = sK11(X2,X3,set_intersection2(X0,X4)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369440,c_96]) ).
tcf(c_392047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,X3))) = sK11(X0,X1,set_intersection2(X2,X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369440,c_93]) ).
tcf(c_392049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,set_intersection2(set_intersection2(X2,X3),X4)),X3)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(set_intersection2(X2,X3),X4))) = sK11(X0,X1,set_intersection2(set_intersection2(X2,X3),X4)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369440,c_59]) ).
tcf(c_392050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,set_intersection2(set_intersection2(X2,X3),X4)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(set_intersection2(X2,X3),X4))) = sK11(X0,X1,set_intersection2(set_intersection2(X2,X3),X4)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369440,c_58]) ).
tcf(c_392051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK11(X0,X2,set_intersection2(relation_inverse_image(X1,X3),X4))),X3)
| ( set_intersection2(relation_inverse_image(X1,X3),X4) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,set_intersection2(relation_inverse_image(X1,X3),X4))) = sK11(X0,X2,set_intersection2(relation_inverse_image(X1,X3),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369440,c_88]) ).
tcf(c_392052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X2,set_intersection2(relation_inverse_image(X1,X3),X4)),relation_dom(X1))
| ( set_intersection2(relation_inverse_image(X1,X3),X4) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,set_intersection2(relation_inverse_image(X1,X3),X4))) = sK11(X0,X2,set_intersection2(relation_inverse_image(X1,X3),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369440,c_87]) ).
tcf(c_392053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X1,X2),X4) = relation_image(X0,X3) )
| ( apply(X0,sK12(X0,X3,set_intersection2(relation_image(X1,X2),X4))) = sK11(X0,X3,set_intersection2(relation_image(X1,X2),X4)) )
| ( apply(X1,sK13(X1,X2,sK11(X0,X3,set_intersection2(relation_image(X1,X2),X4)))) = sK11(X0,X3,set_intersection2(relation_image(X1,X2),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369440,c_112]) ).
tcf(c_392054,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = set_intersection2(empty_set,X2) )
| ( apply(X0,sK12(X0,X1,set_intersection2(empty_set,X2))) = sK11(X0,X1,set_intersection2(empty_set,X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369440,c_372426]) ).
tcf(c_392149,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,sK11(X0,X1,empty_set)),X2)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ( apply(X0,sK12(X0,X1,relation_inverse_image(empty_set,X2))) = sK11(X0,X1,relation_inverse_image(empty_set,X2)) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_369441]) ).
tcf(c_392150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(apply(X3,sK11(X2,X4,relation_inverse_image(X3,X0))),X1)
| ( relation_inverse_image(X3,X0) = relation_image(X2,X4) )
| ( apply(X2,sK12(X2,X4,relation_inverse_image(X3,X0))) = sK11(X2,X4,relation_inverse_image(X3,X0)) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369441,c_321]) ).
tcf(c_392151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X3,X0) = relation_image(X2,X4) )
| ( apply(X2,sK12(X2,X4,relation_inverse_image(X3,X0))) = sK11(X2,X4,relation_inverse_image(X3,X0)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369441,c_320]) ).
tcf(c_392152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X1,X0) = relation_image(X2,X3) )
| ( apply(X2,sK12(X2,X3,relation_inverse_image(X1,X0))) = sK11(X2,X3,relation_inverse_image(X1,X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK11(X2,X3,relation_inverse_image(X1,X0)))) ),
inference(superposition,[status(thm)],[c_369441,c_97]) ).
tcf(c_392153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK11(X2,X4,relation_inverse_image(X3,X0))),X1)
| ( relation_inverse_image(X3,X0) = relation_image(X2,X4) )
| ( apply(X2,sK12(X2,X4,relation_inverse_image(X3,X0))) = sK11(X2,X4,relation_inverse_image(X3,X0)) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369441,c_96]) ).
tcf(c_392154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X1,sK11(X0,X2,relation_inverse_image(X1,X3))),X3)
| ( relation_inverse_image(X1,X3) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,relation_inverse_image(X1,X3))) = sK11(X0,X2,relation_inverse_image(X1,X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369441,c_93]) ).
tcf(c_392155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ( apply(X0,sK12(X0,X3,relation_inverse_image(X1,X2))) = sK11(X0,X3,relation_inverse_image(X1,X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369441,c_91]) ).
tcf(c_392156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK11(X0,X2,relation_inverse_image(X1,set_intersection2(X3,X4)))),X4)
| ( relation_inverse_image(X1,set_intersection2(X3,X4)) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,relation_inverse_image(X1,set_intersection2(X3,X4)))) = sK11(X0,X2,relation_inverse_image(X1,set_intersection2(X3,X4))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369441,c_59]) ).
tcf(c_392157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK11(X0,X2,relation_inverse_image(X1,set_intersection2(X3,X4)))),X3)
| ( relation_inverse_image(X1,set_intersection2(X3,X4)) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,relation_inverse_image(X1,set_intersection2(X3,X4)))) = sK11(X0,X2,relation_inverse_image(X1,set_intersection2(X3,X4))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369441,c_58]) ).
tcf(c_392158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3))
| ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,relation_inverse_image(X2,X3))) = sK11(X0,X1,relation_inverse_image(X2,X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2)) ),
inference(superposition,[status(thm)],[c_369441,c_86]) ).
tcf(c_392159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,apply(X1,sK11(X0,X3,relation_inverse_image(X1,relation_inverse_image(X2,X4))))),X4)
| ( relation_inverse_image(X1,relation_inverse_image(X2,X4)) = relation_image(X0,X3) )
| ( apply(X0,sK12(X0,X3,relation_inverse_image(X1,relation_inverse_image(X2,X4)))) = sK11(X0,X3,relation_inverse_image(X1,relation_inverse_image(X2,X4))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369441,c_88]) ).
tcf(c_392160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK11(X0,X3,relation_inverse_image(X1,relation_inverse_image(X2,X4)))),relation_dom(X2))
| ( relation_inverse_image(X1,relation_inverse_image(X2,X4)) = relation_image(X0,X3) )
| ( apply(X0,sK12(X0,X3,relation_inverse_image(X1,relation_inverse_image(X2,X4)))) = sK11(X0,X3,relation_inverse_image(X1,relation_inverse_image(X2,X4))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369441,c_87]) ).
tcf(c_392161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X1,relation_image(X2,X3)) = relation_image(X0,X4) )
| ( apply(X0,sK12(X0,X4,relation_inverse_image(X1,relation_image(X2,X3)))) = sK11(X0,X4,relation_inverse_image(X1,relation_image(X2,X3))) )
| ( apply(X2,sK13(X2,X3,apply(X1,sK11(X0,X4,relation_inverse_image(X1,relation_image(X2,X3)))))) = apply(X1,sK11(X0,X4,relation_inverse_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369441,c_112]) ).
tcf(c_392162,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = relation_inverse_image(X1,empty_set) )
| ( apply(X0,sK12(X0,X2,relation_inverse_image(X1,empty_set))) = sK11(X0,X2,relation_inverse_image(X1,empty_set)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369441,c_372426]) ).
tcf(c_392184,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,sK11(X0,X1,empty_set)),X2)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ( apply(X0,sK12(X0,X1,relation_inverse_image(empty_set,X2))) = sK11(X0,X1,relation_inverse_image(empty_set,X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_392149,c_368630,c_103]) ).
tcf(c_392530,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X1,empty_set,powerset(X0)),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_380254,c_99]) ).
tcf(c_392547,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,empty_set),relation_dom(empty_set))
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ( apply(X0,sK12(X0,X1,relation_inverse_image(empty_set,X2))) = sK11(X0,X1,relation_inverse_image(empty_set,X2)) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373747,c_369442]) ).
tcf(c_392548,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,relation_inverse_image(empty_set,X2)),empty_set)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ( apply(X0,sK12(X0,X1,relation_inverse_image(empty_set,X2))) = sK11(X0,X1,relation_inverse_image(empty_set,X2)) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373108,c_369442]) ).
tcf(c_392549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,X3,relation_inverse_image(X0,X4)),X1)
| ( relation_inverse_image(X0,X4) = relation_image(X2,X3) )
| ( apply(X2,sK12(X2,X3,relation_inverse_image(X0,X4))) = sK11(X2,X3,relation_inverse_image(X0,X4)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369442,c_321]) ).
tcf(c_392550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,X4) = relation_image(X2,X3) )
| ( apply(X2,sK12(X2,X3,relation_inverse_image(X0,X4))) = sK11(X2,X3,relation_inverse_image(X0,X4)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369442,c_320]) ).
tcf(c_392551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,relation_inverse_image(X0,X3))) = sK11(X1,X2,relation_inverse_image(X0,X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK11(X1,X2,relation_inverse_image(X0,X3))) ),
inference(superposition,[status(thm)],[c_369442,c_97]) ).
tcf(c_392552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,X3,relation_inverse_image(X0,X4)),X1)
| ( relation_inverse_image(X0,X4) = relation_image(X2,X3) )
| ( apply(X2,sK12(X2,X3,relation_inverse_image(X0,X4))) = sK11(X2,X3,relation_inverse_image(X0,X4)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369442,c_96]) ).
tcf(c_392553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,X2,relation_inverse_image(X1,X3)),relation_dom(X1))
| ( relation_inverse_image(X1,X3) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,relation_inverse_image(X1,X3))) = sK11(X0,X2,relation_inverse_image(X1,X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369442,c_93]) ).
tcf(c_392554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,relation_inverse_image(X0,X3))) = sK11(X1,X2,relation_inverse_image(X0,X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369442,c_91]) ).
tcf(c_392562,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,empty_set),empty_set)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ( apply(X0,sK12(X0,X1,relation_inverse_image(empty_set,X2))) = sK11(X0,X1,relation_inverse_image(empty_set,X2)) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_392547,c_373108]) ).
tcf(c_392563,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ( apply(X0,sK12(X0,X1,relation_inverse_image(empty_set,X2))) = sK11(X0,X1,relation_inverse_image(empty_set,X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_392562,c_372426,c_368630,c_103]) ).
tcf(c_392620,plain,
! [X0: $i,X1: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,X1)
| ~ in(X0,relation_dom(empty_set))
| ~ in(empty_set,apply(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_375097,c_369498]) ).
tcf(c_392621,plain,
! [X0: $i,X1: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set)
| ~ in(X0,X1)
| ~ in(empty_set,apply(empty_set,X0)) ),
inference(light_normalisation,[status(thm)],[c_392620,c_373108]) ).
tcf(c_392636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,X4),set_intersection2(X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| ~ subset(relation_image(X0,X1),X3)
| ~ subset(relation_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_65,c_369499]) ).
tcf(c_392637,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),relation_image(X1,relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_67,c_369499]) ).
tcf(c_392638,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_68,c_369499]) ).
tcf(c_392639,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,X0),X2)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(empty_set,X2)
| ~ in(X0,X1)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_375097,c_369499]) ).
tcf(c_392650,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,X0),X2)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(empty_set,X2)
| ~ in(X0,empty_set)
| ~ in(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_392639,c_373108]) ).
tcf(c_392663,plain,
! [X0: $i,X1: $i] :
( subset(sK2(empty_set,X1,powerset(X0)),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_380329,c_99]) ).
tcf(c_392670,plain,
! [X0: $i] :
( ( relation_dom(sK16(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_380413]) ).
tcf(c_392671,plain,
relation_dom(sK16(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_104,c_380413]) ).
tcf(c_392672,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK16(powerset(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_380413]) ).
tcf(c_392673,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK16(powerset(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_380413]) ).
tcf(c_392674,plain,
! [X0: $i] :
( ( relation_dom(sK16(powerset(sK16(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_380413]) ).
tcf(c_392675,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| ( relation_dom(sK16(powerset(sK10(powerset(empty_set),X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_389921,c_380413]) ).
tcf(c_392697,plain,
! [X0: $i,X1: $i] :
( element(apply(empty_set,X0),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,X1)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_375097,c_369500]) ).
tcf(c_392699,plain,
! [X0: $i,X1: $i] :
( element(apply(empty_set,X0),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set)
| ~ in(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_392697,c_373108]) ).
tcf(c_392710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(relation_dom(X0),X1,X2),X2)
| ( set_intersection2(relation_dom(X0),X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X3))
| ~ in(sK2(relation_dom(X0),X1,X2),X3) ),
inference(superposition,[status(thm)],[c_368927,c_369501]) ).
tcf(c_392711,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_dom(X0),X1,X2),X2)
| ( set_intersection2(relation_dom(X0),X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X3))
| ~ in(sK2(relation_dom(X0),X1,X2),X3) ),
inference(superposition,[status(thm)],[c_55,c_369501]) ).
tcf(c_392712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,relation_dom(X1),X2),X2)
| ( set_intersection2(X0,relation_dom(X1)) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X3))
| ~ in(sK2(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_368926,c_369501]) ).
tcf(c_392713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,relation_dom(X1),X2),X2)
| ( set_intersection2(X0,relation_dom(X1)) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X3))
| ~ in(sK2(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_56,c_369501]) ).
tcf(c_392714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,relation_dom(X2)),X1)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_image(X2,X3))
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_368925,c_369501]) ).
tcf(c_392715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,relation_dom(X2)),X0)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_image(X2,X3))
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_368924,c_369501]) ).
tcf(c_392716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X1) = relation_dom(X2) )
| ~ empty(X0)
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_image(X2,X3))
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_368865,c_369501]) ).
tcf(c_392717,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,relation_dom(X2)),X1)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_image(X2,X3))
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_56,c_369501]) ).
tcf(c_392718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,relation_dom(X2)),X0)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_image(X2,X3))
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_55,c_369501]) ).
tcf(c_392719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X3))
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_368932,c_369501]) ).
tcf(c_392720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X3))
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_84,c_369501]) ).
tcf(c_392721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,relation_dom(X1),X2),X2)
| ( relation_inverse_image(X0,relation_dom(X1)) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X3))
| ~ in(apply(X0,sK7(X0,relation_dom(X1),X2)),X3) ),
inference(superposition,[status(thm)],[c_368931,c_369501]) ).
tcf(c_392722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_dom(X1),X2),X2)
| ( relation_inverse_image(X0,relation_dom(X1)) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X3))
| ~ in(apply(X0,sK7(X0,relation_dom(X1),X2)),X3) ),
inference(superposition,[status(thm)],[c_85,c_369501]) ).
tcf(c_392723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X0,sK7(X0,X1,relation_dom(X2))),X1)
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X3))
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_368930,c_369501]) ).
tcf(c_392724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X1,relation_dom(X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X3))
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_368929,c_369501]) ).
tcf(c_392725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X3))
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_368871,c_369501]) ).
tcf(c_392726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_dom(X0))
| ~ empty(relation_image(X2,X3))
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_379483,c_369501]) ).
tcf(c_392727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,relation_dom(X2)),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X3))
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_375319,c_369501]) ).
tcf(c_392728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X1,relation_dom(X2))),X1)
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X3))
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_85,c_369501]) ).
tcf(c_392729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,relation_dom(X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X3))
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_84,c_369501]) ).
tcf(c_392730,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(X0),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X2))
| ~ in(sK10(relation_dom(X0),X1),X2) ),
inference(superposition,[status(thm)],[c_95,c_369501]) ).
tcf(c_392731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X1) = relation_dom(X2) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X3))
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369301,c_369501]) ).
tcf(c_392732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X1,relation_dom(X2)),X1)
| ( relation_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X3))
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369300,c_369501]) ).
tcf(c_392733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_dom(X0))
| ~ empty(relation_image(X2,X3))
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_386602,c_369501]) ).
tcf(c_392734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X1,relation_dom(X2)),relation_dom(X0))
| ( relation_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X3))
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369215,c_369501]) ).
tcf(c_392735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X1) = relation_dom(X2) )
| ( apply(X0,sK12(X0,X1,relation_dom(X2))) = sK11(X0,X1,relation_dom(X2)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X3))
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_108,c_369501]) ).
tcf(c_392736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X1,relation_dom(X2)),X1)
| ( relation_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X3))
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_107,c_369501]) ).
tcf(c_392737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X1,relation_dom(X2)),relation_dom(X0))
| ( relation_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X3))
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_106,c_369501]) ).
tcf(c_392738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X3))
| ~ in(sK12(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369207,c_369501]) ).
tcf(c_392739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X3))
| ~ in(sK12(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_106,c_369501]) ).
tcf(c_392740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,relation_dom(X1),X2),X2)
| ( relation_image(X0,relation_dom(X1)) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X3))
| ~ in(sK12(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_369308,c_369501]) ).
tcf(c_392741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,relation_dom(X1),X2),X2)
| ( relation_image(X0,relation_dom(X1)) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X3))
| ~ in(sK12(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_107,c_369501]) ).
tcf(c_392742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X3))
| ~ in(X2,relation_image(X0,X1))
| ~ in(sK13(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_110,c_369501]) ).
tcf(c_392743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X3))
| ~ in(X2,relation_image(X0,relation_dom(X1)))
| ~ in(sK13(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_111,c_369501]) ).
tcf(c_392744,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X1))
| ~ in(sK16(relation_dom(X0)),X1) ),
inference(superposition,[status(thm)],[c_368976,c_369501]) ).
tcf(c_392745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(relation_dom(X0),X1),X2)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X3))
| ~ in(sK10(set_intersection2(relation_dom(X0),X1),X2),X3) ),
inference(superposition,[status(thm)],[c_368986,c_369501]) ).
tcf(c_392746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X0,relation_dom(X1)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X3))
| ~ in(sK10(set_intersection2(X0,relation_dom(X1)),X2),X3) ),
inference(superposition,[status(thm)],[c_368985,c_369501]) ).
tcf(c_392747,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X2))
| ~ in(sK16(set_intersection2(X0,relation_dom(X1))),X2) ),
inference(superposition,[status(thm)],[c_370750,c_369501]) ).
tcf(c_392748,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_dom(X0),X1))
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X2))
| ~ in(sK16(set_intersection2(relation_dom(X0),X1)),X2) ),
inference(superposition,[status(thm)],[c_370751,c_369501]) ).
tcf(c_392749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X1)
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,relation_dom(X3))
| ~ empty(relation_image(X3,X2))
| ~ in(sK10(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_369021,c_369501]) ).
tcf(c_392750,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,relation_dom(X0))
| ~ in(sK16(X2),X1)
| ~ empty(relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_370747,c_369501]) ).
tcf(c_392751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X0,X1),X2)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X3))
| ~ in(sK10(relation_inverse_image(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_368988,c_369501]) ).
tcf(c_392752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X0,relation_dom(X1)),X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X3))
| ~ in(apply(X0,sK10(relation_inverse_image(X0,relation_dom(X1)),X2)),X3) ),
inference(superposition,[status(thm)],[c_368987,c_369501]) ).
tcf(c_392753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_dom(X0),X1,X2),X4)
| ( set_intersection2(relation_dom(X0),X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ empty(relation_image(X0,X3))
| ~ in(sK2(relation_dom(X0),X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369015,c_369501]) ).
tcf(c_392754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,relation_dom(X4))
| ~ empty(relation_image(X4,X3))
| ~ in(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369015,c_369501]) ).
tcf(c_392755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X1)
| ( set_intersection2(X0,X1) = X2 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,relation_dom(X4))
| ~ empty(relation_image(X4,X3))
| ~ in(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369014,c_369501]) ).
tcf(c_392756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_dom(X0),X1) = X2 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X3))
| ~ in(sK2(relation_dom(X0),X1,X2),X3) ),
inference(superposition,[status(thm)],[c_368868,c_369501]) ).
tcf(c_392757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_dom(X0),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(relation_dom(X0),X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK2(relation_dom(X0),X1,set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368506,c_369501]) ).
tcf(c_392758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_dom(X0),X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(relation_dom(X0),X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK2(relation_dom(X0),X1,set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368484,c_369501]) ).
tcf(c_392759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,set_intersection2(X2,relation_dom(X3))),X0)
| ( set_intersection2(X2,relation_dom(X3)) = set_intersection2(X0,X1) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(X0,X1,set_intersection2(X2,relation_dom(X3))),X4) ),
inference(superposition,[status(thm)],[c_368506,c_369501]) ).
tcf(c_392760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,set_intersection2(X2,relation_dom(X3))),X1)
| ( set_intersection2(X2,relation_dom(X3)) = set_intersection2(X0,X1) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(X0,X1,set_intersection2(X2,relation_dom(X3))),X4) ),
inference(superposition,[status(thm)],[c_368505,c_369501]) ).
tcf(c_392761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,set_intersection2(relation_dom(X2),X3)),X0)
| ( set_intersection2(relation_dom(X2),X3) = set_intersection2(X0,X1) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_image(X2,X4))
| ~ in(sK2(X0,X1,set_intersection2(relation_dom(X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_368484,c_369501]) ).
tcf(c_392762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,set_intersection2(relation_dom(X2),X3)),X1)
| ( set_intersection2(relation_dom(X2),X3) = set_intersection2(X0,X1) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_image(X2,X4))
| ~ in(sK2(X0,X1,set_intersection2(relation_dom(X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_368483,c_369501]) ).
tcf(c_392763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,relation_dom(X3))),X1)
| ( relation_inverse_image(X0,relation_dom(X3)) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(apply(X0,sK2(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X4) ),
inference(superposition,[status(thm)],[c_368816,c_369501]) ).
tcf(c_392764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,relation_dom(X3))),X2)
| ( relation_inverse_image(X0,relation_dom(X3)) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(apply(X0,sK2(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X4) ),
inference(superposition,[status(thm)],[c_368815,c_369501]) ).
tcf(c_392765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK2(relation_dom(X0),X1,relation_inverse_image(X2,X3))),X3)
| ( set_intersection2(relation_dom(X0),X1) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK2(relation_dom(X0),X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368816,c_369501]) ).
tcf(c_392766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_dom(X0),X1,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( set_intersection2(relation_dom(X0),X1) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK2(relation_dom(X0),X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368760,c_369501]) ).
tcf(c_392767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,relation_inverse_image(X2,X3)),X0)
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X1) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_image(X2,X4))
| ~ in(sK2(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368760,c_369501]) ).
tcf(c_392768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,relation_inverse_image(X2,X3)),X1)
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X1) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_image(X2,X4))
| ~ in(sK2(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368759,c_369501]) ).
tcf(c_392769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,relation_dom(X2)),X4)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X4)
| ~ empty(relation_image(X2,X3))
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369012,c_369501]) ).
tcf(c_392770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,relation_dom(X4))
| ~ empty(relation_image(X4,X3))
| ~ in(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369012,c_369501]) ).
tcf(c_392771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_dom(X3) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368503,c_369501]) ).
tcf(c_392772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_dom(X3) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368481,c_369501]) ).
tcf(c_392773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,relation_dom(X1)),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,relation_dom(X1)),X2) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X4))
| ~ in(sK2(set_intersection2(X0,relation_dom(X1)),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_368503,c_369501]) ).
tcf(c_392774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_368481,c_369501]) ).
tcf(c_392775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,X1),X2,relation_dom(X3))),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_dom(X3) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(relation_inverse_image(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368813,c_369501]) ).
tcf(c_392776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,relation_dom(X3)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_dom(X3) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(relation_inverse_image(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368757,c_369501]) ).
tcf(c_392777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,relation_dom(X1)),X2,X3),X3)
| ( set_intersection2(relation_inverse_image(X0,relation_dom(X1)),X2) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(apply(X0,sK2(relation_inverse_image(X0,relation_dom(X1)),X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368813,c_369501]) ).
tcf(c_392778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,X3),X3)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK2(relation_inverse_image(X0,X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_368757,c_369501]) ).
tcf(c_392779,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(X0),X1) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X2))
| ~ in(sK2(relation_dom(X0),X1,relation_dom(X0)),X2) ),
inference(superposition,[status(thm)],[c_368448,c_369501]) ).
tcf(c_392780,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(X1) = empty_set )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X2))
| ~ in(sK2(empty_set,X0,relation_dom(X1)),X2) ),
inference(superposition,[status(thm)],[c_372470,c_369501]) ).
tcf(c_392781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,relation_dom(X1),X2),X4)
| ( set_intersection2(X0,relation_dom(X1)) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X4)
| ~ empty(relation_image(X1,X3))
| ~ in(sK2(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_369014,c_369501]) ).
tcf(c_392782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,relation_dom(X1)) = X2 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X3))
| ~ in(sK2(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_368867,c_369501]) ).
tcf(c_392783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,relation_dom(X1),set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,relation_dom(X1)) = set_intersection2(X2,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X4))
| ~ in(sK2(X0,relation_dom(X1),set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368505,c_369501]) ).
tcf(c_392784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,relation_dom(X1),set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,relation_dom(X1)) = set_intersection2(X2,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X4))
| ~ in(sK2(X0,relation_dom(X1),set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368483,c_369501]) ).
tcf(c_392785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK2(X0,relation_dom(X1),relation_inverse_image(X2,X3))),X3)
| ( set_intersection2(X0,relation_dom(X1)) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(relation_image(X1,X4))
| ~ in(sK2(X0,relation_dom(X1),relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368815,c_369501]) ).
tcf(c_392786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,relation_dom(X1),relation_inverse_image(X2,X3)),relation_dom(X2))
| ( set_intersection2(X0,relation_dom(X1)) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(relation_image(X1,X4))
| ~ in(sK2(X0,relation_dom(X1),relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368759,c_369501]) ).
tcf(c_392787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,relation_dom(X2)),X4)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X1,X4)
| ~ empty(relation_image(X2,X3))
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369013,c_369501]) ).
tcf(c_392788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X1,relation_dom(X4))
| ~ empty(relation_image(X4,X3))
| ~ in(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369013,c_369501]) ).
tcf(c_392789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X1) = relation_dom(X2) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_image(X2,X3))
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_368866,c_369501]) ).
tcf(c_392790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368504,c_369501]) ).
tcf(c_392791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368482,c_369501]) ).
tcf(c_392792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,relation_dom(X2)),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,relation_dom(X2))) = X3 )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_image(X2,X4))
| ~ in(sK2(X0,set_intersection2(X1,relation_dom(X2)),X3),X4) ),
inference(superposition,[status(thm)],[c_368504,c_369501]) ).
tcf(c_392793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X3)
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X4))
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X4) ),
inference(superposition,[status(thm)],[c_368482,c_369501]) ).
tcf(c_392794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,relation_inverse_image(X0,relation_dom(X2)),X3),X3)
| ( set_intersection2(X1,relation_inverse_image(X0,relation_dom(X2))) = X3 )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(apply(X0,sK2(X1,relation_inverse_image(X0,relation_dom(X2)),X3)),X4) ),
inference(superposition,[status(thm)],[c_368814,c_369501]) ).
tcf(c_392795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(X0,relation_inverse_image(X1,X2),relation_dom(X3))),X2)
| ( set_intersection2(X0,relation_inverse_image(X1,X2)) = relation_dom(X3) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(X0,relation_inverse_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368814,c_369501]) ).
tcf(c_392796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,relation_inverse_image(X1,X2),relation_dom(X3)),relation_dom(X1))
| ( set_intersection2(X0,relation_inverse_image(X1,X2)) = relation_dom(X3) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(X0,relation_inverse_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368758,c_369501]) ).
tcf(c_392797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,relation_inverse_image(X1,X2),X3),X3)
| ( set_intersection2(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X4))
| ~ in(sK2(X0,relation_inverse_image(X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_368758,c_369501]) ).
tcf(c_392798,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,relation_dom(X1)) = relation_dom(X1) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X2))
| ~ in(sK2(X0,relation_dom(X1),relation_dom(X1)),X2) ),
inference(superposition,[status(thm)],[c_368460,c_369501]) ).
tcf(c_392799,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(X1) = empty_set )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X2))
| ~ in(sK2(X0,empty_set,relation_dom(X1)),X2) ),
inference(superposition,[status(thm)],[c_372467,c_369501]) ).
tcf(c_392800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,relation_dom(X2)),X4)
| ( relation_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(X1,X4)
| ~ empty(relation_image(X2,X3))
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369299,c_369501]) ).
tcf(c_392801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X1,relation_dom(X4))
| ~ empty(relation_image(X4,X3))
| ~ in(sK12(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369299,c_369501]) ).
tcf(c_392802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X1,X2),relation_dom(X3)),X1)
| ( relation_image(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK11(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369303,c_369501]) ).
tcf(c_392803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X1,X2),relation_dom(X3)),X2)
| ( relation_image(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK11(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369302,c_369501]) ).
tcf(c_392804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,set_intersection2(X1,relation_dom(X2)),X3),X3)
| ( relation_image(X0,set_intersection2(X1,relation_dom(X2))) = X3 )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(sK12(X0,set_intersection2(X1,relation_dom(X2)),X3),X4) ),
inference(superposition,[status(thm)],[c_369302,c_369501]) ).
tcf(c_392805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,set_intersection2(relation_dom(X1),X2),X3),X3)
| ( relation_image(X0,set_intersection2(relation_dom(X1),X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(sK12(X0,set_intersection2(relation_dom(X1),X2),X3),X4) ),
inference(superposition,[status(thm)],[c_369303,c_369501]) ).
tcf(c_392806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,relation_inverse_image(X1,X2),relation_dom(X3)),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X2)) = relation_dom(X3) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK11(X0,relation_inverse_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369305,c_369501]) ).
tcf(c_392807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK12(X0,relation_inverse_image(X1,X2),relation_dom(X3))),X2)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = relation_dom(X3) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK11(X0,relation_inverse_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369304,c_369501]) ).
tcf(c_392808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X1,relation_inverse_image(X0,relation_dom(X2)),X3),X3)
| ( relation_image(X1,relation_inverse_image(X0,relation_dom(X2))) = X3 )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(apply(X0,sK12(X1,relation_inverse_image(X0,relation_dom(X2)),X3)),X4) ),
inference(superposition,[status(thm)],[c_369304,c_369501]) ).
tcf(c_392809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),X3),X3)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(sK12(X0,relation_inverse_image(X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_369305,c_369501]) ).
tcf(c_392810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK12(X0,X1,X2)) = sK11(X0,X1,X2) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,relation_dom(X4))
| ~ empty(relation_image(X4,X3))
| ~ in(sK11(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369436,c_369501]) ).
tcf(c_392811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,X2),X1)
| ( relation_image(X0,X1) = X2 )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,relation_dom(X4))
| ~ empty(relation_image(X4,X3))
| ~ in(sK11(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369307,c_369501]) ).
tcf(c_392812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,relation_dom(X4))
| ~ empty(relation_image(X4,X3))
| ~ in(sK11(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369206,c_369501]) ).
tcf(c_392813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_dom(X1),X2),X4)
| ( relation_image(X0,relation_dom(X1)) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ empty(relation_image(X1,X3))
| ~ in(sK12(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_369307,c_369501]) ).
tcf(c_392814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,relation_dom(X1)) = X2 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X3))
| ~ in(sK12(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_369309,c_369501]) ).
tcf(c_392815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_dom(X1),set_intersection2(X2,X3)),X2)
| ( relation_image(X0,relation_dom(X1)) = set_intersection2(X2,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(sK12(X0,relation_dom(X1),set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369311,c_369501]) ).
tcf(c_392816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_dom(X1),set_intersection2(X2,X3)),X3)
| ( relation_image(X0,relation_dom(X1)) = set_intersection2(X2,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(sK12(X0,relation_dom(X1),set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369310,c_369501]) ).
tcf(c_392817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X2,relation_dom(X3)) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,relation_dom(X3)))) = sK11(X0,X1,set_intersection2(X2,relation_dom(X3))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK11(X0,X1,set_intersection2(X2,relation_dom(X3))),X4) ),
inference(superposition,[status(thm)],[c_369439,c_369501]) ).
tcf(c_392818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,set_intersection2(X2,relation_dom(X3))),X1)
| ( set_intersection2(X2,relation_dom(X3)) = relation_image(X0,X1) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK11(X0,X1,set_intersection2(X2,relation_dom(X3))),X4) ),
inference(superposition,[status(thm)],[c_369310,c_369501]) ).
tcf(c_392819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,set_intersection2(X2,relation_dom(X3))),relation_dom(X0))
| ( set_intersection2(X2,relation_dom(X3)) = relation_image(X0,X1) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK11(X0,X1,set_intersection2(X2,relation_dom(X3))),X4) ),
inference(superposition,[status(thm)],[c_369209,c_369501]) ).
tcf(c_392820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_dom(X2),X3) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(relation_dom(X2),X3))) = sK11(X0,X1,set_intersection2(relation_dom(X2),X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(sK11(X0,X1,set_intersection2(relation_dom(X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_369440,c_369501]) ).
tcf(c_392821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,set_intersection2(relation_dom(X2),X3)),X1)
| ( set_intersection2(relation_dom(X2),X3) = relation_image(X0,X1) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(sK11(X0,X1,set_intersection2(relation_dom(X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_369311,c_369501]) ).
tcf(c_392822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,set_intersection2(relation_dom(X2),X3)),relation_dom(X0))
| ( set_intersection2(relation_dom(X2),X3) = relation_image(X0,X1) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(sK11(X0,X1,set_intersection2(relation_dom(X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_369210,c_369501]) ).
tcf(c_392823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X2,relation_inverse_image(X0,relation_dom(X3))),X2)
| ( relation_inverse_image(X0,relation_dom(X3)) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(apply(X0,sK11(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X4) ),
inference(superposition,[status(thm)],[c_369312,c_369501]) ).
tcf(c_392824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X2,relation_inverse_image(X0,relation_dom(X3))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_dom(X3)) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(apply(X0,sK11(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X4) ),
inference(superposition,[status(thm)],[c_369211,c_369501]) ).
tcf(c_392825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_dom(X1),relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_image(X0,relation_dom(X1)) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(sK12(X0,relation_dom(X1),relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369313,c_369501]) ).
tcf(c_392826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK11(X0,relation_dom(X1),relation_inverse_image(X2,X3))),X3)
| ( relation_image(X0,relation_dom(X1)) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(sK12(X0,relation_dom(X1),relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369312,c_369501]) ).
tcf(c_392827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,relation_inverse_image(X2,X3)),X1)
| ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(sK11(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369313,c_369501]) ).
tcf(c_392828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X0))
| ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(sK11(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369212,c_369501]) ).
tcf(c_392829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,X2),X4)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ empty(relation_image(X0,X3))
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369020,c_369501]) ).
tcf(c_392830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,X2),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,relation_dom(X4))
| ~ empty(relation_image(X4,X3))
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369020,c_369501]) ).
tcf(c_392831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X1,X2)),X1)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,relation_dom(X4))
| ~ empty(relation_image(X4,X3))
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369019,c_369501]) ).
tcf(c_392832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X3))
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_368873,c_369501]) ).
tcf(c_392833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK7(X0,X1,set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368673,c_369501]) ).
tcf(c_392834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK7(X0,X1,set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368672,c_369501]) ).
tcf(c_392835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X1,set_intersection2(X2,relation_dom(X3)))),X1)
| ( set_intersection2(X2,relation_dom(X3)) = relation_inverse_image(X0,X1) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK7(X0,X1,set_intersection2(X2,relation_dom(X3))),X4) ),
inference(superposition,[status(thm)],[c_368700,c_369501]) ).
tcf(c_392836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,set_intersection2(X2,relation_dom(X3))),relation_dom(X0))
| ( set_intersection2(X2,relation_dom(X3)) = relation_inverse_image(X0,X1) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK7(X0,X1,set_intersection2(X2,relation_dom(X3))),X4) ),
inference(superposition,[status(thm)],[c_368672,c_369501]) ).
tcf(c_392837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X1,set_intersection2(relation_dom(X2),X3))),X1)
| ( set_intersection2(relation_dom(X2),X3) = relation_inverse_image(X0,X1) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(sK7(X0,X1,set_intersection2(relation_dom(X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_368701,c_369501]) ).
tcf(c_392838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,set_intersection2(relation_dom(X2),X3)),relation_dom(X0))
| ( set_intersection2(relation_dom(X2),X3) = relation_inverse_image(X0,X1) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(sK7(X0,X1,set_intersection2(relation_dom(X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_368673,c_369501]) ).
tcf(c_392839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,X2,relation_inverse_image(X0,relation_dom(X3))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_dom(X3)) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(apply(X0,sK7(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X4) ),
inference(superposition,[status(thm)],[c_368819,c_369501]) ).
tcf(c_392840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X2)
| ( relation_inverse_image(X0,relation_dom(X3)) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(apply(X0,sK7(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X4) ),
inference(superposition,[status(thm)],[c_368818,c_369501]) ).
tcf(c_392841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X0,X1,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368819,c_369501]) ).
tcf(c_392842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368763,c_369501]) ).
tcf(c_392843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368763,c_369501]) ).
tcf(c_392844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X1,relation_inverse_image(X2,X3))),X1)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368762,c_369501]) ).
tcf(c_392845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,relation_dom(X2)),X4)
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X4)
| ~ empty(relation_image(X2,X3))
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369017,c_369501]) ).
tcf(c_392846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ empty(relation_image(X4,X3))
| ~ subset(relation_dom(X0),relation_dom(X4))
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369017,c_369501]) ).
tcf(c_392847,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X1) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X2))
| ~ in(sK7(X0,X1,relation_dom(X0)),X2) ),
inference(superposition,[status(thm)],[c_368674,c_369501]) ).
tcf(c_392848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,X2),X4)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ empty(relation_image(X0,X3))
| ~ in(sK12(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369206,c_369501]) ).
tcf(c_392849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X1) = X2 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X3))
| ~ in(sK12(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369208,c_369501]) ).
tcf(c_392850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK12(X0,X1,set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369210,c_369501]) ).
tcf(c_392851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK12(X0,X1,set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369209,c_369501]) ).
tcf(c_392852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK12(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369212,c_369501]) ).
tcf(c_392853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK11(X0,X1,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK12(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369211,c_369501]) ).
tcf(c_392854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,relation_dom(X2)),X4)
| ( relation_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X4)
| ~ empty(relation_image(X2,X3))
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369214,c_369501]) ).
tcf(c_392855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ empty(relation_image(X4,X3))
| ~ subset(relation_dom(X0),relation_dom(X4))
| ~ in(sK12(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369214,c_369501]) ).
tcf(c_392856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_dom(X1),X2),X4)
| ( relation_inverse_image(X0,relation_dom(X1)) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ empty(relation_image(X1,X3))
| ~ in(apply(X0,sK7(X0,relation_dom(X1),X2)),X3) ),
inference(superposition,[status(thm)],[c_369019,c_369501]) ).
tcf(c_392857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,relation_dom(X1)) = X2 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X3))
| ~ in(apply(X0,sK7(X0,relation_dom(X1),X2)),X3) ),
inference(superposition,[status(thm)],[c_368872,c_369501]) ).
tcf(c_392858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_dom(X1),set_intersection2(X2,X3)),X2)
| ( relation_inverse_image(X0,relation_dom(X1)) = set_intersection2(X2,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(apply(X0,sK7(X0,relation_dom(X1),set_intersection2(X2,X3))),X4) ),
inference(superposition,[status(thm)],[c_368701,c_369501]) ).
tcf(c_392859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_dom(X1),set_intersection2(X2,X3)),X3)
| ( relation_inverse_image(X0,relation_dom(X1)) = set_intersection2(X2,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(apply(X0,sK7(X0,relation_dom(X1),set_intersection2(X2,X3))),X4) ),
inference(superposition,[status(thm)],[c_368700,c_369501]) ).
tcf(c_392860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X0,relation_dom(X1),relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X0,relation_dom(X1)) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(apply(X0,sK7(X0,relation_dom(X1),relation_inverse_image(X2,X3))),X4) ),
inference(superposition,[status(thm)],[c_368818,c_369501]) ).
tcf(c_392861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_dom(X1),relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X0,relation_dom(X1)) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(apply(X0,sK7(X0,relation_dom(X1),relation_inverse_image(X2,X3))),X4) ),
inference(superposition,[status(thm)],[c_368762,c_369501]) ).
tcf(c_392862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X1,relation_dom(X4))
| ~ empty(relation_image(X4,X3))
| ~ in(apply(X0,sK7(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_369018,c_369501]) ).
tcf(c_392863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X1,relation_dom(X2))),X4)
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(X1,X4)
| ~ empty(relation_image(X2,X3))
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369018,c_369501]) ).
tcf(c_392864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X1,X2),relation_dom(X3))),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK7(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368703,c_369501]) ).
tcf(c_392865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X1,X2),relation_dom(X3))),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK7(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368702,c_369501]) ).
tcf(c_392866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X1,relation_dom(X2)),X3),X3)
| ( relation_inverse_image(X0,set_intersection2(X1,relation_dom(X2))) = X3 )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(apply(X0,sK7(X0,set_intersection2(X1,relation_dom(X2)),X3)),X4) ),
inference(superposition,[status(thm)],[c_368702,c_369501]) ).
tcf(c_392867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(relation_dom(X1),X2),X3),X3)
| ( relation_inverse_image(X0,set_intersection2(relation_dom(X1),X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(apply(X0,sK7(X0,set_intersection2(relation_dom(X1),X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_368703,c_369501]) ).
tcf(c_392868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X2),relation_dom(X3)))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = relation_dom(X3) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK7(X0,relation_inverse_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368817,c_369501]) ).
tcf(c_392869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),relation_dom(X3))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = relation_dom(X3) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK7(X0,relation_inverse_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368761,c_369501]) ).
tcf(c_392870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,relation_inverse_image(X0,relation_dom(X2)),X3),X3)
| ( relation_inverse_image(X1,relation_inverse_image(X0,relation_dom(X2))) = X3 )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(apply(X0,apply(X1,sK7(X1,relation_inverse_image(X0,relation_dom(X2)),X3))),X4) ),
inference(superposition,[status(thm)],[c_368817,c_369501]) ).
tcf(c_392871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),X3),X3)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_368761,c_369501]) ).
tcf(c_392872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,relation_dom(X3)) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,relation_inverse_image(X0,relation_dom(X3)))) = sK11(X1,X2,relation_inverse_image(X0,relation_dom(X3))) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(apply(X0,sK11(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X4) ),
inference(superposition,[status(thm)],[c_369441,c_369501]) ).
tcf(c_392873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,relation_inverse_image(X2,X3))) = sK11(X0,X1,relation_inverse_image(X2,X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(sK11(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369442,c_369501]) ).
tcf(c_392874,plain,
! [X0: $i,X1: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X1,empty_set)
| ~ in(X1,X0)
| ~ empty(relation_image(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_373108,c_369501]) ).
tcf(c_392875,plain,
! [X0: $i,X1: $i] :
( ~ empty(empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set)
| ~ in(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_392874,c_375097]) ).
tcf(c_394739,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,relation_image(X0,X1),X2),X2)
| ( relation_inverse_image(X0,relation_image(X0,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),X2),X2)
| ~ in(sK7(X0,relation_image(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_368932,c_369502]) ).
tcf(c_394743,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,relation_image(X0,X1)) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X1))
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368871,c_369502]) ).
tcf(c_394744,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,relation_image(X0,X1)) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0))
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_369502]) ).
tcf(c_394748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_image(X0,X1),X2),X3)
| ( relation_inverse_image(X0,relation_image(X0,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ in(sK7(X0,relation_image(X0,X1),X2),X2)
| ~ in(sK7(X0,relation_image(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_369020,c_369502]) ).
tcf(c_394749,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_image(X0,X1),X2),relation_dom(X0))
| ( relation_inverse_image(X0,relation_image(X0,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,relation_dom(X0))
| ~ in(sK7(X0,relation_image(X0,X1),X2),X2)
| ~ in(sK7(X0,relation_image(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_369020,c_369502]) ).
tcf(c_394750,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,relation_image(X0,X1),X2)),relation_image(X0,X1))
| ( relation_inverse_image(X0,relation_image(X0,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,relation_dom(X0))
| ~ in(sK7(X0,relation_image(X0,X1),X2),X2)
| ~ in(sK7(X0,relation_image(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_369019,c_369502]) ).
tcf(c_394751,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,relation_image(X0,X1)) = X2 )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),X2),X2)
| ~ in(sK7(X0,relation_image(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_368873,c_369502]) ).
tcf(c_394752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_image(X0,X1),set_intersection2(X2,X3)),X2)
| ( relation_inverse_image(X0,relation_image(X0,X1)) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),set_intersection2(X2,X3)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),set_intersection2(X2,X3)),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_368673,c_369502]) ).
tcf(c_394753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_image(X0,X1),set_intersection2(X2,X3)),X3)
| ( relation_inverse_image(X0,relation_image(X0,X1)) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),set_intersection2(X2,X3)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),set_intersection2(X2,X3)),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_368672,c_369502]) ).
tcf(c_394754,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,relation_image(X0,X1),set_intersection2(X2,relation_dom(X0)))),relation_image(X0,X1))
| ( relation_inverse_image(X0,relation_image(X0,X1)) = set_intersection2(X2,relation_dom(X0)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),set_intersection2(X2,relation_dom(X0))),X1)
| ~ in(sK7(X0,relation_image(X0,X1),set_intersection2(X2,relation_dom(X0))),set_intersection2(X2,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_368700,c_369502]) ).
tcf(c_394755,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_image(X0,X1),set_intersection2(X2,relation_dom(X0))),relation_dom(X0))
| ( relation_inverse_image(X0,relation_image(X0,X1)) = set_intersection2(X2,relation_dom(X0)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),set_intersection2(X2,relation_dom(X0))),X1)
| ~ in(sK7(X0,relation_image(X0,X1),set_intersection2(X2,relation_dom(X0))),set_intersection2(X2,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_368672,c_369502]) ).
tcf(c_394756,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,relation_image(X0,X1),set_intersection2(relation_dom(X0),X2))),relation_image(X0,X1))
| ( relation_inverse_image(X0,relation_image(X0,X1)) = set_intersection2(relation_dom(X0),X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),set_intersection2(relation_dom(X0),X2)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),set_intersection2(relation_dom(X0),X2)),set_intersection2(relation_dom(X0),X2)) ),
inference(superposition,[status(thm)],[c_368701,c_369502]) ).
tcf(c_394757,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_image(X0,X1),set_intersection2(relation_dom(X0),X2)),relation_dom(X0))
| ( relation_inverse_image(X0,relation_image(X0,X1)) = set_intersection2(relation_dom(X0),X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),set_intersection2(relation_dom(X0),X2)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),set_intersection2(relation_dom(X0),X2)),set_intersection2(relation_dom(X0),X2)) ),
inference(superposition,[status(thm)],[c_368673,c_369502]) ).
tcf(c_394758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK7(X0,relation_image(X0,X1),relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X0,relation_image(X0,X1)) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),relation_inverse_image(X2,X3)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368819,c_369502]) ).
tcf(c_394759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_image(X0,X1),relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X0,relation_image(X0,X1)) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),relation_inverse_image(X2,X3)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368763,c_369502]) ).
tcf(c_394760,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_image(X0,X1),relation_inverse_image(X0,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,relation_image(X0,X1)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),relation_inverse_image(X0,X2)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),relation_inverse_image(X0,X2)),relation_inverse_image(X0,X2)) ),
inference(superposition,[status(thm)],[c_368763,c_369502]) ).
tcf(c_394761,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,relation_image(X0,X1),relation_inverse_image(X0,X2))),relation_image(X0,X1))
| ( relation_inverse_image(X0,relation_image(X0,X1)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),relation_inverse_image(X0,X2)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),relation_inverse_image(X0,X2)),relation_inverse_image(X0,X2)) ),
inference(superposition,[status(thm)],[c_368762,c_369502]) ).
tcf(c_394762,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),X2)
| ( relation_inverse_image(X0,relation_image(X0,X1)) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X2)
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369017,c_369502]) ).
tcf(c_394764,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,relation_image(X0,X1)) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368674,c_369502]) ).
tcf(c_394765,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,relation_image(X0,X1),relation_dom(X0))),X2)
| ( relation_inverse_image(X0,relation_image(X0,X1)) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_image(X0,X1),X2)
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369018,c_369502]) ).
tcf(c_394766,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(empty_set,relation_image(empty_set,X0)) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(sK7(empty_set,empty_set,X1),relation_dom(empty_set))
| ~ in(sK7(empty_set,relation_image(empty_set,X0),X1),X1)
| ~ in(sK7(empty_set,relation_image(empty_set,X0),X1),X0) ),
inference(superposition,[status(thm)],[c_375097,c_369502]) ).
tcf(c_394767,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(empty_set,relation_image(empty_set,X0)) = X1 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(sK7(empty_set,relation_image(empty_set,X0),X1),empty_set)
| ~ in(sK7(empty_set,relation_image(empty_set,X0),X1),X1)
| ~ in(sK7(empty_set,relation_image(empty_set,X0),X1),X0) ),
inference(superposition,[status(thm)],[c_373108,c_369502]) ).
tcf(c_394779,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(empty_set,empty_set) = X0 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(sK7(empty_set,empty_set,X0),empty_set)
| ~ in(sK7(empty_set,empty_set,X0),X1)
| ~ in(sK7(empty_set,empty_set,X0),X0) ),
inference(light_normalisation,[status(thm)],[c_394766,c_373108,c_375097]) ).
tcf(c_394944,plain,
! [X0: $i,X1: $i] :
( ~ empty(powerset(X1))
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_368984,c_380683]) ).
tcf(c_394945,plain,
! [X0: $i] : ~ subset(powerset(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_100,c_380683]) ).
tcf(c_394946,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(powerset(X2),X1)
| ~ subset(powerset(X2),X0)
| ~ subset(powerset(set_intersection2(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_65,c_380683]) ).
tcf(c_394950,plain,
! [X0: $i] : ~ empty(powerset(powerset(X0))),
inference(superposition,[status(thm)],[c_368984,c_394945]) ).
tcf(c_394951,plain,
! [X0: $i,X1: $i] :
( ~ subset(powerset(powerset(set_intersection2(X0,X1))),X1)
| ~ subset(powerset(powerset(set_intersection2(X0,X1))),X0) ),
inference(superposition,[status(thm)],[c_65,c_394945]) ).
tcf(c_394964,plain,
! [X0: $i,X1: $i] :
( in(X0,empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,X1)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_373747,c_369503]) ).
tcf(c_394965,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_inverse_image(empty_set,empty_set))
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,X1)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_375097,c_369503]) ).
tcf(c_394966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_inverse_image(X0,relation_image(X0,X1)),X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(relation_inverse_image(X0,relation_image(X0,X1)),X2,X3),X3)
| ~ in(sK2(relation_inverse_image(X0,relation_image(X0,X1)),X2,X3),X2)
| ~ in(sK2(relation_inverse_image(X0,relation_image(X0,X1)),X2,X3),X1)
| ~ in(sK2(relation_inverse_image(X0,relation_image(X0,X1)),X2,X3),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369503,c_54]) ).
tcf(c_394967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X3,X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,X1)
| ~ in(X3,relation_dom(X0))
| ~ subset(relation_inverse_image(X0,relation_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_369503,c_321]) ).
tcf(c_394968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,X1)
| ~ in(X3,relation_dom(X0))
| ~ subset(relation_inverse_image(X0,relation_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_369503,c_320]) ).
tcf(c_394969,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X2,X1)
| ~ in(X2,relation_dom(X0))
| ~ in(relation_inverse_image(X0,relation_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_369503,c_97]) ).
tcf(c_394970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,X1)
| ~ in(X3,relation_dom(X0))
| ~ subset(relation_inverse_image(X0,relation_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_369503,c_96]) ).
tcf(c_394971,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,relation_inverse_image(X1,relation_image(X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_369503,c_93]) ).
tcf(c_394972,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X2,X1)
| ~ in(X2,relation_dom(X0))
| ~ empty(relation_inverse_image(X0,relation_image(X0,X1))) ),
inference(superposition,[status(thm)],[c_369503,c_91]) ).
tcf(c_394973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,relation_inverse_image(X1,relation_image(X1,X2))) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK7(X0,relation_inverse_image(X1,relation_image(X1,X2)),X3),X3)
| ~ in(sK7(X0,relation_inverse_image(X1,relation_image(X1,X2)),X3),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,relation_inverse_image(X1,relation_image(X1,X2)),X3)),X2)
| ~ in(apply(X0,sK7(X0,relation_inverse_image(X1,relation_image(X1,X2)),X3)),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_369503,c_83]) ).
tcf(c_394974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_inverse_image(X0,relation_inverse_image(X2,relation_image(X2,X3))))
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X3)
| ~ in(apply(X0,X1),relation_dom(X2)) ),
inference(superposition,[status(thm)],[c_369503,c_86]) ).
tcf(c_394977,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,relation_inverse_image(X1,relation_image(X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK10(X0,relation_inverse_image(X1,relation_image(X1,X2))),X2)
| ~ in(sK10(X0,relation_inverse_image(X1,relation_image(X1,X2))),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_369503,c_94]) ).
tcf(c_394978,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(powerset(X2),X1)
| ~ in(powerset(X2),relation_dom(X0))
| ~ subset(relation_inverse_image(X0,relation_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_369503,c_372982]) ).
tcf(c_394979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(set_intersection2(X2,X3),X1)
| ~ in(set_intersection2(X2,X3),relation_dom(X0))
| ~ in(relation_inverse_image(X0,relation_image(X0,X1)),X3)
| ~ in(relation_inverse_image(X0,relation_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_369503,c_369080]) ).
tcf(c_394980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,set_intersection2(relation_inverse_image(X1,relation_image(X1,X2)),X3))
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK10(X0,set_intersection2(relation_inverse_image(X1,relation_image(X1,X2)),X3)),X3)
| ~ in(sK10(X0,set_intersection2(relation_inverse_image(X1,relation_image(X1,X2)),X3)),X2)
| ~ in(sK10(X0,set_intersection2(relation_inverse_image(X1,relation_image(X1,X2)),X3)),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_369503,c_368972]) ).
tcf(c_394981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(relation_inverse_image(X0,relation_image(X0,X1)),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,relation_image(X0,X1)),X2),X3,X4),X4)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,relation_image(X0,X1)),X2),X3,X4),X3)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,relation_image(X0,X1)),X2),X3,X4),X2)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,relation_image(X0,X1)),X2),X3,X4),X1)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,relation_image(X0,X1)),X2),X3,X4),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369503,c_368471]) ).
tcf(c_394982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,set_intersection2(relation_inverse_image(X1,relation_image(X1,X2)),X3)) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK7(X0,set_intersection2(relation_inverse_image(X1,relation_image(X1,X2)),X3),X4),X4)
| ~ in(sK7(X0,set_intersection2(relation_inverse_image(X1,relation_image(X1,X2)),X3),X4),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,set_intersection2(relation_inverse_image(X1,relation_image(X1,X2)),X3),X4)),X3)
| ~ in(apply(X0,sK7(X0,set_intersection2(relation_inverse_image(X1,relation_image(X1,X2)),X3),X4)),X2)
| ~ in(apply(X0,sK7(X0,set_intersection2(relation_inverse_image(X1,relation_image(X1,X2)),X3),X4)),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_369503,c_368654]) ).
tcf(c_394984,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_inverse_image(empty_set,empty_set))
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set)
| ~ in(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_394965,c_373108]) ).
tcf(c_395113,plain,
! [X0: $i,X1: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X1,relation_image(empty_set,X0))
| ~ in(empty_set,sK13(empty_set,X0,X1)) ),
inference(superposition,[status(thm)],[c_373108,c_369555]) ).
tcf(c_395114,plain,
! [X0: $i,X1: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X1,empty_set)
| ~ in(empty_set,sK13(empty_set,X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_395113,c_375097]) ).
tcf(c_395125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK13(X1,X2,X0),X4)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X4)
| ~ subset(relation_dom(X1),X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_321]) ).
tcf(c_395126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ empty(X4)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X4)
| ~ subset(relation_dom(X1),X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_320]) ).
tcf(c_395127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X0)
| ~ in(X3,relation_image(X1,X2))
| ~ in(X0,sK13(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_369556,c_97]) ).
tcf(c_395128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X1,X2,X0),X4)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X4)
| ~ subset(relation_dom(X1),X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_96]) ).
tcf(c_395131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X0,X4,X3),X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,X4))
| ~ subset(relation_dom(X0),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_59]) ).
tcf(c_395132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X0,X4,X3),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,X4))
| ~ subset(relation_dom(X0),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_58]) ).
tcf(c_395133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK13(X0,X4,X3)),X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,X4))
| ~ subset(relation_dom(X0),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_88]) ).
tcf(c_395134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X0,X4,X3),relation_dom(X1))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,X4))
| ~ subset(relation_dom(X0),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_87]) ).
tcf(c_395135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(X1,sK13(X1,X2,sK13(X0,X4,X3))) = sK13(X0,X4,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,X4))
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_112]) ).
tcf(c_395136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ empty(relation_image(X4,X3))
| ~ subset(relation_dom(X0),relation_dom(X4))
| ~ in(X2,relation_image(X0,X1))
| ~ in(sK13(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369556,c_369501]) ).
tcf(c_395137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK13(X0,X1,X2),X3)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_image(X0,X1))
| ~ subset(relation_dom(X0),sK10(sK13(X0,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_369556,c_369085]) ).
tcf(c_395138,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),empty_set)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_372426]) ).
tcf(c_395139,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK13(X0,X1,X2))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_image(X0,X1))
| ~ subset(relation_dom(X0),sK16(sK13(X0,X1,X2))) ),
inference(superposition,[status(thm)],[c_369556,c_370746]) ).
tcf(c_395140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,sK13(X0,X3,X4)),X1)
| ( sK13(X0,X3,X4) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_image(X0,X3))
| ~ subset(relation_dom(X0),sK2(X1,X2,sK13(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369556,c_369079]) ).
tcf(c_395141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,sK13(X0,X3,X4)),X2)
| ( sK13(X0,X3,X4) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_image(X0,X3))
| ~ subset(relation_dom(X0),sK2(X1,X2,sK13(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369556,c_369078]) ).
tcf(c_395142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(sK13(X0,X1,X2),X3,X4),X4)
| ( set_intersection2(sK13(X0,X1,X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_image(X0,X1))
| ~ subset(relation_dom(X0),sK2(sK13(X0,X1,X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_369556,c_369076]) ).
tcf(c_395143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,sK13(X0,X2,X3),X4),X4)
| ( set_intersection2(X1,sK13(X0,X2,X3)) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,X2))
| ~ subset(relation_dom(X0),sK2(X1,sK13(X0,X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_369556,c_369077]) ).
tcf(c_395144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X1,sK13(X0,X2,X3),X4),X4)
| ( relation_image(X1,sK13(X0,X2,X3)) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,X2))
| ~ subset(relation_dom(X0),sK12(X1,sK13(X0,X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_369556,c_369298]) ).
tcf(c_395145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK13(X0,X3,X4) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK13(X0,X3,X4))) = sK11(X1,X2,sK13(X0,X3,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X4,relation_image(X0,X3))
| ~ subset(relation_dom(X0),sK11(X1,X2,sK13(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369556,c_369435]) ).
tcf(c_395146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X2,sK13(X0,X3,X4)),X2)
| ( sK13(X0,X3,X4) = relation_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X4,relation_image(X0,X3))
| ~ subset(relation_dom(X0),sK11(X1,X2,sK13(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369556,c_369306]) ).
tcf(c_395147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X2,sK13(X0,X3,X4)),relation_dom(X1))
| ( sK13(X0,X3,X4) = relation_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X4,relation_image(X0,X3))
| ~ subset(relation_dom(X0),sK11(X1,X2,sK13(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369556,c_369205]) ).
tcf(c_395148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,X2,sK13(X0,X3,X4)),relation_dom(X1))
| ( sK13(X0,X3,X4) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X4,relation_image(X0,X3))
| ~ subset(relation_dom(X0),sK7(X1,X2,sK13(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369556,c_369084]) ).
tcf(c_395149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X1,X2,sK13(X0,X3,X4))),X2)
| ( sK13(X0,X3,X4) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X4,relation_image(X0,X3))
| ~ subset(relation_dom(X0),sK7(X1,X2,sK13(X0,X3,X4))) ),
inference(superposition,[status(thm)],[c_369556,c_369083]) ).
tcf(c_395150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,sK13(X0,X2,X3),X4),X4)
| ( relation_inverse_image(X1,sK13(X0,X2,X3)) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,X2))
| ~ subset(relation_dom(X0),apply(X1,sK7(X1,sK13(X0,X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_369556,c_369082]) ).
tcf(c_395369,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK7(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_380722,c_92]) ).
tcf(c_395370,plain,
! [X0: $i,X1: $i] :
( subset(sK7(empty_set,X1,powerset(X0)),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_380722,c_99]) ).
tcf(c_395376,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,X0)
| in(sK10(empty_set,X0),X1) ),
inference(demodulation,[status(thm)],[c_380839,c_368545]) ).
tcf(c_395385,plain,
! [X0: $i,X1: $i] :
( element(sK13(empty_set,X1,X0),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,relation_image(empty_set,X1)) ),
inference(superposition,[status(thm)],[c_373108,c_369557]) ).
tcf(c_395387,plain,
! [X0: $i,X1: $i] :
( element(sK13(empty_set,X1,X0),empty_set)
| ~ in(X0,relation_image(empty_set,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_395385,c_368630,c_103]) ).
tcf(c_395398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(relation_image(X0,X1),X2,X3),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368927,c_369558]) ).
tcf(c_395399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_image(X0,X1),X2,X3),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_55,c_369558]) ).
tcf(c_395400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X1,relation_image(X0,X2),X3),X3)
| ( set_intersection2(X1,relation_image(X0,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368926,c_369558]) ).
tcf(c_395401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,relation_image(X0,X2),X3),X3)
| ( set_intersection2(X1,relation_image(X0,X2)) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_56,c_369558]) ).
tcf(c_395402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,relation_image(X0,X1)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368925,c_369558]) ).
tcf(c_395403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,relation_image(X0,X1)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368924,c_369558]) ).
tcf(c_395404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X2) = set_intersection2(X1,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368865,c_369558]) ).
tcf(c_395405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_image(X0,X1)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_56,c_369558]) ).
tcf(c_395406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_image(X0,X1)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_55,c_369558]) ).
tcf(c_395407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X1,relation_image(X0,X2),X3),X3)
| ( relation_inverse_image(X1,relation_image(X0,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368931,c_369558]) ).
tcf(c_395408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,relation_image(X0,X2),X3),X3)
| ( relation_inverse_image(X1,relation_image(X0,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_85,c_369558]) ).
tcf(c_395409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X1,sK7(X1,X2,relation_image(X0,X3))),X2)
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368930,c_369558]) ).
tcf(c_395410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X1,X2,relation_image(X0,X3)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368929,c_369558]) ).
tcf(c_395411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368871,c_369558]) ).
tcf(c_395412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X2) = relation_image(X1,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X1))
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_369558]) ).
tcf(c_395413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X2,relation_image(X0,X3)),relation_inverse_image(X1,X2))
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_375319,c_369558]) ).
tcf(c_395414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,X2,relation_image(X0,X3))),X2)
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_85,c_369558]) ).
tcf(c_395415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X2,relation_image(X0,X3)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_84,c_369558]) ).
tcf(c_395416,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_image(X0,X1),X2)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_95,c_369558]) ).
tcf(c_395417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X3) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369301,c_369558]) ).
tcf(c_395418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X1,X3,relation_image(X0,X2)),X3)
| ( relation_image(X0,X2) = relation_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369300,c_369558]) ).
tcf(c_395419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X2) = relation_image(X1,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X1))
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_386602,c_369558]) ).
tcf(c_395420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X1,X3,relation_image(X0,X2)),relation_dom(X1))
| ( relation_image(X0,X2) = relation_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369215,c_369558]) ).
tcf(c_395421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,relation_image(X0,X3))) = sK11(X1,X2,relation_image(X0,X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_108,c_369558]) ).
tcf(c_395422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X3,relation_image(X0,X2)),X3)
| ( relation_image(X0,X2) = relation_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_107,c_369558]) ).
tcf(c_395423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X3,relation_image(X0,X2)),relation_dom(X1))
| ( relation_image(X0,X2) = relation_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_106,c_369558]) ).
tcf(c_395424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X1,relation_image(X0,X2),X3),X3)
| ( relation_image(X1,relation_image(X0,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369308,c_369558]) ).
tcf(c_395425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,relation_image(X0,X2),X3),X3)
| ( relation_image(X1,relation_image(X0,X2)) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_107,c_369558]) ).
tcf(c_395426,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_109,c_369558]) ).
tcf(c_395427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(relation_dom(X2))
| ~ in(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_111,c_369558]) ).
tcf(c_395428,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368976,c_369558]) ).
tcf(c_395429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(relation_image(X0,X1),X2),X3)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368986,c_369558]) ).
tcf(c_395430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X1,relation_image(X0,X2)),X3)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368985,c_369558]) ).
tcf(c_395431,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X1,relation_image(X0,X2)))
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370750,c_369558]) ).
tcf(c_395432,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_image(X0,X1),X2))
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370751,c_369558]) ).
tcf(c_395433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369021,c_369558]) ).
tcf(c_395434,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370747,c_369558]) ).
tcf(c_395435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X1,relation_image(X0,X2)),X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368987,c_369558]) ).
tcf(c_395436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X2,X3),X4,X0),X1)
| ( set_intersection2(relation_image(X2,X3),X4) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_369558]) ).
tcf(c_395437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| ( set_intersection2(X3,X4) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369015,c_369558]) ).
tcf(c_395438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| ( set_intersection2(X3,X4) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369014,c_369558]) ).
tcf(c_395439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_image(X0,X2),X3) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368868,c_369558]) ).
tcf(c_395440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X0,X1),X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(relation_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368506,c_369558]) ).
tcf(c_395441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X0,X1),X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368484,c_369558]) ).
tcf(c_395442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X1,relation_image(X0,X2))),X3)
| ( set_intersection2(X1,relation_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368506,c_369558]) ).
tcf(c_395443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X1,relation_image(X0,X2))),X4)
| ( set_intersection2(X1,relation_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368505,c_369558]) ).
tcf(c_395444,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(relation_image(X0,X1),X2)),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368484,c_369558]) ).
tcf(c_395445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(relation_image(X0,X1),X2)),X4)
| ( set_intersection2(relation_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368483,c_369558]) ).
tcf(c_395446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X1,relation_image(X0,X2))),X3)
| ( relation_inverse_image(X1,relation_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368816,c_369558]) ).
tcf(c_395447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X1,relation_image(X0,X2))),X4)
| ( relation_inverse_image(X1,relation_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368815,c_369558]) ).
tcf(c_395448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(relation_image(X0,X2),X3,relation_inverse_image(X1,X4))),X4)
| ( set_intersection2(relation_image(X0,X2),X3) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368816,c_369558]) ).
tcf(c_395449,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X0,X2),X3,relation_inverse_image(X1,X4)),relation_dom(X1))
| ( set_intersection2(relation_image(X0,X2),X3) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368760,c_369558]) ).
tcf(c_395450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X4,relation_image(X2,X3)),X1)
| ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_369558]) ).
tcf(c_395451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| ( set_intersection2(X0,X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369012,c_369558]) ).
tcf(c_395452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_image(X0,X4)),X2)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368503,c_369558]) ).
tcf(c_395453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_image(X0,X4)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368481,c_369558]) ).
tcf(c_395454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,relation_image(X0,X2)),X3,X4),X4)
| ( set_intersection2(set_intersection2(X1,relation_image(X0,X2)),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368503,c_369558]) ).
tcf(c_395455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368481,c_369558]) ).
tcf(c_395456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(relation_inverse_image(X1,X2),X3,relation_image(X0,X4))),X2)
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368813,c_369558]) ).
tcf(c_395457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X1,X2),X3,relation_image(X0,X4)),relation_dom(X1))
| ( set_intersection2(relation_inverse_image(X1,X2),X3) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368757,c_369558]) ).
tcf(c_395458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X1,relation_image(X0,X2)),X3,X4),X4)
| ( set_intersection2(relation_inverse_image(X1,relation_image(X0,X2)),X3) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368813,c_369558]) ).
tcf(c_395459,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_image(X0,X1),X2) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368448,c_369558]) ).
tcf(c_395461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_image(X2,X4),X0),X1)
| ( set_intersection2(X3,relation_image(X2,X4)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_369558]) ).
tcf(c_395462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,relation_image(X0,X3)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368867,c_369558]) ).
tcf(c_395463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,relation_image(X0,X2),set_intersection2(X3,X4)),X4)
| ( set_intersection2(X1,relation_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368505,c_369558]) ).
tcf(c_395464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,relation_image(X0,X2),set_intersection2(X3,X4)),X3)
| ( set_intersection2(X1,relation_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368483,c_369558]) ).
tcf(c_395465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(X2,relation_image(X0,X3),relation_inverse_image(X1,X4))),X4)
| ( set_intersection2(X2,relation_image(X0,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368815,c_369558]) ).
tcf(c_395466,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_image(X0,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| ( set_intersection2(X2,relation_image(X0,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368759,c_369558]) ).
tcf(c_395467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X4,X0,relation_image(X2,X3)),X1)
| ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_369558]) ).
tcf(c_395468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| ( set_intersection2(X3,X0) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369013,c_369558]) ).
tcf(c_395469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X2) = set_intersection2(X3,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368866,c_369558]) ).
tcf(c_395470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_image(X0,X4)),X3)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368504,c_369558]) ).
tcf(c_395471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_image(X0,X4)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368482,c_369558]) ).
tcf(c_395472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,relation_image(X0,X3)),X4),X4)
| ( set_intersection2(X1,set_intersection2(X2,relation_image(X0,X3))) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368504,c_369558]) ).
tcf(c_395473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(relation_image(X0,X2),X3),X4),X4)
| ( set_intersection2(X1,set_intersection2(relation_image(X0,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368482,c_369558]) ).
tcf(c_395474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_inverse_image(X1,relation_image(X0,X3)),X4),X4)
| ( set_intersection2(X2,relation_inverse_image(X1,relation_image(X0,X3))) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368814,c_369558]) ).
tcf(c_395475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(X2,relation_inverse_image(X1,X3),relation_image(X0,X4))),X3)
| ( set_intersection2(X2,relation_inverse_image(X1,X3)) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368814,c_369558]) ).
tcf(c_395476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_inverse_image(X1,X3),relation_image(X0,X4)),relation_dom(X1))
| ( set_intersection2(X2,relation_inverse_image(X1,X3)) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368758,c_369558]) ).
tcf(c_395477,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_image(X0,X2)) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368460,c_369558]) ).
tcf(c_395478,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_372467,c_369558]) ).
tcf(c_395479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X1))
| ~ in(X3,relation_image(X0,X4))
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_369558]) ).
tcf(c_395480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X0,relation_image(X2,X4)),X1)
| ( relation_image(X2,X4) = relation_image(X3,X0) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_369558]) ).
tcf(c_395481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X0,X4),X4)
| ( relation_image(X3,X0) = X4 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369299,c_369558]) ).
tcf(c_395482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,set_intersection2(X2,X3),relation_image(X0,X4)),X2)
| ( relation_image(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369303,c_369558]) ).
tcf(c_395483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,set_intersection2(X2,X3),relation_image(X0,X4)),X3)
| ( relation_image(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369302,c_369558]) ).
tcf(c_395484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X1,set_intersection2(X2,relation_image(X0,X3)),X4),X4)
| ( relation_image(X1,set_intersection2(X2,relation_image(X0,X3))) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369302,c_369558]) ).
tcf(c_395485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X1,set_intersection2(relation_image(X0,X2),X3),X4),X4)
| ( relation_image(X1,set_intersection2(relation_image(X0,X2),X3)) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369303,c_369558]) ).
tcf(c_395486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,relation_inverse_image(X2,X3),relation_image(X0,X4)),relation_dom(X2))
| ( relation_image(X1,relation_inverse_image(X2,X3)) = relation_image(X0,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369305,c_369558]) ).
tcf(c_395487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK12(X1,relation_inverse_image(X2,X3),relation_image(X0,X4))),X3)
| ( relation_image(X1,relation_inverse_image(X2,X3)) = relation_image(X0,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369304,c_369558]) ).
tcf(c_395488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X1,relation_inverse_image(X2,relation_image(X0,X3)),X4),X4)
| ( relation_image(X1,relation_inverse_image(X2,relation_image(X0,X3))) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369304,c_369558]) ).
tcf(c_395489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X3,X4) = X0 )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369436,c_369558]) ).
tcf(c_395490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| ( relation_image(X3,X4) = X0 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369307,c_369558]) ).
tcf(c_395491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),relation_dom(X3))
| ( relation_image(X3,X4) = X0 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369206,c_369558]) ).
tcf(c_395492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,relation_image(X2,X4),X0),X1)
| ( relation_image(X3,relation_image(X2,X4)) = X0 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_369558]) ).
tcf(c_395493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X1,relation_image(X0,X3)) = X2 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369309,c_369558]) ).
tcf(c_395494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X1,relation_image(X0,X2),set_intersection2(X3,X4)),X3)
| ( relation_image(X1,relation_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369311,c_369558]) ).
tcf(c_395495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X1,relation_image(X0,X2),set_intersection2(X3,X4)),X4)
| ( relation_image(X1,relation_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369310,c_369558]) ).
tcf(c_395496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,relation_image(X0,X4)) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,set_intersection2(X3,relation_image(X0,X4)))) = sK11(X1,X2,set_intersection2(X3,relation_image(X0,X4))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369439,c_369558]) ).
tcf(c_395497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X4,set_intersection2(X2,relation_image(X0,X3))),X4)
| ( set_intersection2(X2,relation_image(X0,X3)) = relation_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369310,c_369558]) ).
tcf(c_395498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X4,set_intersection2(X2,relation_image(X0,X3))),relation_dom(X1))
| ( set_intersection2(X2,relation_image(X0,X3)) = relation_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369209,c_369558]) ).
tcf(c_395499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X0,X3),X4) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,set_intersection2(relation_image(X0,X3),X4))) = sK11(X1,X2,set_intersection2(relation_image(X0,X3),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369440,c_369558]) ).
tcf(c_395500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X4,set_intersection2(relation_image(X0,X2),X3)),X4)
| ( set_intersection2(relation_image(X0,X2),X3) = relation_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369311,c_369558]) ).
tcf(c_395501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X4,set_intersection2(relation_image(X0,X2),X3)),relation_dom(X1))
| ( set_intersection2(relation_image(X0,X2),X3) = relation_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369210,c_369558]) ).
tcf(c_395502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X4,relation_inverse_image(X2,relation_image(X0,X3))),X4)
| ( relation_inverse_image(X2,relation_image(X0,X3)) = relation_image(X1,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369312,c_369558]) ).
tcf(c_395503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X4,relation_inverse_image(X2,relation_image(X0,X3))),relation_dom(X1))
| ( relation_inverse_image(X2,relation_image(X0,X3)) = relation_image(X1,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369211,c_369558]) ).
tcf(c_395504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X1,relation_image(X0,X3),relation_inverse_image(X2,X4)),relation_dom(X2))
| ( relation_image(X1,relation_image(X0,X3)) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369313,c_369558]) ).
tcf(c_395505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK11(X1,relation_image(X0,X3),relation_inverse_image(X2,X4))),X4)
| ( relation_image(X1,relation_image(X0,X3)) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369312,c_369558]) ).
tcf(c_395506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),relation_dom(X3))
| ( relation_inverse_image(X3,X4) = X0 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369020,c_369558]) ).
tcf(c_395507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X3,X4,X0)),X4)
| ( relation_inverse_image(X3,X4) = X0 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369019,c_369558]) ).
tcf(c_395508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X1,X4,set_intersection2(X2,relation_image(X0,X3)))),X4)
| ( set_intersection2(X2,relation_image(X0,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368700,c_369558]) ).
tcf(c_395509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,X4,set_intersection2(X2,relation_image(X0,X3))),relation_dom(X1))
| ( set_intersection2(X2,relation_image(X0,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368672,c_369558]) ).
tcf(c_395510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X1,X4,set_intersection2(relation_image(X0,X2),X3))),X4)
| ( set_intersection2(relation_image(X0,X2),X3) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368701,c_369558]) ).
tcf(c_395511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,X4,set_intersection2(relation_image(X0,X2),X3)),relation_dom(X1))
| ( set_intersection2(relation_image(X0,X2),X3) = relation_inverse_image(X1,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368673,c_369558]) ).
tcf(c_395512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,X4,relation_inverse_image(X2,relation_image(X0,X3))),relation_dom(X1))
| ( relation_inverse_image(X2,relation_image(X0,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368819,c_369558]) ).
tcf(c_395513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X1,X4,relation_inverse_image(X2,relation_image(X0,X3)))),X4)
| ( relation_inverse_image(X2,relation_image(X0,X3)) = relation_inverse_image(X1,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368818,c_369558]) ).
tcf(c_395514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,relation_image(X2,X4)),X1)
| ( relation_inverse_image(X0,X3) = relation_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_dom(X2))
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_369558]) ).
tcf(c_395515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| ( relation_inverse_image(X0,X3) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X1))
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369017,c_369558]) ).
tcf(c_395516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X3,relation_image(X2,X4)),X1)
| ( relation_image(X0,X3) = relation_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_dom(X2))
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_369558]) ).
tcf(c_395517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X3,X4),X4)
| ( relation_image(X0,X3) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X1))
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369214,c_369558]) ).
tcf(c_395518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,relation_image(X2,X4),X0),X1)
| ( relation_inverse_image(X3,relation_image(X2,X4)) = X0 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_369558]) ).
tcf(c_395519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X1,relation_image(X0,X3)) = X2 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368872,c_369558]) ).
tcf(c_395520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,relation_image(X0,X2),set_intersection2(X3,X4)),X3)
| ( relation_inverse_image(X1,relation_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368701,c_369558]) ).
tcf(c_395521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,relation_image(X0,X2),set_intersection2(X3,X4)),X4)
| ( relation_inverse_image(X1,relation_image(X0,X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368700,c_369558]) ).
tcf(c_395522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X1,relation_image(X0,X3),relation_inverse_image(X2,X4))),X4)
| ( relation_inverse_image(X1,relation_image(X0,X3)) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368818,c_369558]) ).
tcf(c_395523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,relation_image(X0,X3),relation_inverse_image(X2,X4)),relation_dom(X2))
| ( relation_inverse_image(X1,relation_image(X0,X3)) = relation_inverse_image(X2,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368762,c_369558]) ).
tcf(c_395524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| ( relation_inverse_image(X3,X0) = X4 )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369018,c_369558]) ).
tcf(c_395525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X3,X0,relation_image(X2,X4))),X1)
| ( relation_inverse_image(X3,X0) = relation_image(X2,X4) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_369558]) ).
tcf(c_395526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X1,set_intersection2(X2,X3),relation_image(X0,X4))),X2)
| ( relation_inverse_image(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368703,c_369558]) ).
tcf(c_395527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X1,set_intersection2(X2,X3),relation_image(X0,X4))),X3)
| ( relation_inverse_image(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368702,c_369558]) ).
tcf(c_395528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,set_intersection2(X2,relation_image(X0,X3)),X4),X4)
| ( relation_inverse_image(X1,set_intersection2(X2,relation_image(X0,X3))) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368702,c_369558]) ).
tcf(c_395529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,set_intersection2(relation_image(X0,X2),X3),X4),X4)
| ( relation_inverse_image(X1,set_intersection2(relation_image(X0,X2),X3)) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368703,c_369558]) ).
tcf(c_395530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,apply(X1,sK7(X1,relation_inverse_image(X2,X3),relation_image(X0,X4)))),X3)
| ( relation_inverse_image(X1,relation_inverse_image(X2,X3)) = relation_image(X0,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368817,c_369558]) ).
tcf(c_395531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X1,relation_inverse_image(X2,X3),relation_image(X0,X4))),relation_dom(X2))
| ( relation_inverse_image(X1,relation_inverse_image(X2,X3)) = relation_image(X0,X4) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368761,c_369558]) ).
tcf(c_395532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,relation_inverse_image(X2,relation_image(X0,X3)),X4),X4)
| ( relation_inverse_image(X1,relation_inverse_image(X2,relation_image(X0,X3))) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368817,c_369558]) ).
tcf(c_395533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X2,relation_image(X0,X4)) = relation_image(X1,X3) )
| ( apply(X1,sK12(X1,X3,relation_inverse_image(X2,relation_image(X0,X4)))) = sK11(X1,X3,relation_inverse_image(X2,relation_image(X0,X4))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369441,c_369558]) ).
tcf(c_396899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X3,relation_image(X1,sK10(X0,X2)))
| ~ subset(X0,sK13(X1,sK10(X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_369021,c_369593]) ).
tcf(c_396900,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,sK16(X0)))
| ~ subset(X0,sK13(X1,sK16(X0),X2)) ),
inference(superposition,[status(thm)],[c_370747,c_369593]) ).
tcf(c_396901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X0),X2)
| ( set_intersection2(X2,X3) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X4,relation_image(X1,sK2(X2,X3,X0)))
| ~ subset(X0,sK13(X1,sK2(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369015,c_369593]) ).
tcf(c_396902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X0),X3)
| ( set_intersection2(X2,X3) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X4,relation_image(X1,sK2(X2,X3,X0)))
| ~ subset(X0,sK13(X1,sK2(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369014,c_369593]) ).
tcf(c_396903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X2,X3),X3)
| ( set_intersection2(X0,X2) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X4,relation_image(X1,sK2(X0,X2,X3)))
| ~ subset(X0,sK13(X1,sK2(X0,X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_369012,c_369593]) ).
tcf(c_396904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X0,X3),X3)
| ( set_intersection2(X2,X0) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X4,relation_image(X1,sK2(X2,X0,X3)))
| ~ subset(X0,sK13(X1,sK2(X2,X0,X3),X4)) ),
inference(superposition,[status(thm)],[c_369013,c_369593]) ).
tcf(c_396905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,X2))
| ~ in(X4,relation_image(X1,sK13(X0,X2,X3)))
| ~ subset(relation_dom(X0),sK13(X1,sK13(X0,X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_369556,c_369593]) ).
tcf(c_396906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,X0,X3),X3)
| ( relation_image(X2,X0) = X3 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,relation_image(X1,sK12(X2,X0,X3)))
| ~ subset(X0,sK13(X1,sK12(X2,X0,X3),X4)) ),
inference(superposition,[status(thm)],[c_369299,c_369593]) ).
tcf(c_396907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X2,X3) = X0 )
| ( apply(X2,sK12(X2,X3,X0)) = sK11(X2,X3,X0) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,relation_image(X1,sK11(X2,X3,X0)))
| ~ subset(X0,sK13(X1,sK11(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369436,c_369593]) ).
tcf(c_396908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X3,X0),X3)
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,relation_image(X1,sK11(X2,X3,X0)))
| ~ subset(X0,sK13(X1,sK11(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369307,c_369593]) ).
tcf(c_396909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X3,X0),relation_dom(X2))
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,relation_image(X1,sK11(X2,X3,X0)))
| ~ subset(X0,sK13(X1,sK11(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369206,c_369593]) ).
tcf(c_396910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X3,X0),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,relation_image(X1,sK7(X2,X3,X0)))
| ~ subset(X0,sK13(X1,sK7(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369020,c_369593]) ).
tcf(c_396911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,X3,X0)),X3)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,relation_image(X1,sK7(X2,X3,X0)))
| ~ subset(X0,sK13(X1,sK7(X2,X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_369019,c_369593]) ).
tcf(c_396912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X2,X3),X3)
| ( relation_inverse_image(X0,X2) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X4,relation_image(X1,sK7(X0,X2,X3)))
| ~ subset(relation_dom(X0),sK13(X1,sK7(X0,X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_369017,c_369593]) ).
tcf(c_396913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X2,X3),X3)
| ( relation_image(X0,X2) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X4,relation_image(X1,sK12(X0,X2,X3)))
| ~ subset(relation_dom(X0),sK13(X1,sK12(X0,X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_369214,c_369593]) ).
tcf(c_396914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X0,X3),X3)
| ( relation_inverse_image(X2,X0) = X3 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,relation_image(X1,apply(X2,sK7(X2,X0,X3))))
| ~ subset(X0,sK13(X1,apply(X2,sK7(X2,X0,X3)),X4)) ),
inference(superposition,[status(thm)],[c_369018,c_369593]) ).
tcf(c_397126,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,X2),X0) = X0 )
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_65,c_380931]) ).
tcf(c_397127,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_image(X0,relation_dom(X0)),relation_image(X0,X1)) = relation_image(X0,X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_67,c_380931]) ).
tcf(c_397128,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_image(X0,relation_inverse_image(X0,X1))) = relation_image(X0,relation_inverse_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_380931]) ).
tcf(c_397129,plain,
! [X0: $i] :
( empty(X0)
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_369762,c_380931]) ).
tcf(c_397130,plain,
! [X0: $i] : set_intersection2(X0,sK16(powerset(X0))) = sK16(powerset(X0)),
inference(superposition,[status(thm)],[c_369151,c_380931]) ).
tcf(c_397132,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( set_intersection2(X0,sK10(powerset(X0),X1)) = sK10(powerset(X0),X1) ) ),
inference(superposition,[status(thm)],[c_372645,c_380931]) ).
tcf(c_397136,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X0,X1),
inference(superposition,[status(thm)],[c_380919,c_380931]) ).
tcf(c_397137,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,set_intersection2(X1,X0)) = set_intersection2(X1,X0),
inference(superposition,[status(thm)],[c_380850,c_380931]) ).
tcf(c_397156,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,set_intersection2(X1,X2)) = X0 )
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_65,c_381110]) ).
tcf(c_397157,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_image(X0,X1),relation_image(X0,relation_dom(X0))) = relation_image(X0,X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_67,c_381110]) ).
tcf(c_397158,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_image(X0,relation_inverse_image(X0,X1)),X1) = relation_image(X0,relation_inverse_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_381110]) ).
tcf(c_397159,plain,
! [X0: $i] :
( empty(X0)
| ( set_intersection2(sK15(X0),X0) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_369762,c_381110]) ).
tcf(c_397160,plain,
! [X0: $i] : set_intersection2(sK16(powerset(X0)),X0) = sK16(powerset(X0)),
inference(superposition,[status(thm)],[c_369151,c_381110]) ).
tcf(c_397162,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( set_intersection2(sK10(powerset(X0),X1),X0) = sK10(powerset(X0),X1) ) ),
inference(superposition,[status(thm)],[c_372645,c_381110]) ).
tcf(c_397166,plain,
! [X0: $i,X1: $i] : set_intersection2(set_intersection2(X0,X1),X0) = set_intersection2(X0,X1),
inference(superposition,[status(thm)],[c_380919,c_381110]) ).
tcf(c_397167,plain,
! [X0: $i,X1: $i] : set_intersection2(set_intersection2(X0,X1),X1) = set_intersection2(X0,X1),
inference(superposition,[status(thm)],[c_380850,c_381110]) ).
tcf(c_397190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK13(X1,X2,X0),X4)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X4)
| ~ subset(X2,X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_321]) ).
tcf(c_397191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ empty(X4)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X4)
| ~ subset(X2,X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_320]) ).
tcf(c_397192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X0)
| ~ in(X3,relation_image(X1,X2))
| ~ in(X0,sK13(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_369594,c_97]) ).
tcf(c_397193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X1,X2,X0),X4)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X4)
| ~ subset(X2,X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_96]) ).
tcf(c_397196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X1,X2,X0),X4)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,set_intersection2(X3,X4))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_59]) ).
tcf(c_397197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X1,X2,X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,set_intersection2(X3,X4))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_58]) ).
tcf(c_397198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK13(X1,X2,X0)),X4)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X2,relation_inverse_image(X3,X4))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_88]) ).
tcf(c_397199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X1,X2,X0),relation_dom(X3))
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X2,relation_inverse_image(X3,X4))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_87]) ).
tcf(c_397200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_dom(X3))
| ~ subset(X2,relation_image(X3,X4))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_369558]) ).
tcf(c_397201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(X3,sK13(X3,X4,sK13(X1,X2,X0))) = sK13(X1,X2,X0) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X2,relation_image(X3,X4))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_112]) ).
tcf(c_397202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X1,relation_dom(X4))
| ~ empty(relation_image(X4,X3))
| ~ in(X2,relation_image(X0,X1))
| ~ in(sK13(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369594,c_369501]) ).
tcf(c_397203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK13(X1,X0,X2),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X0))
| ~ subset(X0,sK10(sK13(X1,X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_369594,c_369085]) ).
tcf(c_397204,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,empty_set)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_372426]) ).
tcf(c_397205,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(sK13(X1,X0,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X0))
| ~ subset(X0,sK16(sK13(X1,X0,X2))) ),
inference(superposition,[status(thm)],[c_369594,c_370746]) ).
tcf(c_397206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,sK13(X3,X0,X4)),X1)
| ( sK13(X3,X0,X4) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(X4,relation_image(X3,X0))
| ~ subset(X0,sK2(X1,X2,sK13(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369594,c_369079]) ).
tcf(c_397207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,sK13(X3,X0,X4)),X2)
| ( sK13(X3,X0,X4) = set_intersection2(X1,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(X4,relation_image(X3,X0))
| ~ subset(X0,sK2(X1,X2,sK13(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369594,c_369078]) ).
tcf(c_397208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(sK13(X1,X0,X2),X3,X4),X4)
| ( set_intersection2(sK13(X1,X0,X2),X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X0))
| ~ subset(X0,sK2(sK13(X1,X0,X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_369594,c_369076]) ).
tcf(c_397209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,sK13(X2,X0,X3),X4),X4)
| ( set_intersection2(X1,sK13(X2,X0,X3)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_image(X2,X0))
| ~ subset(X0,sK2(X1,sK13(X2,X0,X3),X4)) ),
inference(superposition,[status(thm)],[c_369594,c_369077]) ).
tcf(c_397210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X3,relation_image(X2,X0))
| ~ in(X4,relation_image(X1,sK13(X2,X0,X3)))
| ~ subset(X0,sK13(X1,sK13(X2,X0,X3),X4)) ),
inference(superposition,[status(thm)],[c_369594,c_369593]) ).
tcf(c_397211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X1,sK13(X2,X0,X3),X4),X4)
| ( relation_image(X1,sK13(X2,X0,X3)) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X3,relation_image(X2,X0))
| ~ subset(X0,sK12(X1,sK13(X2,X0,X3),X4)) ),
inference(superposition,[status(thm)],[c_369594,c_369298]) ).
tcf(c_397212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK13(X3,X0,X4) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK13(X3,X0,X4))) = sK11(X1,X2,sK13(X3,X0,X4)) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X4,relation_image(X3,X0))
| ~ subset(X0,sK11(X1,X2,sK13(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369594,c_369435]) ).
tcf(c_397213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X2,sK13(X3,X0,X4)),X2)
| ( sK13(X3,X0,X4) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X4,relation_image(X3,X0))
| ~ subset(X0,sK11(X1,X2,sK13(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369594,c_369306]) ).
tcf(c_397214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X2,sK13(X3,X0,X4)),relation_dom(X1))
| ( sK13(X3,X0,X4) = relation_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X4,relation_image(X3,X0))
| ~ subset(X0,sK11(X1,X2,sK13(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369594,c_369205]) ).
tcf(c_397215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,X2,sK13(X3,X0,X4)),relation_dom(X1))
| ( sK13(X3,X0,X4) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X4,relation_image(X3,X0))
| ~ subset(X0,sK7(X1,X2,sK13(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369594,c_369084]) ).
tcf(c_397216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X1,X2,sK13(X3,X0,X4))),X2)
| ( sK13(X3,X0,X4) = relation_inverse_image(X1,X2) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X4,relation_image(X3,X0))
| ~ subset(X0,sK7(X1,X2,sK13(X3,X0,X4))) ),
inference(superposition,[status(thm)],[c_369594,c_369083]) ).
tcf(c_397217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,sK13(X2,X0,X3),X4),X4)
| ( relation_inverse_image(X1,sK13(X2,X0,X3)) = X4 )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X3,relation_image(X2,X0))
| ~ subset(X0,apply(X1,sK7(X1,sK13(X2,X0,X3),X4))) ),
inference(superposition,[status(thm)],[c_369594,c_369082]) ).
tcf(c_397555,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK13(X1,powerset(X2),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_369595,c_99]) ).
tcf(c_397568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(relation_image(X0,X1),X2,X3),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368927,c_369596]) ).
tcf(c_397569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_image(X0,X1),X2,X3),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_369596]) ).
tcf(c_397570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,relation_image(X0,X1),X3),X3)
| ( set_intersection2(X2,relation_image(X0,X1)) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368926,c_369596]) ).
tcf(c_397571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,relation_image(X0,X1),X3),X3)
| ( set_intersection2(X2,relation_image(X0,X1)) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_369596]) ).
tcf(c_397572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,relation_image(X0,X1)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368925,c_369596]) ).
tcf(c_397573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X3,relation_image(X0,X1)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368924,c_369596]) ).
tcf(c_397574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X2) = set_intersection2(X1,X3) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368865,c_369596]) ).
tcf(c_397575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_image(X0,X1)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_369596]) ).
tcf(c_397576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_image(X0,X1)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_369596]) ).
tcf(c_397577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,relation_image(X1,X2),X3),X3)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = X3 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368931,c_369596]) ).
tcf(c_397578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_image(X1,X2),X3),X3)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = X3 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_369596]) ).
tcf(c_397579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X0,sK7(X0,X3,relation_image(X1,X2))),X3)
| ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368930,c_369596]) ).
tcf(c_397580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X3,relation_image(X1,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368929,c_369596]) ).
tcf(c_397581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X2) = relation_image(X1,X3) )
| ~ empty(X3)
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368871,c_369596]) ).
tcf(c_397582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_369596]) ).
tcf(c_397583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,relation_image(X1,X2)),relation_inverse_image(X0,X3))
| ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375319,c_369596]) ).
tcf(c_397584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X3,relation_image(X1,X2))),X3)
| ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_369596]) ).
tcf(c_397585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,relation_image(X1,X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_84,c_369596]) ).
tcf(c_397586,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_image(X0,X1),X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_95,c_369596]) ).
tcf(c_397587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X2) = relation_image(X1,X3) )
| ~ empty(X3)
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369301,c_369596]) ).
tcf(c_397588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X3,relation_image(X1,X2)),X3)
| ( relation_image(X0,X3) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369300,c_369596]) ).
tcf(c_397589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X3) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_386602,c_369596]) ).
tcf(c_397590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X3,relation_image(X1,X2)),relation_dom(X0))
| ( relation_image(X0,X3) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369215,c_369596]) ).
tcf(c_397591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X0,sK12(X0,X3,relation_image(X1,X2))) = sK11(X0,X3,relation_image(X1,X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_369596]) ).
tcf(c_397592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_image(X1,X2)),X3)
| ( relation_image(X0,X3) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_369596]) ).
tcf(c_397593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_image(X1,X2)),relation_dom(X0))
| ( relation_image(X0,X3) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_106,c_369596]) ).
tcf(c_397594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,relation_image(X1,X2),X3),X3)
| ( relation_image(X0,relation_image(X1,X2)) = X3 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369308,c_369596]) ).
tcf(c_397595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,relation_image(X1,X2),X3),X3)
| ( relation_image(X0,relation_image(X1,X2)) = X3 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_369596]) ).
tcf(c_397596,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_109,c_369596]) ).
tcf(c_397597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_111,c_369596]) ).
tcf(c_397598,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368976,c_369596]) ).
tcf(c_397599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(relation_image(X0,X1),X2),X3)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368986,c_369596]) ).
tcf(c_397600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X2,relation_image(X0,X1)),X3)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368985,c_369596]) ).
tcf(c_397601,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,relation_image(X0,X1)))
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370750,c_369596]) ).
tcf(c_397602,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_image(X0,X1),X2))
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370751,c_369596]) ).
tcf(c_397603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369021,c_369596]) ).
tcf(c_397604,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370747,c_369596]) ).
tcf(c_397605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X0,relation_image(X1,X2)),X3)
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368987,c_369596]) ).
tcf(c_397606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X2,X3),X4,X0),X1)
| ( set_intersection2(relation_image(X2,X3),X4) = X0 )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_369596]) ).
tcf(c_397607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X3)
| ( set_intersection2(X3,X4) = X0 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369015,c_369596]) ).
tcf(c_397608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X0),X4)
| ( set_intersection2(X3,X4) = X0 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369014,c_369596]) ).
tcf(c_397609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_image(X0,X2),X3) = X1 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368868,c_369596]) ).
tcf(c_397610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X0,X1),X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(relation_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368506,c_369596]) ).
tcf(c_397611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X0,X1),X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368484,c_369596]) ).
tcf(c_397612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X2,relation_image(X0,X1))),X3)
| ( set_intersection2(X2,relation_image(X0,X1)) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368506,c_369596]) ).
tcf(c_397613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X2,relation_image(X0,X1))),X4)
| ( set_intersection2(X2,relation_image(X0,X1)) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368505,c_369596]) ).
tcf(c_397614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(relation_image(X0,X1),X2)),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368484,c_369596]) ).
tcf(c_397615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(relation_image(X0,X1),X2)),X4)
| ( set_intersection2(relation_image(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368483,c_369596]) ).
tcf(c_397616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,relation_image(X1,X2))),X3)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_369596]) ).
tcf(c_397617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_inverse_image(X0,relation_image(X1,X2))),X4)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_369596]) ).
tcf(c_397618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(relation_image(X1,X2),X3,relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(relation_image(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_369596]) ).
tcf(c_397619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X1,X2),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(relation_image(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368760,c_369596]) ).
tcf(c_397620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X4,relation_image(X2,X3)),X1)
| ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_369596]) ).
tcf(c_397621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X3,X4),X4)
| ( set_intersection2(X0,X3) = X4 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369012,c_369596]) ).
tcf(c_397622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)),X3)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368503,c_369596]) ).
tcf(c_397623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368481,c_369596]) ).
tcf(c_397624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,relation_image(X0,X1)),X3,X4),X4)
| ( set_intersection2(set_intersection2(X2,relation_image(X0,X1)),X3) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368503,c_369596]) ).
tcf(c_397625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368481,c_369596]) ).
tcf(c_397626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,X3),X4,relation_image(X1,X2))),X3)
| ( set_intersection2(relation_inverse_image(X0,X3),X4) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_369596]) ).
tcf(c_397627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X3),X4,relation_image(X1,X2)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X3),X4) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368757,c_369596]) ).
tcf(c_397628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,relation_image(X1,X2)),X3,X4),X4)
| ( set_intersection2(relation_inverse_image(X0,relation_image(X1,X2)),X3) = X4 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_369596]) ).
tcf(c_397629,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_image(X0,X1),X2) = relation_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368448,c_369596]) ).
tcf(c_397631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X4,relation_image(X2,X3),X0),X1)
| ( set_intersection2(X4,relation_image(X2,X3)) = X0 )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_369596]) ).
tcf(c_397632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,relation_image(X0,X2)) = X1 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368867,c_369596]) ).
tcf(c_397633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_image(X0,X1),set_intersection2(X3,X4)),X4)
| ( set_intersection2(X2,relation_image(X0,X1)) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368505,c_369596]) ).
tcf(c_397634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_image(X0,X1),set_intersection2(X3,X4)),X3)
| ( set_intersection2(X2,relation_image(X0,X1)) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368483,c_369596]) ).
tcf(c_397635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(X3,relation_image(X1,X2),relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(X3,relation_image(X1,X2)) = relation_inverse_image(X0,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_369596]) ).
tcf(c_397636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_image(X1,X2),relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(X3,relation_image(X1,X2)) = relation_inverse_image(X0,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368759,c_369596]) ).
tcf(c_397637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X4,X0,relation_image(X2,X3)),X1)
| ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_369596]) ).
tcf(c_397638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X0,X4),X4)
| ( set_intersection2(X3,X0) = X4 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369013,c_369596]) ).
tcf(c_397639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X2) = set_intersection2(X3,X1) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368866,c_369596]) ).
tcf(c_397640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)),X4)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368504,c_369596]) ).
tcf(c_397641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368482,c_369596]) ).
tcf(c_397642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,relation_image(X0,X1)),X4),X4)
| ( set_intersection2(X2,set_intersection2(X3,relation_image(X0,X1))) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368504,c_369596]) ).
tcf(c_397643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(relation_image(X0,X1),X3),X4),X4)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X1),X3)) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368482,c_369596]) ).
tcf(c_397644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_inverse_image(X0,relation_image(X1,X2)),X4),X4)
| ( set_intersection2(X3,relation_inverse_image(X0,relation_image(X1,X2))) = X4 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_369596]) ).
tcf(c_397645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(X3,relation_inverse_image(X0,X4),relation_image(X1,X2))),X4)
| ( set_intersection2(X3,relation_inverse_image(X0,X4)) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_369596]) ).
tcf(c_397646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_inverse_image(X0,X4),relation_image(X1,X2)),relation_dom(X0))
| ( set_intersection2(X3,relation_inverse_image(X0,X4)) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368758,c_369596]) ).
tcf(c_397647,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,relation_image(X0,X1)) = relation_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368460,c_369596]) ).
tcf(c_397649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ empty(X4)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X2,relation_image(X3,X4))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_369596]) ).
tcf(c_397650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,X4))
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_369596]) ).
tcf(c_397651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X0,relation_image(X3,X4)),X1)
| ( relation_image(X2,X0) = relation_image(X3,X4) )
| ~ empty(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_369596]) ).
tcf(c_397652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X0,X4),X4)
| ( relation_image(X3,X0) = X4 )
| ~ empty(X2)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369299,c_369596]) ).
tcf(c_397653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X3,X4),relation_image(X1,X2)),X3)
| ( relation_image(X0,set_intersection2(X3,X4)) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_369596]) ).
tcf(c_397654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X3,X4),relation_image(X1,X2)),X4)
| ( relation_image(X0,set_intersection2(X3,X4)) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_369596]) ).
tcf(c_397655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,set_intersection2(X3,relation_image(X1,X2)),X4),X4)
| ( relation_image(X0,set_intersection2(X3,relation_image(X1,X2))) = X4 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_369596]) ).
tcf(c_397656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,set_intersection2(relation_image(X1,X2),X3),X4),X4)
| ( relation_image(X0,set_intersection2(relation_image(X1,X2),X3)) = X4 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_369596]) ).
tcf(c_397657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,relation_inverse_image(X1,X4),relation_image(X2,X3)),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X4)) = relation_image(X2,X3) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369305,c_369596]) ).
tcf(c_397658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK12(X0,relation_inverse_image(X1,X4),relation_image(X2,X3))),X4)
| ( relation_image(X0,relation_inverse_image(X1,X4)) = relation_image(X2,X3) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_369596]) ).
tcf(c_397659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_inverse_image(X1,relation_image(X2,X3)),X4),X4)
| ( relation_image(X0,relation_inverse_image(X1,relation_image(X2,X3))) = X4 )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_369596]) ).
tcf(c_397660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X3,X4) = X0 )
| ( apply(X3,sK12(X3,X4,X0)) = sK11(X3,X4,X0) )
| ~ empty(X2)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369436,c_369596]) ).
tcf(c_397661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),X4)
| ( relation_image(X3,X4) = X0 )
| ~ empty(X2)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369307,c_369596]) ).
tcf(c_397662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X0),relation_dom(X3))
| ( relation_image(X3,X4) = X0 )
| ~ empty(X2)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369206,c_369596]) ).
tcf(c_397663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,relation_image(X3,X4),X0),X1)
| ( relation_image(X2,relation_image(X3,X4)) = X0 )
| ~ empty(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_369596]) ).
tcf(c_397664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,relation_image(X1,X3)) = X2 )
| ~ empty(X3)
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369309,c_369596]) ).
tcf(c_397665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_image(X1,X2),set_intersection2(X3,X4)),X3)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_369596]) ).
tcf(c_397666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_image(X1,X2),set_intersection2(X3,X4)),X4)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_369596]) ).
tcf(c_397667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X4,relation_image(X1,X2)) = relation_image(X0,X3) )
| ( apply(X0,sK12(X0,X3,set_intersection2(X4,relation_image(X1,X2)))) = sK11(X0,X3,set_intersection2(X4,relation_image(X1,X2))) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369439,c_369596]) ).
tcf(c_397668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(X3,relation_image(X1,X2))),X4)
| ( set_intersection2(X3,relation_image(X1,X2)) = relation_image(X0,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_369596]) ).
tcf(c_397669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(X3,relation_image(X1,X2))),relation_dom(X0))
| ( set_intersection2(X3,relation_image(X1,X2)) = relation_image(X0,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369209,c_369596]) ).
tcf(c_397670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X1,X2),X4) = relation_image(X0,X3) )
| ( apply(X0,sK12(X0,X3,set_intersection2(relation_image(X1,X2),X4))) = sK11(X0,X3,set_intersection2(relation_image(X1,X2),X4)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369440,c_369596]) ).
tcf(c_397671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(relation_image(X1,X2),X3)),X4)
| ( set_intersection2(relation_image(X1,X2),X3) = relation_image(X0,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_369596]) ).
tcf(c_397672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,set_intersection2(relation_image(X1,X2),X3)),relation_dom(X0))
| ( set_intersection2(relation_image(X1,X2),X3) = relation_image(X0,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369210,c_369596]) ).
tcf(c_397673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_inverse_image(X1,relation_image(X2,X3))),X4)
| ( relation_inverse_image(X1,relation_image(X2,X3)) = relation_image(X0,X4) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_369596]) ).
tcf(c_397674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_inverse_image(X1,relation_image(X2,X3))),relation_dom(X0))
| ( relation_inverse_image(X1,relation_image(X2,X3)) = relation_image(X0,X4) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369211,c_369596]) ).
tcf(c_397675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_image(X2,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| ( relation_image(X0,relation_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369313,c_369596]) ).
tcf(c_397676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK11(X0,relation_image(X2,X3),relation_inverse_image(X1,X4))),X4)
| ( relation_image(X0,relation_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_369596]) ).
tcf(c_397677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X0),relation_dom(X3))
| ( relation_inverse_image(X3,X4) = X0 )
| ~ empty(X2)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369020,c_369596]) ).
tcf(c_397678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X3,X4,X0)),X4)
| ( relation_inverse_image(X3,X4) = X0 )
| ~ empty(X2)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369019,c_369596]) ).
tcf(c_397679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X4,set_intersection2(X3,relation_image(X1,X2)))),X4)
| ( set_intersection2(X3,relation_image(X1,X2)) = relation_inverse_image(X0,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_369596]) ).
tcf(c_397680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(X3,relation_image(X1,X2))),relation_dom(X0))
| ( set_intersection2(X3,relation_image(X1,X2)) = relation_inverse_image(X0,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_369596]) ).
tcf(c_397681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X4,set_intersection2(relation_image(X1,X2),X3))),X4)
| ( set_intersection2(relation_image(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_369596]) ).
tcf(c_397682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,set_intersection2(relation_image(X1,X2),X3)),relation_dom(X0))
| ( set_intersection2(relation_image(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_369596]) ).
tcf(c_397683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,relation_inverse_image(X1,relation_image(X2,X3))),relation_dom(X0))
| ( relation_inverse_image(X1,relation_image(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368819,c_369596]) ).
tcf(c_397684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X4,relation_inverse_image(X1,relation_image(X2,X3)))),X4)
| ( relation_inverse_image(X1,relation_image(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_369596]) ).
tcf(c_397685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,relation_image(X2,X3)),X1)
| ( relation_inverse_image(X0,X4) = relation_image(X2,X3) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_369596]) ).
tcf(c_397686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,X4),X4)
| ( relation_inverse_image(X0,X3) = X4 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369017,c_369596]) ).
tcf(c_397687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_image(X2,X3)),X1)
| ( relation_image(X0,X4) = relation_image(X2,X3) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_369596]) ).
tcf(c_397688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X3,X4),X4)
| ( relation_image(X0,X3) = X4 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369214,c_369596]) ).
tcf(c_397689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,relation_image(X3,X4),X0),X1)
| ( relation_inverse_image(X2,relation_image(X3,X4)) = X0 )
| ~ empty(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_369596]) ).
tcf(c_397690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,relation_image(X1,X3)) = X2 )
| ~ empty(X3)
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368872,c_369596]) ).
tcf(c_397691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_image(X1,X2),set_intersection2(X3,X4)),X3)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_369596]) ).
tcf(c_397692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_image(X1,X2),set_intersection2(X3,X4)),X4)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_369596]) ).
tcf(c_397693,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X0,relation_image(X2,X3),relation_inverse_image(X1,X4))),X4)
| ( relation_inverse_image(X0,relation_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_369596]) ).
tcf(c_397694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_image(X2,X3),relation_inverse_image(X1,X4)),relation_dom(X1))
| ( relation_inverse_image(X0,relation_image(X2,X3)) = relation_inverse_image(X1,X4) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368762,c_369596]) ).
tcf(c_397695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X0,X4),X4)
| ( relation_inverse_image(X3,X0) = X4 )
| ~ empty(X2)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369018,c_369596]) ).
tcf(c_397696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,X0,relation_image(X3,X4))),X1)
| ( relation_inverse_image(X2,X0) = relation_image(X3,X4) )
| ~ empty(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_369596]) ).
tcf(c_397697,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X3,X4),relation_image(X1,X2))),X3)
| ( relation_inverse_image(X0,set_intersection2(X3,X4)) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_369596]) ).
tcf(c_397698,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X3,X4),relation_image(X1,X2))),X4)
| ( relation_inverse_image(X0,set_intersection2(X3,X4)) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_369596]) ).
tcf(c_397699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X3,relation_image(X1,X2)),X4),X4)
| ( relation_inverse_image(X0,set_intersection2(X3,relation_image(X1,X2))) = X4 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_369596]) ).
tcf(c_397700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(relation_image(X1,X2),X3),X4),X4)
| ( relation_inverse_image(X0,set_intersection2(relation_image(X1,X2),X3)) = X4 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_369596]) ).
tcf(c_397701,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X4),relation_image(X2,X3)))),X4)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X4)) = relation_image(X2,X3) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_369596]) ).
tcf(c_397702,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,relation_inverse_image(X1,X4),relation_image(X2,X3))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X4)) = relation_image(X2,X3) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368761,c_369596]) ).
tcf(c_397703,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X1,relation_image(X2,X3)),X4),X4)
| ( relation_inverse_image(X0,relation_inverse_image(X1,relation_image(X2,X3))) = X4 )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_369596]) ).
tcf(c_397704,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X1,relation_image(X2,X3)) = relation_image(X0,X4) )
| ( apply(X0,sK12(X0,X4,relation_inverse_image(X1,relation_image(X2,X3)))) = sK11(X0,X4,relation_inverse_image(X1,relation_image(X2,X3))) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369441,c_369596]) ).
tcf(c_398903,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_381372]) ).
tcf(c_398904,plain,
! [X0: $i] : relation_dom(set_intersection2(X0,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_104,c_381372]) ).
tcf(c_398905,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(X0,X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_381372]) ).
tcf(c_398906,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(X1,set_intersection2(X2,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_381372]) ).
tcf(c_398907,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(X1,sK16(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_381372]) ).
tcf(c_398908,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X1)
| ( relation_dom(set_intersection2(X0,sK10(powerset(empty_set),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_389921,c_381372]) ).
tcf(c_399152,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,X2,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X2))) ),
inference(superposition,[status(thm)],[c_53,c_369597]) ).
tcf(c_399153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X1,set_intersection2(X3,X2),X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_63,c_369597]) ).
tcf(c_399156,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,empty_set,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(empty_set,X2))) ),
inference(superposition,[status(thm)],[c_368545,c_369597]) ).
tcf(c_399157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK13(X1,set_intersection2(X2,X3),X0),X4)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X4)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_369597,c_321]) ).
tcf(c_399158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ empty(X4)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X4)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_369597,c_320]) ).
tcf(c_399159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X3,relation_image(X1,set_intersection2(X2,X0)))
| ~ in(X0,sK13(X1,set_intersection2(X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_369597,c_97]) ).
tcf(c_399160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X1,set_intersection2(X2,X3),X0),X4)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X4)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_369597,c_96]) ).
tcf(c_399161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK13(X1,set_intersection2(X2,X3),X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_369597,c_93]) ).
tcf(c_399162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_369597,c_91]) ).
tcf(c_399163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X1,set_intersection2(X2,set_intersection2(X3,X4)),X0),X4)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,set_intersection2(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369597,c_59]) ).
tcf(c_399164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X1,set_intersection2(X2,set_intersection2(X3,X4)),X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,set_intersection2(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369597,c_58]) ).
tcf(c_399165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK13(X1,set_intersection2(X2,relation_inverse_image(X3,X4)),X0)),X4)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,relation_inverse_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369597,c_88]) ).
tcf(c_399166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X1,set_intersection2(X2,relation_inverse_image(X3,X4)),X0),relation_dom(X3))
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,relation_inverse_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369597,c_87]) ).
tcf(c_399167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ empty(X4)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,relation_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369597,c_369596]) ).
tcf(c_399168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_dom(X3))
| ~ in(X0,relation_image(X1,set_intersection2(X2,relation_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369597,c_369558]) ).
tcf(c_399169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(X3,sK13(X3,X4,sK13(X1,set_intersection2(X2,relation_image(X3,X4)),X0))) = sK13(X1,set_intersection2(X2,relation_image(X3,X4)),X0) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,relation_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369597,c_112]) ).
tcf(c_399170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(X3,relation_image(X0,set_intersection2(X1,relation_dom(X2))))
| ~ in(sK13(X0,set_intersection2(X1,relation_dom(X2)),X3),X4) ),
inference(superposition,[status(thm)],[c_369597,c_369501]) ).
tcf(c_399171,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,empty_set))) ),
inference(superposition,[status(thm)],[c_369597,c_372426]) ).
tcf(c_399292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X1,set_intersection2(X3,X2),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_63,c_369598]) ).
tcf(c_399296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK13(X1,set_intersection2(X2,X3),X0),X4)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X4)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_369598,c_321]) ).
tcf(c_399297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ empty(X4)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X4)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_369598,c_320]) ).
tcf(c_399298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X3,relation_image(X1,set_intersection2(X0,X2)))
| ~ in(X0,sK13(X1,set_intersection2(X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_369598,c_97]) ).
tcf(c_399299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X1,set_intersection2(X2,X3),X0),X4)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X4)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_369598,c_96]) ).
tcf(c_399300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK13(X1,set_intersection2(X2,X3),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_369598,c_93]) ).
tcf(c_399301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,X3))) ),
inference(superposition,[status(thm)],[c_369598,c_91]) ).
tcf(c_399302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X1,set_intersection2(set_intersection2(X2,X3),X4),X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(set_intersection2(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_369598,c_59]) ).
tcf(c_399303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X1,set_intersection2(set_intersection2(X2,X3),X4),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(set_intersection2(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_369598,c_58]) ).
tcf(c_399304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK13(X1,set_intersection2(relation_inverse_image(X2,X3),X4),X0)),X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(relation_inverse_image(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_369598,c_88]) ).
tcf(c_399305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X1,set_intersection2(relation_inverse_image(X2,X3),X4),X0),relation_dom(X2))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(relation_inverse_image(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_369598,c_87]) ).
tcf(c_399306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(relation_image(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_369598,c_369596]) ).
tcf(c_399307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(relation_dom(X2))
| ~ in(X0,relation_image(X1,set_intersection2(relation_image(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_369598,c_369558]) ).
tcf(c_399308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(X2,sK13(X2,X3,sK13(X1,set_intersection2(relation_image(X2,X3),X4),X0))) = sK13(X1,set_intersection2(relation_image(X2,X3),X4),X0) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(relation_image(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_369598,c_112]) ).
tcf(c_399309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(X3,relation_image(X0,set_intersection2(relation_dom(X1),X2)))
| ~ in(sK13(X0,set_intersection2(relation_dom(X1),X2),X3),X4) ),
inference(superposition,[status(thm)],[c_369598,c_369501]) ).
tcf(c_399310,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(empty_set,X2))) ),
inference(superposition,[status(thm)],[c_369598,c_372426]) ).
tcf(c_399436,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,sK13(X1,empty_set,X0)),X2)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(empty_set,X2))) ),
inference(superposition,[status(thm)],[c_373747,c_369599]) ).
tcf(c_399437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(apply(X2,sK13(X1,relation_inverse_image(X2,X3),X0)),X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X3,X4)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369599,c_321]) ).
tcf(c_399438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ empty(X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X3,X4)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369599,c_320]) ).
tcf(c_399439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X3,relation_image(X2,relation_inverse_image(X1,X0)))
| ~ in(X0,apply(X1,sK13(X2,relation_inverse_image(X1,X0),X3))) ),
inference(superposition,[status(thm)],[c_369599,c_97]) ).
tcf(c_399440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK13(X1,relation_inverse_image(X2,X3),X0)),X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X3,X4)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369599,c_96]) ).
tcf(c_399441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X2,sK13(X1,relation_inverse_image(X2,X3),X0)),X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369599,c_93]) ).
tcf(c_399442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369599,c_91]) ).
tcf(c_399443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK13(X1,relation_inverse_image(X2,set_intersection2(X3,X4)),X0)),X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,set_intersection2(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369599,c_59]) ).
tcf(c_399444,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK13(X1,relation_inverse_image(X2,set_intersection2(X3,X4)),X0)),X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,set_intersection2(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369599,c_58]) ).
tcf(c_399445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X0,relation_inverse_image(X1,X2),X3),relation_inverse_image(X1,X2))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,relation_inverse_image(X1,X2)))
| ~ in(sK13(X0,relation_inverse_image(X1,X2),X3),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_369599,c_86]) ).
tcf(c_399446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,apply(X2,sK13(X1,relation_inverse_image(X2,relation_inverse_image(X3,X4)),X0))),X4)
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,relation_inverse_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369599,c_88]) ).
tcf(c_399447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK13(X1,relation_inverse_image(X2,relation_inverse_image(X3,X4)),X0)),relation_dom(X3))
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,relation_inverse_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369599,c_87]) ).
tcf(c_399448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ empty(X4)
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,relation_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369599,c_369596]) ).
tcf(c_399449,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(relation_dom(X3))
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,relation_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369599,c_369558]) ).
tcf(c_399450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(X3,sK13(X3,X4,apply(X2,sK13(X1,relation_inverse_image(X2,relation_image(X3,X4)),X0)))) = apply(X2,sK13(X1,relation_inverse_image(X2,relation_image(X3,X4)),X0)) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,relation_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369599,c_112]) ).
tcf(c_399451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X2,X4))
| ~ in(X3,relation_image(X1,relation_inverse_image(X0,relation_dom(X2))))
| ~ in(apply(X0,sK13(X1,relation_inverse_image(X0,relation_dom(X2)),X3)),X4) ),
inference(superposition,[status(thm)],[c_369599,c_369501]) ).
tcf(c_399452,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,empty_set))) ),
inference(superposition,[status(thm)],[c_369599,c_372426]) ).
tcf(c_399471,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(empty_set,sK13(X1,empty_set,X0)),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(empty_set,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_399436,c_368630,c_103]) ).
tcf(c_399681,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(relation_dom(X0),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_381426]) ).
tcf(c_399682,plain,
! [X0: $i] : relation_dom(set_intersection2(empty_set,X0)) = empty_set,
inference(superposition,[status(thm)],[c_104,c_381426]) ).
tcf(c_399683,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(set_intersection2(X0,X1),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_381426]) ).
tcf(c_399684,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(set_intersection2(set_intersection2(X1,X0),X2)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_381426]) ).
tcf(c_399685,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(set_intersection2(sK16(powerset(X0)),X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_381426]) ).
tcf(c_399686,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X0)
| ( relation_dom(set_intersection2(sK10(powerset(empty_set),X0),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_389921,c_381426]) ).
tcf(c_399710,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,empty_set,X0),relation_dom(empty_set))
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(empty_set,X2))) ),
inference(superposition,[status(thm)],[c_373747,c_369600]) ).
tcf(c_399712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK13(X1,relation_inverse_image(X2,X3),X0),X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(relation_dom(X2),X4)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369600,c_321]) ).
tcf(c_399713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ empty(X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(relation_dom(X2),X4)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369600,c_320]) ).
tcf(c_399714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X3,relation_image(X1,relation_inverse_image(X0,X2)))
| ~ in(relation_dom(X0),sK13(X1,relation_inverse_image(X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_369600,c_97]) ).
tcf(c_399715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK13(X1,relation_inverse_image(X2,X3),X0),X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(relation_dom(X2),X4)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369600,c_96]) ).
tcf(c_399716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK13(X1,relation_inverse_image(X2,X3),X0),relation_dom(X2))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369600,c_93]) ).
tcf(c_399717,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(relation_dom(X2))
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369600,c_91]) ).
tcf(c_399718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(X3,relation_image(X0,relation_inverse_image(X1,X2)))
| ~ in(sK13(X0,relation_inverse_image(X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_369600,c_369501]) ).
tcf(c_399725,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,empty_set,X0),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(empty_set,X2))) ),
inference(light_normalisation,[status(thm)],[c_399710,c_373108]) ).
tcf(c_399726,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(empty_set,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_399725,c_372426,c_368630,c_103]) ).
tcf(c_399800,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| ( set_intersection2(relation_image(empty_set,X0),X1) = X2 )
| ( apply(empty_set,sK13(empty_set,X0,sK2(relation_image(empty_set,X0),X1,X2))) = sK2(relation_image(empty_set,X0),X1,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_375097,c_369659]) ).
tcf(c_399802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(relation_image(X2,X3),X4,X0),X1)
| ( set_intersection2(relation_image(X2,X3),X4) = X0 )
| ( apply(X2,sK13(X2,X3,sK2(relation_image(X2,X3),X4,X0))) = sK2(relation_image(X2,X3),X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369659,c_321]) ).
tcf(c_399803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X2,X3),X4) = X0 )
| ( apply(X2,sK13(X2,X3,sK2(relation_image(X2,X3),X4,X0))) = sK2(relation_image(X2,X3),X4,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369659,c_320]) ).
tcf(c_399804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_image(X1,X2),X3) = X0 )
| ( apply(X1,sK13(X1,X2,sK2(relation_image(X1,X2),X3,X0))) = sK2(relation_image(X1,X2),X3,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(relation_image(X1,X2),X3,X0)) ),
inference(superposition,[status(thm)],[c_369659,c_97]) ).
tcf(c_399810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(relation_image(X0,X2),X3,relation_inverse_image(X1,X4))),X4)
| ( set_intersection2(relation_image(X0,X2),X3) = relation_inverse_image(X1,X4) )
| ( apply(X0,sK13(X0,X2,sK2(relation_image(X0,X2),X3,relation_inverse_image(X1,X4)))) = sK2(relation_image(X0,X2),X3,relation_inverse_image(X1,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369659,c_88]) ).
tcf(c_399811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X0,X2),X3,relation_inverse_image(X1,X4)),relation_dom(X1))
| ( set_intersection2(relation_image(X0,X2),X3) = relation_inverse_image(X1,X4) )
| ( apply(X0,sK13(X0,X2,sK2(relation_image(X0,X2),X3,relation_inverse_image(X1,X4)))) = sK2(relation_image(X0,X2),X3,relation_inverse_image(X1,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369659,c_87]) ).
tcf(c_399812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X0,X3),X4) = relation_image(X1,X2) )
| ( apply(X0,sK13(X0,X3,sK2(relation_image(X0,X3),X4,relation_image(X1,X2)))) = sK2(relation_image(X0,X3),X4,relation_image(X1,X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369659,c_369596]) ).
tcf(c_399813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X1,X2),X3) = relation_image(X0,X4) )
| ( apply(X1,sK13(X1,X2,sK2(relation_image(X1,X2),X3,relation_image(X0,X4)))) = sK2(relation_image(X1,X2),X3,relation_image(X0,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369659,c_369558]) ).
tcf(c_399814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X0,X2),X3) = relation_image(X1,X4) )
| ( apply(X1,sK13(X1,X4,sK2(relation_image(X0,X2),X3,relation_image(X1,X4)))) = sK2(relation_image(X0,X2),X3,relation_image(X1,X4)) )
| ( apply(X0,sK13(X0,X2,sK2(relation_image(X0,X2),X3,relation_image(X1,X4)))) = sK2(relation_image(X0,X2),X3,relation_image(X1,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369659,c_112]) ).
tcf(c_399815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X0,X1),X2) = relation_dom(X3) )
| ( apply(X0,sK13(X0,X1,sK2(relation_image(X0,X1),X2,relation_dom(X3)))) = sK2(relation_image(X0,X1),X2,relation_dom(X3)) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(relation_image(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369659,c_369501]) ).
tcf(c_399816,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_image(X0,X1),X2) = empty_set )
| ( apply(X0,sK13(X0,X1,sK2(relation_image(X0,X1),X2,empty_set))) = sK2(relation_image(X0,X1),X2,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369659,c_372426]) ).
tcf(c_399821,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| ( set_intersection2(empty_set,X1) = X2 )
| ( apply(empty_set,sK13(empty_set,X0,sK2(empty_set,X1,X2))) = sK2(empty_set,X1,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_399800,c_375097]) ).
tcf(c_399822,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| ( set_intersection2(empty_set,X1) = X2 )
| ( apply(empty_set,sK13(empty_set,X0,sK2(empty_set,X1,X2))) = sK2(empty_set,X1,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_399821,c_368630,c_103]) ).
tcf(c_399897,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,empty_set,X2),X2)
| ( set_intersection2(X1,relation_image(empty_set,X0)) = X2 )
| ( apply(empty_set,sK13(empty_set,X0,sK2(X1,relation_image(empty_set,X0),X2))) = sK2(X1,relation_image(empty_set,X0),X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_375097,c_369660]) ).
tcf(c_399898,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,relation_image(X1,X2)) = X0 )
| ( apply(X1,sK13(X1,X2,sK2(X0,relation_image(X1,X2),X0))) = sK2(X0,relation_image(X1,X2),X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,relation_image(X1,X2),X0),X0)
| ~ in(sK2(X0,relation_image(X1,X2),X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369660,c_54]) ).
tcf(c_399899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,relation_image(X2,X3),X0),X1)
| ( set_intersection2(X4,relation_image(X2,X3)) = X0 )
| ( apply(X2,sK13(X2,X3,sK2(X4,relation_image(X2,X3),X0))) = sK2(X4,relation_image(X2,X3),X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369660,c_321]) ).
tcf(c_399900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X4,relation_image(X2,X3)) = X0 )
| ( apply(X2,sK13(X2,X3,sK2(X4,relation_image(X2,X3),X0))) = sK2(X4,relation_image(X2,X3),X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369660,c_320]) ).
tcf(c_399901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,relation_image(X2,X3)) = X0 )
| ( apply(X2,sK13(X2,X3,sK2(X1,relation_image(X2,X3),X0))) = sK2(X1,relation_image(X2,X3),X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,sK2(X1,relation_image(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_369660,c_97]) ).
tcf(c_399907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(X3,relation_image(X0,X2),relation_inverse_image(X1,X4))),X4)
| ( set_intersection2(X3,relation_image(X0,X2)) = relation_inverse_image(X1,X4) )
| ( apply(X0,sK13(X0,X2,sK2(X3,relation_image(X0,X2),relation_inverse_image(X1,X4)))) = sK2(X3,relation_image(X0,X2),relation_inverse_image(X1,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369660,c_88]) ).
tcf(c_399908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_image(X0,X2),relation_inverse_image(X1,X4)),relation_dom(X1))
| ( set_intersection2(X3,relation_image(X0,X2)) = relation_inverse_image(X1,X4) )
| ( apply(X0,sK13(X0,X2,sK2(X3,relation_image(X0,X2),relation_inverse_image(X1,X4)))) = sK2(X3,relation_image(X0,X2),relation_inverse_image(X1,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369660,c_87]) ).
tcf(c_399909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X4,relation_image(X0,X3)) = relation_image(X1,X2) )
| ( apply(X0,sK13(X0,X3,sK2(X4,relation_image(X0,X3),relation_image(X1,X2)))) = sK2(X4,relation_image(X0,X3),relation_image(X1,X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369660,c_369596]) ).
tcf(c_399910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,relation_image(X1,X2)) = relation_image(X0,X4) )
| ( apply(X1,sK13(X1,X2,sK2(X3,relation_image(X1,X2),relation_image(X0,X4)))) = sK2(X3,relation_image(X1,X2),relation_image(X0,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369660,c_369558]) ).
tcf(c_399911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,relation_image(X0,X2)) = relation_image(X1,X4) )
| ( apply(X1,sK13(X1,X4,sK2(X3,relation_image(X0,X2),relation_image(X1,X4)))) = sK2(X3,relation_image(X0,X2),relation_image(X1,X4)) )
| ( apply(X0,sK13(X0,X2,sK2(X3,relation_image(X0,X2),relation_image(X1,X4)))) = sK2(X3,relation_image(X0,X2),relation_image(X1,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369660,c_112]) ).
tcf(c_399912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X0,relation_image(X1,X2)) = relation_dom(X3) )
| ( apply(X1,sK13(X1,X2,sK2(X0,relation_image(X1,X2),relation_dom(X3)))) = sK2(X0,relation_image(X1,X2),relation_dom(X3)) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(X0,relation_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369660,c_369501]) ).
tcf(c_399913,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,relation_image(X0,X1)) = empty_set )
| ( apply(X0,sK13(X0,X1,sK2(X2,relation_image(X0,X1),empty_set))) = sK2(X2,relation_image(X0,X1),empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369660,c_372426]) ).
tcf(c_399914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),relation_image(X2,X3)) = X0 )
| ( apply(X2,sK13(X2,X3,sK2(set_intersection2(X0,X1),relation_image(X2,X3),X0))) = sK2(set_intersection2(X0,X1),relation_image(X2,X3),X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X0,X1),relation_image(X2,X3),X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),relation_image(X2,X3),X0),X0)
| ~ in(sK2(set_intersection2(X0,X1),relation_image(X2,X3),X0),relation_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_369660,c_368471]) ).
tcf(c_399919,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,empty_set,X2),X2)
| ( set_intersection2(X1,empty_set) = X2 )
| ( apply(empty_set,sK13(empty_set,X0,sK2(X1,empty_set,X2))) = sK2(X1,empty_set,X2) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_399897,c_375097]) ).
tcf(c_399920,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,empty_set,X2),X2)
| ( set_intersection2(X1,empty_set) = X2 )
| ( apply(empty_set,sK13(empty_set,X0,sK2(X1,empty_set,X2))) = sK2(X1,empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_399919,c_368630,c_103]) ).
tcf(c_400047,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_383574]) ).
tcf(c_400048,plain,
relation_dom(relation_dom(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_104,c_383574]) ).
tcf(c_400049,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_383574]) ).
tcf(c_400050,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_383574]) ).
tcf(c_400051,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK16(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_383574]) ).
tcf(c_400052,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| ( relation_dom(relation_dom(relation_dom(sK10(powerset(empty_set),X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_389921,c_383574]) ).
tcf(c_400074,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,empty_set),X2)
| ( set_intersection2(X1,X2) = relation_image(empty_set,X0) )
| ( apply(empty_set,sK13(empty_set,X0,sK2(X1,X2,relation_image(empty_set,X0)))) = sK2(X1,X2,relation_image(empty_set,X0)) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_375097,c_369661]) ).
tcf(c_400075,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = set_intersection2(X0,X0) )
| ( apply(X1,sK13(X1,X2,sK2(X0,X0,relation_image(X1,X2)))) = sK2(X0,X0,relation_image(X1,X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,X0,relation_image(X1,X2)),X0)
| ~ in(sK2(X0,X0,relation_image(X1,X2)),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369661,c_54]) ).
tcf(c_400076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X0,relation_image(X2,X3)),X1)
| ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ( apply(X2,sK13(X2,X3,sK2(X4,X0,relation_image(X2,X3)))) = sK2(X4,X0,relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369661,c_321]) ).
tcf(c_400077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ( apply(X2,sK13(X2,X3,sK2(X4,X0,relation_image(X2,X3)))) = sK2(X4,X0,relation_image(X2,X3)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369661,c_320]) ).
tcf(c_400078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X2,X3) = set_intersection2(X1,X0) )
| ( apply(X2,sK13(X2,X3,sK2(X1,X0,relation_image(X2,X3)))) = sK2(X1,X0,relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,sK2(X1,X0,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369661,c_97]) ).
tcf(c_400084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(X3,relation_inverse_image(X1,X4),relation_image(X0,X2))),X4)
| ( set_intersection2(X3,relation_inverse_image(X1,X4)) = relation_image(X0,X2) )
| ( apply(X0,sK13(X0,X2,sK2(X3,relation_inverse_image(X1,X4),relation_image(X0,X2)))) = sK2(X3,relation_inverse_image(X1,X4),relation_image(X0,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369661,c_88]) ).
tcf(c_400085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_inverse_image(X1,X4),relation_image(X0,X2)),relation_dom(X1))
| ( set_intersection2(X3,relation_inverse_image(X1,X4)) = relation_image(X0,X2) )
| ( apply(X0,sK13(X0,X2,sK2(X3,relation_inverse_image(X1,X4),relation_image(X0,X2)))) = sK2(X3,relation_inverse_image(X1,X4),relation_image(X0,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369661,c_87]) ).
tcf(c_400086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X4,relation_image(X1,X2)) = relation_image(X0,X3) )
| ( apply(X0,sK13(X0,X3,sK2(X4,relation_image(X1,X2),relation_image(X0,X3)))) = sK2(X4,relation_image(X1,X2),relation_image(X0,X3)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369661,c_369596]) ).
tcf(c_400087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,relation_image(X0,X4)) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK2(X3,relation_image(X0,X4),relation_image(X1,X2)))) = sK2(X3,relation_image(X0,X4),relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369661,c_369558]) ).
tcf(c_400088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,relation_image(X1,X4)) = relation_image(X0,X2) )
| ( apply(X1,sK13(X1,X4,sK2(X3,relation_image(X1,X4),relation_image(X0,X2)))) = sK2(X3,relation_image(X1,X4),relation_image(X0,X2)) )
| ( apply(X0,sK13(X0,X2,sK2(X3,relation_image(X1,X4),relation_image(X0,X2)))) = sK2(X3,relation_image(X1,X4),relation_image(X0,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369661,c_112]) ).
tcf(c_400089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X0,relation_dom(X1)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(X0,relation_dom(X1),relation_image(X2,X3)))) = sK2(X0,relation_dom(X1),relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ empty(relation_image(X1,X4))
| ~ in(sK2(X0,relation_dom(X1),relation_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369661,c_369501]) ).
tcf(c_400090,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = set_intersection2(X2,empty_set) )
| ( apply(X0,sK13(X0,X1,sK2(X2,empty_set,relation_image(X0,X1)))) = sK2(X2,empty_set,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369661,c_372426]) ).
tcf(c_400091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X0) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(set_intersection2(X0,X1),X0,relation_image(X2,X3)))) = sK2(set_intersection2(X0,X1),X0,relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,relation_image(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X0,relation_image(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),X0,relation_image(X2,X3)),relation_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_369661,c_368471]) ).
tcf(c_400096,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,empty_set),X2)
| ( set_intersection2(X1,X2) = empty_set )
| ( apply(empty_set,sK13(empty_set,X0,sK2(X1,X2,empty_set))) = sK2(X1,X2,empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_400074,c_375097]) ).
tcf(c_400097,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,empty_set),X2)
| ( set_intersection2(X1,X2) = empty_set )
| ( apply(empty_set,sK13(empty_set,X0,sK2(X1,X2,empty_set))) = sK2(X1,X2,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_400096,c_368630,c_103]) ).
tcf(c_400132,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = X0 )
| ( apply(X1,sK13(X1,X2,sK2(X0,X0,relation_image(X1,X2)))) = sK2(X0,X0,relation_image(X1,X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,X0,relation_image(X1,X2)),X0)
| ~ in(sK2(X0,X0,relation_image(X1,X2)),relation_image(X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_400075,c_53]) ).
tcf(c_400168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X2,X3) = set_intersection2(X0,X1) )
| ( apply(X2,sK13(X2,X3,sK2(set_intersection2(X0,X1),X0,relation_image(X2,X3)))) = sK2(set_intersection2(X0,X1),X0,relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,relation_image(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X0,relation_image(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),X0,relation_image(X2,X3)),relation_image(X2,X3)) ),
inference(light_normalisation,[status(thm)],[c_400091,c_397166]) ).
tcf(c_400198,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,empty_set),X1)
| ( set_intersection2(X1,X2) = relation_image(empty_set,X0) )
| ( apply(empty_set,sK13(empty_set,X0,sK2(X1,X2,relation_image(empty_set,X0)))) = sK2(X1,X2,relation_image(empty_set,X0)) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_375097,c_369662]) ).
tcf(c_400199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X2,X3) = set_intersection2(X0,X1) )
| ( apply(X2,sK13(X2,X3,sK2(X0,X1,relation_image(X2,X3)))) = sK2(X0,X1,relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,relation_image(X2,X3)),X1)
| ~ in(sK2(X0,X1,relation_image(X2,X3)),relation_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_369662,c_54]) ).
tcf(c_400200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X4,relation_image(X2,X3)),X1)
| ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK2(X0,X4,relation_image(X2,X3)))) = sK2(X0,X4,relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369662,c_321]) ).
tcf(c_400201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK2(X0,X4,relation_image(X2,X3)))) = sK2(X0,X4,relation_image(X2,X3)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369662,c_320]) ).
tcf(c_400202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X2,X3) = set_intersection2(X0,X1) )
| ( apply(X2,sK13(X2,X3,sK2(X0,X1,relation_image(X2,X3)))) = sK2(X0,X1,relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,sK2(X0,X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369662,c_97]) ).
tcf(c_400208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(relation_inverse_image(X1,X3),X4,relation_image(X0,X2))),X3)
| ( set_intersection2(relation_inverse_image(X1,X3),X4) = relation_image(X0,X2) )
| ( apply(X0,sK13(X0,X2,sK2(relation_inverse_image(X1,X3),X4,relation_image(X0,X2)))) = sK2(relation_inverse_image(X1,X3),X4,relation_image(X0,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369662,c_88]) ).
tcf(c_400209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X1,X3),X4,relation_image(X0,X2)),relation_dom(X1))
| ( set_intersection2(relation_inverse_image(X1,X3),X4) = relation_image(X0,X2) )
| ( apply(X0,sK13(X0,X2,sK2(relation_inverse_image(X1,X3),X4,relation_image(X0,X2)))) = sK2(relation_inverse_image(X1,X3),X4,relation_image(X0,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369662,c_87]) ).
tcf(c_400210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X1,X2),X4) = relation_image(X0,X3) )
| ( apply(X0,sK13(X0,X3,sK2(relation_image(X1,X2),X4,relation_image(X0,X3)))) = sK2(relation_image(X1,X2),X4,relation_image(X0,X3)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369662,c_369596]) ).
tcf(c_400211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X0,X3),X4) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK2(relation_image(X0,X3),X4,relation_image(X1,X2)))) = sK2(relation_image(X0,X3),X4,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369662,c_369558]) ).
tcf(c_400212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X1,X3),X4) = relation_image(X0,X2) )
| ( apply(X1,sK13(X1,X3,sK2(relation_image(X1,X3),X4,relation_image(X0,X2)))) = sK2(relation_image(X1,X3),X4,relation_image(X0,X2)) )
| ( apply(X0,sK13(X0,X2,sK2(relation_image(X1,X3),X4,relation_image(X0,X2)))) = sK2(relation_image(X1,X3),X4,relation_image(X0,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369662,c_112]) ).
tcf(c_400213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_dom(X0),X1) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(relation_dom(X0),X1,relation_image(X2,X3)))) = sK2(relation_dom(X0),X1,relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK2(relation_dom(X0),X1,relation_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369662,c_369501]) ).
tcf(c_400214,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = set_intersection2(empty_set,X2) )
| ( apply(X0,sK13(X0,X1,sK2(empty_set,X2,relation_image(X0,X1)))) = sK2(empty_set,X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369662,c_372426]) ).
tcf(c_400219,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,empty_set),X1)
| ( set_intersection2(X1,X2) = empty_set )
| ( apply(empty_set,sK13(empty_set,X0,sK2(X1,X2,empty_set))) = sK2(X1,X2,empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_400198,c_375097]) ).
tcf(c_400220,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,empty_set),X1)
| ( set_intersection2(X1,X2) = empty_set )
| ( apply(empty_set,sK13(empty_set,X0,sK2(X1,X2,empty_set))) = sK2(X1,X2,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_400219,c_368630,c_103]) ).
tcf(c_400324,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,X2),X2)
| ( relation_inverse_image(X0,relation_image(empty_set,X1)) = X2 )
| ( apply(empty_set,sK13(empty_set,X1,apply(X0,sK7(X0,relation_image(empty_set,X1),X2)))) = apply(X0,sK7(X0,relation_image(empty_set,X1),X2)) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375097,c_369663]) ).
tcf(c_400325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,relation_image(X3,X4),X0),X1)
| ( relation_inverse_image(X2,relation_image(X3,X4)) = X0 )
| ( apply(X3,sK13(X3,X4,apply(X2,sK7(X2,relation_image(X3,X4),X0)))) = apply(X2,sK7(X2,relation_image(X3,X4),X0)) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369663,c_321]) ).
tcf(c_400326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X2,relation_image(X3,X4)) = X0 )
| ( apply(X3,sK13(X3,X4,apply(X2,sK7(X2,relation_image(X3,X4),X0)))) = apply(X2,sK7(X2,relation_image(X3,X4),X0)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369663,c_320]) ).
tcf(c_400327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X1,relation_image(X2,X3)) = X0 )
| ( apply(X2,sK13(X2,X3,apply(X1,sK7(X1,relation_image(X2,X3),X0)))) = apply(X1,sK7(X1,relation_image(X2,X3),X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,sK7(X1,relation_image(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_369663,c_97]) ).
tcf(c_400333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X0,relation_image(X1,X3),relation_inverse_image(X2,X4))),X4)
| ( relation_inverse_image(X0,relation_image(X1,X3)) = relation_inverse_image(X2,X4) )
| ( apply(X1,sK13(X1,X3,apply(X0,sK7(X0,relation_image(X1,X3),relation_inverse_image(X2,X4))))) = apply(X0,sK7(X0,relation_image(X1,X3),relation_inverse_image(X2,X4))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369663,c_88]) ).
tcf(c_400334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_image(X1,X3),relation_inverse_image(X2,X4)),relation_dom(X2))
| ( relation_inverse_image(X0,relation_image(X1,X3)) = relation_inverse_image(X2,X4) )
| ( apply(X1,sK13(X1,X3,apply(X0,sK7(X0,relation_image(X1,X3),relation_inverse_image(X2,X4))))) = apply(X0,sK7(X0,relation_image(X1,X3),relation_inverse_image(X2,X4))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369663,c_87]) ).
tcf(c_400335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,relation_image(X1,X4)) = relation_image(X2,X3) )
| ( apply(X1,sK13(X1,X4,apply(X0,sK7(X0,relation_image(X1,X4),relation_image(X2,X3))))) = apply(X0,sK7(X0,relation_image(X1,X4),relation_image(X2,X3))) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369663,c_369596]) ).
tcf(c_400336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X1,relation_image(X2,X3)) = relation_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,apply(X1,sK7(X1,relation_image(X2,X3),relation_image(X0,X4))))) = apply(X1,sK7(X1,relation_image(X2,X3),relation_image(X0,X4))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369663,c_369558]) ).
tcf(c_400337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,relation_image(X1,X3)) = relation_image(X2,X4) )
| ( apply(X2,sK13(X2,X4,sK7(X0,relation_image(X1,X3),relation_image(X2,X4)))) = sK7(X0,relation_image(X1,X3),relation_image(X2,X4)) )
| ( apply(X1,sK13(X1,X3,apply(X0,sK7(X0,relation_image(X1,X3),relation_image(X2,X4))))) = apply(X0,sK7(X0,relation_image(X1,X3),relation_image(X2,X4))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369663,c_112]) ).
tcf(c_400338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,relation_image(X1,X2)) = relation_dom(X3) )
| ( apply(X1,sK13(X1,X2,apply(X0,sK7(X0,relation_image(X1,X2),relation_dom(X3))))) = apply(X0,sK7(X0,relation_image(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK7(X0,relation_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369663,c_369501]) ).
tcf(c_400339,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,relation_image(X1,X2)) = empty_set )
| ( apply(X1,sK13(X1,X2,apply(X0,sK7(X0,relation_image(X1,X2),empty_set)))) = apply(X0,sK7(X0,relation_image(X1,X2),empty_set)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369663,c_372426]) ).
tcf(c_400340,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,relation_image(X0,X1)) = relation_dom(X0) )
| ( apply(X0,sK13(X0,X1,apply(X0,sK7(X0,relation_image(X0,X1),relation_dom(X0))))) = apply(X0,sK7(X0,relation_image(X0,X1),relation_dom(X0))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369663,c_369502]) ).
tcf(c_400347,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,X2),X2)
| ( relation_inverse_image(X0,relation_image(empty_set,X1)) = X2 )
| ( apply(empty_set,sK13(empty_set,X1,apply(X0,sK7(X0,relation_image(empty_set,X1),X2)))) = apply(X0,sK7(X0,relation_image(empty_set,X1),X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_400324,c_368630,c_103]) ).
tcf(c_400671,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(relation_dom(X0)),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_383785]) ).
tcf(c_400672,plain,
! [X0: $i] : set_intersection2(relation_dom(empty_set),X0) = empty_set,
inference(superposition,[status(thm)],[c_104,c_383785]) ).
tcf(c_400673,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X0,X1)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_383785]) ).
tcf(c_400674,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(set_intersection2(X1,X0)),X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_383785]) ).
tcf(c_400675,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(sK16(powerset(X0))),X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_383785]) ).
tcf(c_400676,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X0)
| ( set_intersection2(relation_dom(sK10(powerset(empty_set),X0)),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_389921,c_383785]) ).
tcf(c_400692,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_384186]) ).
tcf(c_400693,plain,
! [X0: $i] : set_intersection2(X0,relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_104,c_384186]) ).
tcf(c_400694,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(X0,X2))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_384186]) ).
tcf(c_400695,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_dom(set_intersection2(X2,X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_384186]) ).
tcf(c_400696,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(sK16(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_384186]) ).
tcf(c_400697,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X1)
| ( set_intersection2(X0,relation_dom(sK10(powerset(empty_set),X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_389921,c_384186]) ).
tcf(c_400747,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X2,empty_set)),X2)
| ( relation_inverse_image(X0,X2) = relation_image(empty_set,X1) )
| ( apply(empty_set,sK13(empty_set,X1,sK7(X0,X2,relation_image(empty_set,X1)))) = sK7(X0,X2,relation_image(empty_set,X1)) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375097,c_369664]) ).
tcf(c_400748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(apply(X2,sK7(X2,X0,relation_image(X3,X4))),X1)
| ( relation_inverse_image(X2,X0) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK7(X2,X0,relation_image(X3,X4)))) = sK7(X2,X0,relation_image(X3,X4)) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369664,c_321]) ).
tcf(c_400749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X2,X0) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK7(X2,X0,relation_image(X3,X4)))) = sK7(X2,X0,relation_image(X3,X4)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369664,c_320]) ).
tcf(c_400750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X1,X0) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X1,X0,relation_image(X2,X3)))) = sK7(X1,X0,relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK7(X1,X0,relation_image(X2,X3)))) ),
inference(superposition,[status(thm)],[c_369664,c_97]) ).
tcf(c_400756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X1) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X0,X1,relation_image(X2,X3)))) = sK7(X0,X1,relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_image(X2,X3)),relation_dom(X0))
| ~ in(sK7(X0,X1,relation_image(X2,X3)),relation_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_369664,c_83]) ).
tcf(c_400757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,relation_image(X2,X3)),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X0,X1,relation_image(X2,X3)))) = sK7(X0,X1,relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_image(X2,X3)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369664,c_86]) ).
tcf(c_400758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,apply(X0,sK7(X0,relation_inverse_image(X2,X4),relation_image(X1,X3)))),X4)
| ( relation_inverse_image(X0,relation_inverse_image(X2,X4)) = relation_image(X1,X3) )
| ( apply(X1,sK13(X1,X3,sK7(X0,relation_inverse_image(X2,X4),relation_image(X1,X3)))) = sK7(X0,relation_inverse_image(X2,X4),relation_image(X1,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369664,c_88]) ).
tcf(c_400759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,relation_inverse_image(X2,X4),relation_image(X1,X3))),relation_dom(X2))
| ( relation_inverse_image(X0,relation_inverse_image(X2,X4)) = relation_image(X1,X3) )
| ( apply(X1,sK13(X1,X3,sK7(X0,relation_inverse_image(X2,X4),relation_image(X1,X3)))) = sK7(X0,relation_inverse_image(X2,X4),relation_image(X1,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369664,c_87]) ).
tcf(c_400760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,relation_image(X2,X3)) = relation_image(X1,X4) )
| ( apply(X1,sK13(X1,X4,sK7(X0,relation_image(X2,X3),relation_image(X1,X4)))) = sK7(X0,relation_image(X2,X3),relation_image(X1,X4)) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369664,c_369596]) ).
tcf(c_400761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X1,relation_image(X0,X4)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X1,relation_image(X0,X4),relation_image(X2,X3)))) = sK7(X1,relation_image(X0,X4),relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369664,c_369558]) ).
tcf(c_400762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,relation_image(X2,X3)) = relation_image(X1,X4) )
| ( apply(X1,sK13(X1,X4,sK7(X0,relation_image(X2,X3),relation_image(X1,X4)))) = sK7(X0,relation_image(X2,X3),relation_image(X1,X4)) )
| ( apply(X2,sK13(X2,X3,apply(X0,sK7(X0,relation_image(X2,X3),relation_image(X1,X4))))) = apply(X0,sK7(X0,relation_image(X2,X3),relation_image(X1,X4))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369664,c_112]) ).
tcf(c_400763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,relation_dom(X1)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X0,relation_dom(X1),relation_image(X2,X3)))) = sK7(X0,relation_dom(X1),relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(apply(X0,sK7(X0,relation_dom(X1),relation_image(X2,X3))),X4) ),
inference(superposition,[status(thm)],[c_369664,c_369501]) ).
tcf(c_400764,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = relation_inverse_image(X0,empty_set) )
| ( apply(X1,sK13(X1,X2,sK7(X0,empty_set,relation_image(X1,X2)))) = sK7(X0,empty_set,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369664,c_372426]) ).
tcf(c_400779,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X2,empty_set)),X2)
| ( relation_inverse_image(X0,X2) = relation_image(empty_set,X1) )
| ( apply(empty_set,sK13(empty_set,X1,sK7(X0,X2,relation_image(empty_set,X1)))) = sK7(X0,X2,relation_image(empty_set,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_400747,c_368630,c_103]) ).
tcf(c_400963,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,empty_set),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = relation_image(empty_set,X1) )
| ( apply(empty_set,sK13(empty_set,X1,sK7(X0,X2,relation_image(empty_set,X1)))) = sK7(X0,X2,relation_image(empty_set,X1)) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375097,c_369665]) ).
tcf(c_400964,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,relation_image(X0,X1)),empty_set)
| ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ( apply(X0,sK13(X0,X1,sK7(empty_set,X2,relation_image(X0,X1)))) = sK7(empty_set,X2,relation_image(X0,X1)) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373108,c_369665]) ).
tcf(c_400965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X4,relation_image(X2,X3)),X1)
| ( relation_inverse_image(X0,X4) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X0,X4,relation_image(X2,X3)))) = sK7(X0,X4,relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369665,c_321]) ).
tcf(c_400966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,X4) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X0,X4,relation_image(X2,X3)))) = sK7(X0,X4,relation_image(X2,X3)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369665,c_320]) ).
tcf(c_400967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X1) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X0,X1,relation_image(X2,X3)))) = sK7(X0,X1,relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK7(X0,X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369665,c_97]) ).
tcf(c_400970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK7(X0,X3,relation_image(X1,X2)))) = sK7(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369665,c_91]) ).
tcf(c_400971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,X1) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X0,X1,relation_image(X2,X3)))) = sK7(X0,X1,relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK7(X0,X1,relation_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369665,c_369501]) ).
tcf(c_400972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,relation_image(X0,X1)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X0,relation_image(X0,X1),relation_image(X2,X3)))) = sK7(X0,relation_image(X0,X1),relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X0,X1),relation_image(X2,X3)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),relation_image(X2,X3)),relation_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_369665,c_369502]) ).
tcf(c_400980,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,empty_set),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = relation_image(empty_set,X1) )
| ( apply(empty_set,sK13(empty_set,X1,sK7(X0,X2,relation_image(empty_set,X1)))) = sK7(X0,X2,relation_image(empty_set,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_400963,c_368630,c_103]) ).
tcf(c_400994,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_inverse_image(empty_set,X2) )
| ( apply(X0,sK13(X0,X1,sK7(empty_set,X2,relation_image(X0,X1)))) = sK7(empty_set,X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_400964,c_372426,c_368630,c_103]) ).
tcf(c_401052,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,X1)
| ( apply(empty_set,sK13(empty_set,X0,sK10(relation_image(empty_set,X0),X1))) = sK10(relation_image(empty_set,X0),X1) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_375097,c_369666]) ).
tcf(c_401053,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_image(X0,X1),X2) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK10(relation_image(X0,X1),X2))) = sK10(relation_image(X0,X1),X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_381110]) ).
tcf(c_401054,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,relation_image(X0,X1)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK10(relation_image(X0,X1),X2))) = sK10(relation_image(X0,X1),X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_380931]) ).
tcf(c_401055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_image(X0,X2),X3)
| ( apply(X0,sK13(X0,X2,sK10(relation_image(X0,X2),X1))) = sK10(relation_image(X0,X2),X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_369791]) ).
tcf(c_401056,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(relation_image(X0,X2))
| ( apply(X0,sK13(X0,X2,sK10(relation_image(X0,X2),X1))) = sK10(relation_image(X0,X2),X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_370745]) ).
tcf(c_401057,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = X0 )
| ( apply(X1,sK13(X1,X2,sK10(relation_image(X1,X2),X0))) = sK10(relation_image(X1,X2),X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369666,c_60]) ).
tcf(c_401058,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,relation_dom(X0)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,relation_dom(X0),sK10(relation_image(X0,relation_dom(X0)),relation_image(X0,X1)))) = sK10(relation_image(X0,relation_dom(X0)),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_368586]) ).
tcf(c_401059,plain,
! [X0: $i,X1: $i] :
( empty(relation_image(X0,X1))
| ( apply(X0,sK13(X0,X1,sK10(relation_image(X0,X1),empty_set))) = sK10(relation_image(X0,X1),empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_387335]) ).
tcf(c_401060,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_image(X0,X1),X2)
| ( apply(X0,sK13(X0,X1,sK10(relation_image(X0,X1),empty_set))) = sK10(relation_image(X0,X1),empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_383286]) ).
tcf(c_401061,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = empty_set )
| ( apply(X0,sK13(X0,X1,sK10(relation_image(X0,X1),empty_set))) = sK10(relation_image(X0,X1),empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_369178]) ).
tcf(c_401062,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,relation_inverse_image(X1,relation_image(X0,X2))) = relation_image(X0,X2) )
| ( apply(X0,sK13(X0,X2,sK10(relation_image(X0,X2),relation_image(X1,relation_inverse_image(X1,relation_image(X0,X2)))))) = sK10(relation_image(X0,X2),relation_image(X1,relation_inverse_image(X1,relation_image(X0,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_368596]) ).
tcf(c_401063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,X0),X3)
| ( apply(X1,sK13(X1,X2,sK10(relation_image(X1,X2),X3))) = sK10(relation_image(X1,X2),X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_369666,c_369499]) ).
tcf(c_401064,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,X1)
| ( apply(empty_set,sK13(empty_set,X0,sK10(empty_set,X1))) = sK10(empty_set,X1) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_401052,c_375097]) ).
tcf(c_401173,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK11(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_384724,c_92]) ).
tcf(c_401174,plain,
! [X0: $i,X1: $i] :
( subset(sK11(empty_set,X1,powerset(X0)),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_384724,c_99]) ).
tcf(c_401184,plain,
! [X0: $i] :
( ( sK16(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_385145]) ).
tcf(c_401185,plain,
sK16(powerset(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_104,c_385145]) ).
tcf(c_401186,plain,
! [X0: $i,X1: $i] :
( ( sK16(powerset(relation_dom(set_intersection2(X0,X1)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381102,c_385145]) ).
tcf(c_401187,plain,
! [X0: $i,X1: $i] :
( ( sK16(powerset(relation_dom(set_intersection2(X1,X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380923,c_385145]) ).
tcf(c_401188,plain,
! [X0: $i] :
( ( sK16(powerset(relation_dom(sK16(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380186,c_385145]) ).
tcf(c_401189,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| ( sK16(powerset(relation_dom(sK10(powerset(empty_set),X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_389921,c_385145]) ).
tcf(c_401215,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = relation_image(sK1,X1) )
| ( apply(X0,sK12(X0,X2,relation_image(sK1,X1))) = sK11(X0,X2,relation_image(sK1,X1)) )
| ( apply(sK1,sK13(sK1,X1,sK11(X0,X2,relation_image(sK1,X1)))) = sK11(X0,X2,relation_image(sK1,X1)) )
| ~ relation(sK1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_51,c_369667]) ).
tcf(c_401216,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = relation_image(sK4,X1) )
| ( apply(X0,sK12(X0,X2,relation_image(sK4,X1))) = sK11(X0,X2,relation_image(sK4,X1)) )
| ( apply(sK4,sK13(sK4,X1,sK11(X0,X2,relation_image(sK4,X1)))) = sK11(X0,X2,relation_image(sK4,X1)) )
| ~ relation(sK4)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_76,c_369667]) ).
tcf(c_401217,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = relation_image(empty_set,X1) )
| ( apply(X0,sK12(X0,X2,relation_image(empty_set,X1))) = sK11(X0,X2,relation_image(empty_set,X1)) )
| ( apply(empty_set,sK13(empty_set,X1,sK11(X0,X2,relation_image(empty_set,X1)))) = sK11(X0,X2,relation_image(empty_set,X1)) )
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368630,c_369667]) ).
tcf(c_401218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(relation_dom(X0),X2) = relation_image(X1,X3) )
| ( apply(X1,sK12(X1,X3,relation_image(relation_dom(X0),X2))) = sK11(X1,X3,relation_image(relation_dom(X0),X2)) )
| ( apply(relation_dom(X0),sK13(relation_dom(X0),X2,sK11(X1,X3,relation_image(relation_dom(X0),X2)))) = sK11(X1,X3,relation_image(relation_dom(X0),X2)) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368626,c_369667]) ).
tcf(c_401219,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(set_intersection2(X0,X1),X3) = relation_image(X2,X4) )
| ( apply(X2,sK12(X2,X4,relation_image(set_intersection2(X0,X1),X3))) = sK11(X2,X4,relation_image(set_intersection2(X0,X1),X3)) )
| ( apply(set_intersection2(X0,X1),sK13(set_intersection2(X0,X1),X3,sK11(X2,X4,relation_image(set_intersection2(X0,X1),X3)))) = sK11(X2,X4,relation_image(set_intersection2(X0,X1),X3)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_381376,c_369667]) ).
tcf(c_401220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(set_intersection2(X0,X1),X3) = relation_image(X2,X4) )
| ( apply(X2,sK12(X2,X4,relation_image(set_intersection2(X0,X1),X3))) = sK11(X2,X4,relation_image(set_intersection2(X0,X1),X3)) )
| ( apply(set_intersection2(X0,X1),sK13(set_intersection2(X0,X1),X3,sK11(X2,X4,relation_image(set_intersection2(X0,X1),X3)))) = sK11(X2,X4,relation_image(set_intersection2(X0,X1),X3)) )
| ~ empty(X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_381430,c_369667]) ).
tcf(c_401221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(sK16(powerset(X0)),X2) = relation_image(X1,X3) )
| ( apply(X1,sK12(X1,X3,relation_image(sK16(powerset(X0)),X2))) = sK11(X1,X3,relation_image(sK16(powerset(X0)),X2)) )
| ( apply(sK16(powerset(X0)),sK13(sK16(powerset(X0)),X2,sK11(X1,X3,relation_image(sK16(powerset(X0)),X2)))) = sK11(X1,X3,relation_image(sK16(powerset(X0)),X2)) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_380417,c_369667]) ).
tcf(c_401222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(empty_set),X0)
| ( relation_image(sK10(powerset(empty_set),X0),X2) = relation_image(X1,X3) )
| ( apply(X1,sK12(X1,X3,relation_image(sK10(powerset(empty_set),X0),X2))) = sK11(X1,X3,relation_image(sK10(powerset(empty_set),X0),X2)) )
| ( apply(sK10(powerset(empty_set),X0),sK13(sK10(powerset(empty_set),X0),X2,sK11(X1,X3,relation_image(sK10(powerset(empty_set),X0),X2)))) = sK11(X1,X3,relation_image(sK10(powerset(empty_set),X0),X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(sK10(powerset(empty_set),X0)) ),
inference(superposition,[status(thm)],[c_390528,c_369667]) ).
tcf(c_401223,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = relation_image(empty_set,X1) )
| ( apply(X0,sK12(X0,X2,relation_image(empty_set,X1))) = sK11(X0,X2,relation_image(empty_set,X1)) )
| ( apply(empty_set,sK13(empty_set,X1,sK11(X0,X2,relation_image(empty_set,X1)))) = sK11(X0,X2,relation_image(empty_set,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_401217,c_103]) ).
tcf(c_401229,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = relation_image(sK4,X1) )
| ( apply(X0,sK12(X0,X2,relation_image(sK4,X1))) = sK11(X0,X2,relation_image(sK4,X1)) )
| ( apply(sK4,sK13(sK4,X1,sK11(X0,X2,relation_image(sK4,X1)))) = sK11(X0,X2,relation_image(sK4,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_401216,c_75]) ).
tcf(c_401235,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = relation_image(sK1,X1) )
| ( apply(X0,sK12(X0,X2,relation_image(sK1,X1))) = sK11(X0,X2,relation_image(sK1,X1)) )
| ( apply(sK1,sK13(sK1,X1,sK11(X0,X2,relation_image(sK1,X1)))) = sK11(X0,X2,relation_image(sK1,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_401215,c_50]) ).
tcf(c_401296,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,empty_set),X2)
| ( relation_image(X0,X2) = relation_image(empty_set,X1) )
| ( apply(empty_set,sK13(empty_set,X1,sK11(X0,X2,relation_image(empty_set,X1)))) = sK11(X0,X2,relation_image(empty_set,X1)) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375097,c_369668]) ).
tcf(c_401297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X2,X0,relation_image(X3,X4)),X1)
| ( relation_image(X2,X0) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK11(X2,X0,relation_image(X3,X4)))) = sK11(X2,X0,relation_image(X3,X4)) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369668,c_321]) ).
tcf(c_401298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X2,X0) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK11(X2,X0,relation_image(X3,X4)))) = sK11(X2,X0,relation_image(X3,X4)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369668,c_320]) ).
tcf(c_401299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X1,X0) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK11(X1,X0,relation_image(X2,X3)))) = sK11(X1,X0,relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,sK12(X1,X0,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369668,c_97]) ).
tcf(c_401305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK12(X0,relation_inverse_image(X2,X4),relation_image(X1,X3))),X4)
| ( relation_image(X0,relation_inverse_image(X2,X4)) = relation_image(X1,X3) )
| ( apply(X1,sK13(X1,X3,sK11(X0,relation_inverse_image(X2,X4),relation_image(X1,X3)))) = sK11(X0,relation_inverse_image(X2,X4),relation_image(X1,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369668,c_88]) ).
tcf(c_401306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,relation_inverse_image(X2,X4),relation_image(X1,X3)),relation_dom(X2))
| ( relation_image(X0,relation_inverse_image(X2,X4)) = relation_image(X1,X3) )
| ( apply(X1,sK13(X1,X3,sK11(X0,relation_inverse_image(X2,X4),relation_image(X1,X3)))) = sK11(X0,relation_inverse_image(X2,X4),relation_image(X1,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369668,c_87]) ).
tcf(c_401307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,relation_image(X2,X3)) = relation_image(X1,X4) )
| ( apply(X1,sK13(X1,X4,sK11(X0,relation_image(X2,X3),relation_image(X1,X4)))) = sK11(X0,relation_image(X2,X3),relation_image(X1,X4)) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369668,c_369596]) ).
tcf(c_401308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X1,relation_image(X0,X4)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK11(X1,relation_image(X0,X4),relation_image(X2,X3)))) = sK11(X1,relation_image(X0,X4),relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369668,c_369558]) ).
tcf(c_401309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,relation_image(X2,X4)) = relation_image(X1,X3) )
| ( apply(X2,sK13(X2,X4,sK12(X0,relation_image(X2,X4),relation_image(X1,X3)))) = sK12(X0,relation_image(X2,X4),relation_image(X1,X3)) )
| ( apply(X1,sK13(X1,X3,sK11(X0,relation_image(X2,X4),relation_image(X1,X3)))) = sK11(X0,relation_image(X2,X4),relation_image(X1,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369668,c_112]) ).
tcf(c_401310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,relation_dom(X1)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK11(X0,relation_dom(X1),relation_image(X2,X3)))) = sK11(X0,relation_dom(X1),relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X4))
| ~ in(sK12(X0,relation_dom(X1),relation_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369668,c_369501]) ).
tcf(c_401311,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X1,X2) = relation_image(X0,empty_set) )
| ( apply(X1,sK13(X1,X2,sK11(X0,empty_set,relation_image(X1,X2)))) = sK11(X0,empty_set,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369668,c_372426]) ).
tcf(c_401318,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,empty_set),X2)
| ( relation_image(X0,X2) = relation_image(empty_set,X1) )
| ( apply(empty_set,sK13(empty_set,X1,sK11(X0,X2,relation_image(empty_set,X1)))) = sK11(X0,X2,relation_image(empty_set,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_401296,c_368630,c_103]) ).
tcf(c_401426,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,empty_set),relation_dom(X0))
| ( relation_image(X0,X2) = relation_image(empty_set,X1) )
| ( apply(empty_set,sK13(empty_set,X1,sK11(X0,X2,relation_image(empty_set,X1)))) = sK11(X0,X2,relation_image(empty_set,X1)) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375097,c_369669]) ).
tcf(c_401427,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(empty_set,X2,relation_image(X0,X1)),empty_set)
| ( relation_image(X0,X1) = relation_image(empty_set,X2) )
| ( apply(X0,sK13(X0,X1,sK11(empty_set,X2,relation_image(X0,X1)))) = sK11(empty_set,X2,relation_image(X0,X1)) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_373108,c_369669]) ).
tcf(c_401428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X4,relation_image(X2,X3)),X1)
| ( relation_image(X0,X4) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK11(X0,X4,relation_image(X2,X3)))) = sK11(X0,X4,relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369669,c_321]) ).
tcf(c_401429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,X4) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK11(X0,X4,relation_image(X2,X3)))) = sK11(X0,X4,relation_image(X2,X3)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369669,c_320]) ).
tcf(c_401430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X1) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK11(X0,X1,relation_image(X2,X3)))) = sK11(X0,X1,relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK12(X0,X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369669,c_97]) ).
tcf(c_401433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK11(X0,X3,relation_image(X1,X2)))) = sK11(X0,X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369669,c_91]) ).
tcf(c_401434,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,X1) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK11(X0,X1,relation_image(X2,X3)))) = sK11(X0,X1,relation_image(X2,X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK12(X0,X1,relation_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369669,c_369501]) ).
tcf(c_401442,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,empty_set),relation_dom(X0))
| ( relation_image(X0,X2) = relation_image(empty_set,X1) )
| ( apply(empty_set,sK13(empty_set,X1,sK11(X0,X2,relation_image(empty_set,X1)))) = sK11(X0,X2,relation_image(empty_set,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_401426,c_368630,c_103]) ).
tcf(c_401456,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = relation_image(empty_set,X2) )
| ( apply(X0,sK13(X0,X1,sK11(empty_set,X2,relation_image(X0,X1)))) = sK11(empty_set,X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_401427,c_372426,c_368630,c_103]) ).
tcf(c_401501,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,X0))
| element(sK16(set_intersection2(X0,X2)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_388043,c_321]) ).
tcf(c_401503,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| ~ in(X0,sK16(set_intersection2(X0,X1))) ),
inference(superposition,[status(thm)],[c_388043,c_97]) ).
tcf(c_401504,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,X0))
| in(sK16(set_intersection2(X0,X2)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_388043,c_96]) ).
tcf(c_401505,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| element(sK16(set_intersection2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_388043,c_93]) ).
tcf(c_401507,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,set_intersection2(X0,X1)))
| in(sK16(set_intersection2(set_intersection2(X0,X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_388043,c_59]) ).
tcf(c_401508,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,set_intersection2(X0,X1)))
| in(sK16(set_intersection2(set_intersection2(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_388043,c_58]) ).
tcf(c_401509,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,relation_inverse_image(X0,X1)))
| in(apply(X0,sK16(set_intersection2(relation_inverse_image(X0,X1),X2))),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_388043,c_88]) ).
tcf(c_401510,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,relation_inverse_image(X0,X1)))
| in(sK16(set_intersection2(relation_inverse_image(X0,X1),X2)),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_388043,c_87]) ).
tcf(c_401513,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X2,relation_image(X0,X1)))
| ( apply(X0,sK13(X0,X1,sK16(set_intersection2(relation_image(X0,X1),X2)))) = sK16(set_intersection2(relation_image(X0,X1),X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_388043,c_112]) ).
tcf(c_401514,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X1,relation_dom(X0)))
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X2))
| ~ in(sK16(set_intersection2(relation_dom(X0),X1)),X2) ),
inference(superposition,[status(thm)],[c_388043,c_369501]) ).
tcf(c_401589,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,X2),X2)
| ( relation_image(X0,relation_image(empty_set,X1)) = X2 )
| ( apply(empty_set,sK13(empty_set,X1,sK12(X0,relation_image(empty_set,X1),X2))) = sK12(X0,relation_image(empty_set,X1),X2) )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375097,c_369670]) ).
tcf(c_401590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,relation_image(X3,X4),X0),X1)
| ( relation_image(X2,relation_image(X3,X4)) = X0 )
| ( apply(X3,sK13(X3,X4,sK12(X2,relation_image(X3,X4),X0))) = sK12(X2,relation_image(X3,X4),X0) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369670,c_321]) ).
tcf(c_401591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X2,relation_image(X3,X4)) = X0 )
| ( apply(X3,sK13(X3,X4,sK12(X2,relation_image(X3,X4),X0))) = sK12(X2,relation_image(X3,X4),X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369670,c_320]) ).
tcf(c_401592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X1,relation_image(X2,X3)) = X0 )
| ( apply(X2,sK13(X2,X3,sK12(X1,relation_image(X2,X3),X0))) = sK12(X1,relation_image(X2,X3),X0) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,sK11(X1,relation_image(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_369670,c_97]) ).
tcf(c_401598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK11(X0,relation_image(X1,X3),relation_inverse_image(X2,X4))),X4)
| ( relation_image(X0,relation_image(X1,X3)) = relation_inverse_image(X2,X4) )
| ( apply(X1,sK13(X1,X3,sK12(X0,relation_image(X1,X3),relation_inverse_image(X2,X4)))) = sK12(X0,relation_image(X1,X3),relation_inverse_image(X2,X4)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369670,c_88]) ).
tcf(c_401599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_image(X1,X3),relation_inverse_image(X2,X4)),relation_dom(X2))
| ( relation_image(X0,relation_image(X1,X3)) = relation_inverse_image(X2,X4) )
| ( apply(X1,sK13(X1,X3,sK12(X0,relation_image(X1,X3),relation_inverse_image(X2,X4)))) = sK12(X0,relation_image(X1,X3),relation_inverse_image(X2,X4)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369670,c_87]) ).
tcf(c_401600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,relation_image(X1,X4)) = relation_image(X2,X3) )
| ( apply(X1,sK13(X1,X4,sK12(X0,relation_image(X1,X4),relation_image(X2,X3)))) = sK12(X0,relation_image(X1,X4),relation_image(X2,X3)) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369670,c_369596]) ).
tcf(c_401601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X1,relation_image(X2,X3)) = relation_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK12(X1,relation_image(X2,X3),relation_image(X0,X4)))) = sK12(X1,relation_image(X2,X3),relation_image(X0,X4)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369670,c_369558]) ).
tcf(c_401602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,relation_image(X1,X3)) = relation_image(X2,X4) )
| ( apply(X2,sK13(X2,X4,sK11(X0,relation_image(X1,X3),relation_image(X2,X4)))) = sK11(X0,relation_image(X1,X3),relation_image(X2,X4)) )
| ( apply(X1,sK13(X1,X3,sK12(X0,relation_image(X1,X3),relation_image(X2,X4)))) = sK12(X0,relation_image(X1,X3),relation_image(X2,X4)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369670,c_112]) ).
tcf(c_401603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,relation_image(X1,X2)) = relation_dom(X3) )
| ( apply(X1,sK13(X1,X2,sK12(X0,relation_image(X1,X2),relation_dom(X3)))) = sK12(X0,relation_image(X1,X2),relation_dom(X3)) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X3,X4))
| ~ in(sK11(X0,relation_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369670,c_369501]) ).
tcf(c_401604,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,relation_image(X1,X2)) = empty_set )
| ( apply(X1,sK13(X1,X2,sK12(X0,relation_image(X1,X2),empty_set))) = sK12(X0,relation_image(X1,X2),empty_set) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369670,c_372426]) ).
tcf(c_401611,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,X2),X2)
| ( relation_image(X0,relation_image(empty_set,X1)) = X2 )
| ( apply(empty_set,sK13(empty_set,X1,sK12(X0,relation_image(empty_set,X1),X2))) = sK12(X0,relation_image(empty_set,X1),X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_401589,c_368630,c_103]) ).
tcf(c_401717,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(relation_dom(X0),X1,X2),X2)
| ( set_intersection2(relation_dom(X0),X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK2(relation_dom(X0),X1,X2)))) = apply(X0,sK2(relation_dom(X0),X1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(relation_dom(X0),X1,X2),X3) ),
inference(superposition,[status(thm)],[c_368927,c_369671]) ).
tcf(c_401718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_dom(X0),X1,X2),X2)
| ( set_intersection2(relation_dom(X0),X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK2(relation_dom(X0),X1,X2)))) = apply(X0,sK2(relation_dom(X0),X1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(relation_dom(X0),X1,X2),X3) ),
inference(superposition,[status(thm)],[c_55,c_369671]) ).
tcf(c_401719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,relation_dom(X1),X2),X2)
| ( set_intersection2(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,sK2(X0,relation_dom(X1),X2)))) = apply(X1,sK2(X0,relation_dom(X1),X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_368926,c_369671]) ).
tcf(c_401720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,relation_dom(X1),X2),X2)
| ( set_intersection2(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,sK2(X0,relation_dom(X1),X2)))) = apply(X1,sK2(X0,relation_dom(X1),X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_56,c_369671]) ).
tcf(c_401721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,relation_dom(X2)),X1)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK2(X0,X1,relation_dom(X2))))) = apply(X2,sK2(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_368925,c_369671]) ).
tcf(c_401722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,relation_dom(X2)),X0)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK2(X0,X1,relation_dom(X2))))) = apply(X2,sK2(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_368924,c_369671]) ).
tcf(c_401723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK2(X0,X1,relation_dom(X2))))) = apply(X2,sK2(X0,X1,relation_dom(X2))) )
| ~ empty(X0)
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_368865,c_369671]) ).
tcf(c_401724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,relation_dom(X2)),X1)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK2(X0,X1,relation_dom(X2))))) = apply(X2,sK2(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_56,c_369671]) ).
tcf(c_401725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,relation_dom(X2)),X0)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK2(X0,X1,relation_dom(X2))))) = apply(X2,sK2(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_55,c_369671]) ).
tcf(c_401726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK7(X0,X1,X2)))) = apply(X0,sK7(X0,X1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_368932,c_369671]) ).
tcf(c_401727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK7(X0,X1,X2)))) = apply(X0,sK7(X0,X1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_84,c_369671]) ).
tcf(c_401728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,relation_dom(X1),X2),X2)
| ( relation_inverse_image(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,apply(X0,sK7(X0,relation_dom(X1),X2))))) = apply(X1,apply(X0,sK7(X0,relation_dom(X1),X2))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,relation_dom(X1),X2)),X3) ),
inference(superposition,[status(thm)],[c_368931,c_369671]) ).
tcf(c_401729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_dom(X1),X2),X2)
| ( relation_inverse_image(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,apply(X0,sK7(X0,relation_dom(X1),X2))))) = apply(X1,apply(X0,sK7(X0,relation_dom(X1),X2))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,relation_dom(X1),X2)),X3) ),
inference(superposition,[status(thm)],[c_85,c_369671]) ).
tcf(c_401730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X0,sK7(X0,X1,relation_dom(X2))),X1)
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK7(X0,X1,relation_dom(X2))))) = apply(X2,sK7(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_368930,c_369671]) ).
tcf(c_401731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X1,relation_dom(X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK7(X0,X1,relation_dom(X2))))) = apply(X2,sK7(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_368929,c_369671]) ).
tcf(c_401732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK7(X0,X1,relation_dom(X2))))) = apply(X2,sK7(X0,X1,relation_dom(X2))) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_368871,c_369671]) ).
tcf(c_401733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK7(X0,X1,relation_dom(X2))))) = apply(X2,sK7(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_dom(X0))
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_379483,c_369671]) ).
tcf(c_401734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,relation_dom(X2)),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK7(X0,X1,relation_dom(X2))))) = apply(X2,sK7(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_375319,c_369671]) ).
tcf(c_401735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X1,relation_dom(X2))),X1)
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK7(X0,X1,relation_dom(X2))))) = apply(X2,sK7(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_85,c_369671]) ).
tcf(c_401736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,relation_dom(X2)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK7(X0,X1,relation_dom(X2))))) = apply(X2,sK7(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_84,c_369671]) ).
tcf(c_401737,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(X0),X1)
| ( apply(X0,sK13(X0,X2,apply(X0,sK10(relation_dom(X0),X1)))) = apply(X0,sK10(relation_dom(X0),X1)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK10(relation_dom(X0),X1),X2) ),
inference(superposition,[status(thm)],[c_95,c_369671]) ).
tcf(c_401738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK11(X0,X1,relation_dom(X2))))) = apply(X2,sK11(X0,X1,relation_dom(X2))) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369301,c_369671]) ).
tcf(c_401739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X1,relation_dom(X2)),X1)
| ( relation_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK11(X0,X1,relation_dom(X2))))) = apply(X2,sK11(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369300,c_369671]) ).
tcf(c_401740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK11(X0,X1,relation_dom(X2))))) = apply(X2,sK11(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_dom(X0))
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_386602,c_369671]) ).
tcf(c_401741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X1,relation_dom(X2)),relation_dom(X0))
| ( relation_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK11(X0,X1,relation_dom(X2))))) = apply(X2,sK11(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369215,c_369671]) ).
tcf(c_401742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X1) = relation_dom(X2) )
| ( apply(X0,sK12(X0,X1,relation_dom(X2))) = sK11(X0,X1,relation_dom(X2)) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK11(X0,X1,relation_dom(X2))))) = apply(X2,sK11(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_108,c_369671]) ).
tcf(c_401743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X1,relation_dom(X2)),X1)
| ( relation_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK11(X0,X1,relation_dom(X2))))) = apply(X2,sK11(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_107,c_369671]) ).
tcf(c_401744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X1,relation_dom(X2)),relation_dom(X0))
| ( relation_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK11(X0,X1,relation_dom(X2))))) = apply(X2,sK11(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_106,c_369671]) ).
tcf(c_401745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK12(X0,X1,X2)))) = apply(X0,sK12(X0,X1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK12(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369207,c_369671]) ).
tcf(c_401746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK12(X0,X1,X2)))) = apply(X0,sK12(X0,X1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK12(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_106,c_369671]) ).
tcf(c_401747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,relation_dom(X1),X2),X2)
| ( relation_image(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,sK12(X0,relation_dom(X1),X2)))) = apply(X1,sK12(X0,relation_dom(X1),X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK12(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_369308,c_369671]) ).
tcf(c_401748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,relation_dom(X1),X2),X2)
| ( relation_image(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,sK12(X0,relation_dom(X1),X2)))) = apply(X1,sK12(X0,relation_dom(X1),X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK12(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_107,c_369671]) ).
tcf(c_401749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X0,sK13(X0,X3,apply(X0,sK13(X0,X1,X2)))) = apply(X0,sK13(X0,X1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_image(X0,X1))
| ~ in(sK13(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_110,c_369671]) ).
tcf(c_401750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X1,sK13(X1,X3,apply(X1,sK13(X0,relation_dom(X1),X2)))) = apply(X1,sK13(X0,relation_dom(X1),X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X2,relation_image(X0,relation_dom(X1)))
| ~ in(sK13(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_111,c_369671]) ).
tcf(c_401751,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom(X0))
| ( apply(X0,sK13(X0,X1,apply(X0,sK16(relation_dom(X0))))) = apply(X0,sK16(relation_dom(X0))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK16(relation_dom(X0)),X1) ),
inference(superposition,[status(thm)],[c_368976,c_369671]) ).
tcf(c_401752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(relation_dom(X0),X1),X2)
| ( apply(X0,sK13(X0,X3,apply(X0,sK10(set_intersection2(relation_dom(X0),X1),X2)))) = apply(X0,sK10(set_intersection2(relation_dom(X0),X1),X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK10(set_intersection2(relation_dom(X0),X1),X2),X3) ),
inference(superposition,[status(thm)],[c_368986,c_369671]) ).
tcf(c_401753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_intersection2(X0,relation_dom(X1)),X2)
| ( apply(X1,sK13(X1,X3,apply(X1,sK10(set_intersection2(X0,relation_dom(X1)),X2)))) = apply(X1,sK10(set_intersection2(X0,relation_dom(X1)),X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK10(set_intersection2(X0,relation_dom(X1)),X2),X3) ),
inference(superposition,[status(thm)],[c_368985,c_369671]) ).
tcf(c_401754,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,relation_dom(X1)))
| ( apply(X1,sK13(X1,X2,apply(X1,sK16(set_intersection2(X0,relation_dom(X1)))))) = apply(X1,sK16(set_intersection2(X0,relation_dom(X1)))) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK16(set_intersection2(X0,relation_dom(X1))),X2) ),
inference(superposition,[status(thm)],[c_370750,c_369671]) ).
tcf(c_401755,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X1,relation_dom(X0)))
| ( apply(X0,sK13(X0,X2,apply(X0,sK16(set_intersection2(relation_dom(X0),X1))))) = apply(X0,sK16(set_intersection2(relation_dom(X0),X1))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK16(set_intersection2(relation_dom(X0),X1)),X2) ),
inference(superposition,[status(thm)],[c_388043,c_369671]) ).
tcf(c_401756,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_dom(X0),X1))
| ( apply(X0,sK13(X0,X2,apply(X0,sK16(set_intersection2(relation_dom(X0),X1))))) = apply(X0,sK16(set_intersection2(relation_dom(X0),X1))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK16(set_intersection2(relation_dom(X0),X1)),X2) ),
inference(superposition,[status(thm)],[c_370751,c_369671]) ).
tcf(c_401757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X1)
| ( apply(X3,sK13(X3,X2,apply(X3,sK10(X0,X1)))) = apply(X3,sK10(X0,X1)) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,relation_dom(X3))
| ~ in(sK10(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_369021,c_369671]) ).
tcf(c_401758,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| ( apply(X2,sK13(X2,X1,apply(X2,sK16(X0)))) = apply(X2,sK16(X0)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,relation_dom(X2))
| ~ in(sK16(X0),X1) ),
inference(superposition,[status(thm)],[c_370747,c_369671]) ).
tcf(c_401759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X0,X1),X2)
| ( apply(X0,sK13(X0,X3,apply(X0,sK10(relation_inverse_image(X0,X1),X2)))) = apply(X0,sK10(relation_inverse_image(X0,X1),X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK10(relation_inverse_image(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_368988,c_369671]) ).
tcf(c_401760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X0,relation_dom(X1)),X2)
| ( apply(X1,sK13(X1,X3,apply(X1,apply(X0,sK10(relation_inverse_image(X0,relation_dom(X1)),X2))))) = apply(X1,apply(X0,sK10(relation_inverse_image(X0,relation_dom(X1)),X2))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK10(relation_inverse_image(X0,relation_dom(X1)),X2)),X3) ),
inference(superposition,[status(thm)],[c_368987,c_369671]) ).
tcf(c_401761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_dom(X0),X1,X2),X4)
| ( set_intersection2(relation_dom(X0),X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK2(relation_dom(X0),X1,X2)))) = apply(X0,sK2(relation_dom(X0),X1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ in(sK2(relation_dom(X0),X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369015,c_369671]) ).
tcf(c_401762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 )
| ( apply(X4,sK13(X4,X3,apply(X4,sK2(X0,X1,X2)))) = apply(X4,sK2(X0,X1,X2)) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,relation_dom(X4))
| ~ in(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369015,c_369671]) ).
tcf(c_401763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X1)
| ( set_intersection2(X0,X1) = X2 )
| ( apply(X4,sK13(X4,X3,apply(X4,sK2(X0,X1,X2)))) = apply(X4,sK2(X0,X1,X2)) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,relation_dom(X4))
| ~ in(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369014,c_369671]) ).
tcf(c_401764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_dom(X0),X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK2(relation_dom(X0),X1,X2)))) = apply(X0,sK2(relation_dom(X0),X1,X2)) )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(relation_dom(X0),X1,X2),X3) ),
inference(superposition,[status(thm)],[c_368868,c_369671]) ).
tcf(c_401765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_dom(X0),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(relation_dom(X0),X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK2(relation_dom(X0),X1,set_intersection2(X2,X3))))) = apply(X0,sK2(relation_dom(X0),X1,set_intersection2(X2,X3))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(relation_dom(X0),X1,set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368506,c_369671]) ).
tcf(c_401766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_dom(X0),X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(relation_dom(X0),X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK2(relation_dom(X0),X1,set_intersection2(X2,X3))))) = apply(X0,sK2(relation_dom(X0),X1,set_intersection2(X2,X3))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(relation_dom(X0),X1,set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368484,c_369671]) ).
tcf(c_401767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,set_intersection2(X2,relation_dom(X3))),X0)
| ( set_intersection2(X2,relation_dom(X3)) = set_intersection2(X0,X1) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(X0,X1,set_intersection2(X2,relation_dom(X3)))))) = apply(X3,sK2(X0,X1,set_intersection2(X2,relation_dom(X3)))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(X0,X1,set_intersection2(X2,relation_dom(X3))),X4) ),
inference(superposition,[status(thm)],[c_368506,c_369671]) ).
tcf(c_401768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,set_intersection2(X2,relation_dom(X3))),X1)
| ( set_intersection2(X2,relation_dom(X3)) = set_intersection2(X0,X1) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(X0,X1,set_intersection2(X2,relation_dom(X3)))))) = apply(X3,sK2(X0,X1,set_intersection2(X2,relation_dom(X3)))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(X0,X1,set_intersection2(X2,relation_dom(X3))),X4) ),
inference(superposition,[status(thm)],[c_368505,c_369671]) ).
tcf(c_401769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,set_intersection2(relation_dom(X2),X3)),X0)
| ( set_intersection2(relation_dom(X2),X3) = set_intersection2(X0,X1) )
| ( apply(X2,sK13(X2,X4,apply(X2,sK2(X0,X1,set_intersection2(relation_dom(X2),X3))))) = apply(X2,sK2(X0,X1,set_intersection2(relation_dom(X2),X3))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,set_intersection2(relation_dom(X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_368484,c_369671]) ).
tcf(c_401770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,set_intersection2(relation_dom(X2),X3)),X1)
| ( set_intersection2(relation_dom(X2),X3) = set_intersection2(X0,X1) )
| ( apply(X2,sK13(X2,X4,apply(X2,sK2(X0,X1,set_intersection2(relation_dom(X2),X3))))) = apply(X2,sK2(X0,X1,set_intersection2(relation_dom(X2),X3))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,set_intersection2(relation_dom(X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_368483,c_369671]) ).
tcf(c_401771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,relation_dom(X3))),X1)
| ( relation_inverse_image(X0,relation_dom(X3)) = set_intersection2(X1,X2) )
| ( apply(X3,sK13(X3,X4,apply(X3,apply(X0,sK2(X1,X2,relation_inverse_image(X0,relation_dom(X3))))))) = apply(X3,apply(X0,sK2(X1,X2,relation_inverse_image(X0,relation_dom(X3))))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(apply(X0,sK2(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X4) ),
inference(superposition,[status(thm)],[c_368816,c_369671]) ).
tcf(c_401772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,relation_dom(X3))),X2)
| ( relation_inverse_image(X0,relation_dom(X3)) = set_intersection2(X1,X2) )
| ( apply(X3,sK13(X3,X4,apply(X3,apply(X0,sK2(X1,X2,relation_inverse_image(X0,relation_dom(X3))))))) = apply(X3,apply(X0,sK2(X1,X2,relation_inverse_image(X0,relation_dom(X3))))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(apply(X0,sK2(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X4) ),
inference(superposition,[status(thm)],[c_368815,c_369671]) ).
tcf(c_401773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK2(relation_dom(X0),X1,relation_inverse_image(X2,X3))),X3)
| ( set_intersection2(relation_dom(X0),X1) = relation_inverse_image(X2,X3) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK2(relation_dom(X0),X1,relation_inverse_image(X2,X3))))) = apply(X0,sK2(relation_dom(X0),X1,relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK2(relation_dom(X0),X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368816,c_369671]) ).
tcf(c_401774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_dom(X0),X1,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( set_intersection2(relation_dom(X0),X1) = relation_inverse_image(X2,X3) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK2(relation_dom(X0),X1,relation_inverse_image(X2,X3))))) = apply(X0,sK2(relation_dom(X0),X1,relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK2(relation_dom(X0),X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368760,c_369671]) ).
tcf(c_401775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,relation_inverse_image(X2,X3)),X0)
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X1) )
| ( apply(X2,sK13(X2,X4,apply(X2,sK2(X0,X1,relation_inverse_image(X2,X3))))) = apply(X2,sK2(X0,X1,relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368760,c_369671]) ).
tcf(c_401776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,relation_inverse_image(X2,X3)),X1)
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X1) )
| ( apply(X2,sK13(X2,X4,apply(X2,sK2(X0,X1,relation_inverse_image(X2,X3))))) = apply(X2,sK2(X0,X1,relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368759,c_369671]) ).
tcf(c_401777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,relation_dom(X2)),X4)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK2(X0,X1,relation_dom(X2))))) = apply(X2,sK2(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X4)
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369012,c_369671]) ).
tcf(c_401778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ( apply(X4,sK13(X4,X3,apply(X4,sK2(X0,X1,X2)))) = apply(X4,sK2(X0,X1,X2)) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,relation_dom(X4))
| ~ in(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369012,c_369671]) ).
tcf(c_401779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(set_intersection2(X0,X1),X2,relation_dom(X3))))) = apply(X3,sK2(set_intersection2(X0,X1),X2,relation_dom(X3))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368503,c_369671]) ).
tcf(c_401780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(set_intersection2(X0,X1),X2,relation_dom(X3))))) = apply(X3,sK2(set_intersection2(X0,X1),X2,relation_dom(X3))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368481,c_369671]) ).
tcf(c_401781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,relation_dom(X1)),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,relation_dom(X1)),X2) = X3 )
| ( apply(X1,sK13(X1,X4,apply(X1,sK2(set_intersection2(X0,relation_dom(X1)),X2,X3)))) = apply(X1,sK2(set_intersection2(X0,relation_dom(X1)),X2,X3)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(set_intersection2(X0,relation_dom(X1)),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_368503,c_369671]) ).
tcf(c_401782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = X3 )
| ( apply(X0,sK13(X0,X4,apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,X3)))) = apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,X3)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_368481,c_369671]) ).
tcf(c_401783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,X1),X2,relation_dom(X3))),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(relation_inverse_image(X0,X1),X2,relation_dom(X3))))) = apply(X3,sK2(relation_inverse_image(X0,X1),X2,relation_dom(X3))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK2(relation_inverse_image(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368813,c_369671]) ).
tcf(c_401784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,relation_dom(X3)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(relation_inverse_image(X0,X1),X2,relation_dom(X3))))) = apply(X3,sK2(relation_inverse_image(X0,X1),X2,relation_dom(X3))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK2(relation_inverse_image(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368757,c_369671]) ).
tcf(c_401785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,relation_dom(X1)),X2,X3),X3)
| ( set_intersection2(relation_inverse_image(X0,relation_dom(X1)),X2) = X3 )
| ( apply(X1,sK13(X1,X4,apply(X1,apply(X0,sK2(relation_inverse_image(X0,relation_dom(X1)),X2,X3))))) = apply(X1,apply(X0,sK2(relation_inverse_image(X0,relation_dom(X1)),X2,X3))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK2(relation_inverse_image(X0,relation_dom(X1)),X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368813,c_369671]) ).
tcf(c_401786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,X3),X3)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = X3 )
| ( apply(X0,sK13(X0,X4,apply(X0,sK2(relation_inverse_image(X0,X1),X2,X3)))) = apply(X0,sK2(relation_inverse_image(X0,X1),X2,X3)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(relation_inverse_image(X0,X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_368757,c_369671]) ).
tcf(c_401787,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_dom(X0),X1) = relation_dom(X0) )
| ( apply(X0,sK13(X0,X2,apply(X0,sK2(relation_dom(X0),X1,relation_dom(X0))))) = apply(X0,sK2(relation_dom(X0),X1,relation_dom(X0))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(relation_dom(X0),X1,relation_dom(X0)),X2) ),
inference(superposition,[status(thm)],[c_368448,c_369671]) ).
tcf(c_401788,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(X1) = empty_set )
| ( apply(X1,sK13(X1,X2,apply(X1,sK2(empty_set,X0,relation_dom(X1))))) = apply(X1,sK2(empty_set,X0,relation_dom(X1))) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(empty_set,X0,relation_dom(X1)),X2) ),
inference(superposition,[status(thm)],[c_372470,c_369671]) ).
tcf(c_401789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,relation_dom(X1),X2),X4)
| ( set_intersection2(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,sK2(X0,relation_dom(X1),X2)))) = apply(X1,sK2(X0,relation_dom(X1),X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X4)
| ~ in(sK2(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_369014,c_369671]) ).
tcf(c_401790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,sK2(X0,relation_dom(X1),X2)))) = apply(X1,sK2(X0,relation_dom(X1),X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_368867,c_369671]) ).
tcf(c_401791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,relation_dom(X1),set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,relation_dom(X1)) = set_intersection2(X2,X3) )
| ( apply(X1,sK13(X1,X4,apply(X1,sK2(X0,relation_dom(X1),set_intersection2(X2,X3))))) = apply(X1,sK2(X0,relation_dom(X1),set_intersection2(X2,X3))) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,relation_dom(X1),set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368505,c_369671]) ).
tcf(c_401792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,relation_dom(X1),set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,relation_dom(X1)) = set_intersection2(X2,X3) )
| ( apply(X1,sK13(X1,X4,apply(X1,sK2(X0,relation_dom(X1),set_intersection2(X2,X3))))) = apply(X1,sK2(X0,relation_dom(X1),set_intersection2(X2,X3))) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,relation_dom(X1),set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368483,c_369671]) ).
tcf(c_401793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK2(X0,relation_dom(X1),relation_inverse_image(X2,X3))),X3)
| ( set_intersection2(X0,relation_dom(X1)) = relation_inverse_image(X2,X3) )
| ( apply(X1,sK13(X1,X4,apply(X1,sK2(X0,relation_dom(X1),relation_inverse_image(X2,X3))))) = apply(X1,sK2(X0,relation_dom(X1),relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(sK2(X0,relation_dom(X1),relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368815,c_369671]) ).
tcf(c_401794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,relation_dom(X1),relation_inverse_image(X2,X3)),relation_dom(X2))
| ( set_intersection2(X0,relation_dom(X1)) = relation_inverse_image(X2,X3) )
| ( apply(X1,sK13(X1,X4,apply(X1,sK2(X0,relation_dom(X1),relation_inverse_image(X2,X3))))) = apply(X1,sK2(X0,relation_dom(X1),relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(sK2(X0,relation_dom(X1),relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368759,c_369671]) ).
tcf(c_401795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,relation_dom(X2)),X4)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK2(X0,X1,relation_dom(X2))))) = apply(X2,sK2(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X1,X4)
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369013,c_369671]) ).
tcf(c_401796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ( apply(X4,sK13(X4,X3,apply(X4,sK2(X0,X1,X2)))) = apply(X4,sK2(X0,X1,X2)) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X1,relation_dom(X4))
| ~ in(sK2(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369013,c_369671]) ).
tcf(c_401797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK2(X0,X1,relation_dom(X2))))) = apply(X2,sK2(X0,X1,relation_dom(X2))) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_368866,c_369671]) ).
tcf(c_401798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(X0,set_intersection2(X1,X2),relation_dom(X3))))) = apply(X3,sK2(X0,set_intersection2(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368504,c_369671]) ).
tcf(c_401799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(X0,set_intersection2(X1,X2),relation_dom(X3))))) = apply(X3,sK2(X0,set_intersection2(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368482,c_369671]) ).
tcf(c_401800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,relation_dom(X2)),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,relation_dom(X2))) = X3 )
| ( apply(X2,sK13(X2,X4,apply(X2,sK2(X0,set_intersection2(X1,relation_dom(X2)),X3)))) = apply(X2,sK2(X0,set_intersection2(X1,relation_dom(X2)),X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,set_intersection2(X1,relation_dom(X2)),X3),X4) ),
inference(superposition,[status(thm)],[c_368504,c_369671]) ).
tcf(c_401801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X3)
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = X3 )
| ( apply(X1,sK13(X1,X4,apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),X3)))) = apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),X3)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X4) ),
inference(superposition,[status(thm)],[c_368482,c_369671]) ).
tcf(c_401802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,relation_inverse_image(X0,relation_dom(X2)),X3),X3)
| ( set_intersection2(X1,relation_inverse_image(X0,relation_dom(X2))) = X3 )
| ( apply(X2,sK13(X2,X4,apply(X2,apply(X0,sK2(X1,relation_inverse_image(X0,relation_dom(X2)),X3))))) = apply(X2,apply(X0,sK2(X1,relation_inverse_image(X0,relation_dom(X2)),X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(apply(X0,sK2(X1,relation_inverse_image(X0,relation_dom(X2)),X3)),X4) ),
inference(superposition,[status(thm)],[c_368814,c_369671]) ).
tcf(c_401803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(X0,relation_inverse_image(X1,X2),relation_dom(X3))),X2)
| ( set_intersection2(X0,relation_inverse_image(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(X0,relation_inverse_image(X1,X2),relation_dom(X3))))) = apply(X3,sK2(X0,relation_inverse_image(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(sK2(X0,relation_inverse_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368814,c_369671]) ).
tcf(c_401804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,relation_inverse_image(X1,X2),relation_dom(X3)),relation_dom(X1))
| ( set_intersection2(X0,relation_inverse_image(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(X0,relation_inverse_image(X1,X2),relation_dom(X3))))) = apply(X3,sK2(X0,relation_inverse_image(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(sK2(X0,relation_inverse_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368758,c_369671]) ).
tcf(c_401805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,relation_inverse_image(X1,X2),X3),X3)
| ( set_intersection2(X0,relation_inverse_image(X1,X2)) = X3 )
| ( apply(X1,sK13(X1,X4,apply(X1,sK2(X0,relation_inverse_image(X1,X2),X3)))) = apply(X1,sK2(X0,relation_inverse_image(X1,X2),X3)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,relation_inverse_image(X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_368758,c_369671]) ).
tcf(c_401806,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,relation_dom(X1)) = relation_dom(X1) )
| ( apply(X1,sK13(X1,X2,apply(X1,sK2(X0,relation_dom(X1),relation_dom(X1))))) = apply(X1,sK2(X0,relation_dom(X1),relation_dom(X1))) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,relation_dom(X1),relation_dom(X1)),X2) ),
inference(superposition,[status(thm)],[c_368460,c_369671]) ).
tcf(c_401807,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(X1) = empty_set )
| ( apply(X1,sK13(X1,X2,apply(X1,sK2(X0,empty_set,relation_dom(X1))))) = apply(X1,sK2(X0,empty_set,relation_dom(X1))) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,empty_set,relation_dom(X1)),X2) ),
inference(superposition,[status(thm)],[c_372467,c_369671]) ).
tcf(c_401808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(X4,sK13(X4,X3,apply(X4,sK13(X0,X1,X2)))) = apply(X4,sK13(X0,X1,X2)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X1,relation_dom(X4))
| ~ in(X2,relation_image(X0,X1))
| ~ in(sK13(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369594,c_369671]) ).
tcf(c_401809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(X4,sK13(X4,X3,apply(X4,sK13(X0,X1,X2)))) = apply(X4,sK13(X0,X1,X2)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_dom(X4))
| ~ in(X2,relation_image(X0,X1))
| ~ in(sK13(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369556,c_369671]) ).
tcf(c_401810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(X2,sK13(X2,X4,apply(X2,sK13(X0,set_intersection2(X1,relation_dom(X2)),X3)))) = apply(X2,sK13(X0,set_intersection2(X1,relation_dom(X2)),X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,set_intersection2(X1,relation_dom(X2))))
| ~ in(sK13(X0,set_intersection2(X1,relation_dom(X2)),X3),X4) ),
inference(superposition,[status(thm)],[c_369597,c_369671]) ).
tcf(c_401811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(X1,sK13(X1,X4,apply(X1,sK13(X0,set_intersection2(relation_dom(X1),X2),X3)))) = apply(X1,sK13(X0,set_intersection2(relation_dom(X1),X2),X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,set_intersection2(relation_dom(X1),X2)))
| ~ in(sK13(X0,set_intersection2(relation_dom(X1),X2),X3),X4) ),
inference(superposition,[status(thm)],[c_369598,c_369671]) ).
tcf(c_401812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(X2,sK13(X2,X4,apply(X2,apply(X0,sK13(X1,relation_inverse_image(X0,relation_dom(X2)),X3))))) = apply(X2,apply(X0,sK13(X1,relation_inverse_image(X0,relation_dom(X2)),X3))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X3,relation_image(X1,relation_inverse_image(X0,relation_dom(X2))))
| ~ in(apply(X0,sK13(X1,relation_inverse_image(X0,relation_dom(X2)),X3)),X4) ),
inference(superposition,[status(thm)],[c_369599,c_369671]) ).
tcf(c_401813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(X1,sK13(X1,X4,apply(X1,sK13(X0,relation_inverse_image(X1,X2),X3)))) = apply(X1,sK13(X0,relation_inverse_image(X1,X2),X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,relation_inverse_image(X1,X2)))
| ~ in(sK13(X0,relation_inverse_image(X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_369600,c_369671]) ).
tcf(c_401814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X0,X1),X2) = relation_dom(X3) )
| ( apply(X0,sK13(X0,X1,sK2(relation_image(X0,X1),X2,relation_dom(X3)))) = sK2(relation_image(X0,X1),X2,relation_dom(X3)) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(relation_image(X0,X1),X2,relation_dom(X3))))) = apply(X3,sK2(relation_image(X0,X1),X2,relation_dom(X3))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK2(relation_image(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369659,c_369671]) ).
tcf(c_401815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X0,relation_image(X1,X2)) = relation_dom(X3) )
| ( apply(X1,sK13(X1,X2,sK2(X0,relation_image(X1,X2),relation_dom(X3)))) = sK2(X0,relation_image(X1,X2),relation_dom(X3)) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(X0,relation_image(X1,X2),relation_dom(X3))))) = apply(X3,sK2(X0,relation_image(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(sK2(X0,relation_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369660,c_369671]) ).
tcf(c_401816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X0,relation_dom(X1)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(X0,relation_dom(X1),relation_image(X2,X3)))) = sK2(X0,relation_dom(X1),relation_image(X2,X3)) )
| ( apply(X1,sK13(X1,X4,apply(X1,sK2(X0,relation_dom(X1),relation_image(X2,X3))))) = apply(X1,sK2(X0,relation_dom(X1),relation_image(X2,X3))) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(sK2(X0,relation_dom(X1),relation_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369661,c_369671]) ).
tcf(c_401817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_dom(X0),X1) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(relation_dom(X0),X1,relation_image(X2,X3)))) = sK2(relation_dom(X0),X1,relation_image(X2,X3)) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK2(relation_dom(X0),X1,relation_image(X2,X3))))) = apply(X0,sK2(relation_dom(X0),X1,relation_image(X2,X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK2(relation_dom(X0),X1,relation_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369662,c_369671]) ).
tcf(c_401818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,relation_dom(X2)),X4)
| ( relation_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK11(X0,X1,relation_dom(X2))))) = apply(X2,sK11(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(X1,X4)
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369299,c_369671]) ).
tcf(c_401819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X4,sK13(X4,X3,apply(X4,sK12(X0,X1,X2)))) = apply(X4,sK12(X0,X1,X2)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X1,relation_dom(X4))
| ~ in(sK12(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369299,c_369671]) ).
tcf(c_401820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X1,X2),relation_dom(X3)),X1)
| ( relation_image(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK11(X0,set_intersection2(X1,X2),relation_dom(X3))))) = apply(X3,sK11(X0,set_intersection2(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK11(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369303,c_369671]) ).
tcf(c_401821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,set_intersection2(X1,X2),relation_dom(X3)),X2)
| ( relation_image(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK11(X0,set_intersection2(X1,X2),relation_dom(X3))))) = apply(X3,sK11(X0,set_intersection2(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK11(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369302,c_369671]) ).
tcf(c_401822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,set_intersection2(X1,relation_dom(X2)),X3),X3)
| ( relation_image(X0,set_intersection2(X1,relation_dom(X2))) = X3 )
| ( apply(X2,sK13(X2,X4,apply(X2,sK12(X0,set_intersection2(X1,relation_dom(X2)),X3)))) = apply(X2,sK12(X0,set_intersection2(X1,relation_dom(X2)),X3)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK12(X0,set_intersection2(X1,relation_dom(X2)),X3),X4) ),
inference(superposition,[status(thm)],[c_369302,c_369671]) ).
tcf(c_401823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,set_intersection2(relation_dom(X1),X2),X3),X3)
| ( relation_image(X0,set_intersection2(relation_dom(X1),X2)) = X3 )
| ( apply(X1,sK13(X1,X4,apply(X1,sK12(X0,set_intersection2(relation_dom(X1),X2),X3)))) = apply(X1,sK12(X0,set_intersection2(relation_dom(X1),X2),X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK12(X0,set_intersection2(relation_dom(X1),X2),X3),X4) ),
inference(superposition,[status(thm)],[c_369303,c_369671]) ).
tcf(c_401824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,relation_inverse_image(X1,X2),relation_dom(X3)),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK11(X0,relation_inverse_image(X1,X2),relation_dom(X3))))) = apply(X3,sK11(X0,relation_inverse_image(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK11(X0,relation_inverse_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369305,c_369671]) ).
tcf(c_401825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK12(X0,relation_inverse_image(X1,X2),relation_dom(X3))),X2)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK11(X0,relation_inverse_image(X1,X2),relation_dom(X3))))) = apply(X3,sK11(X0,relation_inverse_image(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK11(X0,relation_inverse_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369304,c_369671]) ).
tcf(c_401826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X1,relation_inverse_image(X0,relation_dom(X2)),X3),X3)
| ( relation_image(X1,relation_inverse_image(X0,relation_dom(X2))) = X3 )
| ( apply(X2,sK13(X2,X4,apply(X2,apply(X0,sK12(X1,relation_inverse_image(X0,relation_dom(X2)),X3))))) = apply(X2,apply(X0,sK12(X1,relation_inverse_image(X0,relation_dom(X2)),X3))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK12(X1,relation_inverse_image(X0,relation_dom(X2)),X3)),X4) ),
inference(superposition,[status(thm)],[c_369304,c_369671]) ).
tcf(c_401827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),X3),X3)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ( apply(X1,sK13(X1,X4,apply(X1,sK12(X0,relation_inverse_image(X1,X2),X3)))) = apply(X1,sK12(X0,relation_inverse_image(X1,X2),X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK12(X0,relation_inverse_image(X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_369305,c_369671]) ).
tcf(c_401828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,relation_image(X1,X2)) = relation_dom(X3) )
| ( apply(X1,sK13(X1,X2,sK12(X0,relation_image(X1,X2),relation_dom(X3)))) = sK12(X0,relation_image(X1,X2),relation_dom(X3)) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK11(X0,relation_image(X1,X2),relation_dom(X3))))) = apply(X3,sK11(X0,relation_image(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK11(X0,relation_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369670,c_369671]) ).
tcf(c_401829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK12(X0,X1,X2)) = sK11(X0,X1,X2) )
| ( apply(X4,sK13(X4,X3,apply(X4,sK11(X0,X1,X2)))) = apply(X4,sK11(X0,X1,X2)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,relation_dom(X4))
| ~ in(sK11(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369436,c_369671]) ).
tcf(c_401830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,X2),X1)
| ( relation_image(X0,X1) = X2 )
| ( apply(X4,sK13(X4,X3,apply(X4,sK11(X0,X1,X2)))) = apply(X4,sK11(X0,X1,X2)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,relation_dom(X4))
| ~ in(sK11(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369307,c_369671]) ).
tcf(c_401831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ( apply(X4,sK13(X4,X3,apply(X4,sK11(X0,X1,X2)))) = apply(X4,sK11(X0,X1,X2)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,relation_dom(X4))
| ~ in(sK11(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369206,c_369671]) ).
tcf(c_401832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_dom(X1),X2),X4)
| ( relation_image(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,sK12(X0,relation_dom(X1),X2)))) = apply(X1,sK12(X0,relation_dom(X1),X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ in(sK12(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_369307,c_369671]) ).
tcf(c_401833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,sK12(X0,relation_dom(X1),X2)))) = apply(X1,sK12(X0,relation_dom(X1),X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK12(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_369309,c_369671]) ).
tcf(c_401834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_dom(X1),set_intersection2(X2,X3)),X2)
| ( relation_image(X0,relation_dom(X1)) = set_intersection2(X2,X3) )
| ( apply(X1,sK13(X1,X4,apply(X1,sK12(X0,relation_dom(X1),set_intersection2(X2,X3))))) = apply(X1,sK12(X0,relation_dom(X1),set_intersection2(X2,X3))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK12(X0,relation_dom(X1),set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369311,c_369671]) ).
tcf(c_401835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_dom(X1),set_intersection2(X2,X3)),X3)
| ( relation_image(X0,relation_dom(X1)) = set_intersection2(X2,X3) )
| ( apply(X1,sK13(X1,X4,apply(X1,sK12(X0,relation_dom(X1),set_intersection2(X2,X3))))) = apply(X1,sK12(X0,relation_dom(X1),set_intersection2(X2,X3))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK12(X0,relation_dom(X1),set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369310,c_369671]) ).
tcf(c_401836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X2,relation_dom(X3)) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,relation_dom(X3)))) = sK11(X0,X1,set_intersection2(X2,relation_dom(X3))) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK11(X0,X1,set_intersection2(X2,relation_dom(X3)))))) = apply(X3,sK11(X0,X1,set_intersection2(X2,relation_dom(X3)))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK11(X0,X1,set_intersection2(X2,relation_dom(X3))),X4) ),
inference(superposition,[status(thm)],[c_369439,c_369671]) ).
tcf(c_401837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,set_intersection2(X2,relation_dom(X3))),X1)
| ( set_intersection2(X2,relation_dom(X3)) = relation_image(X0,X1) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK11(X0,X1,set_intersection2(X2,relation_dom(X3)))))) = apply(X3,sK11(X0,X1,set_intersection2(X2,relation_dom(X3)))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK11(X0,X1,set_intersection2(X2,relation_dom(X3))),X4) ),
inference(superposition,[status(thm)],[c_369310,c_369671]) ).
tcf(c_401838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,set_intersection2(X2,relation_dom(X3))),relation_dom(X0))
| ( set_intersection2(X2,relation_dom(X3)) = relation_image(X0,X1) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK11(X0,X1,set_intersection2(X2,relation_dom(X3)))))) = apply(X3,sK11(X0,X1,set_intersection2(X2,relation_dom(X3)))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK11(X0,X1,set_intersection2(X2,relation_dom(X3))),X4) ),
inference(superposition,[status(thm)],[c_369209,c_369671]) ).
tcf(c_401839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_dom(X2),X3) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(relation_dom(X2),X3))) = sK11(X0,X1,set_intersection2(relation_dom(X2),X3)) )
| ( apply(X2,sK13(X2,X4,apply(X2,sK11(X0,X1,set_intersection2(relation_dom(X2),X3))))) = apply(X2,sK11(X0,X1,set_intersection2(relation_dom(X2),X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,set_intersection2(relation_dom(X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_369440,c_369671]) ).
tcf(c_401840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,set_intersection2(relation_dom(X2),X3)),X1)
| ( set_intersection2(relation_dom(X2),X3) = relation_image(X0,X1) )
| ( apply(X2,sK13(X2,X4,apply(X2,sK11(X0,X1,set_intersection2(relation_dom(X2),X3))))) = apply(X2,sK11(X0,X1,set_intersection2(relation_dom(X2),X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,set_intersection2(relation_dom(X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_369311,c_369671]) ).
tcf(c_401841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,set_intersection2(relation_dom(X2),X3)),relation_dom(X0))
| ( set_intersection2(relation_dom(X2),X3) = relation_image(X0,X1) )
| ( apply(X2,sK13(X2,X4,apply(X2,sK11(X0,X1,set_intersection2(relation_dom(X2),X3))))) = apply(X2,sK11(X0,X1,set_intersection2(relation_dom(X2),X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,set_intersection2(relation_dom(X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_369210,c_369671]) ).
tcf(c_401842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X2,relation_inverse_image(X0,relation_dom(X3))),X2)
| ( relation_inverse_image(X0,relation_dom(X3)) = relation_image(X1,X2) )
| ( apply(X3,sK13(X3,X4,apply(X3,apply(X0,sK11(X1,X2,relation_inverse_image(X0,relation_dom(X3))))))) = apply(X3,apply(X0,sK11(X1,X2,relation_inverse_image(X0,relation_dom(X3))))) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK11(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X4) ),
inference(superposition,[status(thm)],[c_369312,c_369671]) ).
tcf(c_401843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X2,relation_inverse_image(X0,relation_dom(X3))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_dom(X3)) = relation_image(X1,X2) )
| ( apply(X3,sK13(X3,X4,apply(X3,apply(X0,sK11(X1,X2,relation_inverse_image(X0,relation_dom(X3))))))) = apply(X3,apply(X0,sK11(X1,X2,relation_inverse_image(X0,relation_dom(X3))))) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK11(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X4) ),
inference(superposition,[status(thm)],[c_369211,c_369671]) ).
tcf(c_401844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_dom(X1),relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_image(X0,relation_dom(X1)) = relation_inverse_image(X2,X3) )
| ( apply(X1,sK13(X1,X4,apply(X1,sK12(X0,relation_dom(X1),relation_inverse_image(X2,X3))))) = apply(X1,sK12(X0,relation_dom(X1),relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK12(X0,relation_dom(X1),relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369313,c_369671]) ).
tcf(c_401845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK11(X0,relation_dom(X1),relation_inverse_image(X2,X3))),X3)
| ( relation_image(X0,relation_dom(X1)) = relation_inverse_image(X2,X3) )
| ( apply(X1,sK13(X1,X4,apply(X1,sK12(X0,relation_dom(X1),relation_inverse_image(X2,X3))))) = apply(X1,sK12(X0,relation_dom(X1),relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK12(X0,relation_dom(X1),relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369312,c_369671]) ).
tcf(c_401846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,relation_inverse_image(X2,X3)),X1)
| ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ( apply(X2,sK13(X2,X4,apply(X2,sK11(X0,X1,relation_inverse_image(X2,X3))))) = apply(X2,sK11(X0,X1,relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369313,c_369671]) ).
tcf(c_401847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X0))
| ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ( apply(X2,sK13(X2,X4,apply(X2,sK11(X0,X1,relation_inverse_image(X2,X3))))) = apply(X2,sK11(X0,X1,relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369212,c_369671]) ).
tcf(c_401848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,relation_dom(X1)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK11(X0,relation_dom(X1),relation_image(X2,X3)))) = sK11(X0,relation_dom(X1),relation_image(X2,X3)) )
| ( apply(X1,sK13(X1,X4,apply(X1,sK12(X0,relation_dom(X1),relation_image(X2,X3))))) = apply(X1,sK12(X0,relation_dom(X1),relation_image(X2,X3))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK12(X0,relation_dom(X1),relation_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369668,c_369671]) ).
tcf(c_401849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,X2),X4)
| ( relation_inverse_image(X0,X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK7(X0,X1,X2)))) = apply(X0,sK7(X0,X1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369020,c_369671]) ).
tcf(c_401850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,X2),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = X2 )
| ( apply(X4,sK13(X4,X3,apply(X4,sK7(X0,X1,X2)))) = apply(X4,sK7(X0,X1,X2)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,relation_dom(X4))
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369020,c_369671]) ).
tcf(c_401851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X1,X2)),X1)
| ( relation_inverse_image(X0,X1) = X2 )
| ( apply(X4,sK13(X4,X3,apply(X4,sK7(X0,X1,X2)))) = apply(X4,sK7(X0,X1,X2)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,relation_dom(X4))
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369019,c_369671]) ).
tcf(c_401852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK7(X0,X1,X2)))) = apply(X0,sK7(X0,X1,X2)) )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_368873,c_369671]) ).
tcf(c_401853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK7(X0,X1,set_intersection2(X2,X3))))) = apply(X0,sK7(X0,X1,set_intersection2(X2,X3))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368673,c_369671]) ).
tcf(c_401854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_inverse_image(X0,X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK7(X0,X1,set_intersection2(X2,X3))))) = apply(X0,sK7(X0,X1,set_intersection2(X2,X3))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368672,c_369671]) ).
tcf(c_401855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X1,set_intersection2(X2,relation_dom(X3)))),X1)
| ( set_intersection2(X2,relation_dom(X3)) = relation_inverse_image(X0,X1) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK7(X0,X1,set_intersection2(X2,relation_dom(X3)))))) = apply(X3,sK7(X0,X1,set_intersection2(X2,relation_dom(X3)))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK7(X0,X1,set_intersection2(X2,relation_dom(X3))),X4) ),
inference(superposition,[status(thm)],[c_368700,c_369671]) ).
tcf(c_401856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,set_intersection2(X2,relation_dom(X3))),relation_dom(X0))
| ( set_intersection2(X2,relation_dom(X3)) = relation_inverse_image(X0,X1) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK7(X0,X1,set_intersection2(X2,relation_dom(X3)))))) = apply(X3,sK7(X0,X1,set_intersection2(X2,relation_dom(X3)))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK7(X0,X1,set_intersection2(X2,relation_dom(X3))),X4) ),
inference(superposition,[status(thm)],[c_368672,c_369671]) ).
tcf(c_401857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X1,set_intersection2(relation_dom(X2),X3))),X1)
| ( set_intersection2(relation_dom(X2),X3) = relation_inverse_image(X0,X1) )
| ( apply(X2,sK13(X2,X4,apply(X2,sK7(X0,X1,set_intersection2(relation_dom(X2),X3))))) = apply(X2,sK7(X0,X1,set_intersection2(relation_dom(X2),X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,set_intersection2(relation_dom(X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_368701,c_369671]) ).
tcf(c_401858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,set_intersection2(relation_dom(X2),X3)),relation_dom(X0))
| ( set_intersection2(relation_dom(X2),X3) = relation_inverse_image(X0,X1) )
| ( apply(X2,sK13(X2,X4,apply(X2,sK7(X0,X1,set_intersection2(relation_dom(X2),X3))))) = apply(X2,sK7(X0,X1,set_intersection2(relation_dom(X2),X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,set_intersection2(relation_dom(X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_368673,c_369671]) ).
tcf(c_401859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,X2,relation_inverse_image(X0,relation_dom(X3))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_dom(X3)) = relation_inverse_image(X1,X2) )
| ( apply(X3,sK13(X3,X4,apply(X3,apply(X0,sK7(X1,X2,relation_inverse_image(X0,relation_dom(X3))))))) = apply(X3,apply(X0,sK7(X1,X2,relation_inverse_image(X0,relation_dom(X3))))) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X4) ),
inference(superposition,[status(thm)],[c_368819,c_369671]) ).
tcf(c_401860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X2)
| ( relation_inverse_image(X0,relation_dom(X3)) = relation_inverse_image(X1,X2) )
| ( apply(X3,sK13(X3,X4,apply(X3,apply(X0,sK7(X1,X2,relation_inverse_image(X0,relation_dom(X3))))))) = apply(X3,apply(X0,sK7(X1,X2,relation_inverse_image(X0,relation_dom(X3))))) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X4) ),
inference(superposition,[status(thm)],[c_368818,c_369671]) ).
tcf(c_401861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X0,X1,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK7(X0,X1,relation_inverse_image(X2,X3))))) = apply(X0,sK7(X0,X1,relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368819,c_369671]) ).
tcf(c_401862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK7(X0,X1,relation_inverse_image(X2,X3))))) = apply(X0,sK7(X0,X1,relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368763,c_369671]) ).
tcf(c_401863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ( apply(X2,sK13(X2,X4,apply(X2,sK7(X0,X1,relation_inverse_image(X2,X3))))) = apply(X2,sK7(X0,X1,relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368763,c_369671]) ).
tcf(c_401864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X1,relation_inverse_image(X2,X3))),X1)
| ( relation_inverse_image(X0,X1) = relation_inverse_image(X2,X3) )
| ( apply(X2,sK13(X2,X4,apply(X2,sK7(X0,X1,relation_inverse_image(X2,X3))))) = apply(X2,sK7(X0,X1,relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_368762,c_369671]) ).
tcf(c_401865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,X1) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X0,X1,relation_image(X2,X3)))) = sK7(X0,X1,relation_image(X2,X3)) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK7(X0,X1,relation_image(X2,X3))))) = apply(X0,sK7(X0,X1,relation_image(X2,X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369665,c_369671]) ).
tcf(c_401866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,relation_dom(X2)),X4)
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK7(X0,X1,relation_dom(X2))))) = apply(X2,sK7(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X4)
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369017,c_369671]) ).
tcf(c_401867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ( apply(X4,sK13(X4,X3,apply(X4,sK7(X0,X1,X2)))) = apply(X4,sK7(X0,X1,X2)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_dom(X4))
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369017,c_369671]) ).
tcf(c_401868,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X1) = relation_dom(X0) )
| ( apply(X0,sK13(X0,X2,apply(X0,sK7(X0,X1,relation_dom(X0))))) = apply(X0,sK7(X0,X1,relation_dom(X0))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,X1,relation_dom(X0)),X2) ),
inference(superposition,[status(thm)],[c_368674,c_369671]) ).
tcf(c_401869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,X2),X4)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK12(X0,X1,X2)))) = apply(X0,sK12(X0,X1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ in(sK12(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369206,c_369671]) ).
tcf(c_401870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK12(X0,X1,X2)))) = apply(X0,sK12(X0,X1,X2)) )
| ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK12(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369208,c_369671]) ).
tcf(c_401871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK12(X0,X1,set_intersection2(X2,X3))))) = apply(X0,sK12(X0,X1,set_intersection2(X2,X3))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK12(X0,X1,set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369210,c_369671]) ).
tcf(c_401872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK12(X0,X1,set_intersection2(X2,X3))))) = apply(X0,sK12(X0,X1,set_intersection2(X2,X3))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK12(X0,X1,set_intersection2(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369209,c_369671]) ).
tcf(c_401873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK12(X0,X1,relation_inverse_image(X2,X3))))) = apply(X0,sK12(X0,X1,relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK12(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369212,c_369671]) ).
tcf(c_401874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK11(X0,X1,relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK12(X0,X1,relation_inverse_image(X2,X3))))) = apply(X0,sK12(X0,X1,relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK12(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369211,c_369671]) ).
tcf(c_401875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,X1) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK11(X0,X1,relation_image(X2,X3)))) = sK11(X0,X1,relation_image(X2,X3)) )
| ( apply(X0,sK13(X0,X4,apply(X0,sK12(X0,X1,relation_image(X2,X3))))) = apply(X0,sK12(X0,X1,relation_image(X2,X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK12(X0,X1,relation_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369669,c_369671]) ).
tcf(c_401876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X1,relation_dom(X2)),X4)
| ( relation_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK11(X0,X1,relation_dom(X2))))) = apply(X2,sK11(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X4)
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369214,c_369671]) ).
tcf(c_401877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X4,sK13(X4,X3,apply(X4,sK12(X0,X1,X2)))) = apply(X4,sK12(X0,X1,X2)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_dom(X4))
| ~ in(sK12(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369214,c_369671]) ).
tcf(c_401878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_dom(X1),X2),X4)
| ( relation_inverse_image(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,apply(X0,sK7(X0,relation_dom(X1),X2))))) = apply(X1,apply(X0,sK7(X0,relation_dom(X1),X2))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ in(apply(X0,sK7(X0,relation_dom(X1),X2)),X3) ),
inference(superposition,[status(thm)],[c_369019,c_369671]) ).
tcf(c_401879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,apply(X0,sK7(X0,relation_dom(X1),X2))))) = apply(X1,apply(X0,sK7(X0,relation_dom(X1),X2))) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,relation_dom(X1),X2)),X3) ),
inference(superposition,[status(thm)],[c_368872,c_369671]) ).
tcf(c_401880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_dom(X1),set_intersection2(X2,X3)),X2)
| ( relation_inverse_image(X0,relation_dom(X1)) = set_intersection2(X2,X3) )
| ( apply(X1,sK13(X1,X4,apply(X1,apply(X0,sK7(X0,relation_dom(X1),set_intersection2(X2,X3)))))) = apply(X1,apply(X0,sK7(X0,relation_dom(X1),set_intersection2(X2,X3)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,relation_dom(X1),set_intersection2(X2,X3))),X4) ),
inference(superposition,[status(thm)],[c_368701,c_369671]) ).
tcf(c_401881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_dom(X1),set_intersection2(X2,X3)),X3)
| ( relation_inverse_image(X0,relation_dom(X1)) = set_intersection2(X2,X3) )
| ( apply(X1,sK13(X1,X4,apply(X1,apply(X0,sK7(X0,relation_dom(X1),set_intersection2(X2,X3)))))) = apply(X1,apply(X0,sK7(X0,relation_dom(X1),set_intersection2(X2,X3)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,relation_dom(X1),set_intersection2(X2,X3))),X4) ),
inference(superposition,[status(thm)],[c_368700,c_369671]) ).
tcf(c_401882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X0,relation_dom(X1),relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X0,relation_dom(X1)) = relation_inverse_image(X2,X3) )
| ( apply(X1,sK13(X1,X4,apply(X1,apply(X0,sK7(X0,relation_dom(X1),relation_inverse_image(X2,X3)))))) = apply(X1,apply(X0,sK7(X0,relation_dom(X1),relation_inverse_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,relation_dom(X1),relation_inverse_image(X2,X3))),X4) ),
inference(superposition,[status(thm)],[c_368818,c_369671]) ).
tcf(c_401883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_dom(X1),relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X0,relation_dom(X1)) = relation_inverse_image(X2,X3) )
| ( apply(X1,sK13(X1,X4,apply(X1,apply(X0,sK7(X0,relation_dom(X1),relation_inverse_image(X2,X3)))))) = apply(X1,apply(X0,sK7(X0,relation_dom(X1),relation_inverse_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,relation_dom(X1),relation_inverse_image(X2,X3))),X4) ),
inference(superposition,[status(thm)],[c_368762,c_369671]) ).
tcf(c_401884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,relation_dom(X1)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK7(X0,relation_dom(X1),relation_image(X2,X3)))) = sK7(X0,relation_dom(X1),relation_image(X2,X3)) )
| ( apply(X1,sK13(X1,X4,apply(X1,apply(X0,sK7(X0,relation_dom(X1),relation_image(X2,X3)))))) = apply(X1,apply(X0,sK7(X0,relation_dom(X1),relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,relation_dom(X1),relation_image(X2,X3))),X4) ),
inference(superposition,[status(thm)],[c_369664,c_369671]) ).
tcf(c_401885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ( apply(X4,sK13(X4,X3,apply(X4,apply(X0,sK7(X0,X1,X2))))) = apply(X4,apply(X0,sK7(X0,X1,X2))) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X1,relation_dom(X4))
| ~ in(apply(X0,sK7(X0,X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_369018,c_369671]) ).
tcf(c_401886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X1,relation_dom(X2))),X4)
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK7(X0,X1,relation_dom(X2))))) = apply(X2,sK7(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(X1,X4)
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369018,c_369671]) ).
tcf(c_401887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X1,X2),relation_dom(X3))),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK7(X0,set_intersection2(X1,X2),relation_dom(X3))))) = apply(X3,sK7(X0,set_intersection2(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK7(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368703,c_369671]) ).
tcf(c_401888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X1,X2),relation_dom(X3))),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK7(X0,set_intersection2(X1,X2),relation_dom(X3))))) = apply(X3,sK7(X0,set_intersection2(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK7(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368702,c_369671]) ).
tcf(c_401889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X1,relation_dom(X2)),X3),X3)
| ( relation_inverse_image(X0,set_intersection2(X1,relation_dom(X2))) = X3 )
| ( apply(X2,sK13(X2,X4,apply(X2,apply(X0,sK7(X0,set_intersection2(X1,relation_dom(X2)),X3))))) = apply(X2,apply(X0,sK7(X0,set_intersection2(X1,relation_dom(X2)),X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,set_intersection2(X1,relation_dom(X2)),X3)),X4) ),
inference(superposition,[status(thm)],[c_368702,c_369671]) ).
tcf(c_401890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(relation_dom(X1),X2),X3),X3)
| ( relation_inverse_image(X0,set_intersection2(relation_dom(X1),X2)) = X3 )
| ( apply(X1,sK13(X1,X4,apply(X1,apply(X0,sK7(X0,set_intersection2(relation_dom(X1),X2),X3))))) = apply(X1,apply(X0,sK7(X0,set_intersection2(relation_dom(X1),X2),X3))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,set_intersection2(relation_dom(X1),X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_368703,c_369671]) ).
tcf(c_401891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X2),relation_dom(X3)))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK7(X0,relation_inverse_image(X1,X2),relation_dom(X3))))) = apply(X3,sK7(X0,relation_inverse_image(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK7(X0,relation_inverse_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368817,c_369671]) ).
tcf(c_401892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),relation_dom(X3))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK7(X0,relation_inverse_image(X1,X2),relation_dom(X3))))) = apply(X3,sK7(X0,relation_inverse_image(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK7(X0,relation_inverse_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_368761,c_369671]) ).
tcf(c_401893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,relation_inverse_image(X0,relation_dom(X2)),X3),X3)
| ( relation_inverse_image(X1,relation_inverse_image(X0,relation_dom(X2))) = X3 )
| ( apply(X2,sK13(X2,X4,apply(X2,apply(X0,apply(X1,sK7(X1,relation_inverse_image(X0,relation_dom(X2)),X3)))))) = apply(X2,apply(X0,apply(X1,sK7(X1,relation_inverse_image(X0,relation_dom(X2)),X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,apply(X1,sK7(X1,relation_inverse_image(X0,relation_dom(X2)),X3))),X4) ),
inference(superposition,[status(thm)],[c_368817,c_369671]) ).
tcf(c_401894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),X3),X3)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = X3 )
| ( apply(X1,sK13(X1,X4,apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X2),X3))))) = apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X2),X3))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),X3)),X4) ),
inference(superposition,[status(thm)],[c_368761,c_369671]) ).
tcf(c_401895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,relation_image(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK7(X0,relation_image(X1,X2),relation_dom(X3))))) = apply(X3,sK7(X0,relation_image(X1,X2),relation_dom(X3))) )
| ( apply(X1,sK13(X1,X2,apply(X0,sK7(X0,relation_image(X1,X2),relation_dom(X3))))) = apply(X0,sK7(X0,relation_image(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK7(X0,relation_image(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_369663,c_369671]) ).
tcf(c_401896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,relation_dom(X3)) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,relation_inverse_image(X0,relation_dom(X3)))) = sK11(X1,X2,relation_inverse_image(X0,relation_dom(X3))) )
| ( apply(X3,sK13(X3,X4,apply(X3,apply(X0,sK11(X1,X2,relation_inverse_image(X0,relation_dom(X3))))))) = apply(X3,apply(X0,sK11(X1,X2,relation_inverse_image(X0,relation_dom(X3))))) )
| ~ function(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK11(X1,X2,relation_inverse_image(X0,relation_dom(X3)))),X4) ),
inference(superposition,[status(thm)],[c_369441,c_369671]) ).
tcf(c_401897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X2,X3) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,relation_inverse_image(X2,X3))) = sK11(X0,X1,relation_inverse_image(X2,X3)) )
| ( apply(X2,sK13(X2,X4,apply(X2,sK11(X0,X1,relation_inverse_image(X2,X3))))) = apply(X2,sK11(X0,X1,relation_inverse_image(X2,X3))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK11(X0,X1,relation_inverse_image(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_369442,c_369671]) ).
tcf(c_404035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(relation_image(X0,relation_image(X1,X2)),X3,X4),X4)
| ( set_intersection2(relation_image(X0,relation_image(X1,X2)),X3) = X4 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(relation_image(X0,relation_image(X1,X2)),X3,X4)))) = sK13(X0,relation_image(X1,X2),sK2(relation_image(X0,relation_image(X1,X2)),X3,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368927,c_369672]) ).
tcf(c_404036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X0,relation_image(X1,X2)),X3,X4),X4)
| ( set_intersection2(relation_image(X0,relation_image(X1,X2)),X3) = X4 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(relation_image(X0,relation_image(X1,X2)),X3,X4)))) = sK13(X0,relation_image(X1,X2),sK2(relation_image(X0,relation_image(X1,X2)),X3,X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_369672]) ).
tcf(c_404037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,relation_image(X0,relation_image(X1,X2)),X4),X4)
| ( set_intersection2(X3,relation_image(X0,relation_image(X1,X2))) = X4 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,relation_image(X0,relation_image(X1,X2)),X4)))) = sK13(X0,relation_image(X1,X2),sK2(X3,relation_image(X0,relation_image(X1,X2)),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368926,c_369672]) ).
tcf(c_404038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_image(X0,relation_image(X1,X2)),X4),X4)
| ( set_intersection2(X3,relation_image(X0,relation_image(X1,X2))) = X4 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,relation_image(X0,relation_image(X1,X2)),X4)))) = sK13(X0,relation_image(X1,X2),sK2(X3,relation_image(X0,relation_image(X1,X2)),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_369672]) ).
tcf(c_404039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,relation_image(X0,relation_image(X1,X2))),X4)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,X4,relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(X3,X4,relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368925,c_369672]) ).
tcf(c_404040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,relation_image(X0,relation_image(X1,X2))),X3)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,X4,relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(X3,X4,relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368924,c_369672]) ).
tcf(c_404041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,relation_image(X1,X3)) = set_intersection2(X2,X4) )
| ( apply(X1,sK13(X1,X3,sK13(X0,relation_image(X1,X3),sK2(X2,X4,relation_image(X0,relation_image(X1,X3)))))) = sK13(X0,relation_image(X1,X3),sK2(X2,X4,relation_image(X0,relation_image(X1,X3)))) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368865,c_369672]) ).
tcf(c_404042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_image(X0,relation_image(X1,X2))),X4)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,X4,relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(X3,X4,relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_56,c_369672]) ).
tcf(c_404043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_image(X0,relation_image(X1,X2))),X3)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,X4,relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(X3,X4,relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_55,c_369672]) ).
tcf(c_404044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,relation_image(X1,relation_image(X2,X3)),X4),X4)
| ( relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))) = X4 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK7(X0,relation_image(X1,relation_image(X2,X3)),X4))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK7(X0,relation_image(X1,relation_image(X2,X3)),X4))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368931,c_369672]) ).
tcf(c_404045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,relation_image(X1,relation_image(X2,X3)),X4),X4)
| ( relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))) = X4 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK7(X0,relation_image(X1,relation_image(X2,X3)),X4))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK7(X0,relation_image(X1,relation_image(X2,X3)),X4))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_369672]) ).
tcf(c_404046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(apply(X0,sK7(X0,X4,relation_image(X1,relation_image(X2,X3)))),X4)
| ( relation_image(X1,relation_image(X2,X3)) = relation_inverse_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X0,X4,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK7(X0,X4,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368930,c_369672]) ).
tcf(c_404047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X4,relation_image(X1,relation_image(X2,X3))),relation_dom(X0))
| ( relation_image(X1,relation_image(X2,X3)) = relation_inverse_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X0,X4,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK7(X0,X4,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368929,c_369672]) ).
tcf(c_404048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X1,relation_image(X2,X4)) = relation_inverse_image(X0,X3) )
| ( apply(X2,sK13(X2,X4,sK13(X1,relation_image(X2,X4),sK7(X0,X3,relation_image(X1,relation_image(X2,X4)))))) = sK13(X1,relation_image(X2,X4),sK7(X0,X3,relation_image(X1,relation_image(X2,X4)))) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368871,c_369672]) ).
tcf(c_404049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X1,relation_image(X2,X3)) = relation_inverse_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X0,X4,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK7(X0,X4,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_369672]) ).
tcf(c_404050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,relation_image(X1,relation_image(X2,X3))),relation_inverse_image(X0,X4))
| ( relation_image(X1,relation_image(X2,X3)) = relation_inverse_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X0,X4,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK7(X0,X4,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375319,c_369672]) ).
tcf(c_404051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X4,relation_image(X1,relation_image(X2,X3)))),X4)
| ( relation_image(X1,relation_image(X2,X3)) = relation_inverse_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X0,X4,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK7(X0,X4,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_369672]) ).
tcf(c_404052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X4,relation_image(X1,relation_image(X2,X3))),relation_dom(X0))
| ( relation_image(X1,relation_image(X2,X3)) = relation_inverse_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X0,X4,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK7(X0,X4,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_84,c_369672]) ).
tcf(c_404053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_image(X0,relation_image(X1,X2)),X3)
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK10(relation_image(X0,relation_image(X1,X2)),X3)))) = sK13(X0,relation_image(X1,X2),sK10(relation_image(X0,relation_image(X1,X2)),X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_95,c_369672]) ).
tcf(c_404054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X1,relation_image(X2,X4)) = relation_image(X0,X3) )
| ( apply(X2,sK13(X2,X4,sK13(X1,relation_image(X2,X4),sK11(X0,X3,relation_image(X1,relation_image(X2,X4)))))) = sK13(X1,relation_image(X2,X4),sK11(X0,X3,relation_image(X1,relation_image(X2,X4)))) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369301,c_369672]) ).
tcf(c_404055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X4,relation_image(X1,relation_image(X2,X3))),X4)
| ( relation_image(X1,relation_image(X2,X3)) = relation_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X0,X4,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK11(X0,X4,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369300,c_369672]) ).
tcf(c_404056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X1,relation_image(X2,X3)) = relation_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X0,X4,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK11(X0,X4,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_386602,c_369672]) ).
tcf(c_404057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X4,relation_image(X1,relation_image(X2,X3))),relation_dom(X0))
| ( relation_image(X1,relation_image(X2,X3)) = relation_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X0,X4,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK11(X0,X4,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369215,c_369672]) ).
tcf(c_404058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X1,relation_image(X2,X3)) = relation_image(X0,X4) )
| ( apply(X0,sK12(X0,X4,relation_image(X1,relation_image(X2,X3)))) = sK11(X0,X4,relation_image(X1,relation_image(X2,X3))) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X0,X4,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK11(X0,X4,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_369672]) ).
tcf(c_404059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_image(X1,relation_image(X2,X3))),X4)
| ( relation_image(X1,relation_image(X2,X3)) = relation_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X0,X4,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK11(X0,X4,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_369672]) ).
tcf(c_404060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X4,relation_image(X1,relation_image(X2,X3))),relation_dom(X0))
| ( relation_image(X1,relation_image(X2,X3)) = relation_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X0,X4,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK11(X0,X4,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_106,c_369672]) ).
tcf(c_404061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X0,relation_image(X1,relation_image(X2,X3)),X4),X4)
| ( relation_image(X0,relation_image(X1,relation_image(X2,X3))) = X4 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK12(X0,relation_image(X1,relation_image(X2,X3)),X4)))) = sK13(X1,relation_image(X2,X3),sK12(X0,relation_image(X1,relation_image(X2,X3)),X4)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369308,c_369672]) ).
tcf(c_404062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,relation_image(X1,relation_image(X2,X3)),X4),X4)
| ( relation_image(X0,relation_image(X1,relation_image(X2,X3))) = X4 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK12(X0,relation_image(X1,relation_image(X2,X3)),X4)))) = sK13(X1,relation_image(X2,X3),sK12(X0,relation_image(X1,relation_image(X2,X3)),X4)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_369672]) ).
tcf(c_404063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X1,sK13(X1,X2,sK13(X3,relation_image(X1,X2),apply(X3,X0)))) = sK13(X3,relation_image(X1,X2),apply(X3,X0)) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X0,relation_dom(X3))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_109,c_369672]) ).
tcf(c_404064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK13(X1,relation_image(X2,relation_image(X3,X4)),X0)))) = sK13(X2,relation_image(X3,X4),sK13(X1,relation_image(X2,relation_image(X3,X4)),X0)) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_image(X2,relation_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_111,c_369672]) ).
tcf(c_404065,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(relation_image(X0,relation_image(X1,X2)))
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK16(relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK16(relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368976,c_369672]) ).
tcf(c_404066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4)
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK10(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4)))) = sK13(X0,relation_image(X1,X2),sK10(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368986,c_369672]) ).
tcf(c_404067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4)
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK10(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4)))) = sK13(X0,relation_image(X1,X2),sK10(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368985,c_369672]) ).
tcf(c_404068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))))
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK16(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))))))) = sK13(X0,relation_image(X1,X2),sK16(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370750,c_369672]) ).
tcf(c_404069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))))
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK16(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3))))) = sK13(X0,relation_image(X1,X2),sK16(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_388043,c_369672]) ).
tcf(c_404070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3))
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK16(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3))))) = sK13(X0,relation_image(X1,X2),sK16(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370751,c_369672]) ).
tcf(c_404071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(X0,X4)
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK10(X0,X4)))) = sK13(X1,relation_image(X2,X3),sK10(X0,X4)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369021,c_369672]) ).
tcf(c_404072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X0)
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK16(X0)))) = sK13(X1,relation_image(X2,X3),sK16(X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_370747,c_369672]) ).
tcf(c_404073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X4)
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK10(relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X4))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK10(relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X4))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368987,c_369672]) ).
tcf(c_404074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_image(X2,relation_image(X3,X4)),X5,X0),X1)
| ( set_intersection2(relation_image(X2,relation_image(X3,X4)),X5) = X0 )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK2(relation_image(X2,relation_image(X3,X4)),X5,X0)))) = sK13(X2,relation_image(X3,X4),sK2(relation_image(X2,relation_image(X3,X4)),X5,X0)) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_369672]) ).
tcf(c_404075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X0),X4)
| ( set_intersection2(X4,X5) = X0 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,X5,X0)))) = sK13(X1,relation_image(X2,X3),sK2(X4,X5,X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369015,c_369672]) ).
tcf(c_404076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X0),X5)
| ( set_intersection2(X4,X5) = X0 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,X5,X0)))) = sK13(X1,relation_image(X2,X3),sK2(X4,X5,X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369014,c_369672]) ).
tcf(c_404077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X0,relation_image(X1,X3)),X4) = X2 )
| ( apply(X1,sK13(X1,X3,sK13(X0,relation_image(X1,X3),sK2(relation_image(X0,relation_image(X1,X3)),X4,X2)))) = sK13(X0,relation_image(X1,X3),sK2(relation_image(X0,relation_image(X1,X3)),X4,X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368868,c_369672]) ).
tcf(c_404078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_image(X0,relation_image(X1,X2)),X3,set_intersection2(X4,X5)),X5)
| ( set_intersection2(relation_image(X0,relation_image(X1,X2)),X3) = set_intersection2(X4,X5) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(relation_image(X0,relation_image(X1,X2)),X3,set_intersection2(X4,X5))))) = sK13(X0,relation_image(X1,X2),sK2(relation_image(X0,relation_image(X1,X2)),X3,set_intersection2(X4,X5))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368506,c_369672]) ).
tcf(c_404079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_image(X0,relation_image(X1,X2)),X3,set_intersection2(X4,X5)),X4)
| ( set_intersection2(relation_image(X0,relation_image(X1,X2)),X3) = set_intersection2(X4,X5) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(relation_image(X0,relation_image(X1,X2)),X3,set_intersection2(X4,X5))))) = sK13(X0,relation_image(X1,X2),sK2(relation_image(X0,relation_image(X1,X2)),X3,set_intersection2(X4,X5))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368484,c_369672]) ).
tcf(c_404080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,X4,set_intersection2(X5,relation_image(X0,relation_image(X1,X2)))),X3)
| ( set_intersection2(X5,relation_image(X0,relation_image(X1,X2))) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,X4,set_intersection2(X5,relation_image(X0,relation_image(X1,X2))))))) = sK13(X0,relation_image(X1,X2),sK2(X3,X4,set_intersection2(X5,relation_image(X0,relation_image(X1,X2))))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368506,c_369672]) ).
tcf(c_404081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,X4,set_intersection2(X5,relation_image(X0,relation_image(X1,X2)))),X4)
| ( set_intersection2(X5,relation_image(X0,relation_image(X1,X2))) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,X4,set_intersection2(X5,relation_image(X0,relation_image(X1,X2))))))) = sK13(X0,relation_image(X1,X2),sK2(X3,X4,set_intersection2(X5,relation_image(X0,relation_image(X1,X2))))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368505,c_369672]) ).
tcf(c_404082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,X4,set_intersection2(relation_image(X0,relation_image(X1,X2)),X5)),X3)
| ( set_intersection2(relation_image(X0,relation_image(X1,X2)),X5) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,X4,set_intersection2(relation_image(X0,relation_image(X1,X2)),X5))))) = sK13(X0,relation_image(X1,X2),sK2(X3,X4,set_intersection2(relation_image(X0,relation_image(X1,X2)),X5))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368484,c_369672]) ).
tcf(c_404083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,X4,set_intersection2(relation_image(X0,relation_image(X1,X2)),X5)),X4)
| ( set_intersection2(relation_image(X0,relation_image(X1,X2)),X5) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,X4,set_intersection2(relation_image(X0,relation_image(X1,X2)),X5))))) = sK13(X0,relation_image(X1,X2),sK2(X3,X4,set_intersection2(relation_image(X0,relation_image(X1,X2)),X5))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368483,c_369672]) ).
tcf(c_404084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))),X4)
| ( relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))) = set_intersection2(X4,X5) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK2(X4,X5,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK2(X4,X5,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_369672]) ).
tcf(c_404085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))),X5)
| ( relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))) = set_intersection2(X4,X5) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK2(X4,X5,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK2(X4,X5,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_369672]) ).
tcf(c_404086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK2(relation_image(X1,relation_image(X2,X3)),X4,relation_inverse_image(X0,X5))),X5)
| ( set_intersection2(relation_image(X1,relation_image(X2,X3)),X4) = relation_inverse_image(X0,X5) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(relation_image(X1,relation_image(X2,X3)),X4,relation_inverse_image(X0,X5))))) = sK13(X1,relation_image(X2,X3),sK2(relation_image(X1,relation_image(X2,X3)),X4,relation_inverse_image(X0,X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_369672]) ).
tcf(c_404087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_image(X1,relation_image(X2,X3)),X4,relation_inverse_image(X0,X5)),relation_dom(X0))
| ( set_intersection2(relation_image(X1,relation_image(X2,X3)),X4) = relation_inverse_image(X0,X5) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(relation_image(X1,relation_image(X2,X3)),X4,relation_inverse_image(X0,X5))))) = sK13(X1,relation_image(X2,X3),sK2(relation_image(X1,relation_image(X2,X3)),X4,relation_inverse_image(X0,X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368760,c_369672]) ).
tcf(c_404088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,X5,relation_image(X2,relation_image(X3,X4))),X1)
| ( relation_image(X2,relation_image(X3,X4)) = set_intersection2(X0,X5) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK2(X0,X5,relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK2(X0,X5,relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_369672]) ).
tcf(c_404089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,X4,X5),X5)
| ( set_intersection2(X0,X4) = X5 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X0,X4,X5)))) = sK13(X1,relation_image(X2,X3),sK2(X0,X4,X5)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369012,c_369672]) ).
tcf(c_404090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,relation_image(X0,relation_image(X1,X2))),X4)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(set_intersection2(X3,X4),X5) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,X4),X5,relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,X4),X5,relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368503,c_369672]) ).
tcf(c_404091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,relation_image(X0,relation_image(X1,X2))),X3)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(set_intersection2(X3,X4),X5) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,X4),X5,relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,X4),X5,relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368481,c_369672]) ).
tcf(c_404092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4,X5),X5)
| ( set_intersection2(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4) = X5 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4,X5)))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368503,c_369672]) ).
tcf(c_404093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4) = X5 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,X5)))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368481,c_369672]) ).
tcf(c_404094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,X4),X5,relation_image(X1,relation_image(X2,X3)))),X4)
| ( relation_image(X1,relation_image(X2,X3)) = set_intersection2(relation_inverse_image(X0,X4),X5) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(relation_inverse_image(X0,X4),X5,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK2(relation_inverse_image(X0,X4),X5,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_369672]) ).
tcf(c_404095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_inverse_image(X0,X4),X5,relation_image(X1,relation_image(X2,X3))),relation_dom(X0))
| ( relation_image(X1,relation_image(X2,X3)) = set_intersection2(relation_inverse_image(X0,X4),X5) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(relation_inverse_image(X0,X4),X5,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK2(relation_inverse_image(X0,X4),X5,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368757,c_369672]) ).
tcf(c_404096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X4,X5),X5)
| ( set_intersection2(relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X4) = X5 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK2(relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X4,X5))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK2(relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X4,X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_369672]) ).
tcf(c_404097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_image(X0,relation_image(X1,X2)),X3) = relation_image(X0,relation_image(X1,X2)) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(relation_image(X0,relation_image(X1,X2)),X3,relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(relation_image(X0,relation_image(X1,X2)),X3,relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368448,c_369672]) ).
tcf(c_404098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,relation_image(X1,X2)) = empty_set )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(empty_set,X3,relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(empty_set,X3,relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372470,c_369672]) ).
tcf(c_404099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X5,relation_image(X2,relation_image(X3,X4)),X0),X1)
| ( set_intersection2(X5,relation_image(X2,relation_image(X3,X4))) = X0 )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK2(X5,relation_image(X2,relation_image(X3,X4)),X0)))) = sK13(X2,relation_image(X3,X4),sK2(X5,relation_image(X2,relation_image(X3,X4)),X0)) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_369672]) ).
tcf(c_404100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X4,relation_image(X0,relation_image(X1,X3))) = X2 )
| ( apply(X1,sK13(X1,X3,sK13(X0,relation_image(X1,X3),sK2(X4,relation_image(X0,relation_image(X1,X3)),X2)))) = sK13(X0,relation_image(X1,X3),sK2(X4,relation_image(X0,relation_image(X1,X3)),X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368867,c_369672]) ).
tcf(c_404101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,relation_image(X0,relation_image(X1,X2)),set_intersection2(X4,X5)),X5)
| ( set_intersection2(X3,relation_image(X0,relation_image(X1,X2))) = set_intersection2(X4,X5) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,relation_image(X0,relation_image(X1,X2)),set_intersection2(X4,X5))))) = sK13(X0,relation_image(X1,X2),sK2(X3,relation_image(X0,relation_image(X1,X2)),set_intersection2(X4,X5))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368505,c_369672]) ).
tcf(c_404102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,relation_image(X0,relation_image(X1,X2)),set_intersection2(X4,X5)),X4)
| ( set_intersection2(X3,relation_image(X0,relation_image(X1,X2))) = set_intersection2(X4,X5) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,relation_image(X0,relation_image(X1,X2)),set_intersection2(X4,X5))))) = sK13(X0,relation_image(X1,X2),sK2(X3,relation_image(X0,relation_image(X1,X2)),set_intersection2(X4,X5))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368483,c_369672]) ).
tcf(c_404103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK2(X4,relation_image(X1,relation_image(X2,X3)),relation_inverse_image(X0,X5))),X5)
| ( set_intersection2(X4,relation_image(X1,relation_image(X2,X3))) = relation_inverse_image(X0,X5) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,relation_image(X1,relation_image(X2,X3)),relation_inverse_image(X0,X5))))) = sK13(X1,relation_image(X2,X3),sK2(X4,relation_image(X1,relation_image(X2,X3)),relation_inverse_image(X0,X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_369672]) ).
tcf(c_404104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,relation_image(X1,relation_image(X2,X3)),relation_inverse_image(X0,X5)),relation_dom(X0))
| ( set_intersection2(X4,relation_image(X1,relation_image(X2,X3))) = relation_inverse_image(X0,X5) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,relation_image(X1,relation_image(X2,X3)),relation_inverse_image(X0,X5))))) = sK13(X1,relation_image(X2,X3),sK2(X4,relation_image(X1,relation_image(X2,X3)),relation_inverse_image(X0,X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368759,c_369672]) ).
tcf(c_404105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X5,X0,relation_image(X2,relation_image(X3,X4))),X1)
| ( relation_image(X2,relation_image(X3,X4)) = set_intersection2(X5,X0) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK2(X5,X0,relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK2(X5,X0,relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_369672]) ).
tcf(c_404106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X0,X5),X5)
| ( set_intersection2(X4,X0) = X5 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,X0,X5)))) = sK13(X1,relation_image(X2,X3),sK2(X4,X0,X5)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369013,c_369672]) ).
tcf(c_404107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,relation_image(X1,X3)) = set_intersection2(X4,X2) )
| ( apply(X1,sK13(X1,X3,sK13(X0,relation_image(X1,X3),sK2(X4,X2,relation_image(X0,relation_image(X1,X3)))))) = sK13(X0,relation_image(X1,X3),sK2(X4,X2,relation_image(X0,relation_image(X1,X3)))) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368866,c_369672]) ).
tcf(c_404108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),relation_image(X0,relation_image(X1,X2))),X5)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,X5),relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,X5),relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368504,c_369672]) ).
tcf(c_404109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),relation_image(X0,relation_image(X1,X2))),X4)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,X5),relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,X5),relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368482,c_369672]) ).
tcf(c_404110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,relation_image(X0,relation_image(X1,X2))),X5),X5)
| ( set_intersection2(X3,set_intersection2(X4,relation_image(X0,relation_image(X1,X2)))) = X5 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,relation_image(X0,relation_image(X1,X2))),X5)))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,relation_image(X0,relation_image(X1,X2))),X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368504,c_369672]) ).
tcf(c_404111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),X5),X5)
| ( set_intersection2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4)) = X5 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),X5)))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368482,c_369672]) ).
tcf(c_404112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X5),X5)
| ( set_intersection2(X4,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))) = X5 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK2(X4,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X5))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK2(X4,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_369672]) ).
tcf(c_404113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK2(X4,relation_inverse_image(X0,X5),relation_image(X1,relation_image(X2,X3)))),X5)
| ( relation_image(X1,relation_image(X2,X3)) = set_intersection2(X4,relation_inverse_image(X0,X5)) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,relation_inverse_image(X0,X5),relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK2(X4,relation_inverse_image(X0,X5),relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_369672]) ).
tcf(c_404114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,relation_inverse_image(X0,X5),relation_image(X1,relation_image(X2,X3))),relation_dom(X0))
| ( relation_image(X1,relation_image(X2,X3)) = set_intersection2(X4,relation_inverse_image(X0,X5)) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,relation_inverse_image(X0,X5),relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK2(X4,relation_inverse_image(X0,X5),relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368758,c_369672]) ).
tcf(c_404115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,relation_image(X0,relation_image(X1,X2))) = relation_image(X0,relation_image(X1,X2)) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,relation_image(X0,relation_image(X1,X2)),relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(X3,relation_image(X0,relation_image(X1,X2)),relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368460,c_369672]) ).
tcf(c_404116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,relation_image(X1,X2)) = empty_set )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,empty_set,relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(X3,empty_set,relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372467,c_369672]) ).
tcf(c_404117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK13(X5,X0,X4)))) = sK13(X1,relation_image(X2,X3),sK13(X5,X0,X4)) )
| ~ function(X5)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X5)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,relation_image(X5,X0))
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369594,c_369672]) ).
tcf(c_404118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK13(X0,X5,X4)))) = sK13(X1,relation_image(X2,X3),sK13(X0,X5,X4)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X4,relation_image(X0,X5))
| ~ subset(relation_dom(X0),relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369556,c_369672]) ).
tcf(c_404119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( apply(X4,sK13(X4,X5,sK13(X3,relation_image(X4,X5),sK13(X1,set_intersection2(X2,relation_image(X3,relation_image(X4,X5))),X0)))) = sK13(X3,relation_image(X4,X5),sK13(X1,set_intersection2(X2,relation_image(X3,relation_image(X4,X5))),X0)) )
| ~ function(X4)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,relation_image(X3,relation_image(X4,X5))))) ),
inference(superposition,[status(thm)],[c_369597,c_369672]) ).
tcf(c_404120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK13(X1,set_intersection2(relation_image(X2,relation_image(X3,X4)),X5),X0)))) = sK13(X2,relation_image(X3,X4),sK13(X1,set_intersection2(relation_image(X2,relation_image(X3,X4)),X5),X0)) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(relation_image(X2,relation_image(X3,X4)),X5))) ),
inference(superposition,[status(thm)],[c_369598,c_369672]) ).
tcf(c_404121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( apply(X4,sK13(X4,X5,sK13(X3,relation_image(X4,X5),apply(X2,sK13(X1,relation_inverse_image(X2,relation_image(X3,relation_image(X4,X5))),X0))))) = sK13(X3,relation_image(X4,X5),apply(X2,sK13(X1,relation_inverse_image(X2,relation_image(X3,relation_image(X4,X5))),X0))) )
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,relation_image(X3,relation_image(X4,X5))))) ),
inference(superposition,[status(thm)],[c_369599,c_369672]) ).
tcf(c_404122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_image(X1,relation_image(X2,X3)) = set_intersection2(relation_image(X0,X4),X5) )
| ( apply(X0,sK13(X0,X4,sK2(relation_image(X0,X4),X5,relation_image(X1,relation_image(X2,X3))))) = sK2(relation_image(X0,X4),X5,relation_image(X1,relation_image(X2,X3))) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(relation_image(X0,X4),X5,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK2(relation_image(X0,X4),X5,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369659,c_369672]) ).
tcf(c_404123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_image(X1,relation_image(X2,X3)) = set_intersection2(X4,relation_image(X0,X5)) )
| ( apply(X0,sK13(X0,X5,sK2(X4,relation_image(X0,X5),relation_image(X1,relation_image(X2,X3))))) = sK2(X4,relation_image(X0,X5),relation_image(X1,relation_image(X2,X3))) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,relation_image(X0,X5),relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK2(X4,relation_image(X0,X5),relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369660,c_369672]) ).
tcf(c_404124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X4,relation_image(X1,relation_image(X2,X3))) = relation_image(X0,X5) )
| ( apply(X0,sK13(X0,X5,sK2(X4,relation_image(X1,relation_image(X2,X3)),relation_image(X0,X5)))) = sK2(X4,relation_image(X1,relation_image(X2,X3)),relation_image(X0,X5)) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,relation_image(X1,relation_image(X2,X3)),relation_image(X0,X5))))) = sK13(X1,relation_image(X2,X3),sK2(X4,relation_image(X1,relation_image(X2,X3)),relation_image(X0,X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369661,c_369672]) ).
tcf(c_404125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(relation_image(X1,relation_image(X2,X3)),X4) = relation_image(X0,X5) )
| ( apply(X0,sK13(X0,X5,sK2(relation_image(X1,relation_image(X2,X3)),X4,relation_image(X0,X5)))) = sK2(relation_image(X1,relation_image(X2,X3)),X4,relation_image(X0,X5)) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(relation_image(X1,relation_image(X2,X3)),X4,relation_image(X0,X5))))) = sK13(X1,relation_image(X2,X3),sK2(relation_image(X1,relation_image(X2,X3)),X4,relation_image(X0,X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369662,c_369672]) ).
tcf(c_404126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X0,relation_image(X3,relation_image(X4,X5))),X1)
| ( relation_image(X3,relation_image(X4,X5)) = relation_image(X2,X0) )
| ( apply(X4,sK13(X4,X5,sK13(X3,relation_image(X4,X5),sK11(X2,X0,relation_image(X3,relation_image(X4,X5)))))) = sK13(X3,relation_image(X4,X5),sK11(X2,X0,relation_image(X3,relation_image(X4,X5)))) )
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_369672]) ).
tcf(c_404127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X4,X0,X5),X5)
| ( relation_image(X4,X0) = X5 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK12(X4,X0,X5)))) = sK13(X1,relation_image(X2,X3),sK12(X4,X0,X5)) )
| ~ function(X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369299,c_369672]) ).
tcf(c_404128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X0,set_intersection2(X4,X5),relation_image(X1,relation_image(X2,X3))),X4)
| ( relation_image(X0,set_intersection2(X4,X5)) = relation_image(X1,relation_image(X2,X3)) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X0,set_intersection2(X4,X5),relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK11(X0,set_intersection2(X4,X5),relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_369672]) ).
tcf(c_404129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X0,set_intersection2(X4,X5),relation_image(X1,relation_image(X2,X3))),X5)
| ( relation_image(X0,set_intersection2(X4,X5)) = relation_image(X1,relation_image(X2,X3)) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X0,set_intersection2(X4,X5),relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK11(X0,set_intersection2(X4,X5),relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_369672]) ).
tcf(c_404130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X0,set_intersection2(X4,relation_image(X1,relation_image(X2,X3))),X5),X5)
| ( relation_image(X0,set_intersection2(X4,relation_image(X1,relation_image(X2,X3)))) = X5 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK12(X0,set_intersection2(X4,relation_image(X1,relation_image(X2,X3))),X5)))) = sK13(X1,relation_image(X2,X3),sK12(X0,set_intersection2(X4,relation_image(X1,relation_image(X2,X3))),X5)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_369672]) ).
tcf(c_404131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X0,set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5),X5)
| ( relation_image(X0,set_intersection2(relation_image(X1,relation_image(X2,X3)),X4)) = X5 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK12(X0,set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5)))) = sK13(X1,relation_image(X2,X3),sK12(X0,set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_369672]) ).
tcf(c_404132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X0,relation_inverse_image(X1,X5),relation_image(X2,relation_image(X3,X4))),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X5)) = relation_image(X2,relation_image(X3,X4)) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK11(X0,relation_inverse_image(X1,X5),relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK11(X0,relation_inverse_image(X1,X5),relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369305,c_369672]) ).
tcf(c_404133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X1,sK12(X0,relation_inverse_image(X1,X5),relation_image(X2,relation_image(X3,X4)))),X5)
| ( relation_image(X0,relation_inverse_image(X1,X5)) = relation_image(X2,relation_image(X3,X4)) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK11(X0,relation_inverse_image(X1,X5),relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK11(X0,relation_inverse_image(X1,X5),relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_369672]) ).
tcf(c_404134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X0,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4))),X5),X5)
| ( relation_image(X0,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))) = X5 )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),apply(X1,sK12(X0,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4))),X5))))) = sK13(X2,relation_image(X3,X4),apply(X1,sK12(X0,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4))),X5))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_369672]) ).
tcf(c_404135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_image(X0,relation_image(X1,X5)) = relation_image(X2,relation_image(X3,X4)) )
| ( apply(X1,sK13(X1,X5,sK12(X0,relation_image(X1,X5),relation_image(X2,relation_image(X3,X4))))) = sK12(X0,relation_image(X1,X5),relation_image(X2,relation_image(X3,X4))) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK11(X0,relation_image(X1,X5),relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK11(X0,relation_image(X1,X5),relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369670,c_369672]) ).
tcf(c_404136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_image(X4,X5) = X0 )
| ( apply(X4,sK12(X4,X5,X0)) = sK11(X4,X5,X0) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X4,X5,X0)))) = sK13(X1,relation_image(X2,X3),sK11(X4,X5,X0)) )
| ~ function(X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369436,c_369672]) ).
tcf(c_404137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X4,X5,X0),X5)
| ( relation_image(X4,X5) = X0 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X4,X5,X0)))) = sK13(X1,relation_image(X2,X3),sK11(X4,X5,X0)) )
| ~ function(X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369307,c_369672]) ).
tcf(c_404138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X4,X5,X0),relation_dom(X4))
| ( relation_image(X4,X5) = X0 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X4,X5,X0)))) = sK13(X1,relation_image(X2,X3),sK11(X4,X5,X0)) )
| ~ function(X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369206,c_369672]) ).
tcf(c_404139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X2,relation_image(X3,relation_image(X4,X5)),X0),X1)
| ( relation_image(X2,relation_image(X3,relation_image(X4,X5))) = X0 )
| ( apply(X4,sK13(X4,X5,sK13(X3,relation_image(X4,X5),sK12(X2,relation_image(X3,relation_image(X4,X5)),X0)))) = sK13(X3,relation_image(X4,X5),sK12(X2,relation_image(X3,relation_image(X4,X5)),X0)) )
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_369672]) ).
tcf(c_404140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,relation_image(X1,relation_image(X2,X4))) = X3 )
| ( apply(X2,sK13(X2,X4,sK13(X1,relation_image(X2,X4),sK12(X0,relation_image(X1,relation_image(X2,X4)),X3)))) = sK13(X1,relation_image(X2,X4),sK12(X0,relation_image(X1,relation_image(X2,X4)),X3)) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369309,c_369672]) ).
tcf(c_404141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X0,relation_image(X1,relation_image(X2,X3)),set_intersection2(X4,X5)),X4)
| ( relation_image(X0,relation_image(X1,relation_image(X2,X3))) = set_intersection2(X4,X5) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK12(X0,relation_image(X1,relation_image(X2,X3)),set_intersection2(X4,X5))))) = sK13(X1,relation_image(X2,X3),sK12(X0,relation_image(X1,relation_image(X2,X3)),set_intersection2(X4,X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_369672]) ).
tcf(c_404142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X0,relation_image(X1,relation_image(X2,X3)),set_intersection2(X4,X5)),X5)
| ( relation_image(X0,relation_image(X1,relation_image(X2,X3))) = set_intersection2(X4,X5) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK12(X0,relation_image(X1,relation_image(X2,X3)),set_intersection2(X4,X5))))) = sK13(X1,relation_image(X2,X3),sK12(X0,relation_image(X1,relation_image(X2,X3)),set_intersection2(X4,X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_369672]) ).
tcf(c_404143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X5,relation_image(X1,relation_image(X2,X3))) = relation_image(X0,X4) )
| ( apply(X0,sK12(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3))))) = sK11(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3)))) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3))))))) = sK13(X1,relation_image(X2,X3),sK11(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3))))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369439,c_369672]) ).
tcf(c_404144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3)))),X4)
| ( set_intersection2(X5,relation_image(X1,relation_image(X2,X3))) = relation_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3))))))) = sK13(X1,relation_image(X2,X3),sK11(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3))))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_369672]) ).
tcf(c_404145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3)))),relation_dom(X0))
| ( set_intersection2(X5,relation_image(X1,relation_image(X2,X3))) = relation_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3))))))) = sK13(X1,relation_image(X2,X3),sK11(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3))))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369209,c_369672]) ).
tcf(c_404146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(relation_image(X1,relation_image(X2,X3)),X5) = relation_image(X0,X4) )
| ( apply(X0,sK12(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5))) = sK11(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5)) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5))))) = sK13(X1,relation_image(X2,X3),sK11(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369440,c_369672]) ).
tcf(c_404147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5)),X4)
| ( set_intersection2(relation_image(X1,relation_image(X2,X3)),X5) = relation_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5))))) = sK13(X1,relation_image(X2,X3),sK11(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_369672]) ).
tcf(c_404148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5)),relation_dom(X0))
| ( set_intersection2(relation_image(X1,relation_image(X2,X3)),X5) = relation_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK11(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5))))) = sK13(X1,relation_image(X2,X3),sK11(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369210,c_369672]) ).
tcf(c_404149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))),X5)
| ( relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4))) = relation_image(X0,X5) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),apply(X1,sK11(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))))))) = sK13(X2,relation_image(X3,X4),apply(X1,sK11(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_369672]) ).
tcf(c_404150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))),relation_dom(X0))
| ( relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4))) = relation_image(X0,X5) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),apply(X1,sK11(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))))))) = sK13(X2,relation_image(X3,X4),apply(X1,sK11(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369211,c_369672]) ).
tcf(c_404151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X0,relation_image(X2,relation_image(X3,X4)),relation_inverse_image(X1,X5)),relation_dom(X1))
| ( relation_image(X0,relation_image(X2,relation_image(X3,X4))) = relation_inverse_image(X1,X5) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK12(X0,relation_image(X2,relation_image(X3,X4)),relation_inverse_image(X1,X5))))) = sK13(X2,relation_image(X3,X4),sK12(X0,relation_image(X2,relation_image(X3,X4)),relation_inverse_image(X1,X5))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369313,c_369672]) ).
tcf(c_404152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X1,sK11(X0,relation_image(X2,relation_image(X3,X4)),relation_inverse_image(X1,X5))),X5)
| ( relation_image(X0,relation_image(X2,relation_image(X3,X4))) = relation_inverse_image(X1,X5) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK12(X0,relation_image(X2,relation_image(X3,X4)),relation_inverse_image(X1,X5))))) = sK13(X2,relation_image(X3,X4),sK12(X0,relation_image(X2,relation_image(X3,X4)),relation_inverse_image(X1,X5))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_369672]) ).
tcf(c_404153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_image(X0,relation_image(X2,relation_image(X3,X4))) = relation_image(X1,X5) )
| ( apply(X1,sK13(X1,X5,sK11(X0,relation_image(X2,relation_image(X3,X4)),relation_image(X1,X5)))) = sK11(X0,relation_image(X2,relation_image(X3,X4)),relation_image(X1,X5)) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK12(X0,relation_image(X2,relation_image(X3,X4)),relation_image(X1,X5))))) = sK13(X2,relation_image(X3,X4),sK12(X0,relation_image(X2,relation_image(X3,X4)),relation_image(X1,X5))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369668,c_369672]) ).
tcf(c_404154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X4,X5,X0),relation_dom(X4))
| ( relation_inverse_image(X4,X5) = X0 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X4,X5,X0)))) = sK13(X1,relation_image(X2,X3),sK7(X4,X5,X0)) )
| ~ function(X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369020,c_369672]) ).
tcf(c_404155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X4,sK7(X4,X5,X0)),X5)
| ( relation_inverse_image(X4,X5) = X0 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X4,X5,X0)))) = sK13(X1,relation_image(X2,X3),sK7(X4,X5,X0)) )
| ~ function(X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369019,c_369672]) ).
tcf(c_404156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK7(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3))))),X4)
| ( set_intersection2(X5,relation_image(X1,relation_image(X2,X3))) = relation_inverse_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3))))))) = sK13(X1,relation_image(X2,X3),sK7(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3))))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_369672]) ).
tcf(c_404157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3)))),relation_dom(X0))
| ( set_intersection2(X5,relation_image(X1,relation_image(X2,X3))) = relation_inverse_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3))))))) = sK13(X1,relation_image(X2,X3),sK7(X0,X4,set_intersection2(X5,relation_image(X1,relation_image(X2,X3))))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_369672]) ).
tcf(c_404158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK7(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5))),X4)
| ( set_intersection2(relation_image(X1,relation_image(X2,X3)),X5) = relation_inverse_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5))))) = sK13(X1,relation_image(X2,X3),sK7(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_369672]) ).
tcf(c_404159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5)),relation_dom(X0))
| ( set_intersection2(relation_image(X1,relation_image(X2,X3)),X5) = relation_inverse_image(X0,X4) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5))))) = sK13(X1,relation_image(X2,X3),sK7(X0,X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_369672]) ).
tcf(c_404160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))),relation_dom(X0))
| ( relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4))) = relation_inverse_image(X0,X5) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),apply(X1,sK7(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))))))) = sK13(X2,relation_image(X3,X4),apply(X1,sK7(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368819,c_369672]) ).
tcf(c_404161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK7(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4))))),X5)
| ( relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4))) = relation_inverse_image(X0,X5) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),apply(X1,sK7(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))))))) = sK13(X2,relation_image(X3,X4),apply(X1,sK7(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_369672]) ).
tcf(c_404162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,X5,relation_image(X2,relation_image(X3,X4))),X1)
| ( relation_image(X2,relation_image(X3,X4)) = relation_inverse_image(X0,X5) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK7(X0,X5,relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK7(X0,X5,relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_369672]) ).
tcf(c_404163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,X4,X5),X5)
| ( relation_inverse_image(X0,X4) = X5 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X0,X4,X5)))) = sK13(X1,relation_image(X2,X3),sK7(X0,X4,X5)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369017,c_369672]) ).
tcf(c_404164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X0,X5,relation_image(X2,relation_image(X3,X4))),X1)
| ( relation_image(X2,relation_image(X3,X4)) = relation_image(X0,X5) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK11(X0,X5,relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK11(X0,X5,relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_369672]) ).
tcf(c_404165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X0,X4,X5),X5)
| ( relation_image(X0,X4) = X5 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK12(X0,X4,X5)))) = sK13(X1,relation_image(X2,X3),sK12(X0,X4,X5)) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369214,c_369672]) ).
tcf(c_404166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,relation_image(X3,relation_image(X4,X5)),X0),X1)
| ( relation_inverse_image(X2,relation_image(X3,relation_image(X4,X5))) = X0 )
| ( apply(X4,sK13(X4,X5,sK13(X3,relation_image(X4,X5),apply(X2,sK7(X2,relation_image(X3,relation_image(X4,X5)),X0))))) = sK13(X3,relation_image(X4,X5),apply(X2,sK7(X2,relation_image(X3,relation_image(X4,X5)),X0))) )
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_369672]) ).
tcf(c_404167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X0,relation_image(X1,relation_image(X2,X4))) = X3 )
| ( apply(X2,sK13(X2,X4,sK13(X1,relation_image(X2,X4),apply(X0,sK7(X0,relation_image(X1,relation_image(X2,X4)),X3))))) = sK13(X1,relation_image(X2,X4),apply(X0,sK7(X0,relation_image(X1,relation_image(X2,X4)),X3))) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368872,c_369672]) ).
tcf(c_404168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,relation_image(X1,relation_image(X2,X3)),set_intersection2(X4,X5)),X4)
| ( relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))) = set_intersection2(X4,X5) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK7(X0,relation_image(X1,relation_image(X2,X3)),set_intersection2(X4,X5)))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK7(X0,relation_image(X1,relation_image(X2,X3)),set_intersection2(X4,X5)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_369672]) ).
tcf(c_404169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,relation_image(X1,relation_image(X2,X3)),set_intersection2(X4,X5)),X5)
| ( relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))) = set_intersection2(X4,X5) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK7(X0,relation_image(X1,relation_image(X2,X3)),set_intersection2(X4,X5)))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK7(X0,relation_image(X1,relation_image(X2,X3)),set_intersection2(X4,X5)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_369672]) ).
tcf(c_404170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X1,sK7(X0,relation_image(X2,relation_image(X3,X4)),relation_inverse_image(X1,X5))),X5)
| ( relation_inverse_image(X0,relation_image(X2,relation_image(X3,X4))) = relation_inverse_image(X1,X5) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),apply(X0,sK7(X0,relation_image(X2,relation_image(X3,X4)),relation_inverse_image(X1,X5)))))) = sK13(X2,relation_image(X3,X4),apply(X0,sK7(X0,relation_image(X2,relation_image(X3,X4)),relation_inverse_image(X1,X5)))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_369672]) ).
tcf(c_404171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,relation_image(X2,relation_image(X3,X4)),relation_inverse_image(X1,X5)),relation_dom(X1))
| ( relation_inverse_image(X0,relation_image(X2,relation_image(X3,X4))) = relation_inverse_image(X1,X5) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),apply(X0,sK7(X0,relation_image(X2,relation_image(X3,X4)),relation_inverse_image(X1,X5)))))) = sK13(X2,relation_image(X3,X4),apply(X0,sK7(X0,relation_image(X2,relation_image(X3,X4)),relation_inverse_image(X1,X5)))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368762,c_369672]) ).
tcf(c_404172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_inverse_image(X0,relation_image(X2,relation_image(X3,X4))) = relation_image(X1,X5) )
| ( apply(X1,sK13(X1,X5,sK7(X0,relation_image(X2,relation_image(X3,X4)),relation_image(X1,X5)))) = sK7(X0,relation_image(X2,relation_image(X3,X4)),relation_image(X1,X5)) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),apply(X0,sK7(X0,relation_image(X2,relation_image(X3,X4)),relation_image(X1,X5)))))) = sK13(X2,relation_image(X3,X4),apply(X0,sK7(X0,relation_image(X2,relation_image(X3,X4)),relation_image(X1,X5)))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369664,c_369672]) ).
tcf(c_404173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X4,X0,X5),X5)
| ( relation_inverse_image(X4,X0) = X5 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X4,sK7(X4,X0,X5))))) = sK13(X1,relation_image(X2,X3),apply(X4,sK7(X4,X0,X5))) )
| ~ function(X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_369018,c_369672]) ).
tcf(c_404174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK7(X2,X0,relation_image(X3,relation_image(X4,X5)))),X1)
| ( relation_image(X3,relation_image(X4,X5)) = relation_inverse_image(X2,X0) )
| ( apply(X4,sK13(X4,X5,sK13(X3,relation_image(X4,X5),sK7(X2,X0,relation_image(X3,relation_image(X4,X5)))))) = sK13(X3,relation_image(X4,X5),sK7(X2,X0,relation_image(X3,relation_image(X4,X5)))) )
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_369672]) ).
tcf(c_404175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X4,X5),relation_image(X1,relation_image(X2,X3)))),X4)
| ( relation_inverse_image(X0,set_intersection2(X4,X5)) = relation_image(X1,relation_image(X2,X3)) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X0,set_intersection2(X4,X5),relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK7(X0,set_intersection2(X4,X5),relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_369672]) ).
tcf(c_404176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X4,X5),relation_image(X1,relation_image(X2,X3)))),X5)
| ( relation_inverse_image(X0,set_intersection2(X4,X5)) = relation_image(X1,relation_image(X2,X3)) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK7(X0,set_intersection2(X4,X5),relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK7(X0,set_intersection2(X4,X5),relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_369672]) ).
tcf(c_404177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,set_intersection2(X4,relation_image(X1,relation_image(X2,X3))),X5),X5)
| ( relation_inverse_image(X0,set_intersection2(X4,relation_image(X1,relation_image(X2,X3)))) = X5 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK7(X0,set_intersection2(X4,relation_image(X1,relation_image(X2,X3))),X5))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK7(X0,set_intersection2(X4,relation_image(X1,relation_image(X2,X3))),X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_369672]) ).
tcf(c_404178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5),X5)
| ( relation_inverse_image(X0,set_intersection2(relation_image(X1,relation_image(X2,X3)),X4)) = X5 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK7(X0,set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK7(X0,set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_369672]) ).
tcf(c_404179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X5),relation_image(X2,relation_image(X3,X4))))),X5)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X5)) = relation_image(X2,relation_image(X3,X4)) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK7(X0,relation_inverse_image(X1,X5),relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK7(X0,relation_inverse_image(X1,X5),relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_369672]) ).
tcf(c_404180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK7(X0,relation_inverse_image(X1,X5),relation_image(X2,relation_image(X3,X4)))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X5)) = relation_image(X2,relation_image(X3,X4)) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK7(X0,relation_inverse_image(X1,X5),relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK7(X0,relation_inverse_image(X1,X5),relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368761,c_369672]) ).
tcf(c_404181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4))),X5),X5)
| ( relation_inverse_image(X0,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))) = X5 )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4))),X5)))))) = sK13(X2,relation_image(X3,X4),apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4))),X5)))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_369672]) ).
tcf(c_404182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_inverse_image(X0,relation_image(X1,X5)) = relation_image(X2,relation_image(X3,X4)) )
| ( apply(X1,sK13(X1,X5,apply(X0,sK7(X0,relation_image(X1,X5),relation_image(X2,relation_image(X3,X4)))))) = apply(X0,sK7(X0,relation_image(X1,X5),relation_image(X2,relation_image(X3,X4)))) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK7(X0,relation_image(X1,X5),relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK7(X0,relation_image(X1,X5),relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369663,c_369672]) ).
tcf(c_404183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4))) = relation_image(X0,X5) )
| ( apply(X0,sK12(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4))))) = sK11(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),apply(X1,sK11(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))))))) = sK13(X2,relation_image(X3,X4),apply(X1,sK11(X0,X5,relation_inverse_image(X1,relation_image(X2,relation_image(X3,X4)))))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369441,c_369672]) ).
tcf(c_411202,plain,
! [X0: $i] :
( element(sK16(empty_set),empty_set)
| empty(set_intersection2(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_64,c_388051]) ).
tcf(c_411203,plain,
! [X0: $i] :
( element(sK16(empty_set),X0)
| empty(set_intersection2(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_368545,c_388051]) ).
tcf(c_411205,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,powerset(X1)))
| subset(sK16(set_intersection2(X0,powerset(X1))),X1) ),
inference(superposition,[status(thm)],[c_388051,c_99]) ).
tcf(c_411206,plain,
! [X0: $i] :
( empty(empty_set)
| element(sK16(empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_411203,c_368545]) ).
tcf(c_411207,plain,
( empty(empty_set)
| element(sK16(empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_411202,c_64]) ).
tcf(c_411219,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,X2))
| element(sK16(set_intersection2(X2,X0)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_389060,c_321]) ).
tcf(c_411221,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| ~ in(X0,sK16(set_intersection2(X1,X0))) ),
inference(superposition,[status(thm)],[c_389060,c_97]) ).
tcf(c_411222,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(X0,X2))
| in(sK16(set_intersection2(X2,X0)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_389060,c_96]) ).
tcf(c_411223,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,X0))
| element(sK16(set_intersection2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_389060,c_93]) ).
tcf(c_411225,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X1,X2),X0))
| in(sK16(set_intersection2(X0,set_intersection2(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_389060,c_59]) ).
tcf(c_411226,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(set_intersection2(X1,X2),X0))
| in(sK16(set_intersection2(X0,set_intersection2(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_389060,c_58]) ).
tcf(c_411227,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_inverse_image(X0,X2),X1))
| in(apply(X0,sK16(set_intersection2(X1,relation_inverse_image(X0,X2)))),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_389060,c_88]) ).
tcf(c_411228,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_inverse_image(X0,X2),X1))
| in(sK16(set_intersection2(X1,relation_inverse_image(X0,X2))),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_389060,c_87]) ).
tcf(c_411229,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_dom(X1),X0))
| ( apply(X1,sK13(X1,X2,apply(X1,sK16(set_intersection2(X0,relation_dom(X1)))))) = apply(X1,sK16(set_intersection2(X0,relation_dom(X1)))) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK16(set_intersection2(X0,relation_dom(X1))),X2) ),
inference(superposition,[status(thm)],[c_389060,c_369671]) ).
tcf(c_411232,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_image(X0,X1),X2))
| ( apply(X0,sK13(X0,X1,sK16(set_intersection2(X2,relation_image(X0,X1))))) = sK16(set_intersection2(X2,relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_389060,c_112]) ).
tcf(c_411233,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(set_intersection2(relation_dom(X1),X0))
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X2))
| ~ in(sK16(set_intersection2(X0,relation_dom(X1))),X2) ),
inference(superposition,[status(thm)],[c_389060,c_369501]) ).
tcf(c_411235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3))
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK16(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))))))) = sK13(X0,relation_image(X1,X2),sK16(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_389060,c_369672]) ).
tcf(c_411285,plain,
! [X0: $i] :
( ( sK16(powerset(X0)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368984,c_369769]) ).
tcf(c_411287,plain,
! [X0: $i,X1: $i] :
( ( sK16(powerset(set_intersection2(X0,X1))) = set_intersection2(X0,X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381127,c_369769]) ).
tcf(c_411288,plain,
! [X0: $i,X1: $i] :
( ( sK16(powerset(relation_image(X0,X1))) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK10(relation_image(X0,X1),sK16(powerset(relation_image(X0,X1)))))) = sK10(relation_image(X0,X1),sK16(powerset(relation_image(X0,X1)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_369769]) ).
tcf(c_411289,plain,
! [X0: $i] :
( ( sK16(powerset(sK16(powerset(X0)))) = sK16(powerset(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_385170,c_369769]) ).
tcf(c_411290,plain,
! [X0: $i,X1: $i] :
( ( sK16(powerset(set_intersection2(X1,X0))) = set_intersection2(X1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380845,c_369769]) ).
tcf(c_411323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X2,X3),X3)
| ( set_intersection2(X0,X2) = X3 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368984,c_369782]) ).
tcf(c_411325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,X3,X4),X4)
| ( set_intersection2(X2,X3) = X4 )
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369782]) ).
tcf(c_411326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_image(X0,X1),X2,X3),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = X3 )
| ~ relation(X0)
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_67,c_369782]) ).
tcf(c_411327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_image(X0,relation_inverse_image(X0,X1)),X2,X3),X3)
| ( set_intersection2(relation_image(X0,relation_inverse_image(X0,X1)),X2) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_369782]) ).
tcf(c_411329,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),X2)
| ( set_intersection2(sK16(powerset(X0)),X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_369151,c_369782]) ).
tcf(c_411330,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| ( set_intersection2(empty_set,X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_369177,c_369782]) ).
tcf(c_411331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(X0),X1)
| in(sK2(sK10(powerset(X0),X1),X2,X3),X3)
| ( set_intersection2(sK10(powerset(X0),X1),X2) = X3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_372645,c_369782]) ).
tcf(c_411332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381127,c_369782]) ).
tcf(c_411333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X0,X2),X3,X4),X4)
| ( set_intersection2(relation_image(X0,X2),X3) = X4 )
| ( apply(X0,sK13(X0,X2,sK10(relation_image(X0,X2),X1))) = sK10(relation_image(X0,X2),X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_369782]) ).
tcf(c_411334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X0)),X2,X3),X3)
| ( set_intersection2(sK16(powerset(X0)),X2) = X3 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_385170,c_369782]) ).
tcf(c_411335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X0),X3,X4),X4)
| ( set_intersection2(set_intersection2(X2,X0),X3) = X4 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380845,c_369782]) ).
tcf(c_411407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X0,X3),X3)
| ( set_intersection2(X2,X0) = X3 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368984,c_369783]) ).
tcf(c_411409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X2,X4),X4)
| ( set_intersection2(X3,X2) = X4 )
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369783]) ).
tcf(c_411410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,relation_image(X0,X2),X3),X3)
| ( set_intersection2(X1,relation_image(X0,X2)) = X3 )
| ~ relation(X0)
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_67,c_369783]) ).
tcf(c_411411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,relation_image(X0,relation_inverse_image(X0,X1)),X3),X3)
| ( set_intersection2(X2,relation_image(X0,relation_inverse_image(X0,X1))) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_369783]) ).
tcf(c_411413,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK16(powerset(X0)),X2),X2)
| ( set_intersection2(X1,sK16(powerset(X0))) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_369151,c_369783]) ).
tcf(c_411414,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,empty_set,X2),X2)
| ( set_intersection2(X1,empty_set) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_369177,c_369783]) ).
tcf(c_411415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(X0),X2)
| in(sK2(X1,sK10(powerset(X0),X2),X3),X3)
| ( set_intersection2(X1,sK10(powerset(X0),X2)) = X3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_372645,c_369783]) ).
tcf(c_411416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X0,X3),X4),X4)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381127,c_369783]) ).
tcf(c_411417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_image(X0,X2),X4),X4)
| ( set_intersection2(X3,relation_image(X0,X2)) = X4 )
| ( apply(X0,sK13(X0,X2,sK10(relation_image(X0,X2),X1))) = sK10(relation_image(X0,X2),X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_369783]) ).
tcf(c_411418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,sK16(powerset(X0)),X3),X3)
| ( set_intersection2(X2,sK16(powerset(X0))) = X3 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_385170,c_369783]) ).
tcf(c_411419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X0),X4),X4)
| ( set_intersection2(X2,set_intersection2(X3,X0)) = X4 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380845,c_369783]) ).
tcf(c_411500,plain,
! [X0: $i] :
( ( sK16(powerset(relation_dom(X0))) = relation_dom(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_69,c_411285]) ).
tcf(c_411505,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| ( sK16(powerset(sK10(powerset(empty_set),X0))) = sK10(powerset(empty_set),X0) ) ),
inference(superposition,[status(thm)],[c_389921,c_411285]) ).
tcf(c_411517,plain,
! [X0: $i] :
( element(sK16(empty_set),X0)
| empty(set_intersection2(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_64,c_389068]) ).
tcf(c_411518,plain,
! [X0: $i] :
( element(sK16(empty_set),empty_set)
| empty(set_intersection2(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_368545,c_389068]) ).
tcf(c_411520,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(powerset(X0),X1))
| subset(sK16(set_intersection2(powerset(X0),X1)),X0) ),
inference(superposition,[status(thm)],[c_389068,c_99]) ).
tcf(c_411533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X3)
| ( set_intersection2(X2,X3) = X0 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368984,c_369784]) ).
tcf(c_411535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X4)
| ( set_intersection2(X3,X4) = X2 )
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369784]) ).
tcf(c_411536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_image(X0,X1)),X3)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ relation(X0)
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_67,c_369784]) ).
tcf(c_411537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_image(X0,relation_inverse_image(X0,X1))),X3)
| ( relation_image(X0,relation_inverse_image(X0,X1)) = set_intersection2(X2,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_369784]) ).
tcf(c_411539,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,sK16(powerset(X0))),X2)
| ( set_intersection2(X1,X2) = sK16(powerset(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_369151,c_369784]) ).
tcf(c_411540,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,empty_set),X2)
| ( set_intersection2(X1,X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_369177,c_369784]) ).
tcf(c_411541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(X0),X1)
| in(sK2(X2,X3,sK10(powerset(X0),X1)),X3)
| ( sK10(powerset(X0),X1) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_372645,c_369784]) ).
tcf(c_411542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X0,X2)),X4)
| ( set_intersection2(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381127,c_369784]) ).
tcf(c_411543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_image(X0,X2)),X4)
| ( relation_image(X0,X2) = set_intersection2(X3,X4) )
| ( apply(X0,sK13(X0,X2,sK10(relation_image(X0,X2),X1))) = sK10(relation_image(X0,X2),X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_369784]) ).
tcf(c_411544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,sK16(powerset(X0))),X3)
| ( set_intersection2(X2,X3) = sK16(powerset(X0)) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_385170,c_369784]) ).
tcf(c_411545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X2,X0)),X4)
| ( set_intersection2(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380845,c_369784]) ).
tcf(c_411753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X2)
| ( set_intersection2(X2,X3) = X0 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368984,c_369785]) ).
tcf(c_411755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,X2),X3)
| ( set_intersection2(X3,X4) = X2 )
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369785]) ).
tcf(c_411756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_image(X0,X1)),X2)
| ( relation_image(X0,X1) = set_intersection2(X2,X3) )
| ~ relation(X0)
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_67,c_369785]) ).
tcf(c_411757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_image(X0,relation_inverse_image(X0,X1))),X2)
| ( relation_image(X0,relation_inverse_image(X0,X1)) = set_intersection2(X2,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_369785]) ).
tcf(c_411759,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,sK16(powerset(X0))),X1)
| ( set_intersection2(X1,X2) = sK16(powerset(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_369151,c_369785]) ).
tcf(c_411760,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,empty_set),X1)
| ( set_intersection2(X1,X2) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_369177,c_369785]) ).
tcf(c_411761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(X0),X1)
| in(sK2(X2,X3,sK10(powerset(X0),X1)),X2)
| ( sK10(powerset(X0),X1) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_372645,c_369785]) ).
tcf(c_411762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X0,X2)),X3)
| ( set_intersection2(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_381127,c_369785]) ).
tcf(c_411763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_image(X0,X2)),X3)
| ( relation_image(X0,X2) = set_intersection2(X3,X4) )
| ( apply(X0,sK13(X0,X2,sK10(relation_image(X0,X2),X1))) = sK10(relation_image(X0,X2),X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_369785]) ).
tcf(c_411764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,sK16(powerset(X0))),X2)
| ( set_intersection2(X2,X3) = sK16(powerset(X0)) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_385170,c_369785]) ).
tcf(c_411765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,set_intersection2(X2,X0)),X3)
| ( set_intersection2(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_380845,c_369785]) ).
tcf(c_411851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| ~ empty(set_intersection2(X2,X3))
| ~ subset(set_intersection2(X0,X1),X3)
| ~ subset(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_65,c_369786]) ).
tcf(c_411855,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_380850,c_369786]) ).
tcf(c_411886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(empty_set),X1)
| in(sK2(X2,X3,sK10(powerset(empty_set),X1)),X2)
| ( sK10(powerset(empty_set),X1) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_389922,c_369785]) ).
tcf(c_411887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(empty_set),X1)
| in(sK2(X2,X3,sK10(powerset(empty_set),X1)),X3)
| ( sK10(powerset(empty_set),X1) = set_intersection2(X2,X3) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_389922,c_369784]) ).
tcf(c_411888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(empty_set),X2)
| in(sK2(X1,sK10(powerset(empty_set),X2),X3),X3)
| ( set_intersection2(X1,sK10(powerset(empty_set),X2)) = X3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_389922,c_369783]) ).
tcf(c_411889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(empty_set),X1)
| in(sK2(sK10(powerset(empty_set),X1),X2,X3),X3)
| ( set_intersection2(sK10(powerset(empty_set),X1),X2) = X3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_389922,c_369782]) ).
tcf(c_411892,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(powerset(empty_set),X1)
| subset(sK10(powerset(empty_set),X1),X2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_389922,c_369791]) ).
tcf(c_411893,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X1)
| empty(sK10(powerset(empty_set),X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_389922,c_370745]) ).
tcf(c_411894,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X1)
| ( sK10(powerset(empty_set),X1) = X0 )
| ~ subset(X0,sK10(powerset(empty_set),X1)) ),
inference(superposition,[status(thm)],[c_389922,c_60]) ).
tcf(c_411899,plain,
! [X0: $i,X1: $i] :
( subset(powerset(empty_set),X1)
| ( relation_image(X0,relation_inverse_image(X0,sK10(powerset(empty_set),X1))) = sK10(powerset(empty_set),X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_389922,c_368596]) ).
tcf(c_411933,plain,
! [X0: $i] :
( ( sK16(powerset(X0)) = X0 )
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_411285]) ).
tcf(c_411934,plain,
! [X0: $i] :
( ( sK16(powerset(relation_dom(X0))) = empty_set )
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_385145]) ).
tcf(c_411935,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_dom(X0)) = empty_set )
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_384186]) ).
tcf(c_411936,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,sK15(X0)) = sK15(X0) )
| ( set_intersection2(relation_dom(X0),X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_397129,c_383785]) ).
tcf(c_411937,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_383574]) ).
tcf(c_411938,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,sK15(X0)) = sK15(X0) )
| ( relation_dom(set_intersection2(X0,X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_397129,c_381426]) ).
tcf(c_411939,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,sK15(X1)) = sK15(X1) )
| ( relation_dom(set_intersection2(X0,X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_397129,c_381372]) ).
tcf(c_411940,plain,
! [X0: $i] :
( ( relation_dom(sK16(powerset(X0))) = empty_set )
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_380413]) ).
tcf(c_411941,plain,
! [X0: $i] :
( ( sK16(powerset(X0)) = empty_set )
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_380415]) ).
tcf(c_411942,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = empty_set )
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_379213]) ).
tcf(c_411943,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = empty_set )
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_379152]) ).
tcf(c_411944,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_373107]) ).
tcf(c_411945,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = X0 )
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_370147]) ).
tcf(c_411946,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_370079]) ).
tcf(c_411947,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_369156]) ).
tcf(c_411948,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X1) = X0 )
| ( set_intersection2(X1,sK15(X1)) = sK15(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_397129,c_368606]) ).
tcf(c_411949,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_101]) ).
tcf(c_411950,plain,
! [X0: $i] :
( relation(X0)
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_82]) ).
tcf(c_411951,plain,
! [X0: $i] :
( function(X0)
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) ) ),
inference(superposition,[status(thm)],[c_397129,c_77]) ).
tcf(c_411952,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( set_intersection2(X1,sK15(X1)) = sK15(X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_397129,c_52]) ).
tcf(c_411953,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X1) = X2 )
| ( set_intersection2(X2,sK15(X2)) = sK15(X2) )
| ( apply(X0,sK12(X0,X1,X2)) = sK11(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397129,c_369438]) ).
tcf(c_411954,plain,
! [X0: $i] :
( empty(X0)
| ( set_intersection2(relation_dom(X0),sK15(relation_dom(X0))) = sK15(relation_dom(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397129,c_71]) ).
tcf(c_411955,plain,
set_intersection2(sK5,sK15(sK5)) = sK15(sK5),
inference(superposition,[status(thm)],[c_397129,c_78]) ).
tcf(c_411956,plain,
set_intersection2(sK8,sK15(sK8)) = sK15(sK8),
inference(superposition,[status(thm)],[c_397129,c_89]) ).
tcf(c_411957,plain,
! [X0: $i] :
( empty(X0)
| ( set_intersection2(sK15(X0),sK15(sK15(X0))) = sK15(sK15(X0)) ) ),
inference(superposition,[status(thm)],[c_397129,c_118]) ).
tcf(c_411958,plain,
! [X0: $i] : set_intersection2(powerset(X0),sK15(powerset(X0))) = sK15(powerset(X0)),
inference(superposition,[status(thm)],[c_397129,c_120]) ).
tcf(c_411959,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,X2),sK15(set_intersection2(X1,X2))) = sK15(set_intersection2(X1,X2)) )
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_397129,c_368869]) ).
tcf(c_412081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,X3),X3)
| ( relation_inverse_image(X0,X2) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368984,c_369787]) ).
tcf(c_412083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X3,X4),X4)
| ( relation_inverse_image(X2,X3) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(relation_dom(X2),X1)
| ~ subset(relation_dom(X2),X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369787]) ).
tcf(c_412084,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X1,X2),X2)
| ( relation_inverse_image(empty_set,X1) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_373108,c_369787]) ).
tcf(c_412085,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X1,X2),X2)
| ( relation_inverse_image(empty_set,X1) = X2 )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_412084,c_368630,c_103,c_369177]) ).
tcf(c_412114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,X3),X3)
| ( relation_inverse_image(X0,X1) = X3 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368984,c_369788]) ).
tcf(c_412116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X2,X4),X4)
| ( relation_inverse_image(X3,X2) = X4 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369788]) ).
tcf(c_412117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,relation_image(X0,X2),X3),X3)
| ( relation_inverse_image(X1,relation_image(X0,X2)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_67,c_369788]) ).
tcf(c_412118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,relation_image(X0,relation_inverse_image(X0,X2)),X3),X3)
| ( relation_inverse_image(X1,relation_image(X0,relation_inverse_image(X0,X2))) = X3 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_369788]) ).
tcf(c_412120,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK16(powerset(X1)),X2),X2)
| ( relation_inverse_image(X0,sK16(powerset(X1))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369151,c_369788]) ).
tcf(c_412121,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,empty_set,X2),X2)
| ( relation_inverse_image(X0,empty_set) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369177,c_369788]) ).
tcf(c_412122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(X1),X2)
| in(sK7(X0,sK10(powerset(X1),X2),X3),X3)
| ( relation_inverse_image(X0,sK10(powerset(X1),X2)) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372645,c_369788]) ).
tcf(c_412123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X1,X3),X4),X4)
| ( relation_inverse_image(X0,set_intersection2(X1,X3)) = X4 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_381127,c_369788]) ).
tcf(c_412124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,relation_image(X0,X3),X4),X4)
| ( relation_inverse_image(X1,relation_image(X0,X3)) = X4 )
| ( apply(X0,sK13(X0,X3,sK10(relation_image(X0,X3),X2))) = sK10(relation_image(X0,X3),X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_369788]) ).
tcf(c_412125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,sK16(powerset(X1)),X3),X3)
| ( relation_inverse_image(X0,sK16(powerset(X1))) = X3 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_385170,c_369788]) ).
tcf(c_412126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,set_intersection2(X3,X1),X4),X4)
| ( relation_inverse_image(X0,set_intersection2(X3,X1)) = X4 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_380845,c_369788]) ).
tcf(c_412129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(empty_set),X2)
| in(sK7(X0,sK10(powerset(empty_set),X2),X3),X3)
| ( relation_inverse_image(X0,sK10(powerset(empty_set),X2)) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_389922,c_369788]) ).
tcf(c_412376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X3,X1)),X3)
| ( relation_inverse_image(X0,X3) = X1 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368984,c_369789]) ).
tcf(c_412378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK7(X3,X4,X2)),X4)
| ( relation_inverse_image(X3,X4) = X2 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369789]) ).
tcf(c_412379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,X2,relation_image(X0,X3))),X2)
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_67,c_369789]) ).
tcf(c_412380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,X3,relation_image(X0,relation_inverse_image(X0,X2)))),X3)
| ( relation_image(X0,relation_inverse_image(X0,X2)) = relation_inverse_image(X1,X3) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_369789]) ).
tcf(c_412382,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X2,sK16(powerset(X1)))),X2)
| ( relation_inverse_image(X0,X2) = sK16(powerset(X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369151,c_369789]) ).
tcf(c_412383,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X2,empty_set)),X2)
| ( relation_inverse_image(X0,X2) = empty_set )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369177,c_369789]) ).
tcf(c_412384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(X1),X2)
| in(apply(X0,sK7(X0,X3,sK10(powerset(X1),X2))),X3)
| ( sK10(powerset(X1),X2) = relation_inverse_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372645,c_369789]) ).
tcf(c_412385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X3,set_intersection2(X1,X4))),X3)
| ( relation_inverse_image(X0,X3) = set_intersection2(X1,X4) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_381127,c_369789]) ).
tcf(c_412386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK7(X1,X4,relation_image(X0,X3))),X4)
| ( relation_inverse_image(X1,X4) = relation_image(X0,X3) )
| ( apply(X0,sK13(X0,X3,sK10(relation_image(X0,X3),X2))) = sK10(relation_image(X0,X3),X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_369789]) ).
tcf(c_412387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X3,sK16(powerset(X1)))),X3)
| ( relation_inverse_image(X0,X3) = sK16(powerset(X1)) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_385170,c_369789]) ).
tcf(c_412388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK7(X0,X3,set_intersection2(X4,X1))),X3)
| ( relation_inverse_image(X0,X3) = set_intersection2(X4,X1) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_380845,c_369789]) ).
tcf(c_412391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(empty_set),X2)
| in(apply(X0,sK7(X0,X3,sK10(powerset(empty_set),X2))),X3)
| ( sK10(powerset(empty_set),X2) = relation_inverse_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_389922,c_369789]) ).
tcf(c_412494,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK5)
| ~ subset(sK15(sK5),X1)
| ~ in(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_369786]) ).
tcf(c_412495,plain,
( element(sK16(sK15(sK5)),sK5)
| empty(set_intersection2(sK5,sK15(sK5))) ),
inference(superposition,[status(thm)],[c_411955,c_389068]) ).
tcf(c_412496,plain,
( empty(set_intersection2(sK15(sK5),sK5))
| in(sK16(sK15(sK5)),sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_389060]) ).
tcf(c_412497,plain,
( empty(set_intersection2(sK5,sK15(sK5)))
| element(sK16(sK15(sK5)),sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_388051]) ).
tcf(c_412498,plain,
( in(sK16(sK15(sK5)),sK5)
| empty(set_intersection2(sK15(sK5),sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_388043]) ).
tcf(c_412499,plain,
( in(sK16(sK15(sK5)),sK5)
| empty(set_intersection2(sK5,sK15(sK5))) ),
inference(superposition,[status(thm)],[c_411955,c_370751]) ).
tcf(c_412500,plain,
( empty(set_intersection2(sK5,sK15(sK5)))
| in(sK16(sK15(sK5)),sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_370750]) ).
tcf(c_412501,plain,
! [X0: $i] :
( ~ in(X0,sK5)
| ~ in(X0,sK15(sK5))
| ~ in(sK15(sK5),X0) ),
inference(superposition,[status(thm)],[c_411955,c_369080]) ).
tcf(c_412505,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,sK5)
| ~ subset(sK15(sK5),X1)
| ~ in(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_369016]) ).
tcf(c_412507,plain,
! [X0: $i] :
( subset(set_intersection2(sK5,sK15(sK5)),X0)
| in(sK10(sK15(sK5),X0),sK5) ),
inference(superposition,[status(thm)],[c_411955,c_368986]) ).
tcf(c_412508,plain,
subset(sK15(sK5),sK5),
inference(superposition,[status(thm)],[c_411955,c_380919]) ).
tcf(c_412509,plain,
subset(sK15(sK5),sK15(sK5)),
inference(superposition,[status(thm)],[c_411955,c_380850]) ).
tcf(c_412510,plain,
! [X0: $i] :
( subset(set_intersection2(sK5,sK15(sK5)),X0)
| in(sK10(sK15(sK5),X0),sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_368985]) ).
tcf(c_412511,plain,
! [X0: $i] :
( ~ empty(sK15(sK5))
| ~ in(X0,sK5)
| ~ in(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_368869]) ).
tcf(c_412512,plain,
! [X0: $i] :
( ( set_intersection2(sK5,sK15(sK5)) = X0 )
| ~ subset(X0,sK5)
| ~ subset(X0,sK15(sK5))
| ~ subset(sK15(sK5),X0) ),
inference(superposition,[status(thm)],[c_411955,c_368558]) ).
tcf(c_412513,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),sK15(sK5))
| in(sK2(set_intersection2(sK5,sK15(sK5)),X0,X1),X1)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_368503]) ).
tcf(c_412514,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),X1)
| in(sK2(set_intersection2(sK5,sK15(sK5)),X0,X1),sK15(sK5))
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_368503]) ).
tcf(c_412515,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),sK5)
| in(sK2(set_intersection2(sK5,sK15(sK5)),X0,X1),X1)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_368481]) ).
tcf(c_412516,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),X1)
| in(sK2(set_intersection2(sK5,sK15(sK5)),X0,X1),sK5)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_368481]) ).
tcf(c_412517,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = X1 )
| ~ in(sK2(sK15(sK5),X0,X1),sK5)
| ~ in(sK2(set_intersection2(sK5,sK15(sK5)),X0,X1),X1)
| ~ in(sK2(set_intersection2(sK5,sK15(sK5)),X0,X1),X0)
| ~ in(sK2(set_intersection2(sK5,sK15(sK5)),X0,X1),sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_368471]) ).
tcf(c_412519,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,sK15(sK5),X1),X1)
| in(sK12(X0,set_intersection2(sK5,sK15(sK5)),X1),sK5)
| ( relation_image(X0,set_intersection2(sK5,sK15(sK5))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_369303]) ).
tcf(c_412520,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,sK15(sK5),X1),sK5)
| in(sK11(X0,set_intersection2(sK5,sK15(sK5)),X1),X1)
| ( relation_image(X0,set_intersection2(sK5,sK15(sK5))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_369303]) ).
tcf(c_412521,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,sK15(sK5),X1),X1)
| in(sK12(X0,set_intersection2(sK5,sK15(sK5)),X1),sK15(sK5))
| ( relation_image(X0,set_intersection2(sK5,sK15(sK5))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_369302]) ).
tcf(c_412522,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,sK15(sK5),X1),sK15(sK5))
| in(sK11(X0,set_intersection2(sK5,sK15(sK5)),X1),X1)
| ( relation_image(X0,set_intersection2(sK5,sK15(sK5))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_369302]) ).
tcf(c_412523,plain,
! [X0: $i] :
( subset(X0,set_intersection2(sK5,sK15(sK5)))
| ~ in(sK10(X0,sK15(sK5)),sK5)
| ~ in(sK10(X0,set_intersection2(sK5,sK15(sK5))),sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_368972]) ).
tcf(c_412524,plain,
! [X0: $i] :
( element(X0,sK15(sK5))
| ~ in(X0,sK5)
| ~ in(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_368928]) ).
tcf(c_412525,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,set_intersection2(sK5,sK15(sK5)),X1),X1)
| in(apply(X0,sK7(X0,sK15(sK5),X1)),sK5)
| ( relation_inverse_image(X0,set_intersection2(sK5,sK15(sK5))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_368703]) ).
tcf(c_412526,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,sK15(sK5),X1),X1)
| in(apply(X0,sK7(X0,set_intersection2(sK5,sK15(sK5)),X1)),sK5)
| ( relation_inverse_image(X0,set_intersection2(sK5,sK15(sK5))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_368703]) ).
tcf(c_412527,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,set_intersection2(sK5,sK15(sK5)),X1),X1)
| in(apply(X0,sK7(X0,sK15(sK5),X1)),sK15(sK5))
| ( relation_inverse_image(X0,set_intersection2(sK5,sK15(sK5))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_368702]) ).
tcf(c_412528,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,sK15(sK5),X1),X1)
| in(apply(X0,sK7(X0,set_intersection2(sK5,sK15(sK5)),X1)),sK15(sK5))
| ( relation_inverse_image(X0,set_intersection2(sK5,sK15(sK5))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_368702]) ).
tcf(c_412529,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,set_intersection2(sK5,sK15(sK5))) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,set_intersection2(sK5,sK15(sK5)),X1),X1)
| ~ in(apply(X0,sK7(X0,sK15(sK5),X1)),sK5)
| ~ in(sK7(X0,set_intersection2(sK5,sK15(sK5)),X1),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,set_intersection2(sK5,sK15(sK5)),X1)),sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_368654]) ).
tcf(c_412530,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),sK15(sK5))
| in(sK2(X0,set_intersection2(sK5,sK15(sK5)),X1),X1)
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_368504]) ).
tcf(c_412531,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),X1)
| in(sK2(X0,set_intersection2(sK5,sK15(sK5)),X1),sK15(sK5))
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_368504]) ).
tcf(c_412532,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),sK5)
| in(sK2(X0,set_intersection2(sK5,sK15(sK5)),X1),X1)
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_368482]) ).
tcf(c_412533,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),X1)
| in(sK2(X0,set_intersection2(sK5,sK15(sK5)),X1),sK5)
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_368482]) ).
tcf(c_412536,plain,
! [X0: $i] :
( in(X0,sK5)
| ~ in(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_58]) ).
tcf(c_412538,plain,
! [X0: $i] :
( subset(sK15(sK5),X0)
| ~ empty(sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_380845]) ).
tcf(c_412539,plain,
( function(sK15(sK5))
| ~ empty(sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_381376]) ).
tcf(c_412540,plain,
( relation(sK15(sK5))
| ~ empty(sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_381375]) ).
tcf(c_412542,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,sK15(sK5),X0),sK5)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(sK5,sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_411955,c_369598]) ).
tcf(c_412543,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,sK15(sK5),X0),sK15(sK5))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(sK5,sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_411955,c_369597]) ).
tcf(c_412544,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK5)
| ( set_intersection2(sK5,sK15(sK5)) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(sK5,sK15(sK5)))) = sK11(X0,X1,set_intersection2(sK5,sK15(sK5))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_369440]) ).
tcf(c_412545,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK15(sK5))
| ( set_intersection2(sK5,sK15(sK5)) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(sK5,sK15(sK5)))) = sK11(X0,X1,set_intersection2(sK5,sK15(sK5))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_369439]) ).
tcf(c_412546,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK5)
| in(sK12(X0,X1,set_intersection2(sK5,sK15(sK5))),X1)
| ( set_intersection2(sK5,sK15(sK5)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_369311]) ).
tcf(c_412547,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,sK15(sK5)),X1)
| in(sK11(X0,X1,set_intersection2(sK5,sK15(sK5))),sK5)
| ( set_intersection2(sK5,sK15(sK5)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_369311]) ).
tcf(c_412548,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK15(sK5))
| in(sK12(X0,X1,set_intersection2(sK5,sK15(sK5))),X1)
| ( set_intersection2(sK5,sK15(sK5)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_369310]) ).
tcf(c_412549,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,sK15(sK5)),X1)
| in(sK11(X0,X1,set_intersection2(sK5,sK15(sK5))),sK15(sK5))
| ( set_intersection2(sK5,sK15(sK5)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_369310]) ).
tcf(c_412550,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,sK15(sK5)),relation_dom(X0))
| in(sK11(X0,X1,set_intersection2(sK5,sK15(sK5))),sK5)
| ( set_intersection2(sK5,sK15(sK5)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_369210]) ).
tcf(c_412551,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK5)
| in(sK12(X0,X1,set_intersection2(sK5,sK15(sK5))),relation_dom(X0))
| ( set_intersection2(sK5,sK15(sK5)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_369210]) ).
tcf(c_412552,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,sK15(sK5)),relation_dom(X0))
| in(sK11(X0,X1,set_intersection2(sK5,sK15(sK5))),sK15(sK5))
| ( set_intersection2(sK5,sK15(sK5)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_369209]) ).
tcf(c_412553,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK15(sK5))
| in(sK12(X0,X1,set_intersection2(sK5,sK15(sK5))),relation_dom(X0))
| ( set_intersection2(sK5,sK15(sK5)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_369209]) ).
tcf(c_412554,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_inverse_image(X0,sK15(sK5)))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),sK5)
| ~ in(apply(X0,X1),sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_368735]) ).
tcf(c_412555,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,set_intersection2(sK5,sK15(sK5))),sK5)
| in(apply(X0,sK7(X0,X1,sK15(sK5))),X1)
| ( set_intersection2(sK5,sK15(sK5)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_368701]) ).
tcf(c_412556,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),sK5)
| in(apply(X0,sK7(X0,X1,set_intersection2(sK5,sK15(sK5)))),X1)
| ( set_intersection2(sK5,sK15(sK5)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_368701]) ).
tcf(c_412557,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK7(X0,X1,sK15(sK5))),X1)
| in(sK7(X0,X1,set_intersection2(sK5,sK15(sK5))),sK15(sK5))
| ( set_intersection2(sK5,sK15(sK5)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_368700]) ).
tcf(c_412558,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),sK15(sK5))
| in(apply(X0,sK7(X0,X1,set_intersection2(sK5,sK15(sK5)))),X1)
| ( set_intersection2(sK5,sK15(sK5)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_368700]) ).
tcf(c_412559,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),relation_dom(X0))
| in(sK7(X0,X1,set_intersection2(sK5,sK15(sK5))),sK5)
| ( set_intersection2(sK5,sK15(sK5)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_368673]) ).
tcf(c_412560,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),sK5)
| in(sK7(X0,X1,set_intersection2(sK5,sK15(sK5))),relation_dom(X0))
| ( set_intersection2(sK5,sK15(sK5)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_368673]) ).
tcf(c_412561,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),relation_dom(X0))
| in(sK7(X0,X1,set_intersection2(sK5,sK15(sK5))),sK15(sK5))
| ( set_intersection2(sK5,sK15(sK5)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_368672]) ).
tcf(c_412562,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),sK15(sK5))
| in(sK7(X0,X1,set_intersection2(sK5,sK15(sK5))),relation_dom(X0))
| ( set_intersection2(sK5,sK15(sK5)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_368672]) ).
tcf(c_412563,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),X0)
| in(sK2(X0,X1,set_intersection2(sK5,sK15(sK5))),sK15(sK5))
| ( set_intersection2(sK5,sK15(sK5)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411955,c_368506]) ).
tcf(c_412564,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),sK15(sK5))
| in(sK2(X0,X1,set_intersection2(sK5,sK15(sK5))),X0)
| ( set_intersection2(sK5,sK15(sK5)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411955,c_368506]) ).
tcf(c_412565,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),X1)
| in(sK2(X0,X1,set_intersection2(sK5,sK15(sK5))),sK15(sK5))
| ( set_intersection2(sK5,sK15(sK5)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411955,c_368505]) ).
tcf(c_412566,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),sK15(sK5))
| in(sK2(X0,X1,set_intersection2(sK5,sK15(sK5))),X1)
| ( set_intersection2(sK5,sK15(sK5)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411955,c_368505]) ).
tcf(c_412567,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),X0)
| in(sK2(X0,X1,set_intersection2(sK5,sK15(sK5))),sK5)
| ( set_intersection2(sK5,sK15(sK5)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411955,c_368484]) ).
tcf(c_412568,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),sK5)
| in(sK2(X0,X1,set_intersection2(sK5,sK15(sK5))),X0)
| ( set_intersection2(sK5,sK15(sK5)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411955,c_368484]) ).
tcf(c_412569,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),X1)
| in(sK2(X0,X1,set_intersection2(sK5,sK15(sK5))),sK5)
| ( set_intersection2(sK5,sK15(sK5)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411955,c_368483]) ).
tcf(c_412570,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),sK5)
| in(sK2(X0,X1,set_intersection2(sK5,sK15(sK5))),X1)
| ( set_intersection2(sK5,sK15(sK5)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411955,c_368483]) ).
tcf(c_412579,plain,
( empty(sK15(sK5))
| in(sK16(sK15(sK5)),sK5) ),
inference(light_normalisation,[status(thm)],[c_412499,c_411955]) ).
tcf(c_412584,plain,
( empty(sK15(sK5))
| element(sK16(sK15(sK5)),sK5) ),
inference(light_normalisation,[status(thm)],[c_412495,c_411955]) ).
tcf(c_412587,plain,
( empty(sK15(sK5))
| in(sK16(sK15(sK5)),sK15(sK5)) ),
inference(light_normalisation,[status(thm)],[c_412500,c_411955]) ).
tcf(c_412590,plain,
( empty(sK15(sK5))
| element(sK16(sK15(sK5)),sK15(sK5)) ),
inference(light_normalisation,[status(thm)],[c_412497,c_411955]) ).
tcf(c_412593,plain,
! [X0: $i] :
( subset(sK15(sK5),X0)
| in(sK10(sK15(sK5),X0),sK5) ),
inference(light_normalisation,[status(thm)],[c_412507,c_411955]) ).
tcf(c_412602,plain,
! [X0: $i] :
( subset(sK15(sK5),X0)
| in(sK10(sK15(sK5),X0),sK15(sK5)) ),
inference(light_normalisation,[status(thm)],[c_412510,c_411955]) ).
tcf(c_412616,plain,
! [X0: $i] :
( ( sK15(sK5) = X0 )
| ~ subset(X0,sK5)
| ~ subset(X0,sK15(sK5))
| ~ subset(sK15(sK5),X0) ),
inference(light_normalisation,[status(thm)],[c_412512,c_411955]) ).
tcf(c_412621,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,sK15(sK5),X0),sK5)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(sK5))) ),
inference(light_normalisation,[status(thm)],[c_412542,c_411955]) ).
tcf(c_412626,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,sK15(sK5),X0),sK15(sK5))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(sK5))) ),
inference(light_normalisation,[status(thm)],[c_412543,c_411955]) ).
tcf(c_412631,plain,
! [X0: $i] :
( subset(X0,sK15(sK5))
| ~ in(sK10(X0,sK15(sK5)),sK5)
| ~ in(sK10(X0,sK15(sK5)),sK15(sK5)) ),
inference(light_normalisation,[status(thm)],[c_412523,c_411955]) ).
tcf(c_412635,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),sK5)
| in(sK2(X0,X1,sK15(sK5)),X1)
| ( set_intersection2(X0,X1) = sK15(sK5) ) ),
inference(light_normalisation,[status(thm)],[c_412570,c_411955]) ).
tcf(c_412640,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),sK5)
| in(sK2(X0,X1,sK15(sK5)),X0)
| ( set_intersection2(X0,X1) = sK15(sK5) ) ),
inference(light_normalisation,[status(thm)],[c_412568,c_411955]) ).
tcf(c_412645,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),sK5)
| in(sK2(X0,sK15(sK5),X1),X1)
| ( set_intersection2(X0,sK15(sK5)) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_412533,c_411955]) ).
tcf(c_412650,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),sK5)
| in(sK2(sK15(sK5),X0,X1),X1)
| ( set_intersection2(sK15(sK5),X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_412516,c_411955]) ).
tcf(c_412655,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),X1)
| in(sK2(X0,X1,sK15(sK5)),sK15(sK5))
| ( set_intersection2(X0,X1) = sK15(sK5) ) ),
inference(light_normalisation,[status(thm)],[c_412566,c_411955]) ).
tcf(c_412660,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),X0)
| in(sK2(X0,X1,sK15(sK5)),sK15(sK5))
| ( set_intersection2(X0,X1) = sK15(sK5) ) ),
inference(light_normalisation,[status(thm)],[c_412564,c_411955]) ).
tcf(c_412665,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),X1)
| in(sK2(X0,sK15(sK5),X1),sK15(sK5))
| ( set_intersection2(X0,sK15(sK5)) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_412531,c_411955]) ).
tcf(c_412670,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),X1)
| in(sK2(sK15(sK5),X0,X1),sK15(sK5))
| ( set_intersection2(sK15(sK5),X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_412514,c_411955]) ).
tcf(c_412681,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK5)
| in(sK12(X0,X1,sK15(sK5)),X1)
| ( relation_image(X0,X1) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_412547,c_411955]) ).
tcf(c_412688,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,sK15(sK5),X1),sK5)
| in(sK11(X0,sK15(sK5),X1),X1)
| ( relation_image(X0,sK15(sK5)) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_412520,c_411955]) ).
tcf(c_412695,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),sK5)
| in(sK7(X0,X1,sK15(sK5)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_412560,c_411955]) ).
tcf(c_412702,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK5)
| in(sK12(X0,X1,sK15(sK5)),relation_dom(X0))
| ( relation_image(X0,X1) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_412551,c_411955]) ).
tcf(c_412709,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,sK15(sK5)),X1)
| in(sK11(X0,X1,sK15(sK5)),sK15(sK5))
| ( relation_image(X0,X1) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_412549,c_411955]) ).
tcf(c_412716,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,sK15(sK5),X1),X1)
| in(sK12(X0,sK15(sK5),X1),sK15(sK5))
| ( relation_image(X0,sK15(sK5)) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_412522,c_411955]) ).
tcf(c_412723,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),sK15(sK5))
| in(sK7(X0,X1,sK15(sK5)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_412562,c_411955]) ).
tcf(c_412730,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),sK5)
| in(apply(X0,sK7(X0,X1,sK15(sK5))),X1)
| ( relation_inverse_image(X0,X1) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_412556,c_411955]) ).
tcf(c_412737,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK15(sK5))
| in(sK12(X0,X1,sK15(sK5)),relation_dom(X0))
| ( relation_image(X0,X1) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_412553,c_411955]) ).
tcf(c_412744,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,sK15(sK5),X1),X1)
| in(apply(X0,sK7(X0,sK15(sK5),X1)),sK5)
| ( relation_inverse_image(X0,sK15(sK5)) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_412526,c_411955]) ).
tcf(c_412751,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),sK15(sK5))
| in(apply(X0,sK7(X0,X1,sK15(sK5))),X1)
| ( relation_inverse_image(X0,X1) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_412558,c_411955]) ).
tcf(c_412758,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,sK15(sK5),X1),X1)
| in(apply(X0,sK7(X0,sK15(sK5),X1)),sK15(sK5))
| ( relation_inverse_image(X0,sK15(sK5)) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_412528,c_411955]) ).
tcf(c_412765,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK5)
| ( relation_image(X0,X1) = sK15(sK5) )
| ( apply(X0,sK12(X0,X1,sK15(sK5))) = sK11(X0,X1,sK15(sK5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_412544,c_411955]) ).
tcf(c_412771,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK15(sK5))
| ( relation_image(X0,X1) = sK15(sK5) )
| ( apply(X0,sK12(X0,X1,sK15(sK5))) = sK11(X0,X1,sK15(sK5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_412545,c_411955]) ).
tcf(c_412777,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK15(sK5),X0) = X1 )
| ~ in(sK2(sK15(sK5),X0,X1),sK5)
| ~ in(sK2(sK15(sK5),X0,X1),X1)
| ~ in(sK2(sK15(sK5),X0,X1),X0)
| ~ in(sK2(sK15(sK5),X0,X1),sK15(sK5)) ),
inference(light_normalisation,[status(thm)],[c_412517,c_411955]) ).
tcf(c_412783,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,sK15(sK5)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,sK15(sK5),X1),X1)
| ~ in(sK7(X0,sK15(sK5),X1),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,sK15(sK5),X1)),sK5)
| ~ in(apply(X0,sK7(X0,sK15(sK5),X1)),sK15(sK5)) ),
inference(light_normalisation,[status(thm)],[c_412529,c_411955]) ).
tcf(c_412853,plain,
set_intersection2(sK15(sK5),sK5) = sK15(sK5),
inference(superposition,[status(thm)],[c_412508,c_381110]) ).
tcf(c_412857,plain,
( ( sK15(sK5) = sK5 )
| ~ subset(sK5,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_412508,c_60]) ).
tcf(c_412872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,X1),relation_dom(X0))
| ( relation_inverse_image(X0,X3) = X1 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368984,c_369790]) ).
tcf(c_412874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X3,X4,X2),relation_dom(X3))
| ( relation_inverse_image(X3,X4) = X2 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369790]) ).
tcf(c_412875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X2,relation_image(X0,X3)),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = relation_image(X0,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_67,c_369790]) ).
tcf(c_412876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X3,relation_image(X0,relation_inverse_image(X0,X2))),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X0,X2)) = relation_inverse_image(X1,X3) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_369790]) ).
tcf(c_412878,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK16(powerset(X1))),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = sK16(powerset(X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369151,c_369790]) ).
tcf(c_412879,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,empty_set),relation_dom(X0))
| ( relation_inverse_image(X0,X2) = empty_set )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369177,c_369790]) ).
tcf(c_412880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(X1),X2)
| in(sK7(X0,X3,sK10(powerset(X1),X2)),relation_dom(X0))
| ( sK10(powerset(X1),X2) = relation_inverse_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372645,c_369790]) ).
tcf(c_412881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,set_intersection2(X1,X4)),relation_dom(X0))
| ( relation_inverse_image(X0,X3) = set_intersection2(X1,X4) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_381127,c_369790]) ).
tcf(c_412882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X1,X4,relation_image(X0,X3)),relation_dom(X1))
| ( relation_inverse_image(X1,X4) = relation_image(X0,X3) )
| ( apply(X0,sK13(X0,X3,sK10(relation_image(X0,X3),X2))) = sK10(relation_image(X0,X3),X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_369790]) ).
tcf(c_412883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,sK16(powerset(X1))),relation_dom(X0))
| ( relation_inverse_image(X0,X3) = sK16(powerset(X1)) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_385170,c_369790]) ).
tcf(c_412884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X0,X3,set_intersection2(X4,X1)),relation_dom(X0))
| ( relation_inverse_image(X0,X3) = set_intersection2(X4,X1) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_380845,c_369790]) ).
tcf(c_412887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(empty_set),X2)
| in(sK7(X0,X3,sK10(powerset(empty_set),X2)),relation_dom(X0))
| ( sK10(powerset(empty_set),X2) = relation_inverse_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_389922,c_369790]) ).
tcf(c_413125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X3) = X1 )
| ( apply(X0,sK12(X0,X3,X1)) = sK11(X0,X3,X1) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368984,c_369792]) ).
tcf(c_413127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X3,X4) = X2 )
| ( apply(X3,sK12(X3,X4,X2)) = sK11(X3,X4,X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369792]) ).
tcf(c_413128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X3) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,relation_image(X0,X3))) = sK11(X1,X2,relation_image(X0,X3)) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_67,c_369792]) ).
tcf(c_413129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,relation_inverse_image(X0,X2)) = relation_image(X1,X3) )
| ( apply(X1,sK12(X1,X3,relation_image(X0,relation_inverse_image(X0,X2)))) = sK11(X1,X3,relation_image(X0,relation_inverse_image(X0,X2))) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_369792]) ).
tcf(c_413132,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = empty_set )
| ( apply(X0,sK12(X0,X2,empty_set)) = sK11(X0,X2,empty_set) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369177,c_369792]) ).
tcf(c_413133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(X1),X3)
| ( sK10(powerset(X1),X3) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,sK10(powerset(X1),X3))) = sK11(X0,X2,sK10(powerset(X1),X3)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372645,c_369792]) ).
tcf(c_413134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,X3) = set_intersection2(X1,X4) )
| ( apply(X0,sK12(X0,X3,set_intersection2(X1,X4))) = sK11(X0,X3,set_intersection2(X1,X4)) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_381127,c_369792]) ).
tcf(c_413135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,X3) = relation_image(X1,X4) )
| ( apply(X1,sK12(X1,X4,relation_image(X0,X3))) = sK11(X1,X4,relation_image(X0,X3)) )
| ( apply(X0,sK13(X0,X3,sK10(relation_image(X0,X3),X2))) = sK10(relation_image(X0,X3),X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_369792]) ).
tcf(c_413136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X3) = sK16(powerset(X1)) )
| ( apply(X0,sK12(X0,X3,sK16(powerset(X1)))) = sK11(X0,X3,sK16(powerset(X1))) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_385170,c_369792]) ).
tcf(c_413137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,X3) = set_intersection2(X4,X1) )
| ( apply(X0,sK12(X0,X3,set_intersection2(X4,X1))) = sK11(X0,X3,set_intersection2(X4,X1)) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_380845,c_369792]) ).
tcf(c_413140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(empty_set),X3)
| ( sK10(powerset(empty_set),X3) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,sK10(powerset(empty_set),X3))) = sK11(X0,X2,sK10(powerset(empty_set),X3)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_389922,c_369792]) ).
tcf(c_413263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,X1),X3)
| ( relation_image(X0,X3) = X1 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368984,c_369793]) ).
tcf(c_413265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X2),X4)
| ( relation_image(X3,X4) = X2 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369793]) ).
tcf(c_413266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X3,relation_image(X0,X2)),X3)
| ( relation_image(X0,X2) = relation_image(X1,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_67,c_369793]) ).
tcf(c_413267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X3,relation_image(X0,relation_inverse_image(X0,X2))),X3)
| ( relation_image(X0,relation_inverse_image(X0,X2)) = relation_image(X1,X3) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_369793]) ).
tcf(c_413269,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,sK16(powerset(X1))),X2)
| ( relation_image(X0,X2) = sK16(powerset(X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369151,c_369793]) ).
tcf(c_413270,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,empty_set),X2)
| ( relation_image(X0,X2) = empty_set )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369177,c_369793]) ).
tcf(c_413271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(X1),X2)
| in(sK12(X0,X3,sK10(powerset(X1),X2)),X3)
| ( sK10(powerset(X1),X2) = relation_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372645,c_369793]) ).
tcf(c_413272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X3,set_intersection2(X1,X4)),X3)
| ( relation_image(X0,X3) = set_intersection2(X1,X4) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_381127,c_369793]) ).
tcf(c_413273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X4,relation_image(X0,X3)),X4)
| ( relation_image(X0,X3) = relation_image(X1,X4) )
| ( apply(X0,sK13(X0,X3,sK10(relation_image(X0,X3),X2))) = sK10(relation_image(X0,X3),X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_369793]) ).
tcf(c_413274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,sK16(powerset(X1))),X3)
| ( relation_image(X0,X3) = sK16(powerset(X1)) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_385170,c_369793]) ).
tcf(c_413275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X3,set_intersection2(X4,X1)),X3)
| ( relation_image(X0,X3) = set_intersection2(X4,X1) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_380845,c_369793]) ).
tcf(c_413278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(empty_set),X2)
| in(sK12(X0,X3,sK10(powerset(empty_set),X2)),X3)
| ( sK10(powerset(empty_set),X2) = relation_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_389922,c_369793]) ).
tcf(c_413405,plain,
~ empty(sK15(sK5)),
inference(global_subsumption_just,[status(thm)],[c_412539,c_78,c_6041]) ).
tcf(c_413407,plain,
set_intersection2(sK15(sK5),sK15(sK15(sK5))) = sK15(sK15(sK5)),
inference(superposition,[status(thm)],[c_397129,c_413405]) ).
tcf(c_413420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,X1),relation_dom(X0))
| ( relation_image(X0,X3) = X1 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368984,c_369794]) ).
tcf(c_413422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X3,X4,X2),relation_dom(X3))
| ( relation_image(X3,X4) = X2 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369794]) ).
tcf(c_413423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X3,relation_image(X0,X2)),relation_dom(X1))
| ( relation_image(X0,X2) = relation_image(X1,X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_67,c_369794]) ).
tcf(c_413424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X3,relation_image(X0,relation_inverse_image(X0,X2))),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X0,X2)) = relation_image(X1,X3) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_369794]) ).
tcf(c_413426,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,sK16(powerset(X1))),relation_dom(X0))
| ( relation_image(X0,X2) = sK16(powerset(X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369151,c_369794]) ).
tcf(c_413427,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,empty_set),relation_dom(X0))
| ( relation_image(X0,X2) = empty_set )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369177,c_369794]) ).
tcf(c_413428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(X1),X2)
| in(sK12(X0,X3,sK10(powerset(X1),X2)),relation_dom(X0))
| ( sK10(powerset(X1),X2) = relation_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372645,c_369794]) ).
tcf(c_413429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X3,set_intersection2(X1,X4)),relation_dom(X0))
| ( relation_image(X0,X3) = set_intersection2(X1,X4) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_381127,c_369794]) ).
tcf(c_413430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X1,X4,relation_image(X0,X3)),relation_dom(X1))
| ( relation_image(X0,X3) = relation_image(X1,X4) )
| ( apply(X0,sK13(X0,X3,sK10(relation_image(X0,X3),X2))) = sK10(relation_image(X0,X3),X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_369794]) ).
tcf(c_413431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,sK16(powerset(X1))),relation_dom(X0))
| ( relation_image(X0,X3) = sK16(powerset(X1)) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_385170,c_369794]) ).
tcf(c_413432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X0,X3,set_intersection2(X4,X1)),relation_dom(X0))
| ( relation_image(X0,X3) = set_intersection2(X4,X1) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_380845,c_369794]) ).
tcf(c_413435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(empty_set),X2)
| in(sK12(X0,X3,sK10(powerset(empty_set),X2)),relation_dom(X0))
| ( sK10(powerset(empty_set),X2) = relation_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_389922,c_369794]) ).
tcf(c_413530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X2,X3),X3)
| ( relation_image(X0,X2) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368984,c_369795]) ).
tcf(c_413532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,X3,X4),X4)
| ( relation_image(X2,X3) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(relation_dom(X2),X1)
| ~ subset(relation_dom(X2),X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369795]) ).
tcf(c_413533,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(empty_set,X1,X2),X2)
| ( relation_image(empty_set,X1) = X2 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_373108,c_369795]) ).
tcf(c_413534,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(empty_set,X1,X2),X2)
| ( relation_image(empty_set,X1) = X2 )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_413533,c_368630,c_103,c_369177]) ).
tcf(c_413613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,X3),X3)
| ( relation_image(X0,X1) = X3 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368984,c_369796]) ).
tcf(c_413615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X3,X2,X4),X4)
| ( relation_image(X3,X2) = X4 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_369796]) ).
tcf(c_413616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,relation_image(X0,X2),X3),X3)
| ( relation_image(X1,relation_image(X0,X2)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_67,c_369796]) ).
tcf(c_413617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,relation_image(X0,relation_inverse_image(X0,X2)),X3),X3)
| ( relation_image(X1,relation_image(X0,relation_inverse_image(X0,X2))) = X3 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_68,c_369796]) ).
tcf(c_413619,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,sK16(powerset(X1)),X2),X2)
| ( relation_image(X0,sK16(powerset(X1))) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369151,c_369796]) ).
tcf(c_413620,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,empty_set,X2),X2)
| ( relation_image(X0,empty_set) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369177,c_369796]) ).
tcf(c_413621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(X1),X2)
| in(sK11(X0,sK10(powerset(X1),X2),X3),X3)
| ( relation_image(X0,sK10(powerset(X1),X2)) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_372645,c_369796]) ).
tcf(c_413622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,set_intersection2(X1,X3),X4),X4)
| ( relation_image(X0,set_intersection2(X1,X3)) = X4 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_381127,c_369796]) ).
tcf(c_413623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X1,relation_image(X0,X3),X4),X4)
| ( relation_image(X1,relation_image(X0,X3)) = X4 )
| ( apply(X0,sK13(X0,X3,sK10(relation_image(X0,X3),X2))) = sK10(relation_image(X0,X3),X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369666,c_369796]) ).
tcf(c_413624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,sK16(powerset(X1)),X3),X3)
| ( relation_image(X0,sK16(powerset(X1))) = X3 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_385170,c_369796]) ).
tcf(c_413625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X0,set_intersection2(X3,X1),X4),X4)
| ( relation_image(X0,set_intersection2(X3,X1)) = X4 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_380845,c_369796]) ).
tcf(c_413628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(powerset(empty_set),X2)
| in(sK11(X0,sK10(powerset(empty_set),X2),X3),X3)
| ( relation_image(X0,sK10(powerset(empty_set),X2)) = X3 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_389922,c_369796]) ).
tcf(c_413825,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK8)
| ~ subset(sK15(sK8),X1)
| ~ in(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_369786]) ).
tcf(c_413826,plain,
( element(sK16(sK15(sK8)),sK8)
| empty(set_intersection2(sK8,sK15(sK8))) ),
inference(superposition,[status(thm)],[c_411956,c_389068]) ).
tcf(c_413827,plain,
( empty(set_intersection2(sK15(sK8),sK8))
| in(sK16(sK15(sK8)),sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_389060]) ).
tcf(c_413828,plain,
( empty(set_intersection2(sK8,sK15(sK8)))
| element(sK16(sK15(sK8)),sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_388051]) ).
tcf(c_413829,plain,
( in(sK16(sK15(sK8)),sK8)
| empty(set_intersection2(sK15(sK8),sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_388043]) ).
tcf(c_413830,plain,
( in(sK16(sK15(sK8)),sK8)
| empty(set_intersection2(sK8,sK15(sK8))) ),
inference(superposition,[status(thm)],[c_411956,c_370751]) ).
tcf(c_413831,plain,
( empty(set_intersection2(sK8,sK15(sK8)))
| in(sK16(sK15(sK8)),sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_370750]) ).
tcf(c_413832,plain,
! [X0: $i] :
( ~ in(X0,sK8)
| ~ in(X0,sK15(sK8))
| ~ in(sK15(sK8),X0) ),
inference(superposition,[status(thm)],[c_411956,c_369080]) ).
tcf(c_413836,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,sK8)
| ~ subset(sK15(sK8),X1)
| ~ in(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_369016]) ).
tcf(c_413838,plain,
! [X0: $i] :
( subset(set_intersection2(sK8,sK15(sK8)),X0)
| in(sK10(sK15(sK8),X0),sK8) ),
inference(superposition,[status(thm)],[c_411956,c_368986]) ).
tcf(c_413839,plain,
subset(sK15(sK8),sK8),
inference(superposition,[status(thm)],[c_411956,c_380919]) ).
tcf(c_413840,plain,
subset(sK15(sK8),sK15(sK8)),
inference(superposition,[status(thm)],[c_411956,c_380850]) ).
tcf(c_413841,plain,
! [X0: $i] :
( subset(set_intersection2(sK8,sK15(sK8)),X0)
| in(sK10(sK15(sK8),X0),sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_368985]) ).
tcf(c_413842,plain,
! [X0: $i] :
( ~ empty(sK15(sK8))
| ~ in(X0,sK8)
| ~ in(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_368869]) ).
tcf(c_413843,plain,
! [X0: $i] :
( ( set_intersection2(sK8,sK15(sK8)) = X0 )
| ~ subset(X0,sK8)
| ~ subset(X0,sK15(sK8))
| ~ subset(sK15(sK8),X0) ),
inference(superposition,[status(thm)],[c_411956,c_368558]) ).
tcf(c_413844,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),sK15(sK8))
| in(sK2(set_intersection2(sK8,sK15(sK8)),X0,X1),X1)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_368503]) ).
tcf(c_413845,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),X1)
| in(sK2(set_intersection2(sK8,sK15(sK8)),X0,X1),sK15(sK8))
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_368503]) ).
tcf(c_413846,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),sK8)
| in(sK2(set_intersection2(sK8,sK15(sK8)),X0,X1),X1)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_368481]) ).
tcf(c_413847,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),X1)
| in(sK2(set_intersection2(sK8,sK15(sK8)),X0,X1),sK8)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_368481]) ).
tcf(c_413848,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = X1 )
| ~ in(sK2(sK15(sK8),X0,X1),sK8)
| ~ in(sK2(set_intersection2(sK8,sK15(sK8)),X0,X1),X1)
| ~ in(sK2(set_intersection2(sK8,sK15(sK8)),X0,X1),X0)
| ~ in(sK2(set_intersection2(sK8,sK15(sK8)),X0,X1),sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_368471]) ).
tcf(c_413850,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,sK15(sK8),X1),X1)
| in(sK12(X0,set_intersection2(sK8,sK15(sK8)),X1),sK8)
| ( relation_image(X0,set_intersection2(sK8,sK15(sK8))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_369303]) ).
tcf(c_413851,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,sK15(sK8),X1),sK8)
| in(sK11(X0,set_intersection2(sK8,sK15(sK8)),X1),X1)
| ( relation_image(X0,set_intersection2(sK8,sK15(sK8))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_369303]) ).
tcf(c_413852,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,sK15(sK8),X1),X1)
| in(sK12(X0,set_intersection2(sK8,sK15(sK8)),X1),sK15(sK8))
| ( relation_image(X0,set_intersection2(sK8,sK15(sK8))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_369302]) ).
tcf(c_413853,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,sK15(sK8),X1),sK15(sK8))
| in(sK11(X0,set_intersection2(sK8,sK15(sK8)),X1),X1)
| ( relation_image(X0,set_intersection2(sK8,sK15(sK8))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_369302]) ).
tcf(c_413854,plain,
! [X0: $i] :
( subset(X0,set_intersection2(sK8,sK15(sK8)))
| ~ in(sK10(X0,sK15(sK8)),sK8)
| ~ in(sK10(X0,set_intersection2(sK8,sK15(sK8))),sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_368972]) ).
tcf(c_413855,plain,
! [X0: $i] :
( element(X0,sK15(sK8))
| ~ in(X0,sK8)
| ~ in(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_368928]) ).
tcf(c_413856,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,set_intersection2(sK8,sK15(sK8)),X1),X1)
| in(apply(X0,sK7(X0,sK15(sK8),X1)),sK8)
| ( relation_inverse_image(X0,set_intersection2(sK8,sK15(sK8))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_368703]) ).
tcf(c_413857,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,sK15(sK8),X1),X1)
| in(apply(X0,sK7(X0,set_intersection2(sK8,sK15(sK8)),X1)),sK8)
| ( relation_inverse_image(X0,set_intersection2(sK8,sK15(sK8))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_368703]) ).
tcf(c_413858,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,set_intersection2(sK8,sK15(sK8)),X1),X1)
| in(apply(X0,sK7(X0,sK15(sK8),X1)),sK15(sK8))
| ( relation_inverse_image(X0,set_intersection2(sK8,sK15(sK8))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_368702]) ).
tcf(c_413859,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,sK15(sK8),X1),X1)
| in(apply(X0,sK7(X0,set_intersection2(sK8,sK15(sK8)),X1)),sK15(sK8))
| ( relation_inverse_image(X0,set_intersection2(sK8,sK15(sK8))) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_368702]) ).
tcf(c_413860,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,set_intersection2(sK8,sK15(sK8))) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,set_intersection2(sK8,sK15(sK8)),X1),X1)
| ~ in(apply(X0,sK7(X0,sK15(sK8),X1)),sK8)
| ~ in(sK7(X0,set_intersection2(sK8,sK15(sK8)),X1),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,set_intersection2(sK8,sK15(sK8)),X1)),sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_368654]) ).
tcf(c_413861,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),sK15(sK8))
| in(sK2(X0,set_intersection2(sK8,sK15(sK8)),X1),X1)
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_368504]) ).
tcf(c_413862,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),X1)
| in(sK2(X0,set_intersection2(sK8,sK15(sK8)),X1),sK15(sK8))
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_368504]) ).
tcf(c_413863,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),sK8)
| in(sK2(X0,set_intersection2(sK8,sK15(sK8)),X1),X1)
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_368482]) ).
tcf(c_413864,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),X1)
| in(sK2(X0,set_intersection2(sK8,sK15(sK8)),X1),sK8)
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_368482]) ).
tcf(c_413867,plain,
! [X0: $i] :
( in(X0,sK8)
| ~ in(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_58]) ).
tcf(c_413869,plain,
! [X0: $i] :
( subset(sK15(sK8),X0)
| ~ empty(sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_380845]) ).
tcf(c_413870,plain,
( function(sK15(sK8))
| ~ empty(sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_381376]) ).
tcf(c_413871,plain,
( relation(sK15(sK8))
| ~ empty(sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_381375]) ).
tcf(c_413873,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,sK15(sK8),X0),sK8)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(sK8,sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_411956,c_369598]) ).
tcf(c_413874,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,sK15(sK8),X0),sK15(sK8))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(sK8,sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_411956,c_369597]) ).
tcf(c_413875,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK8)
| ( set_intersection2(sK8,sK15(sK8)) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(sK8,sK15(sK8)))) = sK11(X0,X1,set_intersection2(sK8,sK15(sK8))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_369440]) ).
tcf(c_413876,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK15(sK8))
| ( set_intersection2(sK8,sK15(sK8)) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(sK8,sK15(sK8)))) = sK11(X0,X1,set_intersection2(sK8,sK15(sK8))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_369439]) ).
tcf(c_413877,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK8)
| in(sK12(X0,X1,set_intersection2(sK8,sK15(sK8))),X1)
| ( set_intersection2(sK8,sK15(sK8)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_369311]) ).
tcf(c_413878,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,sK15(sK8)),X1)
| in(sK11(X0,X1,set_intersection2(sK8,sK15(sK8))),sK8)
| ( set_intersection2(sK8,sK15(sK8)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_369311]) ).
tcf(c_413879,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK15(sK8))
| in(sK12(X0,X1,set_intersection2(sK8,sK15(sK8))),X1)
| ( set_intersection2(sK8,sK15(sK8)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_369310]) ).
tcf(c_413880,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,sK15(sK8)),X1)
| in(sK11(X0,X1,set_intersection2(sK8,sK15(sK8))),sK15(sK8))
| ( set_intersection2(sK8,sK15(sK8)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_369310]) ).
tcf(c_413881,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,sK15(sK8)),relation_dom(X0))
| in(sK11(X0,X1,set_intersection2(sK8,sK15(sK8))),sK8)
| ( set_intersection2(sK8,sK15(sK8)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_369210]) ).
tcf(c_413882,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK8)
| in(sK12(X0,X1,set_intersection2(sK8,sK15(sK8))),relation_dom(X0))
| ( set_intersection2(sK8,sK15(sK8)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_369210]) ).
tcf(c_413883,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,sK15(sK8)),relation_dom(X0))
| in(sK11(X0,X1,set_intersection2(sK8,sK15(sK8))),sK15(sK8))
| ( set_intersection2(sK8,sK15(sK8)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_369209]) ).
tcf(c_413884,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK15(sK8))
| in(sK12(X0,X1,set_intersection2(sK8,sK15(sK8))),relation_dom(X0))
| ( set_intersection2(sK8,sK15(sK8)) = relation_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_369209]) ).
tcf(c_413885,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_inverse_image(X0,sK15(sK8)))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),sK8)
| ~ in(apply(X0,X1),sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_368735]) ).
tcf(c_413886,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,set_intersection2(sK8,sK15(sK8))),sK8)
| in(apply(X0,sK7(X0,X1,sK15(sK8))),X1)
| ( set_intersection2(sK8,sK15(sK8)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_368701]) ).
tcf(c_413887,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),sK8)
| in(apply(X0,sK7(X0,X1,set_intersection2(sK8,sK15(sK8)))),X1)
| ( set_intersection2(sK8,sK15(sK8)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_368701]) ).
tcf(c_413888,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK7(X0,X1,sK15(sK8))),X1)
| in(sK7(X0,X1,set_intersection2(sK8,sK15(sK8))),sK15(sK8))
| ( set_intersection2(sK8,sK15(sK8)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_368700]) ).
tcf(c_413889,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),sK15(sK8))
| in(apply(X0,sK7(X0,X1,set_intersection2(sK8,sK15(sK8)))),X1)
| ( set_intersection2(sK8,sK15(sK8)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_368700]) ).
tcf(c_413890,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),relation_dom(X0))
| in(sK7(X0,X1,set_intersection2(sK8,sK15(sK8))),sK8)
| ( set_intersection2(sK8,sK15(sK8)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_368673]) ).
tcf(c_413891,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),sK8)
| in(sK7(X0,X1,set_intersection2(sK8,sK15(sK8))),relation_dom(X0))
| ( set_intersection2(sK8,sK15(sK8)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_368673]) ).
tcf(c_413892,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),relation_dom(X0))
| in(sK7(X0,X1,set_intersection2(sK8,sK15(sK8))),sK15(sK8))
| ( set_intersection2(sK8,sK15(sK8)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_368672]) ).
tcf(c_413893,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),sK15(sK8))
| in(sK7(X0,X1,set_intersection2(sK8,sK15(sK8))),relation_dom(X0))
| ( set_intersection2(sK8,sK15(sK8)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_368672]) ).
tcf(c_413894,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),X0)
| in(sK2(X0,X1,set_intersection2(sK8,sK15(sK8))),sK15(sK8))
| ( set_intersection2(sK8,sK15(sK8)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411956,c_368506]) ).
tcf(c_413895,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),sK15(sK8))
| in(sK2(X0,X1,set_intersection2(sK8,sK15(sK8))),X0)
| ( set_intersection2(sK8,sK15(sK8)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411956,c_368506]) ).
tcf(c_413896,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),X1)
| in(sK2(X0,X1,set_intersection2(sK8,sK15(sK8))),sK15(sK8))
| ( set_intersection2(sK8,sK15(sK8)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411956,c_368505]) ).
tcf(c_413897,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),sK15(sK8))
| in(sK2(X0,X1,set_intersection2(sK8,sK15(sK8))),X1)
| ( set_intersection2(sK8,sK15(sK8)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411956,c_368505]) ).
tcf(c_413898,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),X0)
| in(sK2(X0,X1,set_intersection2(sK8,sK15(sK8))),sK8)
| ( set_intersection2(sK8,sK15(sK8)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411956,c_368484]) ).
tcf(c_413899,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),sK8)
| in(sK2(X0,X1,set_intersection2(sK8,sK15(sK8))),X0)
| ( set_intersection2(sK8,sK15(sK8)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411956,c_368484]) ).
tcf(c_413900,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),X1)
| in(sK2(X0,X1,set_intersection2(sK8,sK15(sK8))),sK8)
| ( set_intersection2(sK8,sK15(sK8)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411956,c_368483]) ).
tcf(c_413901,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),sK8)
| in(sK2(X0,X1,set_intersection2(sK8,sK15(sK8))),X1)
| ( set_intersection2(sK8,sK15(sK8)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_411956,c_368483]) ).
tcf(c_413910,plain,
( empty(sK15(sK8))
| in(sK16(sK15(sK8)),sK8) ),
inference(light_normalisation,[status(thm)],[c_413830,c_411956]) ).
tcf(c_413915,plain,
( empty(sK15(sK8))
| element(sK16(sK15(sK8)),sK8) ),
inference(light_normalisation,[status(thm)],[c_413826,c_411956]) ).
tcf(c_413918,plain,
( empty(sK15(sK8))
| in(sK16(sK15(sK8)),sK15(sK8)) ),
inference(light_normalisation,[status(thm)],[c_413831,c_411956]) ).
tcf(c_413921,plain,
( empty(sK15(sK8))
| element(sK16(sK15(sK8)),sK15(sK8)) ),
inference(light_normalisation,[status(thm)],[c_413828,c_411956]) ).
tcf(c_413924,plain,
! [X0: $i] :
( subset(sK15(sK8),X0)
| in(sK10(sK15(sK8),X0),sK8) ),
inference(light_normalisation,[status(thm)],[c_413838,c_411956]) ).
tcf(c_413933,plain,
! [X0: $i] :
( subset(sK15(sK8),X0)
| in(sK10(sK15(sK8),X0),sK15(sK8)) ),
inference(light_normalisation,[status(thm)],[c_413841,c_411956]) ).
tcf(c_413947,plain,
! [X0: $i] :
( ( sK15(sK8) = X0 )
| ~ subset(X0,sK8)
| ~ subset(X0,sK15(sK8))
| ~ subset(sK15(sK8),X0) ),
inference(light_normalisation,[status(thm)],[c_413843,c_411956]) ).
tcf(c_413952,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,sK15(sK8),X0),sK8)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(sK8))) ),
inference(light_normalisation,[status(thm)],[c_413873,c_411956]) ).
tcf(c_413957,plain,
! [X0: $i,X1: $i] :
( in(sK13(X1,sK15(sK8),X0),sK15(sK8))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK15(sK8))) ),
inference(light_normalisation,[status(thm)],[c_413874,c_411956]) ).
tcf(c_413962,plain,
! [X0: $i] :
( subset(X0,sK15(sK8))
| ~ in(sK10(X0,sK15(sK8)),sK8)
| ~ in(sK10(X0,sK15(sK8)),sK15(sK8)) ),
inference(light_normalisation,[status(thm)],[c_413854,c_411956]) ).
tcf(c_413966,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),sK8)
| in(sK2(X0,X1,sK15(sK8)),X1)
| ( set_intersection2(X0,X1) = sK15(sK8) ) ),
inference(light_normalisation,[status(thm)],[c_413901,c_411956]) ).
tcf(c_413971,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),sK8)
| in(sK2(X0,X1,sK15(sK8)),X0)
| ( set_intersection2(X0,X1) = sK15(sK8) ) ),
inference(light_normalisation,[status(thm)],[c_413899,c_411956]) ).
tcf(c_413976,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),sK8)
| in(sK2(X0,sK15(sK8),X1),X1)
| ( set_intersection2(X0,sK15(sK8)) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_413864,c_411956]) ).
tcf(c_413981,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),sK8)
| in(sK2(sK15(sK8),X0,X1),X1)
| ( set_intersection2(sK15(sK8),X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_413847,c_411956]) ).
tcf(c_413986,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),X1)
| in(sK2(X0,X1,sK15(sK8)),sK15(sK8))
| ( set_intersection2(X0,X1) = sK15(sK8) ) ),
inference(light_normalisation,[status(thm)],[c_413897,c_411956]) ).
tcf(c_413991,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),X0)
| in(sK2(X0,X1,sK15(sK8)),sK15(sK8))
| ( set_intersection2(X0,X1) = sK15(sK8) ) ),
inference(light_normalisation,[status(thm)],[c_413895,c_411956]) ).
tcf(c_413996,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),X1)
| in(sK2(X0,sK15(sK8),X1),sK15(sK8))
| ( set_intersection2(X0,sK15(sK8)) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_413862,c_411956]) ).
tcf(c_414001,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),X1)
| in(sK2(sK15(sK8),X0,X1),sK15(sK8))
| ( set_intersection2(sK15(sK8),X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_413845,c_411956]) ).
tcf(c_414012,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK8)
| in(sK12(X0,X1,sK15(sK8)),X1)
| ( relation_image(X0,X1) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_413878,c_411956]) ).
tcf(c_414019,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,sK15(sK8),X1),sK8)
| in(sK11(X0,sK15(sK8),X1),X1)
| ( relation_image(X0,sK15(sK8)) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_413851,c_411956]) ).
tcf(c_414026,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),sK8)
| in(sK7(X0,X1,sK15(sK8)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_413891,c_411956]) ).
tcf(c_414033,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK8)
| in(sK12(X0,X1,sK15(sK8)),relation_dom(X0))
| ( relation_image(X0,X1) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_413882,c_411956]) ).
tcf(c_414040,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,sK15(sK8)),X1)
| in(sK11(X0,X1,sK15(sK8)),sK15(sK8))
| ( relation_image(X0,X1) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_413880,c_411956]) ).
tcf(c_414047,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,sK15(sK8),X1),X1)
| in(sK12(X0,sK15(sK8),X1),sK15(sK8))
| ( relation_image(X0,sK15(sK8)) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_413853,c_411956]) ).
tcf(c_414054,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),sK15(sK8))
| in(sK7(X0,X1,sK15(sK8)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_413893,c_411956]) ).
tcf(c_414061,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),sK8)
| in(apply(X0,sK7(X0,X1,sK15(sK8))),X1)
| ( relation_inverse_image(X0,X1) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_413887,c_411956]) ).
tcf(c_414068,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK15(sK8))
| in(sK12(X0,X1,sK15(sK8)),relation_dom(X0))
| ( relation_image(X0,X1) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_413884,c_411956]) ).
tcf(c_414075,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,sK15(sK8),X1),X1)
| in(apply(X0,sK7(X0,sK15(sK8),X1)),sK8)
| ( relation_inverse_image(X0,sK15(sK8)) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_413857,c_411956]) ).
tcf(c_414082,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),sK15(sK8))
| in(apply(X0,sK7(X0,X1,sK15(sK8))),X1)
| ( relation_inverse_image(X0,X1) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_413889,c_411956]) ).
tcf(c_414089,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,sK15(sK8),X1),X1)
| in(apply(X0,sK7(X0,sK15(sK8),X1)),sK15(sK8))
| ( relation_inverse_image(X0,sK15(sK8)) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_413859,c_411956]) ).
tcf(c_414096,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK8)
| ( relation_image(X0,X1) = sK15(sK8) )
| ( apply(X0,sK12(X0,X1,sK15(sK8))) = sK11(X0,X1,sK15(sK8)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_413875,c_411956]) ).
tcf(c_414102,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK15(sK8))
| ( relation_image(X0,X1) = sK15(sK8) )
| ( apply(X0,sK12(X0,X1,sK15(sK8))) = sK11(X0,X1,sK15(sK8)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(light_normalisation,[status(thm)],[c_413876,c_411956]) ).
tcf(c_414108,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK15(sK8),X0) = X1 )
| ~ in(sK2(sK15(sK8),X0,X1),sK8)
| ~ in(sK2(sK15(sK8),X0,X1),X1)
| ~ in(sK2(sK15(sK8),X0,X1),X0)
| ~ in(sK2(sK15(sK8),X0,X1),sK15(sK8)) ),
inference(light_normalisation,[status(thm)],[c_413848,c_411956]) ).
tcf(c_414114,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,sK15(sK8)) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK7(X0,sK15(sK8),X1),X1)
| ~ in(sK7(X0,sK15(sK8),X1),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,sK15(sK8),X1)),sK8)
| ~ in(apply(X0,sK7(X0,sK15(sK8),X1)),sK15(sK8)) ),
inference(light_normalisation,[status(thm)],[c_413860,c_411956]) ).
tcf(c_414437,plain,
set_intersection2(sK15(sK8),sK8) = sK15(sK8),
inference(superposition,[status(thm)],[c_413839,c_381110]) ).
tcf(c_414441,plain,
( ( sK15(sK8) = sK8 )
| ~ subset(sK8,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_413839,c_60]) ).
tcf(c_414476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| ~ empty(set_intersection2(X2,X3))
| ~ subset(relation_image(X0,X1),X3)
| ~ subset(relation_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_65,c_369797]) ).
tcf(c_414477,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,X2)
| ~ in(X1,relation_dom(X0))
| ~ empty(relation_image(X0,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_67,c_369797]) ).
tcf(c_414478,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_68,c_369797]) ).
tcf(c_414479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X1,sK13(X1,X2,sK10(relation_image(X1,X2),X3))) = sK10(relation_image(X1,X2),X3) )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_369666,c_369797]) ).
tcf(c_414480,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(X2)
| ~ subset(empty_set,X2)
| ~ in(X0,X1)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_375097,c_369797]) ).
tcf(c_414491,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(X2)
| ~ subset(empty_set,X2)
| ~ in(X0,empty_set)
| ~ in(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_414480,c_373108]) ).
tcf(c_414515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(relation_image(X0,X2),X3,X4),X4)
| ( set_intersection2(relation_image(X0,X2),X3) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368927,c_369798]) ).
tcf(c_414516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X0,X2),X3,X4),X4)
| ( set_intersection2(relation_image(X0,X2),X3) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_55,c_369798]) ).
tcf(c_414517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,relation_image(X0,X3),X4),X4)
| ( set_intersection2(X2,relation_image(X0,X3)) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368926,c_369798]) ).
tcf(c_414518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,relation_image(X0,X3),X4),X4)
| ( set_intersection2(X2,relation_image(X0,X3)) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_56,c_369798]) ).
tcf(c_414519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,relation_image(X0,X2)),X4)
| ( relation_image(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368925,c_369798]) ).
tcf(c_414520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,relation_image(X0,X2)),X3)
| ( relation_image(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368924,c_369798]) ).
tcf(c_414521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,X3) = set_intersection2(X2,X4) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368865,c_369798]) ).
tcf(c_414522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_image(X0,X2)),X4)
| ( relation_image(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_56,c_369798]) ).
tcf(c_414523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_image(X0,X2)),X3)
| ( relation_image(X0,X2) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_55,c_369798]) ).
tcf(c_414524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,relation_image(X0,X3),X4),X4)
| ( relation_inverse_image(X2,relation_image(X0,X3)) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368931,c_369798]) ).
tcf(c_414525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,relation_image(X0,X3),X4),X4)
| ( relation_inverse_image(X2,relation_image(X0,X3)) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_85,c_369798]) ).
tcf(c_414526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(apply(X2,sK7(X2,X3,relation_image(X0,X4))),X3)
| ( relation_inverse_image(X2,X3) = relation_image(X0,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368930,c_369798]) ).
tcf(c_414527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,X3,relation_image(X0,X4)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = relation_image(X0,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368929,c_369798]) ).
tcf(c_414528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X2,X3) = relation_image(X0,X4) )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368871,c_369798]) ).
tcf(c_414529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X2,X3) = relation_image(X0,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_dom(X2))
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_379483,c_369798]) ).
tcf(c_414530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X3,relation_image(X0,X4)),relation_inverse_image(X2,X3))
| ( relation_inverse_image(X2,X3) = relation_image(X0,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_375319,c_369798]) ).
tcf(c_414531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,X3,relation_image(X0,X4))),X3)
| ( relation_inverse_image(X2,X3) = relation_image(X0,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_85,c_369798]) ).
tcf(c_414532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X3,relation_image(X0,X4)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = relation_image(X0,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_84,c_369798]) ).
tcf(c_414533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_image(X0,X2),X3)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_95,c_369798]) ).
tcf(c_414534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,X4) = relation_image(X2,X3) )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369301,c_369798]) ).
tcf(c_414535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X2,X4,relation_image(X0,X3)),X4)
| ( relation_image(X0,X3) = relation_image(X2,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369300,c_369798]) ).
tcf(c_414536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,X3) = relation_image(X2,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_dom(X2))
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_386602,c_369798]) ).
tcf(c_414537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X2,X4,relation_image(X0,X3)),relation_dom(X2))
| ( relation_image(X0,X3) = relation_image(X2,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369215,c_369798]) ).
tcf(c_414538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,X4) = relation_image(X2,X3) )
| ( apply(X2,sK12(X2,X3,relation_image(X0,X4))) = sK11(X2,X3,relation_image(X0,X4)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_108,c_369798]) ).
tcf(c_414539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X4,relation_image(X0,X3)),X4)
| ( relation_image(X0,X3) = relation_image(X2,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_107,c_369798]) ).
tcf(c_414540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X4,relation_image(X0,X3)),relation_dom(X2))
| ( relation_image(X0,X3) = relation_image(X2,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_106,c_369798]) ).
tcf(c_414541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,relation_image(X0,X3),X4),X4)
| ( relation_image(X2,relation_image(X0,X3)) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369308,c_369798]) ).
tcf(c_414542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,relation_image(X0,X3),X4),X4)
| ( relation_image(X2,relation_image(X0,X3)) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_107,c_369798]) ).
tcf(c_414543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X3)
| ~ subset(relation_dom(X1),X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_109,c_369798]) ).
tcf(c_414544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ empty(X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(relation_dom(X2),X4)
| ~ in(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_111,c_369798]) ).
tcf(c_414545,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(relation_image(X0,X2))
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368976,c_369798]) ).
tcf(c_414546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(set_intersection2(relation_image(X0,X2),X3),X4)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368986,c_369798]) ).
tcf(c_414547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(set_intersection2(X2,relation_image(X0,X3)),X4)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368985,c_369798]) ).
tcf(c_414549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(set_intersection2(X2,relation_image(X0,X3)))
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370750,c_369798]) ).
tcf(c_414551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(set_intersection2(relation_image(X0,X2),X3))
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370751,c_369798]) ).
tcf(c_414552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(X0,X4)
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369021,c_369798]) ).
tcf(c_414553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X0)
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370747,c_369798]) ).
tcf(c_414554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(relation_inverse_image(X2,relation_image(X0,X3)),X4)
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368987,c_369798]) ).
tcf(c_414555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_image(X0,X4),X5,X2),X3)
| ( set_intersection2(relation_image(X0,X4),X5) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369015,c_369798]) ).
tcf(c_414556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X0),X4)
| ( set_intersection2(X4,X5) = X0 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369015,c_369798]) ).
tcf(c_414557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X0),X5)
| ( set_intersection2(X4,X5) = X0 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369014,c_369798]) ).
tcf(c_414558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X0,X3),X4) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368868,c_369798]) ).
tcf(c_414559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_image(X0,X2),X3,set_intersection2(X4,X5)),X5)
| ( set_intersection2(relation_image(X0,X2),X3) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368506,c_369798]) ).
tcf(c_414560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_image(X0,X2),X3,set_intersection2(X4,X5)),X4)
| ( set_intersection2(relation_image(X0,X2),X3) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368484,c_369798]) ).
tcf(c_414561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,set_intersection2(X2,relation_image(X0,X3))),X4)
| ( set_intersection2(X2,relation_image(X0,X3)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368506,c_369798]) ).
tcf(c_414562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,set_intersection2(X2,relation_image(X0,X3))),X5)
| ( set_intersection2(X2,relation_image(X0,X3)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368505,c_369798]) ).
tcf(c_414563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,set_intersection2(relation_image(X0,X2),X3)),X4)
| ( set_intersection2(relation_image(X0,X2),X3) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368484,c_369798]) ).
tcf(c_414564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,set_intersection2(relation_image(X0,X2),X3)),X5)
| ( set_intersection2(relation_image(X0,X2),X3) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368483,c_369798]) ).
tcf(c_414565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,relation_inverse_image(X2,relation_image(X0,X3))),X4)
| ( relation_inverse_image(X2,relation_image(X0,X3)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368816,c_369798]) ).
tcf(c_414566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,relation_inverse_image(X2,relation_image(X0,X3))),X5)
| ( relation_inverse_image(X2,relation_image(X0,X3)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368815,c_369798]) ).
tcf(c_414567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK2(relation_image(X0,X3),X4,relation_inverse_image(X2,X5))),X5)
| ( set_intersection2(relation_image(X0,X3),X4) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368816,c_369798]) ).
tcf(c_414568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_image(X0,X3),X4,relation_inverse_image(X2,X5)),relation_dom(X2))
| ( set_intersection2(relation_image(X0,X3),X4) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368760,c_369798]) ).
tcf(c_414569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,X5,relation_image(X0,X4)),X3)
| ( relation_image(X0,X4) = set_intersection2(X2,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369012,c_369798]) ).
tcf(c_414570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,X4,X5),X5)
| ( set_intersection2(X0,X4) = X5 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369012,c_369798]) ).
tcf(c_414571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,relation_image(X0,X5)),X3)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368503,c_369798]) ).
tcf(c_414572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,relation_image(X0,X5)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368481,c_369798]) ).
tcf(c_414573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,relation_image(X0,X3)),X4,X5),X5)
| ( set_intersection2(set_intersection2(X2,relation_image(X0,X3)),X4) = X5 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368503,c_369798]) ).
tcf(c_414574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X0,X2),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4) = X5 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368481,c_369798]) ).
tcf(c_414575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK2(relation_inverse_image(X2,X3),X4,relation_image(X0,X5))),X3)
| ( set_intersection2(relation_inverse_image(X2,X3),X4) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368813,c_369798]) ).
tcf(c_414576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_inverse_image(X2,X3),X4,relation_image(X0,X5)),relation_dom(X2))
| ( set_intersection2(relation_inverse_image(X2,X3),X4) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368757,c_369798]) ).
tcf(c_414577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_inverse_image(X2,relation_image(X0,X3)),X4,X5),X5)
| ( set_intersection2(relation_inverse_image(X2,relation_image(X0,X3)),X4) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368813,c_369798]) ).
tcf(c_414578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_image(X0,X2),X3) = relation_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368448,c_369798]) ).
tcf(c_414580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,relation_image(X0,X5),X2),X3)
| ( set_intersection2(X4,relation_image(X0,X5)) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369014,c_369798]) ).
tcf(c_414581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,relation_image(X0,X4)) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368867,c_369798]) ).
tcf(c_414582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,relation_image(X0,X3),set_intersection2(X4,X5)),X5)
| ( set_intersection2(X2,relation_image(X0,X3)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368505,c_369798]) ).
tcf(c_414583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,relation_image(X0,X3),set_intersection2(X4,X5)),X4)
| ( set_intersection2(X2,relation_image(X0,X3)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368483,c_369798]) ).
tcf(c_414584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK2(X3,relation_image(X0,X4),relation_inverse_image(X2,X5))),X5)
| ( set_intersection2(X3,relation_image(X0,X4)) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368815,c_369798]) ).
tcf(c_414585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,relation_image(X0,X4),relation_inverse_image(X2,X5)),relation_dom(X2))
| ( set_intersection2(X3,relation_image(X0,X4)) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368759,c_369798]) ).
tcf(c_414586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X5,X2,relation_image(X0,X4)),X3)
| ( relation_image(X0,X4) = set_intersection2(X5,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369013,c_369798]) ).
tcf(c_414587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X0,X5),X5)
| ( set_intersection2(X4,X0) = X5 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369013,c_369798]) ).
tcf(c_414588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X0,X3) = set_intersection2(X4,X2) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368866,c_369798]) ).
tcf(c_414589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,X4),relation_image(X0,X5)),X4)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368504,c_369798]) ).
tcf(c_414590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,X4),relation_image(X0,X5)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368482,c_369798]) ).
tcf(c_414591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,relation_image(X0,X4)),X5),X5)
| ( set_intersection2(X2,set_intersection2(X3,relation_image(X0,X4))) = X5 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368504,c_369798]) ).
tcf(c_414592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(relation_image(X0,X3),X4),X5),X5)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X3),X4)) = X5 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368482,c_369798]) ).
tcf(c_414593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,relation_inverse_image(X2,relation_image(X0,X4)),X5),X5)
| ( set_intersection2(X3,relation_inverse_image(X2,relation_image(X0,X4))) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368814,c_369798]) ).
tcf(c_414594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK2(X3,relation_inverse_image(X2,X4),relation_image(X0,X5))),X4)
| ( set_intersection2(X3,relation_inverse_image(X2,X4)) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368814,c_369798]) ).
tcf(c_414595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,relation_inverse_image(X2,X4),relation_image(X0,X5)),relation_dom(X2))
| ( set_intersection2(X3,relation_inverse_image(X2,X4)) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368758,c_369798]) ).
tcf(c_414596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,relation_image(X0,X3)) = relation_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368460,c_369798]) ).
tcf(c_414597,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X0,X2) = empty_set )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_372467,c_369798]) ).
tcf(c_414598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ empty(X5)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(relation_dom(X3),X5)
| ~ subset(X2,relation_image(X3,X4))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_369798]) ).
tcf(c_414599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ empty(X5)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X1),X5)
| ~ in(X3,relation_image(X0,X4))
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_369798]) ).
tcf(c_414600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ empty(X5)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(relation_dom(X3),X5)
| ~ in(X0,relation_image(X1,set_intersection2(X2,relation_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369597,c_369798]) ).
tcf(c_414601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ empty(X5)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(relation_dom(X2),X5)
| ~ in(X0,relation_image(X1,set_intersection2(relation_image(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_369598,c_369798]) ).
tcf(c_414602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ empty(X5)
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(relation_dom(X3),X5)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,relation_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369599,c_369798]) ).
tcf(c_414603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(relation_image(X2,X3),X4) = relation_image(X0,X5) )
| ( apply(X2,sK13(X2,X3,sK2(relation_image(X2,X3),X4,relation_image(X0,X5)))) = sK2(relation_image(X2,X3),X4,relation_image(X0,X5)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369659,c_369798]) ).
tcf(c_414604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X4,relation_image(X2,X3)) = relation_image(X0,X5) )
| ( apply(X2,sK13(X2,X3,sK2(X4,relation_image(X2,X3),relation_image(X0,X5)))) = sK2(X4,relation_image(X2,X3),relation_image(X0,X5)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369660,c_369798]) ).
tcf(c_414605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X4,relation_image(X0,X5)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(X4,relation_image(X0,X5),relation_image(X2,X3)))) = sK2(X4,relation_image(X0,X5),relation_image(X2,X3)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369661,c_369798]) ).
tcf(c_414606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(relation_image(X0,X4),X5) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(relation_image(X0,X4),X5,relation_image(X2,X3)))) = sK2(relation_image(X0,X4),X5,relation_image(X2,X3)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369662,c_369798]) ).
tcf(c_414607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X4,X2,relation_image(X0,X5)),X3)
| ( relation_image(X0,X5) = relation_image(X4,X2) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369299,c_369798]) ).
tcf(c_414608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X4,X0,X5),X5)
| ( relation_image(X4,X0) = X5 )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369299,c_369798]) ).
tcf(c_414609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,set_intersection2(X3,X4),relation_image(X0,X5)),X3)
| ( relation_image(X2,set_intersection2(X3,X4)) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369303,c_369798]) ).
tcf(c_414610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,set_intersection2(X3,X4),relation_image(X0,X5)),X4)
| ( relation_image(X2,set_intersection2(X3,X4)) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369302,c_369798]) ).
tcf(c_414611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X2,set_intersection2(X3,relation_image(X0,X4)),X5),X5)
| ( relation_image(X2,set_intersection2(X3,relation_image(X0,X4))) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369302,c_369798]) ).
tcf(c_414612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X2,set_intersection2(relation_image(X0,X3),X4),X5),X5)
| ( relation_image(X2,set_intersection2(relation_image(X0,X3),X4)) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369303,c_369798]) ).
tcf(c_414613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,relation_inverse_image(X3,X4),relation_image(X0,X5)),relation_dom(X3))
| ( relation_image(X2,relation_inverse_image(X3,X4)) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369305,c_369798]) ).
tcf(c_414614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X3,sK12(X2,relation_inverse_image(X3,X4),relation_image(X0,X5))),X4)
| ( relation_image(X2,relation_inverse_image(X3,X4)) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369304,c_369798]) ).
tcf(c_414615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X2,relation_inverse_image(X3,relation_image(X0,X4)),X5),X5)
| ( relation_image(X2,relation_inverse_image(X3,relation_image(X0,X4))) = X5 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369304,c_369798]) ).
tcf(c_414616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_image(X2,relation_image(X3,X4)) = relation_image(X0,X5) )
| ( apply(X3,sK13(X3,X4,sK12(X2,relation_image(X3,X4),relation_image(X0,X5)))) = sK12(X2,relation_image(X3,X4),relation_image(X0,X5)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369670,c_369798]) ).
tcf(c_414617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_image(X4,X5) = X0 )
| ( apply(X4,sK12(X4,X5,X0)) = sK11(X4,X5,X0) )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369436,c_369798]) ).
tcf(c_414618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X4,X5,X0),X5)
| ( relation_image(X4,X5) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369307,c_369798]) ).
tcf(c_414619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X4,X5,X0),relation_dom(X4))
| ( relation_image(X4,X5) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369206,c_369798]) ).
tcf(c_414620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X4,relation_image(X0,X5),X2),X3)
| ( relation_image(X4,relation_image(X0,X5)) = X2 )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369307,c_369798]) ).
tcf(c_414621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X2,relation_image(X0,X4)) = X3 )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369309,c_369798]) ).
tcf(c_414622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X2,relation_image(X0,X3),set_intersection2(X4,X5)),X4)
| ( relation_image(X2,relation_image(X0,X3)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369311,c_369798]) ).
tcf(c_414623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X2,relation_image(X0,X3),set_intersection2(X4,X5)),X5)
| ( relation_image(X2,relation_image(X0,X3)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369310,c_369798]) ).
tcf(c_414624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X4,relation_image(X0,X5)) = relation_image(X2,X3) )
| ( apply(X2,sK12(X2,X3,set_intersection2(X4,relation_image(X0,X5)))) = sK11(X2,X3,set_intersection2(X4,relation_image(X0,X5))) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369439,c_369798]) ).
tcf(c_414625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X5,set_intersection2(X3,relation_image(X0,X4))),X5)
| ( set_intersection2(X3,relation_image(X0,X4)) = relation_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369310,c_369798]) ).
tcf(c_414626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X5,set_intersection2(X3,relation_image(X0,X4))),relation_dom(X2))
| ( set_intersection2(X3,relation_image(X0,X4)) = relation_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369209,c_369798]) ).
tcf(c_414627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(relation_image(X0,X4),X5) = relation_image(X2,X3) )
| ( apply(X2,sK12(X2,X3,set_intersection2(relation_image(X0,X4),X5))) = sK11(X2,X3,set_intersection2(relation_image(X0,X4),X5)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369440,c_369798]) ).
tcf(c_414628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X5,set_intersection2(relation_image(X0,X3),X4)),X5)
| ( set_intersection2(relation_image(X0,X3),X4) = relation_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369311,c_369798]) ).
tcf(c_414629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X5,set_intersection2(relation_image(X0,X3),X4)),relation_dom(X2))
| ( set_intersection2(relation_image(X0,X3),X4) = relation_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369210,c_369798]) ).
tcf(c_414630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X5,relation_inverse_image(X3,relation_image(X0,X4))),X5)
| ( relation_inverse_image(X3,relation_image(X0,X4)) = relation_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369312,c_369798]) ).
tcf(c_414631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X5,relation_inverse_image(X3,relation_image(X0,X4))),relation_dom(X2))
| ( relation_inverse_image(X3,relation_image(X0,X4)) = relation_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369211,c_369798]) ).
tcf(c_414632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X2,relation_image(X0,X4),relation_inverse_image(X3,X5)),relation_dom(X3))
| ( relation_image(X2,relation_image(X0,X4)) = relation_inverse_image(X3,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369313,c_369798]) ).
tcf(c_414633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X3,sK11(X2,relation_image(X0,X4),relation_inverse_image(X3,X5))),X5)
| ( relation_image(X2,relation_image(X0,X4)) = relation_inverse_image(X3,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369312,c_369798]) ).
tcf(c_414634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_image(X2,relation_image(X0,X5)) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK11(X2,relation_image(X0,X5),relation_image(X3,X4)))) = sK11(X2,relation_image(X0,X5),relation_image(X3,X4)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369668,c_369798]) ).
tcf(c_414635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X4,X5,X0),relation_dom(X4))
| ( relation_inverse_image(X4,X5) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369020,c_369798]) ).
tcf(c_414636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X4,sK7(X4,X5,X0)),X5)
| ( relation_inverse_image(X4,X5) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369019,c_369798]) ).
tcf(c_414637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK7(X2,X5,set_intersection2(X3,relation_image(X0,X4)))),X5)
| ( set_intersection2(X3,relation_image(X0,X4)) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368700,c_369798]) ).
tcf(c_414638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,X5,set_intersection2(X3,relation_image(X0,X4))),relation_dom(X2))
| ( set_intersection2(X3,relation_image(X0,X4)) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368672,c_369798]) ).
tcf(c_414639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK7(X2,X5,set_intersection2(relation_image(X0,X3),X4))),X5)
| ( set_intersection2(relation_image(X0,X3),X4) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368701,c_369798]) ).
tcf(c_414640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,X5,set_intersection2(relation_image(X0,X3),X4)),relation_dom(X2))
| ( set_intersection2(relation_image(X0,X3),X4) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368673,c_369798]) ).
tcf(c_414641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,X5,relation_inverse_image(X3,relation_image(X0,X4))),relation_dom(X2))
| ( relation_inverse_image(X3,relation_image(X0,X4)) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368819,c_369798]) ).
tcf(c_414642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK7(X2,X5,relation_inverse_image(X3,relation_image(X0,X4)))),X5)
| ( relation_inverse_image(X3,relation_image(X0,X4)) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368818,c_369798]) ).
tcf(c_414643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,X4,relation_image(X2,X5)),X1)
| ( relation_inverse_image(X0,X4) = relation_image(X2,X5) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X2),X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_369798]) ).
tcf(c_414644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,X4,X5),X5)
| ( relation_inverse_image(X0,X4) = X5 )
| ~ empty(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X1),X3)
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369017,c_369798]) ).
tcf(c_414645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X0,X4,relation_image(X2,X5)),X1)
| ( relation_image(X0,X4) = relation_image(X2,X5) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X2),X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_369798]) ).
tcf(c_414646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X0,X4,X5),X5)
| ( relation_image(X0,X4) = X5 )
| ~ empty(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X1),X3)
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369214,c_369798]) ).
tcf(c_414647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X4,relation_image(X0,X5),X2),X3)
| ( relation_inverse_image(X4,relation_image(X0,X5)) = X2 )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369019,c_369798]) ).
tcf(c_414648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X2,relation_image(X0,X4)) = X3 )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368872,c_369798]) ).
tcf(c_414649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,relation_image(X0,X3),set_intersection2(X4,X5)),X4)
| ( relation_inverse_image(X2,relation_image(X0,X3)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368701,c_369798]) ).
tcf(c_414650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,relation_image(X0,X3),set_intersection2(X4,X5)),X5)
| ( relation_inverse_image(X2,relation_image(X0,X3)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368700,c_369798]) ).
tcf(c_414651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X3,sK7(X2,relation_image(X0,X4),relation_inverse_image(X3,X5))),X5)
| ( relation_inverse_image(X2,relation_image(X0,X4)) = relation_inverse_image(X3,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368818,c_369798]) ).
tcf(c_414652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,relation_image(X0,X4),relation_inverse_image(X3,X5)),relation_dom(X3))
| ( relation_inverse_image(X2,relation_image(X0,X4)) = relation_inverse_image(X3,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368762,c_369798]) ).
tcf(c_414653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_inverse_image(X2,relation_image(X0,X5)) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK7(X2,relation_image(X0,X5),relation_image(X3,X4)))) = sK7(X2,relation_image(X0,X5),relation_image(X3,X4)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369664,c_369798]) ).
tcf(c_414654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X4,X0,X5),X5)
| ( relation_inverse_image(X4,X0) = X5 )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369018,c_369798]) ).
tcf(c_414655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X4,sK7(X4,X2,relation_image(X0,X5))),X3)
| ( relation_inverse_image(X4,X2) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369018,c_369798]) ).
tcf(c_414656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK7(X2,set_intersection2(X3,X4),relation_image(X0,X5))),X3)
| ( relation_inverse_image(X2,set_intersection2(X3,X4)) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368703,c_369798]) ).
tcf(c_414657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK7(X2,set_intersection2(X3,X4),relation_image(X0,X5))),X4)
| ( relation_inverse_image(X2,set_intersection2(X3,X4)) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368702,c_369798]) ).
tcf(c_414658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,set_intersection2(X3,relation_image(X0,X4)),X5),X5)
| ( relation_inverse_image(X2,set_intersection2(X3,relation_image(X0,X4))) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368702,c_369798]) ).
tcf(c_414659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,set_intersection2(relation_image(X0,X3),X4),X5),X5)
| ( relation_inverse_image(X2,set_intersection2(relation_image(X0,X3),X4)) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368703,c_369798]) ).
tcf(c_414660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X3,apply(X2,sK7(X2,relation_inverse_image(X3,X4),relation_image(X0,X5)))),X4)
| ( relation_inverse_image(X2,relation_inverse_image(X3,X4)) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368817,c_369798]) ).
tcf(c_414661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK7(X2,relation_inverse_image(X3,X4),relation_image(X0,X5))),relation_dom(X3))
| ( relation_inverse_image(X2,relation_inverse_image(X3,X4)) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368761,c_369798]) ).
tcf(c_414662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,relation_inverse_image(X3,relation_image(X0,X4)),X5),X5)
| ( relation_inverse_image(X2,relation_inverse_image(X3,relation_image(X0,X4))) = X5 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_368817,c_369798]) ).
tcf(c_414663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_inverse_image(X2,relation_image(X3,X4)) = relation_image(X0,X5) )
| ( apply(X3,sK13(X3,X4,apply(X2,sK7(X2,relation_image(X3,X4),relation_image(X0,X5))))) = apply(X2,sK7(X2,relation_image(X3,X4),relation_image(X0,X5))) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369663,c_369798]) ).
tcf(c_414664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_inverse_image(X3,relation_image(X0,X5)) = relation_image(X2,X4) )
| ( apply(X2,sK12(X2,X4,relation_inverse_image(X3,relation_image(X0,X5)))) = sK11(X2,X4,relation_inverse_image(X3,relation_image(X0,X5))) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369441,c_369798]) ).
tcf(c_414665,plain,
! [X0: $i,X1: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(X0)
| ~ in(X1,empty_set)
| ~ subset(relation_dom(empty_set),X0) ),
inference(superposition,[status(thm)],[c_375097,c_369798]) ).
tcf(c_414666,plain,
! [X0: $i,X1: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(X1)
| ~ subset(empty_set,X1)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_414665,c_373108]) ).
tcf(c_416535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(relation_image(X2,X0),X3,X4),X4)
| ( set_intersection2(relation_image(X2,X0),X3) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368927,c_369799]) ).
tcf(c_416536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(relation_image(X2,X0),X3,X4),X4)
| ( set_intersection2(relation_image(X2,X0),X3) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_55,c_369799]) ).
tcf(c_416537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,relation_image(X2,X0),X4),X4)
| ( set_intersection2(X3,relation_image(X2,X0)) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368926,c_369799]) ).
tcf(c_416538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,relation_image(X2,X0),X4),X4)
| ( set_intersection2(X3,relation_image(X2,X0)) = X4 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_369799]) ).
tcf(c_416539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,relation_image(X2,X0)),X4)
| ( relation_image(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368925,c_369799]) ).
tcf(c_416540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,X4,relation_image(X2,X0)),X3)
| ( relation_image(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368924,c_369799]) ).
tcf(c_416541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368865,c_369799]) ).
tcf(c_416542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_image(X2,X0)),X4)
| ( relation_image(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_56,c_369799]) ).
tcf(c_416543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,X4,relation_image(X2,X0)),X3)
| ( relation_image(X2,X0) = set_intersection2(X3,X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_55,c_369799]) ).
tcf(c_416544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,relation_image(X3,X0),X4),X4)
| ( relation_inverse_image(X2,relation_image(X3,X0)) = X4 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368931,c_369799]) ).
tcf(c_416545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,relation_image(X3,X0),X4),X4)
| ( relation_inverse_image(X2,relation_image(X3,X0)) = X4 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_85,c_369799]) ).
tcf(c_416546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(apply(X2,sK7(X2,X4,relation_image(X3,X0))),X4)
| ( relation_inverse_image(X2,X4) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368930,c_369799]) ).
tcf(c_416547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,X4,relation_image(X3,X0)),relation_dom(X2))
| ( relation_inverse_image(X2,X4) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368929,c_369799]) ).
tcf(c_416548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X2,X4) = relation_image(X3,X0) )
| ~ empty(X4)
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368871,c_369799]) ).
tcf(c_416549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X2,X4) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_379483,c_369799]) ).
tcf(c_416550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X4,relation_image(X3,X0)),relation_inverse_image(X2,X4))
| ( relation_inverse_image(X2,X4) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_375319,c_369799]) ).
tcf(c_416551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK7(X2,X4,relation_image(X3,X0))),X4)
| ( relation_inverse_image(X2,X4) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_85,c_369799]) ).
tcf(c_416552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X2,X4,relation_image(X3,X0)),relation_dom(X2))
| ( relation_inverse_image(X2,X4) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_369799]) ).
tcf(c_416553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_image(X2,X0),X3)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_95,c_369799]) ).
tcf(c_416554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X2,X4) = relation_image(X3,X0) )
| ~ empty(X4)
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369301,c_369799]) ).
tcf(c_416555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X2,X4,relation_image(X3,X0)),X4)
| ( relation_image(X2,X4) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369300,c_369799]) ).
tcf(c_416556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X2,X4) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_386602,c_369799]) ).
tcf(c_416557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X2,X4,relation_image(X3,X0)),relation_dom(X2))
| ( relation_image(X2,X4) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369215,c_369799]) ).
tcf(c_416558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X2,X4) = relation_image(X3,X0) )
| ( apply(X2,sK12(X2,X4,relation_image(X3,X0))) = sK11(X2,X4,relation_image(X3,X0)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_108,c_369799]) ).
tcf(c_416559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X4,relation_image(X3,X0)),X4)
| ( relation_image(X2,X4) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_369799]) ).
tcf(c_416560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK12(X2,X4,relation_image(X3,X0)),relation_dom(X2))
| ( relation_image(X2,X4) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_106,c_369799]) ).
tcf(c_416561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,relation_image(X3,X0),X4),X4)
| ( relation_image(X2,relation_image(X3,X0)) = X4 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369308,c_369799]) ).
tcf(c_416562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK11(X2,relation_image(X3,X0),X4),X4)
| ( relation_image(X2,relation_image(X3,X0)) = X4 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_369799]) ).
tcf(c_416563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_109,c_369799]) ).
tcf(c_416564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ empty(X4)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X3,X4)
| ~ in(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_111,c_369799]) ).
tcf(c_416565,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(relation_image(X2,X0))
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368976,c_369799]) ).
tcf(c_416566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(set_intersection2(relation_image(X2,X0),X3),X4)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368986,c_369799]) ).
tcf(c_416567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(set_intersection2(X3,relation_image(X2,X0)),X4)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368985,c_369799]) ).
tcf(c_416569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(set_intersection2(X3,relation_image(X2,X0)))
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370750,c_369799]) ).
tcf(c_416571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(set_intersection2(relation_image(X2,X0),X3))
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370751,c_369799]) ).
tcf(c_416572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(X0,X4)
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369021,c_369799]) ).
tcf(c_416573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X0)
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370747,c_369799]) ).
tcf(c_416574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(relation_inverse_image(X2,relation_image(X3,X0)),X4)
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368987,c_369799]) ).
tcf(c_416575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_image(X4,X2),X5,X0),X1)
| ( set_intersection2(relation_image(X4,X2),X5) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_369799]) ).
tcf(c_416576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X0),X4)
| ( set_intersection2(X4,X5) = X0 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369015,c_369799]) ).
tcf(c_416577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X0),X5)
| ( set_intersection2(X4,X5) = X0 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369014,c_369799]) ).
tcf(c_416578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_image(X2,X0),X4) = X3 )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368868,c_369799]) ).
tcf(c_416579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_image(X2,X0),X3,set_intersection2(X4,X5)),X5)
| ( set_intersection2(relation_image(X2,X0),X3) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368506,c_369799]) ).
tcf(c_416580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_image(X2,X0),X3,set_intersection2(X4,X5)),X4)
| ( set_intersection2(relation_image(X2,X0),X3) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368484,c_369799]) ).
tcf(c_416581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,set_intersection2(X3,relation_image(X2,X0))),X4)
| ( set_intersection2(X3,relation_image(X2,X0)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368506,c_369799]) ).
tcf(c_416582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,set_intersection2(X3,relation_image(X2,X0))),X5)
| ( set_intersection2(X3,relation_image(X2,X0)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368505,c_369799]) ).
tcf(c_416583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,set_intersection2(relation_image(X2,X0),X3)),X4)
| ( set_intersection2(relation_image(X2,X0),X3) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368484,c_369799]) ).
tcf(c_416584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,set_intersection2(relation_image(X2,X0),X3)),X5)
| ( set_intersection2(relation_image(X2,X0),X3) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368483,c_369799]) ).
tcf(c_416585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,relation_inverse_image(X2,relation_image(X3,X0))),X4)
| ( relation_inverse_image(X2,relation_image(X3,X0)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368816,c_369799]) ).
tcf(c_416586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,relation_inverse_image(X2,relation_image(X3,X0))),X5)
| ( relation_inverse_image(X2,relation_image(X3,X0)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368815,c_369799]) ).
tcf(c_416587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK2(relation_image(X3,X0),X4,relation_inverse_image(X2,X5))),X5)
| ( set_intersection2(relation_image(X3,X0),X4) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368816,c_369799]) ).
tcf(c_416588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_image(X3,X0),X4,relation_inverse_image(X2,X5)),relation_dom(X2))
| ( set_intersection2(relation_image(X3,X0),X4) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368760,c_369799]) ).
tcf(c_416589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,X5,relation_image(X4,X2)),X1)
| ( relation_image(X4,X2) = set_intersection2(X0,X5) )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_369799]) ).
tcf(c_416590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,X4,X5),X5)
| ( set_intersection2(X0,X4) = X5 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369012,c_369799]) ).
tcf(c_416591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,relation_image(X2,X0)),X4)
| ( set_intersection2(set_intersection2(X3,X4),X5) = relation_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368503,c_369799]) ).
tcf(c_416592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,relation_image(X2,X0)),X3)
| ( set_intersection2(set_intersection2(X3,X4),X5) = relation_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368481,c_369799]) ).
tcf(c_416593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,relation_image(X2,X0)),X4,X5),X5)
| ( set_intersection2(set_intersection2(X3,relation_image(X2,X0)),X4) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368503,c_369799]) ).
tcf(c_416594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X2,X0),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_image(X2,X0),X3),X4) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368481,c_369799]) ).
tcf(c_416595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK2(relation_inverse_image(X2,X4),X5,relation_image(X3,X0))),X4)
| ( set_intersection2(relation_inverse_image(X2,X4),X5) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368813,c_369799]) ).
tcf(c_416596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_inverse_image(X2,X4),X5,relation_image(X3,X0)),relation_dom(X2))
| ( set_intersection2(relation_inverse_image(X2,X4),X5) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368757,c_369799]) ).
tcf(c_416597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(relation_inverse_image(X2,relation_image(X3,X0)),X4,X5),X5)
| ( set_intersection2(relation_inverse_image(X2,relation_image(X3,X0)),X4) = X5 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368813,c_369799]) ).
tcf(c_416598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_image(X2,X0),X3) = relation_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368448,c_369799]) ).
tcf(c_416600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X5,relation_image(X4,X2),X0),X1)
| ( set_intersection2(X5,relation_image(X4,X2)) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_369799]) ).
tcf(c_416601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X4,relation_image(X2,X0)) = X3 )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368867,c_369799]) ).
tcf(c_416602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,relation_image(X2,X0),set_intersection2(X4,X5)),X5)
| ( set_intersection2(X3,relation_image(X2,X0)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368505,c_369799]) ).
tcf(c_416603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,relation_image(X2,X0),set_intersection2(X4,X5)),X4)
| ( set_intersection2(X3,relation_image(X2,X0)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368483,c_369799]) ).
tcf(c_416604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK2(X4,relation_image(X3,X0),relation_inverse_image(X2,X5))),X5)
| ( set_intersection2(X4,relation_image(X3,X0)) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368815,c_369799]) ).
tcf(c_416605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,relation_image(X3,X0),relation_inverse_image(X2,X5)),relation_dom(X2))
| ( set_intersection2(X4,relation_image(X3,X0)) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368759,c_369799]) ).
tcf(c_416606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X5,X0,relation_image(X4,X2)),X1)
| ( relation_image(X4,X2) = set_intersection2(X5,X0) )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_369799]) ).
tcf(c_416607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X0,X5),X5)
| ( set_intersection2(X4,X0) = X5 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369013,c_369799]) ).
tcf(c_416608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X2,X0) = set_intersection2(X4,X3) )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368866,c_369799]) ).
tcf(c_416609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),relation_image(X2,X0)),X5)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = relation_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368504,c_369799]) ).
tcf(c_416610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),relation_image(X2,X0)),X4)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = relation_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368482,c_369799]) ).
tcf(c_416611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,relation_image(X2,X0)),X5),X5)
| ( set_intersection2(X3,set_intersection2(X4,relation_image(X2,X0))) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368504,c_369799]) ).
tcf(c_416612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(relation_image(X2,X0),X4),X5),X5)
| ( set_intersection2(X3,set_intersection2(relation_image(X2,X0),X4)) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368482,c_369799]) ).
tcf(c_416613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,relation_inverse_image(X2,relation_image(X3,X0)),X5),X5)
| ( set_intersection2(X4,relation_inverse_image(X2,relation_image(X3,X0))) = X5 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368814,c_369799]) ).
tcf(c_416614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK2(X4,relation_inverse_image(X2,X5),relation_image(X3,X0))),X5)
| ( set_intersection2(X4,relation_inverse_image(X2,X5)) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368814,c_369799]) ).
tcf(c_416615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,relation_inverse_image(X2,X5),relation_image(X3,X0)),relation_dom(X2))
| ( set_intersection2(X4,relation_inverse_image(X2,X5)) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368758,c_369799]) ).
tcf(c_416616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,relation_image(X2,X0)) = relation_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368460,c_369799]) ).
tcf(c_416617,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_image(X2,X0) = empty_set )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_372467,c_369799]) ).
tcf(c_416618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ empty(X5)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X4,X5)
| ~ subset(X2,relation_image(X3,X4))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_369799]) ).
tcf(c_416619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ empty(X5)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X2,X5)
| ~ in(X3,relation_image(X0,X4))
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_369799]) ).
tcf(c_416620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ empty(X5)
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ subset(X4,X5)
| ~ in(X0,relation_image(X1,set_intersection2(X2,relation_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369597,c_369799]) ).
tcf(c_416621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ empty(X5)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X3,X5)
| ~ in(X0,relation_image(X1,set_intersection2(relation_image(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_369598,c_369799]) ).
tcf(c_416622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ empty(X5)
| ~ function(X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X4,X5)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,relation_image(X3,X4)))) ),
inference(superposition,[status(thm)],[c_369599,c_369799]) ).
tcf(c_416623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(relation_image(X2,X4),X5) = relation_image(X3,X0) )
| ( apply(X2,sK13(X2,X4,sK2(relation_image(X2,X4),X5,relation_image(X3,X0)))) = sK2(relation_image(X2,X4),X5,relation_image(X3,X0)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369659,c_369799]) ).
tcf(c_416624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X5,relation_image(X2,X4)) = relation_image(X3,X0) )
| ( apply(X2,sK13(X2,X4,sK2(X5,relation_image(X2,X4),relation_image(X3,X0)))) = sK2(X5,relation_image(X2,X4),relation_image(X3,X0)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369660,c_369799]) ).
tcf(c_416625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X5,relation_image(X3,X0)) = relation_image(X2,X4) )
| ( apply(X2,sK13(X2,X4,sK2(X5,relation_image(X3,X0),relation_image(X2,X4)))) = sK2(X5,relation_image(X3,X0),relation_image(X2,X4)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369661,c_369799]) ).
tcf(c_416626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(relation_image(X3,X0),X5) = relation_image(X2,X4) )
| ( apply(X2,sK13(X2,X4,sK2(relation_image(X3,X0),X5,relation_image(X2,X4)))) = sK2(relation_image(X3,X0),X5,relation_image(X2,X4)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369662,c_369799]) ).
tcf(c_416627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X4,X0,relation_image(X5,X2)),X1)
| ( relation_image(X4,X0) = relation_image(X5,X2) )
| ~ empty(X3)
| ~ function(X5)
| ~ function(X4)
| ~ relation(X5)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_369799]) ).
tcf(c_416628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X4,X0,X5),X5)
| ( relation_image(X4,X0) = X5 )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369299,c_369799]) ).
tcf(c_416629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,set_intersection2(X4,X5),relation_image(X3,X0)),X4)
| ( relation_image(X2,set_intersection2(X4,X5)) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369303,c_369799]) ).
tcf(c_416630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,set_intersection2(X4,X5),relation_image(X3,X0)),X5)
| ( relation_image(X2,set_intersection2(X4,X5)) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369302,c_369799]) ).
tcf(c_416631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X2,set_intersection2(X4,relation_image(X3,X0)),X5),X5)
| ( relation_image(X2,set_intersection2(X4,relation_image(X3,X0))) = X5 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369302,c_369799]) ).
tcf(c_416632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X2,set_intersection2(relation_image(X3,X0),X4),X5),X5)
| ( relation_image(X2,set_intersection2(relation_image(X3,X0),X4)) = X5 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369303,c_369799]) ).
tcf(c_416633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,relation_inverse_image(X3,X5),relation_image(X4,X0)),relation_dom(X3))
| ( relation_image(X2,relation_inverse_image(X3,X5)) = relation_image(X4,X0) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369305,c_369799]) ).
tcf(c_416634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X3,sK12(X2,relation_inverse_image(X3,X5),relation_image(X4,X0))),X5)
| ( relation_image(X2,relation_inverse_image(X3,X5)) = relation_image(X4,X0) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369304,c_369799]) ).
tcf(c_416635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X2,relation_inverse_image(X3,relation_image(X4,X0)),X5),X5)
| ( relation_image(X2,relation_inverse_image(X3,relation_image(X4,X0))) = X5 )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369304,c_369799]) ).
tcf(c_416636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_image(X2,relation_image(X3,X5)) = relation_image(X4,X0) )
| ( apply(X3,sK13(X3,X5,sK12(X2,relation_image(X3,X5),relation_image(X4,X0)))) = sK12(X2,relation_image(X3,X5),relation_image(X4,X0)) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369670,c_369799]) ).
tcf(c_416637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_image(X4,X5) = X0 )
| ( apply(X4,sK12(X4,X5,X0)) = sK11(X4,X5,X0) )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369436,c_369799]) ).
tcf(c_416638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X4,X5,X0),X5)
| ( relation_image(X4,X5) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369307,c_369799]) ).
tcf(c_416639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X4,X5,X0),relation_dom(X4))
| ( relation_image(X4,X5) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369206,c_369799]) ).
tcf(c_416640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X4,relation_image(X5,X2),X0),X1)
| ( relation_image(X4,relation_image(X5,X2)) = X0 )
| ~ empty(X3)
| ~ function(X5)
| ~ function(X4)
| ~ relation(X5)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_369799]) ).
tcf(c_416641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_image(X2,relation_image(X3,X0)) = X4 )
| ~ empty(X4)
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369309,c_369799]) ).
tcf(c_416642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X2,relation_image(X3,X0),set_intersection2(X4,X5)),X4)
| ( relation_image(X2,relation_image(X3,X0)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369311,c_369799]) ).
tcf(c_416643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X2,relation_image(X3,X0),set_intersection2(X4,X5)),X5)
| ( relation_image(X2,relation_image(X3,X0)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369310,c_369799]) ).
tcf(c_416644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X5,relation_image(X3,X0)) = relation_image(X2,X4) )
| ( apply(X2,sK12(X2,X4,set_intersection2(X5,relation_image(X3,X0)))) = sK11(X2,X4,set_intersection2(X5,relation_image(X3,X0))) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369439,c_369799]) ).
tcf(c_416645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X5,set_intersection2(X4,relation_image(X3,X0))),X5)
| ( set_intersection2(X4,relation_image(X3,X0)) = relation_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369310,c_369799]) ).
tcf(c_416646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X5,set_intersection2(X4,relation_image(X3,X0))),relation_dom(X2))
| ( set_intersection2(X4,relation_image(X3,X0)) = relation_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369209,c_369799]) ).
tcf(c_416647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(relation_image(X3,X0),X5) = relation_image(X2,X4) )
| ( apply(X2,sK12(X2,X4,set_intersection2(relation_image(X3,X0),X5))) = sK11(X2,X4,set_intersection2(relation_image(X3,X0),X5)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369440,c_369799]) ).
tcf(c_416648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X5,set_intersection2(relation_image(X3,X0),X4)),X5)
| ( set_intersection2(relation_image(X3,X0),X4) = relation_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369311,c_369799]) ).
tcf(c_416649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X5,set_intersection2(relation_image(X3,X0),X4)),relation_dom(X2))
| ( set_intersection2(relation_image(X3,X0),X4) = relation_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369210,c_369799]) ).
tcf(c_416650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X5,relation_inverse_image(X3,relation_image(X4,X0))),X5)
| ( relation_inverse_image(X3,relation_image(X4,X0)) = relation_image(X2,X5) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369312,c_369799]) ).
tcf(c_416651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X5,relation_inverse_image(X3,relation_image(X4,X0))),relation_dom(X2))
| ( relation_inverse_image(X3,relation_image(X4,X0)) = relation_image(X2,X5) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369211,c_369799]) ).
tcf(c_416652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X2,relation_image(X4,X0),relation_inverse_image(X3,X5)),relation_dom(X3))
| ( relation_image(X2,relation_image(X4,X0)) = relation_inverse_image(X3,X5) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369313,c_369799]) ).
tcf(c_416653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X3,sK11(X2,relation_image(X4,X0),relation_inverse_image(X3,X5))),X5)
| ( relation_image(X2,relation_image(X4,X0)) = relation_inverse_image(X3,X5) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369312,c_369799]) ).
tcf(c_416654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_image(X2,relation_image(X4,X0)) = relation_image(X3,X5) )
| ( apply(X3,sK13(X3,X5,sK11(X2,relation_image(X4,X0),relation_image(X3,X5)))) = sK11(X2,relation_image(X4,X0),relation_image(X3,X5)) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369668,c_369799]) ).
tcf(c_416655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X4,X5,X0),relation_dom(X4))
| ( relation_inverse_image(X4,X5) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369020,c_369799]) ).
tcf(c_416656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X4,sK7(X4,X5,X0)),X5)
| ( relation_inverse_image(X4,X5) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369019,c_369799]) ).
tcf(c_416657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK7(X2,X5,set_intersection2(X4,relation_image(X3,X0)))),X5)
| ( set_intersection2(X4,relation_image(X3,X0)) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368700,c_369799]) ).
tcf(c_416658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,X5,set_intersection2(X4,relation_image(X3,X0))),relation_dom(X2))
| ( set_intersection2(X4,relation_image(X3,X0)) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368672,c_369799]) ).
tcf(c_416659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK7(X2,X5,set_intersection2(relation_image(X3,X0),X4))),X5)
| ( set_intersection2(relation_image(X3,X0),X4) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368701,c_369799]) ).
tcf(c_416660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,X5,set_intersection2(relation_image(X3,X0),X4)),relation_dom(X2))
| ( set_intersection2(relation_image(X3,X0),X4) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368673,c_369799]) ).
tcf(c_416661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,X5,relation_inverse_image(X3,relation_image(X4,X0))),relation_dom(X2))
| ( relation_inverse_image(X3,relation_image(X4,X0)) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368819,c_369799]) ).
tcf(c_416662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK7(X2,X5,relation_inverse_image(X3,relation_image(X4,X0)))),X5)
| ( relation_inverse_image(X3,relation_image(X4,X0)) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368818,c_369799]) ).
tcf(c_416663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,X5,relation_image(X4,X2)),X1)
| ( relation_inverse_image(X0,X5) = relation_image(X4,X2) )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_369799]) ).
tcf(c_416664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,X4,X5),X5)
| ( relation_inverse_image(X0,X4) = X5 )
| ~ empty(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369017,c_369799]) ).
tcf(c_416665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X0,X5,relation_image(X4,X2)),X1)
| ( relation_image(X0,X5) = relation_image(X4,X2) )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_369799]) ).
tcf(c_416666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X0,X4,X5),X5)
| ( relation_image(X0,X4) = X5 )
| ~ empty(X3)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369214,c_369799]) ).
tcf(c_416667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X4,relation_image(X5,X2),X0),X1)
| ( relation_inverse_image(X4,relation_image(X5,X2)) = X0 )
| ~ empty(X3)
| ~ function(X5)
| ~ function(X4)
| ~ relation(X5)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_369799]) ).
tcf(c_416668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X2,relation_image(X3,X0)) = X4 )
| ~ empty(X4)
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368872,c_369799]) ).
tcf(c_416669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,relation_image(X3,X0),set_intersection2(X4,X5)),X4)
| ( relation_inverse_image(X2,relation_image(X3,X0)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368701,c_369799]) ).
tcf(c_416670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,relation_image(X3,X0),set_intersection2(X4,X5)),X5)
| ( relation_inverse_image(X2,relation_image(X3,X0)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368700,c_369799]) ).
tcf(c_416671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X3,sK7(X2,relation_image(X4,X0),relation_inverse_image(X3,X5))),X5)
| ( relation_inverse_image(X2,relation_image(X4,X0)) = relation_inverse_image(X3,X5) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368818,c_369799]) ).
tcf(c_416672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,relation_image(X4,X0),relation_inverse_image(X3,X5)),relation_dom(X3))
| ( relation_inverse_image(X2,relation_image(X4,X0)) = relation_inverse_image(X3,X5) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368762,c_369799]) ).
tcf(c_416673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_inverse_image(X2,relation_image(X4,X0)) = relation_image(X3,X5) )
| ( apply(X3,sK13(X3,X5,sK7(X2,relation_image(X4,X0),relation_image(X3,X5)))) = sK7(X2,relation_image(X4,X0),relation_image(X3,X5)) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369664,c_369799]) ).
tcf(c_416674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X4,X0,X5),X5)
| ( relation_inverse_image(X4,X0) = X5 )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369018,c_369799]) ).
tcf(c_416675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X4,sK7(X4,X0,relation_image(X5,X2))),X1)
| ( relation_inverse_image(X4,X0) = relation_image(X5,X2) )
| ~ empty(X3)
| ~ function(X5)
| ~ function(X4)
| ~ relation(X5)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_369799]) ).
tcf(c_416676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK7(X2,set_intersection2(X4,X5),relation_image(X3,X0))),X4)
| ( relation_inverse_image(X2,set_intersection2(X4,X5)) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368703,c_369799]) ).
tcf(c_416677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK7(X2,set_intersection2(X4,X5),relation_image(X3,X0))),X5)
| ( relation_inverse_image(X2,set_intersection2(X4,X5)) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368702,c_369799]) ).
tcf(c_416678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,set_intersection2(X4,relation_image(X3,X0)),X5),X5)
| ( relation_inverse_image(X2,set_intersection2(X4,relation_image(X3,X0))) = X5 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368702,c_369799]) ).
tcf(c_416679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,set_intersection2(relation_image(X3,X0),X4),X5),X5)
| ( relation_inverse_image(X2,set_intersection2(relation_image(X3,X0),X4)) = X5 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368703,c_369799]) ).
tcf(c_416680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X3,apply(X2,sK7(X2,relation_inverse_image(X3,X5),relation_image(X4,X0)))),X5)
| ( relation_inverse_image(X2,relation_inverse_image(X3,X5)) = relation_image(X4,X0) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368817,c_369799]) ).
tcf(c_416681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK7(X2,relation_inverse_image(X3,X5),relation_image(X4,X0))),relation_dom(X3))
| ( relation_inverse_image(X2,relation_inverse_image(X3,X5)) = relation_image(X4,X0) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368761,c_369799]) ).
tcf(c_416682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,relation_inverse_image(X3,relation_image(X4,X0)),X5),X5)
| ( relation_inverse_image(X2,relation_inverse_image(X3,relation_image(X4,X0))) = X5 )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368817,c_369799]) ).
tcf(c_416683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_inverse_image(X2,relation_image(X3,X5)) = relation_image(X4,X0) )
| ( apply(X3,sK13(X3,X5,apply(X2,sK7(X2,relation_image(X3,X5),relation_image(X4,X0))))) = apply(X2,sK7(X2,relation_image(X3,X5),relation_image(X4,X0))) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369663,c_369799]) ).
tcf(c_416684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_inverse_image(X3,relation_image(X4,X0)) = relation_image(X2,X5) )
| ( apply(X2,sK12(X2,X5,relation_inverse_image(X3,relation_image(X4,X0)))) = sK11(X2,X5,relation_inverse_image(X3,relation_image(X4,X0))) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369441,c_369799]) ).
tcf(c_416685,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ empty(X1)
| ~ in(X2,empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_375097,c_369799]) ).
tcf(c_418533,plain,
~ empty(sK15(sK8)),
inference(global_subsumption_just,[status(thm)],[c_413870,c_89,c_6042]) ).
tcf(c_418535,plain,
set_intersection2(sK15(sK8),sK15(sK15(sK8))) = sK15(sK15(sK8)),
inference(superposition,[status(thm)],[c_397129,c_418533]) ).
tcf(c_418545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X0,X2,X3),X1)
| in(sK2(X0,X2,X3),X3)
| ( set_intersection2(X0,X2) = X3 )
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_369926,c_99]) ).
tcf(c_418546,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X0),X2)
| ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,X2)
| ~ in(sK2(X0,X1,X0),X1)
| ~ in(sK2(X0,X1,X0),X0) ),
inference(superposition,[status(thm)],[c_369926,c_54]) ).
tcf(c_418547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X4,X2),X3)
| element(sK2(X0,X4,X2),X1)
| ( set_intersection2(X0,X4) = X2 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369926,c_321]) ).
tcf(c_418548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X4,X2),X1)
| ( set_intersection2(X0,X4) = X2 )
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369926,c_320]) ).
tcf(c_418549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X1,X2,X0),X3)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X1,X3)
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369926,c_97]) ).
tcf(c_418550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X4,X2),X1)
| in(sK2(X0,X4,X2),X3)
| ( set_intersection2(X0,X4) = X2 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369926,c_96]) ).
tcf(c_418557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X1,relation_dom(X2)),X4)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK2(X0,X1,relation_dom(X2))))) = apply(X2,sK2(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X4)
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369926,c_369671]) ).
tcf(c_418558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X0,X5,relation_image(X4,X2)),X1)
| ( relation_image(X4,X2) = set_intersection2(X0,X5) )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369926,c_369799]) ).
tcf(c_418559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X2,X5,relation_image(X0,X4)),X3)
| ( relation_image(X0,X4) = set_intersection2(X2,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369926,c_369798]) ).
tcf(c_418560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X4,relation_image(X2,X3)),X1)
| ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369926,c_369596]) ).
tcf(c_418561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X4,relation_image(X2,X3)),X1)
| ( relation_image(X2,X3) = set_intersection2(X0,X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369926,c_369558]) ).
tcf(c_418563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X1,relation_dom(X2)),X4)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X4)
| ~ empty(relation_image(X2,X3))
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369926,c_369501]) ).
tcf(c_418564,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X2,empty_set),X1)
| ( set_intersection2(X0,X2) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369926,c_372426]) ).
tcf(c_418565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X0),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ subset(set_intersection2(X0,X1),X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_369926,c_368471]) ).
tcf(c_418566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X0,X5,relation_image(X2,relation_image(X3,X4))),X1)
| ( relation_image(X2,relation_image(X3,X4)) = set_intersection2(X0,X5) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK2(X0,X5,relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK2(X0,X5,relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369926,c_369672]) ).
tcf(c_418673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X0,X3),X1)
| in(sK2(X2,X0,X3),X3)
| ( set_intersection2(X2,X0) = X3 )
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_369927,c_99]) ).
tcf(c_418674,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X0),X2)
| ( set_intersection2(X0,X1) = X0 )
| ~ subset(X1,X2)
| ~ in(sK2(X0,X1,X0),X1)
| ~ in(sK2(X0,X1,X0),X0) ),
inference(superposition,[status(thm)],[c_369927,c_54]) ).
tcf(c_418675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X0,X2),X3)
| element(sK2(X4,X0,X2),X1)
| ( set_intersection2(X4,X0) = X2 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369927,c_321]) ).
tcf(c_418676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X0,X2),X1)
| ( set_intersection2(X4,X0) = X2 )
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369927,c_320]) ).
tcf(c_418677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X1,X2,X0),X3)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X2,X3)
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369927,c_97]) ).
tcf(c_418678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X0,X2),X1)
| in(sK2(X4,X0,X2),X3)
| ( set_intersection2(X4,X0) = X2 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369927,c_96]) ).
tcf(c_418685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X1,relation_dom(X2)),X4)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK2(X0,X1,relation_dom(X2))))) = apply(X2,sK2(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X1,X4)
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369927,c_369671]) ).
tcf(c_418686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X5,X0,relation_image(X4,X2)),X1)
| ( relation_image(X4,X2) = set_intersection2(X5,X0) )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369927,c_369799]) ).
tcf(c_418687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X5,X2,relation_image(X0,X4)),X3)
| ( relation_image(X0,X4) = set_intersection2(X5,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369927,c_369798]) ).
tcf(c_418688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X0,relation_image(X2,X3)),X1)
| ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369927,c_369596]) ).
tcf(c_418689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X0,relation_image(X2,X3)),X1)
| ( relation_image(X2,X3) = set_intersection2(X4,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369927,c_369558]) ).
tcf(c_418691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,X1,relation_dom(X2)),X4)
| ( set_intersection2(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X1,X4)
| ~ empty(relation_image(X2,X3))
| ~ in(sK2(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369927,c_369501]) ).
tcf(c_418692,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X2,X0,empty_set),X1)
| ( set_intersection2(X2,X0) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369927,c_372426]) ).
tcf(c_418693,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X0),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ subset(X2,X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_369927,c_368471]) ).
tcf(c_418694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X5,X0,relation_image(X2,relation_image(X3,X4))),X1)
| ( relation_image(X2,relation_image(X3,X4)) = set_intersection2(X5,X0) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK2(X5,X0,relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK2(X5,X0,relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369927,c_369672]) ).
tcf(c_418836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X3,X0),X1)
| in(sK2(X2,X3,X0),X3)
| ( set_intersection2(X2,X3) = X0 )
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_369928,c_99]) ).
tcf(c_418837,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X0,X1),X2)
| ( set_intersection2(X0,X0) = X1 )
| ~ subset(X1,X2)
| ~ in(sK2(X0,X0,X1),X1)
| ~ in(sK2(X0,X0,X1),X0) ),
inference(superposition,[status(thm)],[c_369928,c_54]) ).
tcf(c_418838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X2,X0),X3)
| element(sK2(X4,X2,X0),X1)
| ( set_intersection2(X4,X2) = X0 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369928,c_321]) ).
tcf(c_418839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X2,X0),X1)
| ( set_intersection2(X4,X2) = X0 )
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369928,c_320]) ).
tcf(c_418840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X1,X0,X2),X3)
| ( set_intersection2(X1,X0) = X2 )
| ~ subset(X2,X3)
| ~ in(X0,sK2(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_369928,c_97]) ).
tcf(c_418841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,X2,X0),X1)
| in(sK2(X4,X2,X0),X3)
| ( set_intersection2(X4,X2) = X0 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369928,c_96]) ).
tcf(c_418848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,relation_dom(X1),X2),X4)
| ( set_intersection2(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,sK2(X0,relation_dom(X1),X2)))) = apply(X1,sK2(X0,relation_dom(X1),X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X4)
| ~ in(sK2(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_369928,c_369671]) ).
tcf(c_418849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X5,relation_image(X4,X2),X0),X1)
| ( set_intersection2(X5,relation_image(X4,X2)) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369928,c_369799]) ).
tcf(c_418850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X4,relation_image(X0,X5),X2),X3)
| ( set_intersection2(X4,relation_image(X0,X5)) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369928,c_369798]) ).
tcf(c_418851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X4,relation_image(X2,X3),X0),X1)
| ( set_intersection2(X4,relation_image(X2,X3)) = X0 )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369928,c_369596]) ).
tcf(c_418852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,relation_image(X2,X4),X0),X1)
| ( set_intersection2(X3,relation_image(X2,X4)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369928,c_369558]) ).
tcf(c_418854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,relation_dom(X1),X2),X4)
| ( set_intersection2(X0,relation_dom(X1)) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X4)
| ~ empty(relation_image(X1,X3))
| ~ in(sK2(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_369928,c_369501]) ).
tcf(c_418855,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X2,empty_set,X0),X1)
| ( set_intersection2(X2,empty_set) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369928,c_372426]) ).
tcf(c_418856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X0,X2),X3)
| ( set_intersection2(set_intersection2(X0,X1),X0) = X2 )
| ~ subset(X2,X3)
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X1)
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X0) ),
inference(superposition,[status(thm)],[c_369928,c_368471]) ).
tcf(c_418857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X5,relation_image(X2,relation_image(X3,X4)),X0),X1)
| ( set_intersection2(X5,relation_image(X2,relation_image(X3,X4))) = X0 )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK2(X5,relation_image(X2,relation_image(X3,X4)),X0)))) = sK13(X2,relation_image(X3,X4),sK2(X5,relation_image(X2,relation_image(X3,X4)),X0)) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369928,c_369672]) ).
tcf(c_418896,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X0,X1),X2)
| ( X0 = X1 )
| ~ subset(X1,X2)
| ~ in(sK2(X0,X0,X1),X1)
| ~ in(sK2(X0,X0,X1),X0) ),
inference(light_normalisation,[status(thm)],[c_418837,c_53]) ).
tcf(c_418923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X0,X2),X3)
| ( set_intersection2(X0,X1) = X2 )
| ~ subset(X2,X3)
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X1)
| ~ in(sK2(set_intersection2(X0,X1),X0,X2),X0) ),
inference(light_normalisation,[status(thm)],[c_418856,c_397166]) ).
tcf(c_418952,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),sK5)
| element(sK2(sK15(sK5),X0,X1),X1)
| ( set_intersection2(sK15(sK5),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_368927,c_412536]) ).
tcf(c_418954,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),sK5)
| element(sK2(X0,sK15(sK5),X1),X1)
| ( set_intersection2(X0,sK15(sK5)) = X1 ) ),
inference(superposition,[status(thm)],[c_368926,c_412536]) ).
tcf(c_418956,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),sK5)
| element(sK2(X0,X1,sK15(sK5)),X1)
| ( set_intersection2(X0,X1) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_368925,c_412536]) ).
tcf(c_418957,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),sK5)
| element(sK2(X0,X1,sK15(sK5)),X0)
| ( set_intersection2(X0,X1) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_368924,c_412536]) ).
tcf(c_418958,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK5)),sK5)
| ( set_intersection2(X0,X1) = sK15(sK5) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368865,c_412536]) ).
tcf(c_418961,plain,
! [X0: $i,X1: $i] :
( element(sK7(X0,sK15(sK5),X1),X1)
| in(apply(X0,sK7(X0,sK15(sK5),X1)),sK5)
| ( relation_inverse_image(X0,sK15(sK5)) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368931,c_412536]) ).
tcf(c_418963,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),sK5)
| element(apply(X0,sK7(X0,X1,sK15(sK5))),X1)
| ( relation_inverse_image(X0,X1) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368930,c_412536]) ).
tcf(c_418964,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),sK5)
| element(sK7(X0,X1,sK15(sK5)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368929,c_412536]) ).
tcf(c_418965,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),sK5)
| ( relation_inverse_image(X0,X1) = sK15(sK5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368871,c_412536]) ).
tcf(c_418966,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),sK5)
| ( relation_inverse_image(X0,X1) = sK15(sK5) )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_412536]) ).
tcf(c_418967,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK5)),sK5)
| in(sK7(X0,X1,sK15(sK5)),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375319,c_412536]) ).
tcf(c_418971,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK5)
| ( relation_image(X0,X1) = sK15(sK5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369301,c_412536]) ).
tcf(c_418972,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK5)
| element(sK12(X0,X1,sK15(sK5)),X1)
| ( relation_image(X0,X1) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369300,c_412536]) ).
tcf(c_418973,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK5)
| ( relation_image(X0,X1) = sK15(sK5) )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_386602,c_412536]) ).
tcf(c_418974,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK5)),sK5)
| element(sK12(X0,X1,sK15(sK5)),relation_dom(X0))
| ( relation_image(X0,X1) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369215,c_412536]) ).
tcf(c_418978,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,sK15(sK5),X1),sK5)
| element(sK11(X0,sK15(sK5),X1),X1)
| ( relation_image(X0,sK15(sK5)) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369308,c_412536]) ).
tcf(c_418982,plain,
! [X0: $i,X1: $i] :
( subset(set_intersection2(sK15(sK5),X0),X1)
| in(sK10(set_intersection2(sK15(sK5),X0),X1),sK5) ),
inference(superposition,[status(thm)],[c_368986,c_412536]) ).
tcf(c_418983,plain,
! [X0: $i,X1: $i] :
( subset(set_intersection2(X0,sK15(sK5)),X1)
| in(sK10(set_intersection2(X0,sK15(sK5)),X1),sK5) ),
inference(superposition,[status(thm)],[c_368985,c_412536]) ).
tcf(c_418984,plain,
! [X0: $i] :
( empty(set_intersection2(sK15(sK5),X0))
| in(sK16(set_intersection2(X0,sK15(sK5))),sK5) ),
inference(superposition,[status(thm)],[c_389060,c_412536]) ).
tcf(c_418985,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK15(sK5)))
| in(sK16(set_intersection2(X0,sK15(sK5))),sK5) ),
inference(superposition,[status(thm)],[c_370750,c_412536]) ).
tcf(c_418986,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK15(sK5)))
| in(sK16(set_intersection2(sK15(sK5),X0)),sK5) ),
inference(superposition,[status(thm)],[c_388043,c_412536]) ).
tcf(c_418987,plain,
! [X0: $i] :
( empty(set_intersection2(sK15(sK5),X0))
| in(sK16(set_intersection2(sK15(sK5),X0)),sK5) ),
inference(superposition,[status(thm)],[c_370751,c_412536]) ).
tcf(c_418988,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK10(X0,X1),sK5)
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_369021,c_412536]) ).
tcf(c_418989,plain,
! [X0: $i] :
( empty(X0)
| in(sK16(X0),sK5)
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_370747,c_412536]) ).
tcf(c_418990,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(X0,sK15(sK5)),X1)
| in(apply(X0,sK10(relation_inverse_image(X0,sK15(sK5)),X1)),sK5)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368987,c_412536]) ).
tcf(c_418991,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X2,X0),sK5)
| in(sK2(sK15(sK5),X2,X0),X1)
| ( set_intersection2(sK15(sK5),X2) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_412536]) ).
tcf(c_418992,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),sK5)
| in(sK2(X1,X2,X0),X1)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_369015,c_412536]) ).
tcf(c_418993,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),sK5)
| in(sK2(X1,X2,X0),X2)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_369014,c_412536]) ).
tcf(c_418994,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X1,X0),sK5)
| ( set_intersection2(sK15(sK5),X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368868,c_412536]) ).
tcf(c_418995,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X0,set_intersection2(X1,X2)),sK5)
| in(sK2(sK15(sK5),X0,set_intersection2(X1,X2)),X2)
| ( set_intersection2(sK15(sK5),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368506,c_412536]) ).
tcf(c_418996,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X0,set_intersection2(X1,X2)),sK5)
| in(sK2(sK15(sK5),X0,set_intersection2(X1,X2)),X1)
| ( set_intersection2(sK15(sK5),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368484,c_412536]) ).
tcf(c_418997,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,set_intersection2(X0,sK15(sK5))),sK5)
| in(sK2(X1,X2,set_intersection2(X0,sK15(sK5))),X1)
| ( set_intersection2(X0,sK15(sK5)) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368506,c_412536]) ).
tcf(c_418998,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,set_intersection2(X0,sK15(sK5))),sK5)
| in(sK2(X1,X2,set_intersection2(X0,sK15(sK5))),X2)
| ( set_intersection2(X0,sK15(sK5)) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368505,c_412536]) ).
tcf(c_418999,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,set_intersection2(sK15(sK5),X0)),sK5)
| in(sK2(X1,X2,set_intersection2(sK15(sK5),X0)),X1)
| ( set_intersection2(sK15(sK5),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368484,c_412536]) ).
tcf(c_419000,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,set_intersection2(sK15(sK5),X0)),sK5)
| in(sK2(X1,X2,set_intersection2(sK15(sK5),X0)),X2)
| ( set_intersection2(sK15(sK5),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368483,c_412536]) ).
tcf(c_419001,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,sK15(sK5))),X1)
| in(apply(X0,sK2(X1,X2,relation_inverse_image(X0,sK15(sK5)))),sK5)
| ( relation_inverse_image(X0,sK15(sK5)) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_412536]) ).
tcf(c_419002,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,sK15(sK5))),X2)
| in(apply(X0,sK2(X1,X2,relation_inverse_image(X0,sK15(sK5)))),sK5)
| ( relation_inverse_image(X0,sK15(sK5)) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_412536]) ).
tcf(c_419003,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X1,relation_inverse_image(X0,X2)),sK5)
| in(apply(X0,sK2(sK15(sK5),X1,relation_inverse_image(X0,X2))),X2)
| ( set_intersection2(sK15(sK5),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_412536]) ).
tcf(c_419004,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X1,relation_inverse_image(X0,X2)),sK5)
| in(sK2(sK15(sK5),X1,relation_inverse_image(X0,X2)),relation_dom(X0))
| ( set_intersection2(sK15(sK5),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368760,c_412536]) ).
tcf(c_419005,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,sK15(sK5)),sK5)
| element(sK2(X0,X2,sK15(sK5)),X1)
| ( set_intersection2(X0,X2) = sK15(sK5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369926,c_412536]) ).
tcf(c_419006,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,sK15(sK5)),sK5)
| in(sK2(X0,X2,sK15(sK5)),X1)
| ( set_intersection2(X0,X2) = sK15(sK5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_412536]) ).
tcf(c_419007,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),sK5)
| in(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_369012,c_412536]) ).
tcf(c_419008,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),sK5)
| in(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_368503,c_412536]) ).
tcf(c_419009,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),sK5)
| in(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_368481,c_412536]) ).
tcf(c_419010,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,sK15(sK5)),X1,X2),sK5)
| in(sK2(set_intersection2(X0,sK15(sK5)),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,sK15(sK5)),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368503,c_412536]) ).
tcf(c_419011,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),sK5)
| in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(sK15(sK5),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368481,c_412536]) ).
tcf(c_419012,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,sK15(sK5)),sK5)
| in(apply(X0,sK2(relation_inverse_image(X0,X1),X2,sK15(sK5))),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_412536]) ).
tcf(c_419013,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,sK15(sK5)),sK5)
| in(sK2(relation_inverse_image(X0,X1),X2,sK15(sK5)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368757,c_412536]) ).
tcf(c_419014,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_inverse_image(X0,sK15(sK5)),X1,X2),X2)
| in(apply(X0,sK2(relation_inverse_image(X0,sK15(sK5)),X1,X2)),sK5)
| ( set_intersection2(relation_inverse_image(X0,sK15(sK5)),X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_412536]) ).
tcf(c_419015,plain,
! [X0: $i] :
( in(sK2(sK15(sK5),X0,sK15(sK5)),sK5)
| ( set_intersection2(sK15(sK5),X0) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_368448,c_412536]) ).
tcf(c_419016,plain,
! [X0: $i] :
( in(sK2(empty_set,X0,sK15(sK5)),sK5)
| ( sK15(sK5) = empty_set ) ),
inference(superposition,[status(thm)],[c_372470,c_412536]) ).
tcf(c_419017,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,sK15(sK5),X0),sK5)
| element(sK2(X2,sK15(sK5),X0),X1)
| ( set_intersection2(X2,sK15(sK5)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369928,c_412536]) ).
tcf(c_419018,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,sK15(sK5),X0),sK5)
| in(sK2(X2,sK15(sK5),X0),X1)
| ( set_intersection2(X2,sK15(sK5)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_412536]) ).
tcf(c_419019,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK15(sK5),X0),sK5)
| ( set_intersection2(X1,sK15(sK5)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368867,c_412536]) ).
tcf(c_419020,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK15(sK5),set_intersection2(X1,X2)),sK5)
| in(sK2(X0,sK15(sK5),set_intersection2(X1,X2)),X2)
| ( set_intersection2(X0,sK15(sK5)) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368505,c_412536]) ).
tcf(c_419021,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK15(sK5),set_intersection2(X1,X2)),sK5)
| in(sK2(X0,sK15(sK5),set_intersection2(X1,X2)),X1)
| ( set_intersection2(X0,sK15(sK5)) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368483,c_412536]) ).
tcf(c_419022,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK5),relation_inverse_image(X0,X2)),sK5)
| in(apply(X0,sK2(X1,sK15(sK5),relation_inverse_image(X0,X2))),X2)
| ( set_intersection2(X1,sK15(sK5)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_412536]) ).
tcf(c_419023,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK5),relation_inverse_image(X0,X2)),sK5)
| in(sK2(X1,sK15(sK5),relation_inverse_image(X0,X2)),relation_dom(X0))
| ( set_intersection2(X1,sK15(sK5)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368759,c_412536]) ).
tcf(c_419024,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X0,sK15(sK5)),sK5)
| element(sK2(X2,X0,sK15(sK5)),X1)
| ( set_intersection2(X2,X0) = sK15(sK5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369927,c_412536]) ).
tcf(c_419025,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X0,sK15(sK5)),sK5)
| in(sK2(X2,X0,sK15(sK5)),X1)
| ( set_intersection2(X2,X0) = sK15(sK5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_412536]) ).
tcf(c_419026,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,X2),sK5)
| in(sK2(X1,X0,X2),X2)
| ( set_intersection2(X1,X0) = X2 )
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_369013,c_412536]) ).
tcf(c_419027,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,sK15(sK5)),sK5)
| ( set_intersection2(X1,X0) = sK15(sK5) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368866,c_412536]) ).
tcf(c_419028,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK5)),sK5)
| in(sK2(X0,set_intersection2(X1,X2),sK15(sK5)),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_368504,c_412536]) ).
tcf(c_419029,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK5)),sK5)
| in(sK2(X0,set_intersection2(X1,X2),sK15(sK5)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_368482,c_412536]) ).
tcf(c_419030,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,sK15(sK5)),X2),sK5)
| in(sK2(X0,set_intersection2(X1,sK15(sK5)),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,sK15(sK5))) = X2 ) ),
inference(superposition,[status(thm)],[c_368504,c_412536]) ).
tcf(c_419031,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(sK15(sK5),X1),X2),sK5)
| in(sK2(X0,set_intersection2(sK15(sK5),X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(sK15(sK5),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_368482,c_412536]) ).
tcf(c_419032,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,relation_inverse_image(X0,sK15(sK5)),X2),X2)
| in(apply(X0,sK2(X1,relation_inverse_image(X0,sK15(sK5)),X2)),sK5)
| ( set_intersection2(X1,relation_inverse_image(X0,sK15(sK5))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_412536]) ).
tcf(c_419033,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),sK15(sK5)),sK5)
| in(apply(X0,sK2(X1,relation_inverse_image(X0,X2),sK15(sK5))),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_412536]) ).
tcf(c_419034,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),sK15(sK5)),sK5)
| in(sK2(X1,relation_inverse_image(X0,X2),sK15(sK5)),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368758,c_412536]) ).
tcf(c_419035,plain,
! [X0: $i] :
( in(sK2(X0,sK15(sK5),sK15(sK5)),sK5)
| ( set_intersection2(X0,sK15(sK5)) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_368460,c_412536]) ).
tcf(c_419036,plain,
! [X0: $i] :
( in(sK2(X0,empty_set,sK15(sK5)),sK5)
| ( sK15(sK5) = empty_set ) ),
inference(superposition,[status(thm)],[c_372467,c_412536]) ).
tcf(c_419037,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,X2,X0),sK5)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,sK15(sK5))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_412536]) ).
tcf(c_419038,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,X2,X0),sK5)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),sK15(sK5))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_412536]) ).
tcf(c_419039,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,set_intersection2(X2,sK15(sK5)),X0),sK5)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_369597,c_412536]) ).
tcf(c_419040,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,set_intersection2(sK15(sK5),X2),X0),sK5)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(sK15(sK5),X2))) ),
inference(superposition,[status(thm)],[c_369598,c_412536]) ).
tcf(c_419041,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X2,sK13(X1,relation_inverse_image(X2,sK15(sK5)),X0)),sK5)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_369599,c_412536]) ).
tcf(c_419042,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_image(X0,X1),X2,sK15(sK5)),sK5)
| ( set_intersection2(relation_image(X0,X1),X2) = sK15(sK5) )
| ( apply(X0,sK13(X0,X1,sK2(relation_image(X0,X1),X2,sK15(sK5)))) = sK2(relation_image(X0,X1),X2,sK15(sK5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369659,c_412536]) ).
tcf(c_419043,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,relation_image(X0,X1),sK15(sK5)),sK5)
| ( set_intersection2(X2,relation_image(X0,X1)) = sK15(sK5) )
| ( apply(X0,sK13(X0,X1,sK2(X2,relation_image(X0,X1),sK15(sK5)))) = sK2(X2,relation_image(X0,X1),sK15(sK5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369660,c_412536]) ).
tcf(c_419044,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,sK15(sK5),relation_image(X0,X1)),sK5)
| ( set_intersection2(X2,sK15(sK5)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,sK15(sK5),relation_image(X0,X1)))) = sK2(X2,sK15(sK5),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369661,c_412536]) ).
tcf(c_419045,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X2,relation_image(X0,X1)),sK5)
| ( set_intersection2(sK15(sK5),X2) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(sK15(sK5),X2,relation_image(X0,X1)))) = sK2(sK15(sK5),X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369662,c_412536]) ).
tcf(c_419046,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X2,X0,sK15(sK5)),sK5)
| in(sK12(X2,X0,sK15(sK5)),X1)
| ( relation_image(X2,X0) = sK15(sK5) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_412536]) ).
tcf(c_419047,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X1,X0,X2),sK5)
| in(sK11(X1,X0,X2),X2)
| ( relation_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_369299,c_412536]) ).
tcf(c_419048,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,set_intersection2(X1,X2),sK15(sK5)),sK5)
| in(sK12(X0,set_intersection2(X1,X2),sK15(sK5)),X1)
| ( relation_image(X0,set_intersection2(X1,X2)) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_412536]) ).
tcf(c_419049,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,set_intersection2(X1,X2),sK15(sK5)),sK5)
| in(sK12(X0,set_intersection2(X1,X2),sK15(sK5)),X2)
| ( relation_image(X0,set_intersection2(X1,X2)) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_412536]) ).
tcf(c_419050,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,set_intersection2(X1,sK15(sK5)),X2),sK5)
| in(sK11(X0,set_intersection2(X1,sK15(sK5)),X2),X2)
| ( relation_image(X0,set_intersection2(X1,sK15(sK5))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_412536]) ).
tcf(c_419051,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,set_intersection2(sK15(sK5),X1),X2),sK5)
| in(sK11(X0,set_intersection2(sK15(sK5),X1),X2),X2)
| ( relation_image(X0,set_intersection2(sK15(sK5),X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_412536]) ).
tcf(c_419052,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),sK15(sK5)),sK5)
| in(sK12(X0,relation_inverse_image(X1,X2),sK15(sK5)),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X2)) = sK15(sK5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369305,c_412536]) ).
tcf(c_419053,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),sK15(sK5)),sK5)
| in(apply(X1,sK12(X0,relation_inverse_image(X1,X2),sK15(sK5))),X2)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = sK15(sK5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_412536]) ).
tcf(c_419054,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,relation_inverse_image(X1,sK15(sK5)),X2),X2)
| in(apply(X1,sK12(X0,relation_inverse_image(X1,sK15(sK5)),X2)),sK5)
| ( relation_image(X0,relation_inverse_image(X1,sK15(sK5))) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_412536]) ).
tcf(c_419055,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,relation_image(X1,X2),sK15(sK5)),sK5)
| ( relation_image(X0,relation_image(X1,X2)) = sK15(sK5) )
| ( apply(X1,sK13(X1,X2,sK12(X0,relation_image(X1,X2),sK15(sK5)))) = sK12(X0,relation_image(X1,X2),sK15(sK5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369670,c_412536]) ).
tcf(c_419056,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X1,X2,X0),sK5)
| ( relation_image(X1,X2) = X0 )
| ( apply(X1,sK12(X1,X2,X0)) = sK11(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_369436,c_412536]) ).
tcf(c_419057,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X1,X2,X0),sK5)
| in(sK12(X1,X2,X0),X2)
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_369307,c_412536]) ).
tcf(c_419058,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X1,X2,X0),sK5)
| in(sK12(X1,X2,X0),relation_dom(X1))
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_369206,c_412536]) ).
tcf(c_419059,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X2,sK15(sK5),X0),sK5)
| in(sK11(X2,sK15(sK5),X0),X1)
| ( relation_image(X2,sK15(sK5)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_412536]) ).
tcf(c_419060,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,sK15(sK5),X1),sK5)
| ( relation_image(X0,sK15(sK5)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369309,c_412536]) ).
tcf(c_419061,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,sK15(sK5),set_intersection2(X1,X2)),sK5)
| in(sK11(X0,sK15(sK5),set_intersection2(X1,X2)),X1)
| ( relation_image(X0,sK15(sK5)) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_412536]) ).
tcf(c_419062,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,sK15(sK5),set_intersection2(X1,X2)),sK5)
| in(sK11(X0,sK15(sK5),set_intersection2(X1,X2)),X2)
| ( relation_image(X0,sK15(sK5)) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_412536]) ).
tcf(c_419063,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,set_intersection2(X2,sK15(sK5))),sK5)
| ( set_intersection2(X2,sK15(sK5)) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,sK15(sK5)))) = sK11(X0,X1,set_intersection2(X2,sK15(sK5))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369439,c_412536]) ).
tcf(c_419064,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,set_intersection2(X1,sK15(sK5))),sK5)
| in(sK12(X0,X2,set_intersection2(X1,sK15(sK5))),X2)
| ( set_intersection2(X1,sK15(sK5)) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_412536]) ).
tcf(c_419065,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,set_intersection2(X1,sK15(sK5))),sK5)
| in(sK12(X0,X2,set_intersection2(X1,sK15(sK5))),relation_dom(X0))
| ( set_intersection2(X1,sK15(sK5)) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369209,c_412536]) ).
tcf(c_419066,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,set_intersection2(sK15(sK5),X2)),sK5)
| ( set_intersection2(sK15(sK5),X2) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(sK15(sK5),X2))) = sK11(X0,X1,set_intersection2(sK15(sK5),X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369440,c_412536]) ).
tcf(c_419067,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,set_intersection2(sK15(sK5),X1)),sK5)
| in(sK12(X0,X2,set_intersection2(sK15(sK5),X1)),X2)
| ( set_intersection2(sK15(sK5),X1) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_412536]) ).
tcf(c_419068,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,set_intersection2(sK15(sK5),X1)),sK5)
| in(sK12(X0,X2,set_intersection2(sK15(sK5),X1)),relation_dom(X0))
| ( set_intersection2(sK15(sK5),X1) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369210,c_412536]) ).
tcf(c_419069,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,relation_inverse_image(X1,sK15(sK5))),X2)
| in(apply(X1,sK11(X0,X2,relation_inverse_image(X1,sK15(sK5)))),sK5)
| ( relation_inverse_image(X1,sK15(sK5)) = relation_image(X0,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_412536]) ).
tcf(c_419070,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,relation_inverse_image(X1,sK15(sK5))),relation_dom(X0))
| in(apply(X1,sK11(X0,X2,relation_inverse_image(X1,sK15(sK5)))),sK5)
| ( relation_inverse_image(X1,sK15(sK5)) = relation_image(X0,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369211,c_412536]) ).
tcf(c_419071,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,sK15(sK5),relation_inverse_image(X1,X2)),sK5)
| in(sK11(X0,sK15(sK5),relation_inverse_image(X1,X2)),relation_dom(X1))
| ( relation_image(X0,sK15(sK5)) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369313,c_412536]) ).
tcf(c_419072,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,sK15(sK5),relation_inverse_image(X1,X2)),sK5)
| in(apply(X1,sK11(X0,sK15(sK5),relation_inverse_image(X1,X2))),X2)
| ( relation_image(X0,sK15(sK5)) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_412536]) ).
tcf(c_419073,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,sK15(sK5),relation_image(X1,X2)),sK5)
| ( relation_image(X0,sK15(sK5)) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK11(X0,sK15(sK5),relation_image(X1,X2)))) = sK11(X0,sK15(sK5),relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369668,c_412536]) ).
tcf(c_419074,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X2,X0),sK5)
| in(sK7(X1,X2,X0),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_369020,c_412536]) ).
tcf(c_419075,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X2,X0),sK5)
| in(apply(X1,sK7(X1,X2,X0)),X2)
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_369019,c_412536]) ).
tcf(c_419076,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,set_intersection2(X1,sK15(sK5))),sK5)
| in(apply(X0,sK7(X0,X2,set_intersection2(X1,sK15(sK5)))),X2)
| ( set_intersection2(X1,sK15(sK5)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_412536]) ).
tcf(c_419077,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,set_intersection2(X1,sK15(sK5))),sK5)
| in(sK7(X0,X2,set_intersection2(X1,sK15(sK5))),relation_dom(X0))
| ( set_intersection2(X1,sK15(sK5)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_412536]) ).
tcf(c_419078,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,set_intersection2(sK15(sK5),X1)),sK5)
| in(apply(X0,sK7(X0,X2,set_intersection2(sK15(sK5),X1))),X2)
| ( set_intersection2(sK15(sK5),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_412536]) ).
tcf(c_419079,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,set_intersection2(sK15(sK5),X1)),sK5)
| in(sK7(X0,X2,set_intersection2(sK15(sK5),X1)),relation_dom(X0))
| ( set_intersection2(sK15(sK5),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_412536]) ).
tcf(c_419080,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,sK15(sK5))),relation_dom(X0))
| in(apply(X1,sK7(X0,X2,relation_inverse_image(X1,sK15(sK5)))),sK5)
| ( relation_inverse_image(X1,sK15(sK5)) = relation_inverse_image(X0,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368819,c_412536]) ).
tcf(c_419081,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,sK7(X0,X2,relation_inverse_image(X1,sK15(sK5)))),sK5)
| in(apply(X0,sK7(X0,X2,relation_inverse_image(X1,sK15(sK5)))),X2)
| ( relation_inverse_image(X1,sK15(sK5)) = relation_inverse_image(X0,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_412536]) ).
tcf(c_419082,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK15(sK5)),sK5)
| in(sK7(X0,X2,sK15(sK5)),X1)
| ( relation_inverse_image(X0,X2) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_412536]) ).
tcf(c_419083,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),sK5)
| in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK15(sK5)) ),
inference(superposition,[status(thm)],[c_369017,c_412536]) ).
tcf(c_419084,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,sK15(sK5)),sK5)
| in(sK12(X0,X2,sK15(sK5)),X1)
| ( relation_image(X0,X2) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_412536]) ).
tcf(c_419085,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,X2),sK5)
| in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK15(sK5)) ),
inference(superposition,[status(thm)],[c_369214,c_412536]) ).
tcf(c_419086,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X2,sK15(sK5),X0),X1)
| in(apply(X2,sK7(X2,sK15(sK5),X0)),sK5)
| ( relation_inverse_image(X2,sK15(sK5)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_412536]) ).
tcf(c_419087,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK7(X0,sK15(sK5),X1)),sK5)
| ( relation_inverse_image(X0,sK15(sK5)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368872,c_412536]) ).
tcf(c_419088,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK15(sK5),set_intersection2(X1,X2)),X1)
| in(apply(X0,sK7(X0,sK15(sK5),set_intersection2(X1,X2))),sK5)
| ( relation_inverse_image(X0,sK15(sK5)) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_412536]) ).
tcf(c_419089,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK15(sK5),set_intersection2(X1,X2)),X2)
| in(apply(X0,sK7(X0,sK15(sK5),set_intersection2(X1,X2))),sK5)
| ( relation_inverse_image(X0,sK15(sK5)) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_412536]) ).
tcf(c_419090,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,sK15(sK5),relation_inverse_image(X1,X2))),sK5)
| in(apply(X1,sK7(X0,sK15(sK5),relation_inverse_image(X1,X2))),X2)
| ( relation_inverse_image(X0,sK15(sK5)) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_412536]) ).
tcf(c_419091,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK15(sK5),relation_inverse_image(X1,X2)),relation_dom(X1))
| in(apply(X0,sK7(X0,sK15(sK5),relation_inverse_image(X1,X2))),sK5)
| ( relation_inverse_image(X0,sK15(sK5)) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368762,c_412536]) ).
tcf(c_419092,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,sK15(sK5),relation_image(X1,X2))),sK5)
| ( relation_inverse_image(X0,sK15(sK5)) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK7(X0,sK15(sK5),relation_image(X1,X2)))) = sK7(X0,sK15(sK5),relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369664,c_412536]) ).
tcf(c_419093,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X0,X2),X2)
| in(apply(X1,sK7(X1,X0,X2)),sK5)
| ( relation_inverse_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_369018,c_412536]) ).
tcf(c_419094,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X2,X0,sK15(sK5)),sK5)
| in(apply(X2,sK7(X2,X0,sK15(sK5))),X1)
| ( relation_inverse_image(X2,X0) = sK15(sK5) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_412536]) ).
tcf(c_419095,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,set_intersection2(X1,X2),sK15(sK5)),sK5)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),sK15(sK5))),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_412536]) ).
tcf(c_419096,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,set_intersection2(X1,X2),sK15(sK5)),sK5)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),sK15(sK5))),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_412536]) ).
tcf(c_419097,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,set_intersection2(X1,sK15(sK5)),X2),X2)
| in(apply(X0,sK7(X0,set_intersection2(X1,sK15(sK5)),X2)),sK5)
| ( relation_inverse_image(X0,set_intersection2(X1,sK15(sK5))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_412536]) ).
tcf(c_419098,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,set_intersection2(sK15(sK5),X1),X2),X2)
| in(apply(X0,sK7(X0,set_intersection2(sK15(sK5),X1),X2)),sK5)
| ( relation_inverse_image(X0,set_intersection2(sK15(sK5),X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_412536]) ).
tcf(c_419099,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),sK15(sK5)),sK5)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X2),sK15(sK5)))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = sK15(sK5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_412536]) ).
tcf(c_419100,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),sK15(sK5)),sK5)
| in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),sK15(sK5))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = sK15(sK5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368761,c_412536]) ).
tcf(c_419101,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_inverse_image(X1,sK15(sK5)),X2),X2)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,sK15(sK5)),X2))),sK5)
| ( relation_inverse_image(X0,relation_inverse_image(X1,sK15(sK5))) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_412536]) ).
tcf(c_419102,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_image(X1,X2),sK15(sK5)),sK5)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = sK15(sK5) )
| ( apply(X1,sK13(X1,X2,apply(X0,sK7(X0,relation_image(X1,X2),sK15(sK5))))) = apply(X0,sK7(X0,relation_image(X1,X2),sK15(sK5))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369663,c_412536]) ).
tcf(c_419103,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,sK11(X0,X2,relation_inverse_image(X1,sK15(sK5)))),sK5)
| ( relation_inverse_image(X1,sK15(sK5)) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,relation_inverse_image(X1,sK15(sK5)))) = sK11(X0,X2,relation_inverse_image(X1,sK15(sK5))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369441,c_412536]) ).
tcf(c_420175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X2,X3,X0),X1)
| in(sK2(X2,X3,X0),X2)
| ( set_intersection2(X2,X3) = X0 )
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_369929,c_99]) ).
tcf(c_420176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,X2),X3)
| ( set_intersection2(X0,X1) = X2 )
| ~ subset(X2,X3)
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1) ),
inference(superposition,[status(thm)],[c_369929,c_54]) ).
tcf(c_420177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,X4,X0),X3)
| element(sK2(X2,X4,X0),X1)
| ( set_intersection2(X2,X4) = X0 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369929,c_321]) ).
tcf(c_420178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,X4,X0),X1)
| ( set_intersection2(X2,X4) = X0 )
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369929,c_320]) ).
tcf(c_420179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X1,X2),X3)
| ( set_intersection2(X0,X1) = X2 )
| ~ subset(X2,X3)
| ~ in(X0,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_369929,c_97]) ).
tcf(c_420180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,X4,X0),X1)
| in(sK2(X2,X4,X0),X3)
| ( set_intersection2(X2,X4) = X0 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369929,c_96]) ).
tcf(c_420187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(relation_dom(X0),X1,X2),X4)
| ( set_intersection2(relation_dom(X0),X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK2(relation_dom(X0),X1,X2)))) = apply(X0,sK2(relation_dom(X0),X1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ in(sK2(relation_dom(X0),X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369929,c_369671]) ).
tcf(c_420188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(relation_image(X4,X2),X5,X0),X1)
| ( set_intersection2(relation_image(X4,X2),X5) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369929,c_369799]) ).
tcf(c_420189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(relation_image(X0,X4),X5,X2),X3)
| ( set_intersection2(relation_image(X0,X4),X5) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369929,c_369798]) ).
tcf(c_420190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(relation_image(X2,X3),X4,X0),X1)
| ( set_intersection2(relation_image(X2,X3),X4) = X0 )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369929,c_369596]) ).
tcf(c_420191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(relation_image(X2,X3),X4,X0),X1)
| ( set_intersection2(relation_image(X2,X3),X4) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369929,c_369558]) ).
tcf(c_420193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(relation_dom(X0),X1,X2),X4)
| ( set_intersection2(relation_dom(X0),X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ empty(relation_image(X0,X3))
| ~ in(sK2(relation_dom(X0),X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369929,c_369501]) ).
tcf(c_420194,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(empty_set,X2,X0),X1)
| ( set_intersection2(empty_set,X2) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369929,c_372426]) ).
tcf(c_420195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(relation_image(X2,relation_image(X3,X4)),X5,X0),X1)
| ( set_intersection2(relation_image(X2,relation_image(X3,X4)),X5) = X0 )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK2(relation_image(X2,relation_image(X3,X4)),X5,X0)))) = sK13(X2,relation_image(X3,X4),sK2(relation_image(X2,relation_image(X3,X4)),X5,X0)) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369929,c_369672]) ).
tcf(c_420196,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X2,X0),sK5)
| element(sK2(sK15(sK5),X2,X0),X1)
| ( set_intersection2(sK15(sK5),X2) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369929,c_412536]) ).
tcf(c_420321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(X4,set_intersection2(X2,X3))
| ~ in(X4,X1)
| ~ in(X4,X0)
| ~ subset(set_intersection2(X0,X1),X3)
| ~ subset(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_65,c_369930]) ).
tcf(c_420324,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_380919,c_369930]) ).
tcf(c_420325,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_380850,c_369930]) ).
tcf(c_420331,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK5)
| ~ subset(sK15(sK5),X1)
| ~ in(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_369930]) ).
tcf(c_420332,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK8)
| ~ subset(sK15(sK8),X1)
| ~ in(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_369930]) ).
tcf(c_420365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK7(X0,X2,X3),X1)
| in(sK7(X0,X2,X3),X3)
| ( relation_inverse_image(X0,X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),powerset(X1)) ),
inference(superposition,[status(thm)],[c_369931,c_99]) ).
tcf(c_420366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X4,X2),X3)
| element(sK7(X0,X4,X2),X1)
| ( relation_inverse_image(X0,X4) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369931,c_321]) ).
tcf(c_420367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X4,X2),X1)
| ( relation_inverse_image(X0,X4) = X2 )
| ~ empty(X3)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369931,c_320]) ).
tcf(c_420368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X1,X2,X0),X3)
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ in(X0,sK7(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369931,c_97]) ).
tcf(c_420376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X1,relation_dom(X2)),X4)
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK7(X0,X1,relation_dom(X2))))) = apply(X2,sK7(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X4)
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369931,c_369671]) ).
tcf(c_420377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK7(X0,X5,relation_image(X4,X2)),X1)
| ( relation_inverse_image(X0,X5) = relation_image(X4,X2) )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369931,c_369799]) ).
tcf(c_420378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK7(X0,X4,relation_image(X2,X5)),X1)
| ( relation_inverse_image(X0,X4) = relation_image(X2,X5) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X2),X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369931,c_369798]) ).
tcf(c_420379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X4,relation_image(X2,X3)),X1)
| ( relation_inverse_image(X0,X4) = relation_image(X2,X3) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369931,c_369596]) ).
tcf(c_420380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X3,relation_image(X2,X4)),X1)
| ( relation_inverse_image(X0,X3) = relation_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_dom(X2))
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369931,c_369558]) ).
tcf(c_420382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X1,relation_dom(X2)),X4)
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X4)
| ~ empty(relation_image(X2,X3))
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369931,c_369501]) ).
tcf(c_420383,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,X2,empty_set),X1)
| ( relation_inverse_image(X0,X2) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369931,c_372426]) ).
tcf(c_420384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK7(X0,X5,relation_image(X2,relation_image(X3,X4))),X1)
| ( relation_image(X2,relation_image(X3,X4)) = relation_inverse_image(X0,X5) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK7(X0,X5,relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK7(X0,X5,relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369931,c_369672]) ).
tcf(c_420385,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK15(sK5)),sK5)
| element(sK7(X0,X2,sK15(sK5)),X1)
| ( relation_inverse_image(X0,X2) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369931,c_412536]) ).
tcf(c_420386,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,relation_image(X0,X1),relation_dom(X0)),X2)
| ( relation_inverse_image(X0,relation_image(X0,X1)) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X2)
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369931,c_369502]) ).
tcf(c_420691,plain,
in(sK16(sK15(sK5)),sK5),
inference(global_subsumption_just,[status(thm)],[c_412579,c_78,c_6041,c_36351]) ).
tcf(c_420693,plain,
! [X0: $i] :
( element(sK16(sK15(sK5)),X0)
| ~ subset(sK5,X0) ),
inference(superposition,[status(thm)],[c_420691,c_321]) ).
tcf(c_420694,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ subset(sK5,X0) ),
inference(superposition,[status(thm)],[c_420691,c_320]) ).
tcf(c_420695,plain,
~ in(sK5,sK16(sK15(sK5))),
inference(superposition,[status(thm)],[c_420691,c_97]) ).
tcf(c_420696,plain,
! [X0: $i] :
( in(sK16(sK15(sK5)),X0)
| ~ subset(sK5,X0) ),
inference(superposition,[status(thm)],[c_420691,c_96]) ).
tcf(c_420697,plain,
element(sK16(sK15(sK5)),sK5),
inference(superposition,[status(thm)],[c_420691,c_93]) ).
tcf(c_420718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X4,X0,X2),X3)
| element(apply(X4,sK7(X4,X0,X2)),X1)
| ( relation_inverse_image(X4,X0) = X2 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369932,c_321]) ).
tcf(c_420719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(apply(X4,sK7(X4,X0,X2)),X1)
| ( relation_inverse_image(X4,X0) = X2 )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369932,c_320]) ).
tcf(c_420720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X1,sK7(X1,X2,X0)),X3)
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,sK7(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369932,c_97]) ).
tcf(c_420721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK7(X4,X0,X2),X3)
| element(apply(X4,sK7(X4,X0,X2)),X1)
| ( relation_inverse_image(X4,X0) = X2 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369932,c_96]) ).
tcf(c_420728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(apply(X0,sK7(X0,X1,relation_dom(X2))),X4)
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK7(X0,X1,relation_dom(X2))))) = apply(X2,sK7(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(X1,X4)
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369932,c_369671]) ).
tcf(c_420729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(apply(X4,sK7(X4,X0,relation_image(X5,X2))),X1)
| ( relation_inverse_image(X4,X0) = relation_image(X5,X2) )
| ~ empty(X3)
| ~ function(X5)
| ~ function(X4)
| ~ relation(X5)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369932,c_369799]) ).
tcf(c_420730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(apply(X4,sK7(X4,X2,relation_image(X0,X5))),X3)
| ( relation_inverse_image(X4,X2) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369932,c_369798]) ).
tcf(c_420731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(apply(X2,sK7(X2,X0,relation_image(X3,X4))),X1)
| ( relation_inverse_image(X2,X0) = relation_image(X3,X4) )
| ~ empty(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369932,c_369596]) ).
tcf(c_420732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(apply(X3,sK7(X3,X0,relation_image(X2,X4))),X1)
| ( relation_inverse_image(X3,X0) = relation_image(X2,X4) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369932,c_369558]) ).
tcf(c_420734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(apply(X0,sK7(X0,X1,relation_dom(X2))),X4)
| ( relation_inverse_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(X1,X4)
| ~ empty(relation_image(X2,X3))
| ~ in(sK7(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369932,c_369501]) ).
tcf(c_420735,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(X2,sK7(X2,X0,empty_set)),X1)
| ( relation_inverse_image(X2,X0) = empty_set )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369932,c_372426]) ).
tcf(c_420736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(apply(X2,sK7(X2,X0,relation_image(X3,relation_image(X4,X5)))),X1)
| ( relation_image(X3,relation_image(X4,X5)) = relation_inverse_image(X2,X0) )
| ( apply(X4,sK13(X4,X5,sK13(X3,relation_image(X4,X5),sK7(X2,X0,relation_image(X3,relation_image(X4,X5)))))) = sK13(X3,relation_image(X4,X5),sK7(X2,X0,relation_image(X3,relation_image(X4,X5)))) )
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369932,c_369672]) ).
tcf(c_420737,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X2,X0,sK15(sK5)),sK5)
| element(apply(X2,sK7(X2,X0,sK15(sK5))),X1)
| ( relation_inverse_image(X2,X0) = sK15(sK5) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369932,c_412536]) ).
tcf(c_420738,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(X0,sK7(X0,relation_image(X0,X1),relation_dom(X0))),X2)
| ( relation_inverse_image(X0,relation_image(X0,X1)) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_image(X0,X1),X2)
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),X1)
| ~ in(sK7(X0,relation_image(X0,X1),relation_dom(X0)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369932,c_369502]) ).
tcf(c_420740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X0,X3),X3)
| subset(apply(X2,sK7(X2,X0,X3)),X1)
| ( relation_inverse_image(X2,X0) = X3 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_369932,c_99]) ).
tcf(c_420894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK7(X2,X3,X0),X1)
| in(apply(X2,sK7(X2,X3,X0)),X3)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_369933,c_99]) ).
tcf(c_420895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X4,X2,X0),X1)
| element(apply(X4,sK7(X4,X2,X0)),X3)
| ( relation_inverse_image(X4,X2) = X0 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369933,c_321]) ).
tcf(c_420896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X4,X2,X0),X1)
| ( relation_inverse_image(X4,X2) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369933,c_320]) ).
tcf(c_420897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X1,X0,X2),X3)
| ( relation_inverse_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,apply(X1,sK7(X1,X0,X2))) ),
inference(superposition,[status(thm)],[c_369933,c_97]) ).
tcf(c_420898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X4,X2,X0),X1)
| in(apply(X4,sK7(X4,X2,X0)),X3)
| ( relation_inverse_image(X4,X2) = X0 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369933,c_96]) ).
tcf(c_420903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X1,X2),X3)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ in(sK7(X0,X1,X2),X2)
| ~ in(sK7(X0,X1,X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369933,c_83]) ).
tcf(c_420904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X1,X2),X3)
| in(sK7(X0,X1,X2),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ in(sK7(X0,X1,X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369933,c_86]) ).
tcf(c_420907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,relation_dom(X1),X2),X4)
| ( relation_inverse_image(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,apply(X0,sK7(X0,relation_dom(X1),X2))))) = apply(X1,apply(X0,sK7(X0,relation_dom(X1),X2))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ in(apply(X0,sK7(X0,relation_dom(X1),X2)),X3) ),
inference(superposition,[status(thm)],[c_369933,c_369671]) ).
tcf(c_420908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK7(X4,relation_image(X5,X2),X0),X1)
| ( relation_inverse_image(X4,relation_image(X5,X2)) = X0 )
| ~ empty(X3)
| ~ function(X5)
| ~ function(X4)
| ~ relation(X5)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369933,c_369799]) ).
tcf(c_420909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK7(X4,relation_image(X0,X5),X2),X3)
| ( relation_inverse_image(X4,relation_image(X0,X5)) = X2 )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369933,c_369798]) ).
tcf(c_420910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X2,relation_image(X3,X4),X0),X1)
| ( relation_inverse_image(X2,relation_image(X3,X4)) = X0 )
| ~ empty(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369933,c_369596]) ).
tcf(c_420911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X3,relation_image(X2,X4),X0),X1)
| ( relation_inverse_image(X3,relation_image(X2,X4)) = X0 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369933,c_369558]) ).
tcf(c_420913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,relation_dom(X1),X2),X4)
| ( relation_inverse_image(X0,relation_dom(X1)) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ empty(relation_image(X1,X3))
| ~ in(apply(X0,sK7(X0,relation_dom(X1),X2)),X3) ),
inference(superposition,[status(thm)],[c_369933,c_369501]) ).
tcf(c_420914,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X2,empty_set,X0),X1)
| ( relation_inverse_image(X2,empty_set) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369933,c_372426]) ).
tcf(c_420915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK7(X2,relation_image(X3,relation_image(X4,X5)),X0),X1)
| ( relation_inverse_image(X2,relation_image(X3,relation_image(X4,X5))) = X0 )
| ( apply(X4,sK13(X4,X5,sK13(X3,relation_image(X4,X5),apply(X2,sK7(X2,relation_image(X3,relation_image(X4,X5)),X0))))) = sK13(X3,relation_image(X4,X5),apply(X2,sK7(X2,relation_image(X3,relation_image(X4,X5)),X0))) )
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369933,c_369672]) ).
tcf(c_420916,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X2,sK15(sK5),X0),X1)
| in(apply(X2,sK7(X2,sK15(sK5),X0)),sK5)
| ( relation_inverse_image(X2,sK15(sK5)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369933,c_412536]) ).
tcf(c_421064,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(empty_set,X2,X0),empty_set)
| element(sK7(empty_set,X2,X0),X1)
| ( relation_inverse_image(empty_set,X2) = X0 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_373108,c_369934]) ).
tcf(c_421066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK7(X2,X3,X0),X1)
| in(sK7(X2,X3,X0),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_369934,c_99]) ).
tcf(c_421068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X4,X2),X3)
| ( relation_inverse_image(X0,X4) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369934,c_320]) ).
tcf(c_421069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X1,X2),X3)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ in(relation_dom(X0),sK7(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_369934,c_97]) ).
tcf(c_421072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X2,X3,X0),X1)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369934,c_91]) ).
tcf(c_421073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X1,X2),X4)
| ( relation_inverse_image(X0,X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK7(X0,X1,X2)))) = apply(X0,sK7(X0,X1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369934,c_369671]) ).
tcf(c_421074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK7(X0,X1,X2),X4)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ empty(relation_image(X0,X3))
| ~ in(sK7(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369934,c_369501]) ).
tcf(c_421075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,relation_image(X0,X1),X2),X3)
| ( relation_inverse_image(X0,relation_image(X0,X1)) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ in(sK7(X0,relation_image(X0,X1),X2),X2)
| ~ in(sK7(X0,relation_image(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_369934,c_369502]) ).
tcf(c_421082,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(empty_set,X2,X0),X1)
| ( relation_inverse_image(empty_set,X2) = X0 )
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_421064,c_372426,c_368630,c_103]) ).
tcf(c_421153,plain,
! [X0: $i,X1: $i] :
( ~ subset(sK5,X1)
| ~ subset(sK5,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_420694]) ).
tcf(c_421164,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| subset(sK10(X0,X2),X1)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_369935,c_99]) ).
tcf(c_421181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK11(X2,X3,X0),X1)
| ( relation_image(X2,X3) = X0 )
| ( apply(X2,sK12(X2,X3,X0)) = sK11(X2,X3,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_369936,c_99]) ).
tcf(c_421201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK11(X2,X3,X0),X1)
| in(sK12(X2,X3,X0),X3)
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_369937,c_99]) ).
tcf(c_421202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X4,X2,X0),X3)
| element(sK11(X4,X2,X0),X1)
| ( relation_image(X4,X2) = X0 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369937,c_321]) ).
tcf(c_421203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X4,X2,X0),X1)
| ( relation_image(X4,X2) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369937,c_320]) ).
tcf(c_421204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X1,X0,X2),X3)
| ( relation_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,sK12(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_369937,c_97]) ).
tcf(c_421205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X4,X2,X0),X1)
| in(sK12(X4,X2,X0),X3)
| ( relation_image(X4,X2) = X0 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369937,c_96]) ).
tcf(c_421212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X0,relation_dom(X1),X2),X4)
| ( relation_image(X0,relation_dom(X1)) = X2 )
| ( apply(X1,sK13(X1,X3,apply(X1,sK12(X0,relation_dom(X1),X2)))) = apply(X1,sK12(X0,relation_dom(X1),X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ in(sK12(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_369937,c_369671]) ).
tcf(c_421213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK11(X4,relation_image(X5,X2),X0),X1)
| ( relation_image(X4,relation_image(X5,X2)) = X0 )
| ~ empty(X3)
| ~ function(X5)
| ~ function(X4)
| ~ relation(X5)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369937,c_369799]) ).
tcf(c_421214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK11(X4,relation_image(X0,X5),X2),X3)
| ( relation_image(X4,relation_image(X0,X5)) = X2 )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369937,c_369798]) ).
tcf(c_421215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X2,relation_image(X3,X4),X0),X1)
| ( relation_image(X2,relation_image(X3,X4)) = X0 )
| ~ empty(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369937,c_369596]) ).
tcf(c_421216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X3,relation_image(X2,X4),X0),X1)
| ( relation_image(X3,relation_image(X2,X4)) = X0 )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369937,c_369558]) ).
tcf(c_421218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X0,relation_dom(X1),X2),X4)
| ( relation_image(X0,relation_dom(X1)) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ empty(relation_image(X1,X3))
| ~ in(sK12(X0,relation_dom(X1),X2),X3) ),
inference(superposition,[status(thm)],[c_369937,c_369501]) ).
tcf(c_421219,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK11(X2,empty_set,X0),X1)
| ( relation_image(X2,empty_set) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369937,c_372426]) ).
tcf(c_421220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK11(X2,relation_image(X3,relation_image(X4,X5)),X0),X1)
| ( relation_image(X2,relation_image(X3,relation_image(X4,X5))) = X0 )
| ( apply(X4,sK13(X4,X5,sK13(X3,relation_image(X4,X5),sK12(X2,relation_image(X3,relation_image(X4,X5)),X0)))) = sK13(X3,relation_image(X4,X5),sK12(X2,relation_image(X3,relation_image(X4,X5)),X0)) )
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369937,c_369672]) ).
tcf(c_421221,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X2,sK15(sK5),X0),sK5)
| element(sK11(X2,sK15(sK5),X0),X1)
| ( relation_image(X2,sK15(sK5)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369937,c_412536]) ).
tcf(c_421354,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(empty_set,X2,X0),empty_set)
| element(sK11(empty_set,X2,X0),X1)
| ( relation_image(empty_set,X2) = X0 )
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_373108,c_369938]) ).
tcf(c_421356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK11(X2,X3,X0),X1)
| in(sK12(X2,X3,X0),relation_dom(X2))
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_369938,c_99]) ).
tcf(c_421357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X4,X2),X1)
| element(sK11(X0,X4,X2),X3)
| ( relation_image(X0,X4) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369938,c_321]) ).
tcf(c_421358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X0,X4,X2),X3)
| ( relation_image(X0,X4) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369938,c_320]) ).
tcf(c_421359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X0,X1,X2),X3)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ in(relation_dom(X0),sK12(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_369938,c_97]) ).
tcf(c_421362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X2,X3,X0),X1)
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369938,c_91]) ).
tcf(c_421363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X0,X1,X2),X4)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK13(X0,X3,apply(X0,sK12(X0,X1,X2)))) = apply(X0,sK12(X0,X1,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ in(sK12(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369938,c_369671]) ).
tcf(c_421364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK11(X0,X1,X2),X4)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X4)
| ~ empty(relation_image(X0,X3))
| ~ in(sK12(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_369938,c_369501]) ).
tcf(c_421371,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK11(empty_set,X2,X0),X1)
| ( relation_image(empty_set,X2) = X0 )
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_421354,c_372426,c_368630,c_103]) ).
tcf(c_421436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK12(X0,X2,X3),X1)
| in(sK11(X0,X2,X3),X3)
| ( relation_image(X0,X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),powerset(X1)) ),
inference(superposition,[status(thm)],[c_369939,c_99]) ).
tcf(c_421438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X4,X2),X1)
| ( relation_image(X0,X4) = X2 )
| ~ empty(X3)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369939,c_320]) ).
tcf(c_421439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X1,X2,X0),X3)
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ in(X0,sK11(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369939,c_97]) ).
tcf(c_421447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X1,relation_dom(X2)),X4)
| ( relation_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK11(X0,X1,relation_dom(X2))))) = apply(X2,sK11(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X4)
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369939,c_369671]) ).
tcf(c_421448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK12(X0,X5,relation_image(X4,X2)),X1)
| ( relation_image(X0,X5) = relation_image(X4,X2) )
| ~ empty(X3)
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369939,c_369799]) ).
tcf(c_421449,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK12(X0,X4,relation_image(X2,X5)),X1)
| ( relation_image(X0,X4) = relation_image(X2,X5) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X2),X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369939,c_369798]) ).
tcf(c_421450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X4,relation_image(X2,X3)),X1)
| ( relation_image(X0,X4) = relation_image(X2,X3) )
| ~ empty(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369939,c_369596]) ).
tcf(c_421451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X3,relation_image(X2,X4)),X1)
| ( relation_image(X0,X3) = relation_image(X2,X4) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_dom(X2))
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369939,c_369558]) ).
tcf(c_421453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X1,relation_dom(X2)),X4)
| ( relation_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X4)
| ~ empty(relation_image(X2,X3))
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369939,c_369501]) ).
tcf(c_421454,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK12(X0,X2,empty_set),X1)
| ( relation_image(X0,X2) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369939,c_372426]) ).
tcf(c_421455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK12(X0,X5,relation_image(X2,relation_image(X3,X4))),X1)
| ( relation_image(X2,relation_image(X3,X4)) = relation_image(X0,X5) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK11(X0,X5,relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK11(X0,X5,relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369939,c_369672]) ).
tcf(c_421456,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,sK15(sK5)),sK5)
| element(sK12(X0,X2,sK15(sK5)),X1)
| ( relation_image(X0,X2) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369939,c_412536]) ).
tcf(c_421593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK12(X2,X0,X3),X1)
| in(sK11(X2,X0,X3),X3)
| ( relation_image(X2,X0) = X3 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_369940,c_99]) ).
tcf(c_421594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X4,X0,X2),X1)
| element(sK11(X4,X0,X2),X3)
| ( relation_image(X4,X0) = X2 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369940,c_321]) ).
tcf(c_421595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X4,X0,X2),X1)
| ( relation_image(X4,X0) = X2 )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369940,c_320]) ).
tcf(c_421596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X1,X2,X0),X3)
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,sK11(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_369940,c_97]) ).
tcf(c_421597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X4,X0,X2),X1)
| in(sK11(X4,X0,X2),X3)
| ( relation_image(X4,X0) = X2 )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369940,c_96]) ).
tcf(c_421604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X1,relation_dom(X2)),X4)
| ( relation_image(X0,X1) = relation_dom(X2) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK11(X0,X1,relation_dom(X2))))) = apply(X2,sK11(X0,X1,relation_dom(X2))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(X1,X4)
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369940,c_369671]) ).
tcf(c_421605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK12(X4,X0,relation_image(X5,X2)),X1)
| ( relation_image(X4,X0) = relation_image(X5,X2) )
| ~ empty(X3)
| ~ function(X5)
| ~ function(X4)
| ~ relation(X5)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369940,c_369799]) ).
tcf(c_421606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK12(X4,X2,relation_image(X0,X5)),X3)
| ( relation_image(X0,X5) = relation_image(X4,X2) )
| ~ empty(X1)
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369940,c_369798]) ).
tcf(c_421607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X2,X0,relation_image(X3,X4)),X1)
| ( relation_image(X2,X0) = relation_image(X3,X4) )
| ~ empty(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369940,c_369596]) ).
tcf(c_421608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X3,X0,relation_image(X2,X4)),X1)
| ( relation_image(X2,X4) = relation_image(X3,X0) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369940,c_369558]) ).
tcf(c_421610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK12(X0,X1,relation_dom(X2)),X4)
| ( relation_image(X0,X1) = relation_dom(X2) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(X1,X4)
| ~ empty(relation_image(X2,X3))
| ~ in(sK11(X0,X1,relation_dom(X2)),X3) ),
inference(superposition,[status(thm)],[c_369940,c_369501]) ).
tcf(c_421611,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK12(X2,X0,empty_set),X1)
| ( relation_image(X2,X0) = empty_set )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369940,c_372426]) ).
tcf(c_421612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK12(X2,X0,relation_image(X3,relation_image(X4,X5))),X1)
| ( relation_image(X3,relation_image(X4,X5)) = relation_image(X2,X0) )
| ( apply(X4,sK13(X4,X5,sK13(X3,relation_image(X4,X5),sK11(X2,X0,relation_image(X3,relation_image(X4,X5)))))) = sK13(X3,relation_image(X4,X5),sK11(X2,X0,relation_image(X3,relation_image(X4,X5)))) )
| ~ function(X4)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369940,c_369672]) ).
tcf(c_421613,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X2,X0,sK15(sK5)),sK5)
| element(sK12(X2,X0,sK15(sK5)),X1)
| ( relation_image(X2,X0) = sK15(sK5) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369940,c_412536]) ).
tcf(c_421989,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),sK8)
| element(sK2(sK15(sK8),X0,X1),X1)
| ( set_intersection2(sK15(sK8),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_368927,c_413867]) ).
tcf(c_421991,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),sK8)
| element(sK2(X0,sK15(sK8),X1),X1)
| ( set_intersection2(X0,sK15(sK8)) = X1 ) ),
inference(superposition,[status(thm)],[c_368926,c_413867]) ).
tcf(c_421993,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),sK8)
| element(sK2(X0,X1,sK15(sK8)),X1)
| ( set_intersection2(X0,X1) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_368925,c_413867]) ).
tcf(c_421994,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),sK8)
| element(sK2(X0,X1,sK15(sK8)),X0)
| ( set_intersection2(X0,X1) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_368924,c_413867]) ).
tcf(c_421995,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK15(sK8)),sK8)
| ( set_intersection2(X0,X1) = sK15(sK8) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368865,c_413867]) ).
tcf(c_421998,plain,
! [X0: $i,X1: $i] :
( element(sK7(X0,sK15(sK8),X1),X1)
| in(apply(X0,sK7(X0,sK15(sK8),X1)),sK8)
| ( relation_inverse_image(X0,sK15(sK8)) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368931,c_413867]) ).
tcf(c_422000,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),sK8)
| element(apply(X0,sK7(X0,X1,sK15(sK8))),X1)
| ( relation_inverse_image(X0,X1) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368930,c_413867]) ).
tcf(c_422001,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),sK8)
| element(sK7(X0,X1,sK15(sK8)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368929,c_413867]) ).
tcf(c_422002,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),sK8)
| ( relation_inverse_image(X0,X1) = sK15(sK8) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368871,c_413867]) ).
tcf(c_422003,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),sK8)
| ( relation_inverse_image(X0,X1) = sK15(sK8) )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_413867]) ).
tcf(c_422004,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK15(sK8)),sK8)
| in(sK7(X0,X1,sK15(sK8)),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375319,c_413867]) ).
tcf(c_422008,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK8)
| ( relation_image(X0,X1) = sK15(sK8) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369301,c_413867]) ).
tcf(c_422009,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK8)
| element(sK12(X0,X1,sK15(sK8)),X1)
| ( relation_image(X0,X1) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369300,c_413867]) ).
tcf(c_422010,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK8)
| ( relation_image(X0,X1) = sK15(sK8) )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_386602,c_413867]) ).
tcf(c_422011,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1,sK15(sK8)),sK8)
| element(sK12(X0,X1,sK15(sK8)),relation_dom(X0))
| ( relation_image(X0,X1) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369215,c_413867]) ).
tcf(c_422015,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,sK15(sK8),X1),sK8)
| element(sK11(X0,sK15(sK8),X1),X1)
| ( relation_image(X0,sK15(sK8)) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369308,c_413867]) ).
tcf(c_422019,plain,
! [X0: $i,X1: $i] :
( subset(set_intersection2(sK15(sK8),X0),X1)
| in(sK10(set_intersection2(sK15(sK8),X0),X1),sK8) ),
inference(superposition,[status(thm)],[c_368986,c_413867]) ).
tcf(c_422020,plain,
! [X0: $i,X1: $i] :
( subset(set_intersection2(X0,sK15(sK8)),X1)
| in(sK10(set_intersection2(X0,sK15(sK8)),X1),sK8) ),
inference(superposition,[status(thm)],[c_368985,c_413867]) ).
tcf(c_422021,plain,
! [X0: $i] :
( empty(set_intersection2(sK15(sK8),X0))
| in(sK16(set_intersection2(X0,sK15(sK8))),sK8) ),
inference(superposition,[status(thm)],[c_389060,c_413867]) ).
tcf(c_422022,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK15(sK8)))
| in(sK16(set_intersection2(X0,sK15(sK8))),sK8) ),
inference(superposition,[status(thm)],[c_370750,c_413867]) ).
tcf(c_422023,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK15(sK8)))
| in(sK16(set_intersection2(sK15(sK8),X0)),sK8) ),
inference(superposition,[status(thm)],[c_388043,c_413867]) ).
tcf(c_422024,plain,
! [X0: $i] :
( empty(set_intersection2(sK15(sK8),X0))
| in(sK16(set_intersection2(sK15(sK8),X0)),sK8) ),
inference(superposition,[status(thm)],[c_370751,c_413867]) ).
tcf(c_422025,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK10(X0,X1),sK8)
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_369021,c_413867]) ).
tcf(c_422026,plain,
! [X0: $i] :
( empty(X0)
| in(sK16(X0),sK8)
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_370747,c_413867]) ).
tcf(c_422027,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(X0,sK15(sK8)),X1)
| in(apply(X0,sK10(relation_inverse_image(X0,sK15(sK8)),X1)),sK8)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368987,c_413867]) ).
tcf(c_422028,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X2,X0),sK8)
| element(sK2(sK15(sK8),X2,X0),X1)
| ( set_intersection2(sK15(sK8),X2) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369929,c_413867]) ).
tcf(c_422029,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X2,X0),sK8)
| in(sK2(sK15(sK8),X2,X0),X1)
| ( set_intersection2(sK15(sK8),X2) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_413867]) ).
tcf(c_422030,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),sK8)
| in(sK2(X1,X2,X0),X1)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_369015,c_413867]) ).
tcf(c_422031,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),sK8)
| in(sK2(X1,X2,X0),X2)
| ( set_intersection2(X1,X2) = X0 )
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_369014,c_413867]) ).
tcf(c_422032,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X1,X0),sK8)
| ( set_intersection2(sK15(sK8),X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368868,c_413867]) ).
tcf(c_422033,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X0,set_intersection2(X1,X2)),sK8)
| in(sK2(sK15(sK8),X0,set_intersection2(X1,X2)),X2)
| ( set_intersection2(sK15(sK8),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368506,c_413867]) ).
tcf(c_422034,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X0,set_intersection2(X1,X2)),sK8)
| in(sK2(sK15(sK8),X0,set_intersection2(X1,X2)),X1)
| ( set_intersection2(sK15(sK8),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368484,c_413867]) ).
tcf(c_422035,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,set_intersection2(X0,sK15(sK8))),sK8)
| in(sK2(X1,X2,set_intersection2(X0,sK15(sK8))),X1)
| ( set_intersection2(X0,sK15(sK8)) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368506,c_413867]) ).
tcf(c_422036,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,set_intersection2(X0,sK15(sK8))),sK8)
| in(sK2(X1,X2,set_intersection2(X0,sK15(sK8))),X2)
| ( set_intersection2(X0,sK15(sK8)) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368505,c_413867]) ).
tcf(c_422037,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,set_intersection2(sK15(sK8),X0)),sK8)
| in(sK2(X1,X2,set_intersection2(sK15(sK8),X0)),X1)
| ( set_intersection2(sK15(sK8),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368484,c_413867]) ).
tcf(c_422038,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,set_intersection2(sK15(sK8),X0)),sK8)
| in(sK2(X1,X2,set_intersection2(sK15(sK8),X0)),X2)
| ( set_intersection2(sK15(sK8),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368483,c_413867]) ).
tcf(c_422039,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,sK15(sK8))),X1)
| in(apply(X0,sK2(X1,X2,relation_inverse_image(X0,sK15(sK8)))),sK8)
| ( relation_inverse_image(X0,sK15(sK8)) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_413867]) ).
tcf(c_422040,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,sK15(sK8))),X2)
| in(apply(X0,sK2(X1,X2,relation_inverse_image(X0,sK15(sK8)))),sK8)
| ( relation_inverse_image(X0,sK15(sK8)) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_413867]) ).
tcf(c_422041,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X1,relation_inverse_image(X0,X2)),sK8)
| in(apply(X0,sK2(sK15(sK8),X1,relation_inverse_image(X0,X2))),X2)
| ( set_intersection2(sK15(sK8),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_413867]) ).
tcf(c_422042,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X1,relation_inverse_image(X0,X2)),sK8)
| in(sK2(sK15(sK8),X1,relation_inverse_image(X0,X2)),relation_dom(X0))
| ( set_intersection2(sK15(sK8),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368760,c_413867]) ).
tcf(c_422043,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,sK15(sK8)),sK8)
| element(sK2(X0,X2,sK15(sK8)),X1)
| ( set_intersection2(X0,X2) = sK15(sK8) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369926,c_413867]) ).
tcf(c_422044,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,sK15(sK8)),sK8)
| in(sK2(X0,X2,sK15(sK8)),X1)
| ( set_intersection2(X0,X2) = sK15(sK8) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_413867]) ).
tcf(c_422045,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),sK8)
| in(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_369012,c_413867]) ).
tcf(c_422046,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),sK8)
| in(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_368503,c_413867]) ).
tcf(c_422047,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),sK8)
| in(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_368481,c_413867]) ).
tcf(c_422048,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,sK15(sK8)),X1,X2),sK8)
| in(sK2(set_intersection2(X0,sK15(sK8)),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,sK15(sK8)),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368503,c_413867]) ).
tcf(c_422049,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),sK8)
| in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(sK15(sK8),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368481,c_413867]) ).
tcf(c_422050,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,sK15(sK8)),sK8)
| in(apply(X0,sK2(relation_inverse_image(X0,X1),X2,sK15(sK8))),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_413867]) ).
tcf(c_422051,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,sK15(sK8)),sK8)
| in(sK2(relation_inverse_image(X0,X1),X2,sK15(sK8)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368757,c_413867]) ).
tcf(c_422052,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_inverse_image(X0,sK15(sK8)),X1,X2),X2)
| in(apply(X0,sK2(relation_inverse_image(X0,sK15(sK8)),X1,X2)),sK8)
| ( set_intersection2(relation_inverse_image(X0,sK15(sK8)),X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_413867]) ).
tcf(c_422053,plain,
! [X0: $i] :
( in(sK2(sK15(sK8),X0,sK15(sK8)),sK8)
| ( set_intersection2(sK15(sK8),X0) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_368448,c_413867]) ).
tcf(c_422054,plain,
! [X0: $i] :
( in(sK2(empty_set,X0,sK15(sK8)),sK8)
| ( sK15(sK8) = empty_set ) ),
inference(superposition,[status(thm)],[c_372470,c_413867]) ).
tcf(c_422055,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,sK15(sK8),X0),sK8)
| element(sK2(X2,sK15(sK8),X0),X1)
| ( set_intersection2(X2,sK15(sK8)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369928,c_413867]) ).
tcf(c_422056,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,sK15(sK8),X0),sK8)
| in(sK2(X2,sK15(sK8),X0),X1)
| ( set_intersection2(X2,sK15(sK8)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_413867]) ).
tcf(c_422057,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK15(sK8),X0),sK8)
| ( set_intersection2(X1,sK15(sK8)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368867,c_413867]) ).
tcf(c_422058,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK15(sK8),set_intersection2(X1,X2)),sK8)
| in(sK2(X0,sK15(sK8),set_intersection2(X1,X2)),X2)
| ( set_intersection2(X0,sK15(sK8)) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368505,c_413867]) ).
tcf(c_422059,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK15(sK8),set_intersection2(X1,X2)),sK8)
| in(sK2(X0,sK15(sK8),set_intersection2(X1,X2)),X1)
| ( set_intersection2(X0,sK15(sK8)) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_368483,c_413867]) ).
tcf(c_422060,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK8),relation_inverse_image(X0,X2)),sK8)
| in(apply(X0,sK2(X1,sK15(sK8),relation_inverse_image(X0,X2))),X2)
| ( set_intersection2(X1,sK15(sK8)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_413867]) ).
tcf(c_422061,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK8),relation_inverse_image(X0,X2)),sK8)
| in(sK2(X1,sK15(sK8),relation_inverse_image(X0,X2)),relation_dom(X0))
| ( set_intersection2(X1,sK15(sK8)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368759,c_413867]) ).
tcf(c_422062,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X0,sK15(sK8)),sK8)
| element(sK2(X2,X0,sK15(sK8)),X1)
| ( set_intersection2(X2,X0) = sK15(sK8) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369927,c_413867]) ).
tcf(c_422063,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X0,sK15(sK8)),sK8)
| in(sK2(X2,X0,sK15(sK8)),X1)
| ( set_intersection2(X2,X0) = sK15(sK8) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_413867]) ).
tcf(c_422064,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,X2),sK8)
| in(sK2(X1,X0,X2),X2)
| ( set_intersection2(X1,X0) = X2 )
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_369013,c_413867]) ).
tcf(c_422065,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,sK15(sK8)),sK8)
| ( set_intersection2(X1,X0) = sK15(sK8) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368866,c_413867]) ).
tcf(c_422066,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK8)),sK8)
| in(sK2(X0,set_intersection2(X1,X2),sK15(sK8)),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_368504,c_413867]) ).
tcf(c_422067,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK8)),sK8)
| in(sK2(X0,set_intersection2(X1,X2),sK15(sK8)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_368482,c_413867]) ).
tcf(c_422068,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,sK15(sK8)),X2),sK8)
| in(sK2(X0,set_intersection2(X1,sK15(sK8)),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,sK15(sK8))) = X2 ) ),
inference(superposition,[status(thm)],[c_368504,c_413867]) ).
tcf(c_422069,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(sK15(sK8),X1),X2),sK8)
| in(sK2(X0,set_intersection2(sK15(sK8),X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(sK15(sK8),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_368482,c_413867]) ).
tcf(c_422070,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,relation_inverse_image(X0,sK15(sK8)),X2),X2)
| in(apply(X0,sK2(X1,relation_inverse_image(X0,sK15(sK8)),X2)),sK8)
| ( set_intersection2(X1,relation_inverse_image(X0,sK15(sK8))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_413867]) ).
tcf(c_422071,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),sK15(sK8)),sK8)
| in(apply(X0,sK2(X1,relation_inverse_image(X0,X2),sK15(sK8))),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_413867]) ).
tcf(c_422072,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),sK15(sK8)),sK8)
| in(sK2(X1,relation_inverse_image(X0,X2),sK15(sK8)),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368758,c_413867]) ).
tcf(c_422073,plain,
! [X0: $i] :
( in(sK2(X0,sK15(sK8),sK15(sK8)),sK8)
| ( set_intersection2(X0,sK15(sK8)) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_368460,c_413867]) ).
tcf(c_422074,plain,
! [X0: $i] :
( in(sK2(X0,empty_set,sK15(sK8)),sK8)
| ( sK15(sK8) = empty_set ) ),
inference(superposition,[status(thm)],[c_372467,c_413867]) ).
tcf(c_422075,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,X2,X0),sK8)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,sK15(sK8))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_413867]) ).
tcf(c_422076,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,X2,X0),sK8)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),sK15(sK8))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369556,c_413867]) ).
tcf(c_422077,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,set_intersection2(X2,sK15(sK8)),X0),sK8)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_369597,c_413867]) ).
tcf(c_422078,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,set_intersection2(sK15(sK8),X2),X0),sK8)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(sK15(sK8),X2))) ),
inference(superposition,[status(thm)],[c_369598,c_413867]) ).
tcf(c_422079,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X2,sK13(X1,relation_inverse_image(X2,sK15(sK8)),X0)),sK8)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_369599,c_413867]) ).
tcf(c_422080,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_image(X0,X1),X2,sK15(sK8)),sK8)
| ( set_intersection2(relation_image(X0,X1),X2) = sK15(sK8) )
| ( apply(X0,sK13(X0,X1,sK2(relation_image(X0,X1),X2,sK15(sK8)))) = sK2(relation_image(X0,X1),X2,sK15(sK8)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369659,c_413867]) ).
tcf(c_422081,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,relation_image(X0,X1),sK15(sK8)),sK8)
| ( set_intersection2(X2,relation_image(X0,X1)) = sK15(sK8) )
| ( apply(X0,sK13(X0,X1,sK2(X2,relation_image(X0,X1),sK15(sK8)))) = sK2(X2,relation_image(X0,X1),sK15(sK8)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369660,c_413867]) ).
tcf(c_422082,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,sK15(sK8),relation_image(X0,X1)),sK8)
| ( set_intersection2(X2,sK15(sK8)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,sK15(sK8),relation_image(X0,X1)))) = sK2(X2,sK15(sK8),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369661,c_413867]) ).
tcf(c_422083,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X2,relation_image(X0,X1)),sK8)
| ( set_intersection2(sK15(sK8),X2) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(sK15(sK8),X2,relation_image(X0,X1)))) = sK2(sK15(sK8),X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369662,c_413867]) ).
tcf(c_422084,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X2,X0,sK15(sK8)),sK8)
| element(sK12(X2,X0,sK15(sK8)),X1)
| ( relation_image(X2,X0) = sK15(sK8) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369940,c_413867]) ).
tcf(c_422085,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X2,X0,sK15(sK8)),sK8)
| in(sK12(X2,X0,sK15(sK8)),X1)
| ( relation_image(X2,X0) = sK15(sK8) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_413867]) ).
tcf(c_422086,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X1,X0,X2),sK8)
| in(sK11(X1,X0,X2),X2)
| ( relation_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_369299,c_413867]) ).
tcf(c_422087,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,set_intersection2(X1,X2),sK15(sK8)),sK8)
| in(sK12(X0,set_intersection2(X1,X2),sK15(sK8)),X1)
| ( relation_image(X0,set_intersection2(X1,X2)) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_413867]) ).
tcf(c_422088,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,set_intersection2(X1,X2),sK15(sK8)),sK8)
| in(sK12(X0,set_intersection2(X1,X2),sK15(sK8)),X2)
| ( relation_image(X0,set_intersection2(X1,X2)) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_413867]) ).
tcf(c_422089,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,set_intersection2(X1,sK15(sK8)),X2),sK8)
| in(sK11(X0,set_intersection2(X1,sK15(sK8)),X2),X2)
| ( relation_image(X0,set_intersection2(X1,sK15(sK8))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_413867]) ).
tcf(c_422090,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,set_intersection2(sK15(sK8),X1),X2),sK8)
| in(sK11(X0,set_intersection2(sK15(sK8),X1),X2),X2)
| ( relation_image(X0,set_intersection2(sK15(sK8),X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_413867]) ).
tcf(c_422091,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),sK15(sK8)),sK8)
| in(sK12(X0,relation_inverse_image(X1,X2),sK15(sK8)),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X2)) = sK15(sK8) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369305,c_413867]) ).
tcf(c_422092,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),sK15(sK8)),sK8)
| in(apply(X1,sK12(X0,relation_inverse_image(X1,X2),sK15(sK8))),X2)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = sK15(sK8) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_413867]) ).
tcf(c_422093,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,relation_inverse_image(X1,sK15(sK8)),X2),X2)
| in(apply(X1,sK12(X0,relation_inverse_image(X1,sK15(sK8)),X2)),sK8)
| ( relation_image(X0,relation_inverse_image(X1,sK15(sK8))) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_413867]) ).
tcf(c_422094,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,relation_image(X1,X2),sK15(sK8)),sK8)
| ( relation_image(X0,relation_image(X1,X2)) = sK15(sK8) )
| ( apply(X1,sK13(X1,X2,sK12(X0,relation_image(X1,X2),sK15(sK8)))) = sK12(X0,relation_image(X1,X2),sK15(sK8)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369670,c_413867]) ).
tcf(c_422095,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X1,X2,X0),sK8)
| ( relation_image(X1,X2) = X0 )
| ( apply(X1,sK12(X1,X2,X0)) = sK11(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_369436,c_413867]) ).
tcf(c_422096,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X1,X2,X0),sK8)
| in(sK12(X1,X2,X0),X2)
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_369307,c_413867]) ).
tcf(c_422097,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X1,X2,X0),sK8)
| in(sK12(X1,X2,X0),relation_dom(X1))
| ( relation_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_369206,c_413867]) ).
tcf(c_422098,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X2,sK15(sK8),X0),sK8)
| element(sK11(X2,sK15(sK8),X0),X1)
| ( relation_image(X2,sK15(sK8)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369937,c_413867]) ).
tcf(c_422099,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X2,sK15(sK8),X0),sK8)
| in(sK11(X2,sK15(sK8),X0),X1)
| ( relation_image(X2,sK15(sK8)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_413867]) ).
tcf(c_422100,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,sK15(sK8),X1),sK8)
| ( relation_image(X0,sK15(sK8)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369309,c_413867]) ).
tcf(c_422101,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,sK15(sK8),set_intersection2(X1,X2)),sK8)
| in(sK11(X0,sK15(sK8),set_intersection2(X1,X2)),X1)
| ( relation_image(X0,sK15(sK8)) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_413867]) ).
tcf(c_422102,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,sK15(sK8),set_intersection2(X1,X2)),sK8)
| in(sK11(X0,sK15(sK8),set_intersection2(X1,X2)),X2)
| ( relation_image(X0,sK15(sK8)) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_413867]) ).
tcf(c_422103,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,set_intersection2(X2,sK15(sK8))),sK8)
| ( set_intersection2(X2,sK15(sK8)) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,sK15(sK8)))) = sK11(X0,X1,set_intersection2(X2,sK15(sK8))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369439,c_413867]) ).
tcf(c_422104,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,set_intersection2(X1,sK15(sK8))),sK8)
| in(sK12(X0,X2,set_intersection2(X1,sK15(sK8))),X2)
| ( set_intersection2(X1,sK15(sK8)) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_413867]) ).
tcf(c_422105,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,set_intersection2(X1,sK15(sK8))),sK8)
| in(sK12(X0,X2,set_intersection2(X1,sK15(sK8))),relation_dom(X0))
| ( set_intersection2(X1,sK15(sK8)) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369209,c_413867]) ).
tcf(c_422106,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,set_intersection2(sK15(sK8),X2)),sK8)
| ( set_intersection2(sK15(sK8),X2) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(sK15(sK8),X2))) = sK11(X0,X1,set_intersection2(sK15(sK8),X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369440,c_413867]) ).
tcf(c_422107,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,set_intersection2(sK15(sK8),X1)),sK8)
| in(sK12(X0,X2,set_intersection2(sK15(sK8),X1)),X2)
| ( set_intersection2(sK15(sK8),X1) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_413867]) ).
tcf(c_422108,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,set_intersection2(sK15(sK8),X1)),sK8)
| in(sK12(X0,X2,set_intersection2(sK15(sK8),X1)),relation_dom(X0))
| ( set_intersection2(sK15(sK8),X1) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369210,c_413867]) ).
tcf(c_422109,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,relation_inverse_image(X1,sK15(sK8))),X2)
| in(apply(X1,sK11(X0,X2,relation_inverse_image(X1,sK15(sK8)))),sK8)
| ( relation_inverse_image(X1,sK15(sK8)) = relation_image(X0,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_413867]) ).
tcf(c_422110,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,relation_inverse_image(X1,sK15(sK8))),relation_dom(X0))
| in(apply(X1,sK11(X0,X2,relation_inverse_image(X1,sK15(sK8)))),sK8)
| ( relation_inverse_image(X1,sK15(sK8)) = relation_image(X0,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369211,c_413867]) ).
tcf(c_422111,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,sK15(sK8),relation_inverse_image(X1,X2)),sK8)
| in(sK11(X0,sK15(sK8),relation_inverse_image(X1,X2)),relation_dom(X1))
| ( relation_image(X0,sK15(sK8)) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369313,c_413867]) ).
tcf(c_422112,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,sK15(sK8),relation_inverse_image(X1,X2)),sK8)
| in(apply(X1,sK11(X0,sK15(sK8),relation_inverse_image(X1,X2))),X2)
| ( relation_image(X0,sK15(sK8)) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_413867]) ).
tcf(c_422113,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,sK15(sK8),relation_image(X1,X2)),sK8)
| ( relation_image(X0,sK15(sK8)) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK11(X0,sK15(sK8),relation_image(X1,X2)))) = sK11(X0,sK15(sK8),relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369668,c_413867]) ).
tcf(c_422114,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X2,X0),sK8)
| in(sK7(X1,X2,X0),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_369020,c_413867]) ).
tcf(c_422115,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X2,X0),sK8)
| in(apply(X1,sK7(X1,X2,X0)),X2)
| ( relation_inverse_image(X1,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_369019,c_413867]) ).
tcf(c_422116,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,set_intersection2(X1,sK15(sK8))),sK8)
| in(apply(X0,sK7(X0,X2,set_intersection2(X1,sK15(sK8)))),X2)
| ( set_intersection2(X1,sK15(sK8)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_413867]) ).
tcf(c_422117,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,set_intersection2(X1,sK15(sK8))),sK8)
| in(sK7(X0,X2,set_intersection2(X1,sK15(sK8))),relation_dom(X0))
| ( set_intersection2(X1,sK15(sK8)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_413867]) ).
tcf(c_422118,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,set_intersection2(sK15(sK8),X1)),sK8)
| in(apply(X0,sK7(X0,X2,set_intersection2(sK15(sK8),X1))),X2)
| ( set_intersection2(sK15(sK8),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_413867]) ).
tcf(c_422119,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,set_intersection2(sK15(sK8),X1)),sK8)
| in(sK7(X0,X2,set_intersection2(sK15(sK8),X1)),relation_dom(X0))
| ( set_intersection2(sK15(sK8),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_413867]) ).
tcf(c_422120,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,relation_inverse_image(X1,sK15(sK8))),relation_dom(X0))
| in(apply(X1,sK7(X0,X2,relation_inverse_image(X1,sK15(sK8)))),sK8)
| ( relation_inverse_image(X1,sK15(sK8)) = relation_inverse_image(X0,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368819,c_413867]) ).
tcf(c_422121,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,sK7(X0,X2,relation_inverse_image(X1,sK15(sK8)))),sK8)
| in(apply(X0,sK7(X0,X2,relation_inverse_image(X1,sK15(sK8)))),X2)
| ( relation_inverse_image(X1,sK15(sK8)) = relation_inverse_image(X0,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_413867]) ).
tcf(c_422122,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK15(sK8)),sK8)
| element(sK7(X0,X2,sK15(sK8)),X1)
| ( relation_inverse_image(X0,X2) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369931,c_413867]) ).
tcf(c_422123,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK15(sK8)),sK8)
| in(sK7(X0,X2,sK15(sK8)),X1)
| ( relation_inverse_image(X0,X2) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_413867]) ).
tcf(c_422124,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,X2),sK8)
| in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK15(sK8)) ),
inference(superposition,[status(thm)],[c_369017,c_413867]) ).
tcf(c_422125,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,sK15(sK8)),sK8)
| element(sK12(X0,X2,sK15(sK8)),X1)
| ( relation_image(X0,X2) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369939,c_413867]) ).
tcf(c_422126,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,sK15(sK8)),sK8)
| in(sK12(X0,X2,sK15(sK8)),X1)
| ( relation_image(X0,X2) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_413867]) ).
tcf(c_422127,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,X2),sK8)
| in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK15(sK8)) ),
inference(superposition,[status(thm)],[c_369214,c_413867]) ).
tcf(c_422128,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X2,sK15(sK8),X0),X1)
| in(apply(X2,sK7(X2,sK15(sK8),X0)),sK8)
| ( relation_inverse_image(X2,sK15(sK8)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369933,c_413867]) ).
tcf(c_422129,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X2,sK15(sK8),X0),X1)
| in(apply(X2,sK7(X2,sK15(sK8),X0)),sK8)
| ( relation_inverse_image(X2,sK15(sK8)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_413867]) ).
tcf(c_422130,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK7(X0,sK15(sK8),X1)),sK8)
| ( relation_inverse_image(X0,sK15(sK8)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368872,c_413867]) ).
tcf(c_422131,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK15(sK8),set_intersection2(X1,X2)),X1)
| in(apply(X0,sK7(X0,sK15(sK8),set_intersection2(X1,X2))),sK8)
| ( relation_inverse_image(X0,sK15(sK8)) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_413867]) ).
tcf(c_422132,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK15(sK8),set_intersection2(X1,X2)),X2)
| in(apply(X0,sK7(X0,sK15(sK8),set_intersection2(X1,X2))),sK8)
| ( relation_inverse_image(X0,sK15(sK8)) = set_intersection2(X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_413867]) ).
tcf(c_422133,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,sK15(sK8),relation_inverse_image(X1,X2))),sK8)
| in(apply(X1,sK7(X0,sK15(sK8),relation_inverse_image(X1,X2))),X2)
| ( relation_inverse_image(X0,sK15(sK8)) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_413867]) ).
tcf(c_422134,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK15(sK8),relation_inverse_image(X1,X2)),relation_dom(X1))
| in(apply(X0,sK7(X0,sK15(sK8),relation_inverse_image(X1,X2))),sK8)
| ( relation_inverse_image(X0,sK15(sK8)) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368762,c_413867]) ).
tcf(c_422135,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,sK15(sK8),relation_image(X1,X2))),sK8)
| ( relation_inverse_image(X0,sK15(sK8)) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK7(X0,sK15(sK8),relation_image(X1,X2)))) = sK7(X0,sK15(sK8),relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369664,c_413867]) ).
tcf(c_422136,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X1,X0,X2),X2)
| in(apply(X1,sK7(X1,X0,X2)),sK8)
| ( relation_inverse_image(X1,X0) = X2 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_369018,c_413867]) ).
tcf(c_422137,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X2,X0,sK15(sK8)),sK8)
| element(apply(X2,sK7(X2,X0,sK15(sK8))),X1)
| ( relation_inverse_image(X2,X0) = sK15(sK8) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369932,c_413867]) ).
tcf(c_422138,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X2,X0,sK15(sK8)),sK8)
| in(apply(X2,sK7(X2,X0,sK15(sK8))),X1)
| ( relation_inverse_image(X2,X0) = sK15(sK8) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_413867]) ).
tcf(c_422139,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,set_intersection2(X1,X2),sK15(sK8)),sK8)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),sK15(sK8))),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_413867]) ).
tcf(c_422140,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,set_intersection2(X1,X2),sK15(sK8)),sK8)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),sK15(sK8))),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_413867]) ).
tcf(c_422141,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,set_intersection2(X1,sK15(sK8)),X2),X2)
| in(apply(X0,sK7(X0,set_intersection2(X1,sK15(sK8)),X2)),sK8)
| ( relation_inverse_image(X0,set_intersection2(X1,sK15(sK8))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_413867]) ).
tcf(c_422142,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,set_intersection2(sK15(sK8),X1),X2),X2)
| in(apply(X0,sK7(X0,set_intersection2(sK15(sK8),X1),X2)),sK8)
| ( relation_inverse_image(X0,set_intersection2(sK15(sK8),X1)) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_413867]) ).
tcf(c_422143,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),sK15(sK8)),sK8)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X2),sK15(sK8)))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = sK15(sK8) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_413867]) ).
tcf(c_422144,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),sK15(sK8)),sK8)
| in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),sK15(sK8))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = sK15(sK8) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368761,c_413867]) ).
tcf(c_422145,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_inverse_image(X1,sK15(sK8)),X2),X2)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,sK15(sK8)),X2))),sK8)
| ( relation_inverse_image(X0,relation_inverse_image(X1,sK15(sK8))) = X2 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_413867]) ).
tcf(c_422146,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,relation_image(X1,X2),sK15(sK8)),sK8)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = sK15(sK8) )
| ( apply(X1,sK13(X1,X2,apply(X0,sK7(X0,relation_image(X1,X2),sK15(sK8))))) = apply(X0,sK7(X0,relation_image(X1,X2),sK15(sK8))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369663,c_413867]) ).
tcf(c_422147,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,sK11(X0,X2,relation_inverse_image(X1,sK15(sK8)))),sK8)
| ( relation_inverse_image(X1,sK15(sK8)) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,relation_inverse_image(X1,sK15(sK8)))) = sK11(X0,X2,relation_inverse_image(X1,sK15(sK8))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369441,c_413867]) ).
tcf(c_423316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(apply(X0,X4),set_intersection2(X2,X3))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| ~ subset(relation_image(X0,X1),X3)
| ~ subset(relation_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_65,c_369941]) ).
tcf(c_423317,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(X1,X0),relation_image(X1,relation_dom(X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_67,c_369941]) ).
tcf(c_423318,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(X1,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_68,c_369941]) ).
tcf(c_423319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X1,X0),X3)
| ( apply(X1,sK13(X1,X2,sK10(relation_image(X1,X2),X3))) = sK10(relation_image(X1,X2),X3) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_369666,c_369941]) ).
tcf(c_423320,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(empty_set,X0),X2)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(empty_set,X2)
| ~ in(X0,X1)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_375097,c_369941]) ).
tcf(c_423331,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(empty_set,X0),X2)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(empty_set,X2)
| ~ in(X0,empty_set)
| ~ in(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_423320,c_373108]) ).
tcf(c_423387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK13(X1,X2,X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),powerset(X3))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369942,c_99]) ).
tcf(c_423404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK13(X1,X2,X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,powerset(X3))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369943,c_99]) ).
tcf(c_423410,plain,
in(sK16(sK15(sK8)),sK8),
inference(global_subsumption_just,[status(thm)],[c_413910,c_89,c_6042,c_36612]) ).
tcf(c_423412,plain,
! [X0: $i] :
( element(sK16(sK15(sK8)),X0)
| ~ subset(sK8,X0) ),
inference(superposition,[status(thm)],[c_423410,c_321]) ).
tcf(c_423413,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ subset(sK8,X0) ),
inference(superposition,[status(thm)],[c_423410,c_320]) ).
tcf(c_423414,plain,
~ in(sK8,sK16(sK15(sK8))),
inference(superposition,[status(thm)],[c_423410,c_97]) ).
tcf(c_423415,plain,
! [X0: $i] :
( in(sK16(sK15(sK8)),X0)
| ~ subset(sK8,X0) ),
inference(superposition,[status(thm)],[c_423410,c_96]) ).
tcf(c_423416,plain,
element(sK16(sK15(sK8)),sK8),
inference(superposition,[status(thm)],[c_423410,c_93]) ).
tcf(c_423425,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ in(sK2(X0,X1,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_370073,c_6327,c_21733]) ).
tcf(c_423440,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,set_intersection2(X1,X2)) = X0 )
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),X2)
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),X1) ),
inference(superposition,[status(thm)],[c_57,c_423425]) ).
tcf(c_423441,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,powerset(X1)) = X0 )
| ~ subset(sK2(X0,powerset(X1),X0),X1) ),
inference(superposition,[status(thm)],[c_369138,c_423425]) ).
tcf(c_423456,plain,
! [X0: $i,X1: $i] :
( in(sK2(relation_inverse_image(X0,X1),relation_dom(X0),relation_inverse_image(X0,X1)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),relation_dom(X0)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368759,c_423425]) ).
tcf(c_423466,plain,
! [X0: $i,X1: $i] :
( in(sK2(relation_inverse_image(X0,X1),relation_dom(X0),relation_inverse_image(X0,X1)),relation_inverse_image(X0,X1))
| ( set_intersection2(relation_inverse_image(X0,X1),relation_dom(X0)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368757,c_423425]) ).
tcf(c_423478,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,X1),X1)
| ( set_intersection2(X1,X0) = X1 )
| ~ subset(X0,X0) ),
inference(superposition,[status(thm)],[c_369013,c_423425]) ).
tcf(c_423480,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),set_intersection2(X0,X1)),X1)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_368504,c_423425]) ).
tcf(c_423481,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),set_intersection2(X0,X1)),X0)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_368482,c_423425]) ).
tcf(c_423482,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,X1),relation_inverse_image(X0,X1),relation_inverse_image(X0,X1))),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_423425]) ).
tcf(c_423483,plain,
! [X0: $i,X1: $i] :
( in(sK2(relation_inverse_image(X0,X1),relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368758,c_423425]) ).
tcf(c_423489,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_image(X0,X1),relation_image(X0,X1)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(relation_image(X0,X1),relation_image(X0,X1),relation_image(X0,X1)))) = sK2(relation_image(X0,X1),relation_image(X0,X1),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369662,c_423425]) ).
tcf(c_423490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,relation_inverse_image(X0,set_intersection2(X2,X3))) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(X1,relation_inverse_image(X0,set_intersection2(X2,X3)),X1),relation_dom(X0))
| ~ in(apply(X0,sK2(X1,relation_inverse_image(X0,set_intersection2(X2,X3)),X1)),X3)
| ~ in(apply(X0,sK2(X1,relation_inverse_image(X0,set_intersection2(X2,X3)),X1)),X2) ),
inference(superposition,[status(thm)],[c_368735,c_423425]) ).
tcf(c_423491,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,relation_inverse_image(X1,relation_image(X1,X2))) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,relation_inverse_image(X1,relation_image(X1,X2)),X0),X2)
| ~ in(sK2(X0,relation_inverse_image(X1,relation_image(X1,X2)),X0),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_369503,c_423425]) ).
tcf(c_423524,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X1)
| ( set_intersection2(sK10(X0,X1),X2) = sK10(X0,X1) )
| ~ subset(X0,sK2(sK10(X0,X1),X2,sK10(X0,X1))) ),
inference(superposition,[status(thm)],[c_369021,c_370076]) ).
tcf(c_423525,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( set_intersection2(sK16(X0),X1) = sK16(X0) )
| ~ subset(X0,sK2(sK16(X0),X1,sK16(X0))) ),
inference(superposition,[status(thm)],[c_370747,c_370076]) ).
tcf(c_423526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X0),X1)
| ( set_intersection2(X1,X2) = X0 )
| ( set_intersection2(sK2(X1,X2,X0),X3) = sK2(X1,X2,X0) )
| ~ subset(X0,sK2(sK2(X1,X2,X0),X3,sK2(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_369015,c_370076]) ).
tcf(c_423527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,X0),X2)
| ( set_intersection2(X1,X2) = X0 )
| ( set_intersection2(sK2(X1,X2,X0),X3) = sK2(X1,X2,X0) )
| ~ subset(X0,sK2(sK2(X1,X2,X0),X3,sK2(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_369014,c_370076]) ).
tcf(c_423528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ( set_intersection2(sK2(X0,X1,X2),X3) = sK2(X0,X1,X2) )
| ~ subset(X0,sK2(sK2(X0,X1,X2),X3,sK2(X0,X1,X2))) ),
inference(superposition,[status(thm)],[c_369012,c_370076]) ).
tcf(c_423529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X0,X2),X2)
| ( set_intersection2(X1,X0) = X2 )
| ( set_intersection2(sK2(X1,X0,X2),X3) = sK2(X1,X0,X2) )
| ~ subset(X0,sK2(sK2(X1,X0,X2),X3,sK2(X1,X0,X2))) ),
inference(superposition,[status(thm)],[c_369013,c_370076]) ).
tcf(c_423530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(sK13(X1,X0,X2),X3) = sK13(X1,X0,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X0))
| ~ subset(X0,sK2(sK13(X1,X0,X2),X3,sK13(X1,X0,X2))) ),
inference(superposition,[status(thm)],[c_369594,c_370076]) ).
tcf(c_423531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(sK13(X0,X1,X2),X3) = sK13(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_image(X0,X1))
| ~ subset(relation_dom(X0),sK2(sK13(X0,X1,X2),X3,sK13(X0,X1,X2))) ),
inference(superposition,[status(thm)],[c_369556,c_370076]) ).
tcf(c_423532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,X0,X2),X2)
| ( relation_image(X1,X0) = X2 )
| ( set_intersection2(sK12(X1,X0,X2),X3) = sK12(X1,X0,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(sK12(X1,X0,X2),X3,sK12(X1,X0,X2))) ),
inference(superposition,[status(thm)],[c_369299,c_370076]) ).
tcf(c_423533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X1,X2) = X0 )
| ( apply(X1,sK12(X1,X2,X0)) = sK11(X1,X2,X0) )
| ( set_intersection2(sK11(X1,X2,X0),X3) = sK11(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(sK11(X1,X2,X0),X3,sK11(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_369436,c_370076]) ).
tcf(c_423534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,X0),X2)
| ( relation_image(X1,X2) = X0 )
| ( set_intersection2(sK11(X1,X2,X0),X3) = sK11(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(sK11(X1,X2,X0),X3,sK11(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_369307,c_370076]) ).
tcf(c_423535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,X0),relation_dom(X1))
| ( relation_image(X1,X2) = X0 )
| ( set_intersection2(sK11(X1,X2,X0),X3) = sK11(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(sK11(X1,X2,X0),X3,sK11(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_369206,c_370076]) ).
tcf(c_423536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X2,X0),relation_dom(X1))
| ( relation_inverse_image(X1,X2) = X0 )
| ( set_intersection2(sK7(X1,X2,X0),X3) = sK7(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(sK7(X1,X2,X0),X3,sK7(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_369020,c_370076]) ).
tcf(c_423537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,X2,X0)),X2)
| ( relation_inverse_image(X1,X2) = X0 )
| ( set_intersection2(sK7(X1,X2,X0),X3) = sK7(X1,X2,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(sK7(X1,X2,X0),X3,sK7(X1,X2,X0))) ),
inference(superposition,[status(thm)],[c_369019,c_370076]) ).
tcf(c_423538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ( set_intersection2(sK7(X0,X1,X2),X3) = sK7(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(sK7(X0,X1,X2),X3,sK7(X0,X1,X2))) ),
inference(superposition,[status(thm)],[c_369017,c_370076]) ).
tcf(c_423539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( set_intersection2(sK12(X0,X1,X2),X3) = sK12(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(sK12(X0,X1,X2),X3,sK12(X0,X1,X2))) ),
inference(superposition,[status(thm)],[c_369214,c_370076]) ).
tcf(c_423540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X0,X2),X2)
| ( relation_inverse_image(X1,X0) = X2 )
| ( set_intersection2(apply(X1,sK7(X1,X0,X2)),X3) = apply(X1,sK7(X1,X0,X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(apply(X1,sK7(X1,X0,X2)),X3,apply(X1,sK7(X1,X0,X2)))) ),
inference(superposition,[status(thm)],[c_369018,c_370076]) ).
tcf(c_423674,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,X0)
| ~ in(sK2(X0,X1,X0),X1)
| ~ in(sK2(X0,X1,X0),X0) ),
inference(superposition,[status(thm)],[c_370077,c_54]) ).
tcf(c_423675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X3,X0),X2)
| ( set_intersection2(X0,X3) = X0 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370077,c_321]) ).
tcf(c_423676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X3) = X0 )
| ~ empty(X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370077,c_320]) ).
tcf(c_423677,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X2) = X1 )
| ~ subset(X1,X0)
| ~ in(X0,sK2(X1,X2,X1)) ),
inference(superposition,[status(thm)],[c_370077,c_97]) ).
tcf(c_423678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X3,X0),X2)
| ( set_intersection2(X0,X3) = X0 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370077,c_96]) ).
tcf(c_423681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X3,X0),X2)
| ( set_intersection2(X0,X3) = X0 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370077,c_59]) ).
tcf(c_423682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X3,X0),X1)
| ( set_intersection2(X0,X3) = X0 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370077,c_58]) ).
tcf(c_423683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK2(X0,X3,X0)),X2)
| ( set_intersection2(X0,X3) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370077,c_88]) ).
tcf(c_423684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X3,X0),relation_dom(X1))
| ( set_intersection2(X0,X3) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370077,c_87]) ).
tcf(c_423685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ( apply(X3,sK13(X3,X2,apply(X3,sK2(X0,X1,X0)))) = apply(X3,sK2(X0,X1,X0)) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,relation_dom(X3))
| ~ in(sK2(X0,X1,X0),X2) ),
inference(superposition,[status(thm)],[c_370077,c_369671]) ).
tcf(c_423686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X0,X4) = X0 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370077,c_369799]) ).
tcf(c_423687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X0,X4) = X0 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370077,c_369798]) ).
tcf(c_423688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X3) = X0 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370077,c_369596]) ).
tcf(c_423689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X3) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370077,c_369558]) ).
tcf(c_423690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X3) = X0 )
| ( apply(X1,sK13(X1,X2,sK2(X0,X3,X0))) = sK2(X0,X3,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370077,c_112]) ).
tcf(c_423691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,relation_dom(X3))
| ~ empty(relation_image(X3,X2))
| ~ in(sK2(X0,X1,X0),X2) ),
inference(superposition,[status(thm)],[c_370077,c_369501]) ).
tcf(c_423692,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X0,X1,X0),X2)
| ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,sK10(sK2(X0,X1,X0),X2)) ),
inference(superposition,[status(thm)],[c_370077,c_369085]) ).
tcf(c_423693,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_370077,c_372426]) ).
tcf(c_423694,plain,
! [X0: $i,X1: $i] :
( empty(sK2(X0,X1,X0))
| ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,sK16(sK2(X0,X1,X0))) ),
inference(superposition,[status(thm)],[c_370077,c_370746]) ).
tcf(c_423695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,sK2(X0,X3,X0)),X1)
| ( set_intersection2(X0,X3) = X0 )
| ( sK2(X0,X3,X0) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X0,X3,X0))) ),
inference(superposition,[status(thm)],[c_370077,c_369079]) ).
tcf(c_423696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,sK2(X0,X3,X0)),X2)
| ( set_intersection2(X0,X3) = X0 )
| ( sK2(X0,X3,X0) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X0,X3,X0))) ),
inference(superposition,[status(thm)],[c_370077,c_369078]) ).
tcf(c_423697,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK2(X0,X1,X0),X2,X3),X3)
| ( set_intersection2(X0,X1) = X0 )
| ( set_intersection2(sK2(X0,X1,X0),X2) = X3 )
| ~ subset(X0,sK2(sK2(X0,X1,X0),X2,X3)) ),
inference(superposition,[status(thm)],[c_370077,c_369076]) ).
tcf(c_423698,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ subset(set_intersection2(X0,X1),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_370077,c_368471]) ).
tcf(c_423699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,sK2(X0,X2,X0),X3),X3)
| ( set_intersection2(X0,X2) = X0 )
| ( set_intersection2(X1,sK2(X0,X2,X0)) = X3 )
| ~ subset(X0,sK2(X1,sK2(X0,X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_370077,c_369077]) ).
tcf(c_423700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X2) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X3,relation_image(X1,sK2(X0,X2,X0)))
| ~ subset(X0,sK13(X1,sK2(X0,X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_370077,c_369593]) ).
tcf(c_423701,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X0,X4) = X0 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X0,X4,X0)))) = sK13(X1,relation_image(X2,X3),sK2(X0,X4,X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_370077,c_369672]) ).
tcf(c_423702,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,sK2(X0,X2,X0),X3),X3)
| ( set_intersection2(X0,X2) = X0 )
| ( relation_image(X1,sK2(X0,X2,X0)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK2(X0,X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_370077,c_369298]) ).
tcf(c_423703,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X3) = X0 )
| ( sK2(X0,X3,X0) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK2(X0,X3,X0))) = sK11(X1,X2,sK2(X0,X3,X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X0,X3,X0))) ),
inference(superposition,[status(thm)],[c_370077,c_369435]) ).
tcf(c_423704,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,sK2(X0,X3,X0)),X2)
| ( set_intersection2(X0,X3) = X0 )
| ( sK2(X0,X3,X0) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X0,X3,X0))) ),
inference(superposition,[status(thm)],[c_370077,c_369306]) ).
tcf(c_423705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,sK2(X0,X3,X0)),relation_dom(X1))
| ( set_intersection2(X0,X3) = X0 )
| ( sK2(X0,X3,X0) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X0,X3,X0))) ),
inference(superposition,[status(thm)],[c_370077,c_369205]) ).
tcf(c_423706,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,X0),sK5)
| ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_370077,c_412536]) ).
tcf(c_423707,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,X0),sK8)
| ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_370077,c_413867]) ).
tcf(c_423708,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X2,sK2(X0,X3,X0)),relation_dom(X1))
| ( set_intersection2(X0,X3) = X0 )
| ( sK2(X0,X3,X0) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X0,X3,X0))) ),
inference(superposition,[status(thm)],[c_370077,c_369084]) ).
tcf(c_423709,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,X2,sK2(X0,X3,X0))),X2)
| ( set_intersection2(X0,X3) = X0 )
| ( sK2(X0,X3,X0) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X0,X3,X0))) ),
inference(superposition,[status(thm)],[c_370077,c_369083]) ).
tcf(c_423710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,sK2(X0,X2,X0),X3),X3)
| ( set_intersection2(X0,X2) = X0 )
| ( relation_inverse_image(X1,sK2(X0,X2,X0)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK2(X0,X2,X0),X3))) ),
inference(superposition,[status(thm)],[c_370077,c_369082]) ).
tcf(c_423712,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X0 )
| ( set_intersection2(sK2(X0,X1,X0),X2) = sK2(X0,X1,X0) )
| ~ subset(X0,sK2(sK2(X0,X1,X0),X2,sK2(X0,X1,X0))) ),
inference(superposition,[status(thm)],[c_370077,c_370076]) ).
tcf(c_423871,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_423698,c_380919]) ).
tcf(c_424104,plain,
! [X0: $i,X1: $i] :
( ~ subset(sK8,X1)
| ~ subset(sK8,X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_423413]) ).
tcf(c_424113,plain,
! [X0: $i,X1: $i] :
( subset(sK2(powerset(X0),X1,powerset(X0)),X0)
| ( set_intersection2(powerset(X0),X1) = powerset(X0) ) ),
inference(superposition,[status(thm)],[c_370078,c_99]) ).
tcf(c_424127,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,X0),X0)
| ( set_intersection2(set_intersection2(X0,X0),X1) = set_intersection2(X0,X0) ) ),
inference(superposition,[status(thm)],[c_53,c_370080]) ).
tcf(c_424128,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X1,X0)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_63,c_370080]) ).
tcf(c_424130,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,empty_set),empty_set)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = set_intersection2(X0,empty_set) ) ),
inference(superposition,[status(thm)],[c_64,c_370080]) ).
tcf(c_424131,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,empty_set),X0)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = set_intersection2(empty_set,X0) ) ),
inference(superposition,[status(thm)],[c_368545,c_370080]) ).
tcf(c_424132,plain,
! [X0: $i] :
( in(sK2(sK15(sK5),X0,sK15(sK5)),sK15(sK5))
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = set_intersection2(sK5,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_411955,c_370080]) ).
tcf(c_424133,plain,
! [X0: $i] :
( in(sK2(sK15(sK8),X0,sK15(sK8)),sK15(sK8))
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = set_intersection2(sK8,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_411956,c_370080]) ).
tcf(c_424134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X2,X0),X3,set_intersection2(X2,X0)),X1)
| ( set_intersection2(set_intersection2(X2,X0),X3) = set_intersection2(X2,X0) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370080,c_321]) ).
tcf(c_424135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X2,X0),X3) = set_intersection2(X2,X0) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370080,c_320]) ).
tcf(c_424136,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X1,X0),X2) = set_intersection2(X1,X0) )
| ~ in(X0,sK2(set_intersection2(X1,X0),X2,set_intersection2(X1,X0))) ),
inference(superposition,[status(thm)],[c_370080,c_97]) ).
tcf(c_424137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X2,X0),X3,set_intersection2(X2,X0)),X1)
| ( set_intersection2(set_intersection2(X2,X0),X3) = set_intersection2(X2,X0) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370080,c_96]) ).
tcf(c_424138,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_370080,c_93]) ).
tcf(c_424140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,set_intersection2(X1,X2)),X3,set_intersection2(X0,set_intersection2(X1,X2))),X2)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3) = set_intersection2(X0,set_intersection2(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_370080,c_59]) ).
tcf(c_424141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,set_intersection2(X1,X2)),X3,set_intersection2(X0,set_intersection2(X1,X2))),X1)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3) = set_intersection2(X0,set_intersection2(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_370080,c_58]) ).
tcf(c_424142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3,set_intersection2(X1,relation_inverse_image(X0,X2)))),X2)
| ( set_intersection2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3) = set_intersection2(X1,relation_inverse_image(X0,X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370080,c_88]) ).
tcf(c_424143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3,set_intersection2(X1,relation_inverse_image(X0,X2))),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3) = set_intersection2(X1,relation_inverse_image(X0,X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370080,c_87]) ).
tcf(c_424144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,relation_dom(X1)),X2) = set_intersection2(X0,relation_dom(X1)) )
| ( apply(X1,sK13(X1,X3,apply(X1,sK2(set_intersection2(X0,relation_dom(X1)),X2,set_intersection2(X0,relation_dom(X1)))))) = apply(X1,sK2(set_intersection2(X0,relation_dom(X1)),X2,set_intersection2(X0,relation_dom(X1)))) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(set_intersection2(X0,relation_dom(X1)),X2,set_intersection2(X0,relation_dom(X1))),X3) ),
inference(superposition,[status(thm)],[c_370080,c_369671]) ).
tcf(c_424145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X3,relation_image(X2,X0)),X4) = set_intersection2(X3,relation_image(X2,X0)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370080,c_369799]) ).
tcf(c_424146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X2,relation_image(X0,X3)),X4) = set_intersection2(X2,relation_image(X0,X3)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370080,c_369798]) ).
tcf(c_424147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X2,relation_image(X0,X1)),X3) = set_intersection2(X2,relation_image(X0,X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370080,c_369596]) ).
tcf(c_424148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X1,relation_image(X0,X2)),X3) = set_intersection2(X1,relation_image(X0,X2)) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370080,c_369558]) ).
tcf(c_424149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X2,relation_image(X0,X1)),X3) = set_intersection2(X2,relation_image(X0,X1)) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,relation_image(X0,X1)),X3,set_intersection2(X2,relation_image(X0,X1))))) = sK2(set_intersection2(X2,relation_image(X0,X1)),X3,set_intersection2(X2,relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370080,c_112]) ).
tcf(c_424150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,relation_dom(X1)),X2) = set_intersection2(X0,relation_dom(X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X3))
| ~ in(sK2(set_intersection2(X0,relation_dom(X1)),X2,set_intersection2(X0,relation_dom(X1))),X3) ),
inference(superposition,[status(thm)],[c_370080,c_369501]) ).
tcf(c_424151,plain,
! [X0: $i,X1: $i] : set_intersection2(set_intersection2(X0,empty_set),X1) = set_intersection2(X0,empty_set),
inference(superposition,[status(thm)],[c_370080,c_372426]) ).
tcf(c_424152,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,X0),X1) = set_intersection2(X0,X0) )
| ~ in(sK2(set_intersection2(X0,X0),X1,set_intersection2(X0,X0)),X1)
| ~ in(sK2(set_intersection2(X0,X0),X1,set_intersection2(X0,X0)),X0)
| ~ in(sK2(set_intersection2(X0,X0),X1,set_intersection2(X0,X0)),set_intersection2(X0,X0)) ),
inference(superposition,[status(thm)],[c_370080,c_368471]) ).
tcf(c_424153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4) = set_intersection2(X3,relation_image(X0,relation_image(X1,X2))) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4,set_intersection2(X3,relation_image(X0,relation_image(X1,X2))))))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4,set_intersection2(X3,relation_image(X0,relation_image(X1,X2))))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370080,c_369672]) ).
tcf(c_424154,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,sK15(sK5)),X1,set_intersection2(X0,sK15(sK5))),sK5)
| ( set_intersection2(set_intersection2(X0,sK15(sK5)),X1) = set_intersection2(X0,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_370080,c_412536]) ).
tcf(c_424155,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,sK15(sK8)),X1,set_intersection2(X0,sK15(sK8))),sK8)
| ( set_intersection2(set_intersection2(X0,sK15(sK8)),X1) = set_intersection2(X0,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_370080,c_413867]) ).
tcf(c_424158,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X0,empty_set),X1)
| ( set_intersection2(empty_set,X0) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_424131,c_368545]) ).
tcf(c_424159,plain,
! [X0: $i] :
( in(sK2(empty_set,X0,empty_set),empty_set)
| ( set_intersection2(empty_set,X0) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_424130,c_64]) ).
tcf(c_424170,plain,
! [X0: $i] :
( in(sK2(sK15(sK8),X0,sK15(sK8)),sK15(sK8))
| ( set_intersection2(sK15(sK8),X0) = sK15(sK8) ) ),
inference(light_normalisation,[status(thm)],[c_424133,c_411956]) ).
tcf(c_424173,plain,
! [X0: $i] :
( in(sK2(sK15(sK5),X0,sK15(sK5)),sK15(sK5))
| ( set_intersection2(sK15(sK5),X0) = sK15(sK5) ) ),
inference(light_normalisation,[status(thm)],[c_424132,c_411955]) ).
tcf(c_424282,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X1,X0)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_63,c_370081]) ).
tcf(c_424284,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,empty_set),X0)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = set_intersection2(X0,empty_set) ) ),
inference(superposition,[status(thm)],[c_64,c_370081]) ).
tcf(c_424285,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,empty_set),empty_set)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = set_intersection2(empty_set,X0) ) ),
inference(superposition,[status(thm)],[c_368545,c_370081]) ).
tcf(c_424286,plain,
! [X0: $i] :
( in(sK2(sK15(sK5),X0,sK15(sK5)),sK5)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = set_intersection2(sK5,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_411955,c_370081]) ).
tcf(c_424287,plain,
! [X0: $i] :
( in(sK2(sK15(sK8),X0,sK15(sK8)),sK8)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = set_intersection2(sK8,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_411956,c_370081]) ).
tcf(c_424288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X2),X3,set_intersection2(X0,X2)),X1)
| ( set_intersection2(set_intersection2(X0,X2),X3) = set_intersection2(X0,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370081,c_321]) ).
tcf(c_424289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X2),X3) = set_intersection2(X0,X2) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370081,c_320]) ).
tcf(c_424290,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ in(X0,sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))) ),
inference(superposition,[status(thm)],[c_370081,c_97]) ).
tcf(c_424291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X2),X3,set_intersection2(X0,X2)),X1)
| ( set_intersection2(set_intersection2(X0,X2),X3) = set_intersection2(X0,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370081,c_96]) ).
tcf(c_424292,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_370081,c_93]) ).
tcf(c_424294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(set_intersection2(X0,X1),X2)),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(set_intersection2(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_370081,c_59]) ).
tcf(c_424295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(set_intersection2(X0,X1),X2)),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(set_intersection2(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_370081,c_58]) ).
tcf(c_424296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,set_intersection2(relation_inverse_image(X0,X1),X2))),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = set_intersection2(relation_inverse_image(X0,X1),X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370081,c_88]) ).
tcf(c_424297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,set_intersection2(relation_inverse_image(X0,X1),X2)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = set_intersection2(relation_inverse_image(X0,X1),X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370081,c_87]) ).
tcf(c_424298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = set_intersection2(relation_dom(X0),X1) )
| ( apply(X0,sK13(X0,X3,apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(relation_dom(X0),X1))))) = apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(relation_dom(X0),X1))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(relation_dom(X0),X1)),X3) ),
inference(superposition,[status(thm)],[c_370081,c_369671]) ).
tcf(c_424299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(relation_image(X2,X0),X3),X4) = set_intersection2(relation_image(X2,X0),X3) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370081,c_369799]) ).
tcf(c_424300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4) = set_intersection2(relation_image(X0,X2),X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370081,c_369798]) ).
tcf(c_424301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = set_intersection2(relation_image(X0,X1),X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370081,c_369596]) ).
tcf(c_424302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = set_intersection2(relation_image(X0,X1),X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370081,c_369558]) ).
tcf(c_424303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = set_intersection2(relation_image(X0,X1),X2) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),X3,set_intersection2(relation_image(X0,X1),X2)))) = sK2(set_intersection2(relation_image(X0,X1),X2),X3,set_intersection2(relation_image(X0,X1),X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370081,c_112]) ).
tcf(c_424304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = set_intersection2(relation_dom(X0),X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X3))
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(relation_dom(X0),X1)),X3) ),
inference(superposition,[status(thm)],[c_370081,c_369501]) ).
tcf(c_424305,plain,
! [X0: $i,X1: $i] : set_intersection2(set_intersection2(empty_set,X0),X1) = set_intersection2(empty_set,X0),
inference(superposition,[status(thm)],[c_370081,c_372426]) ).
tcf(c_424307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4) = set_intersection2(relation_image(X0,relation_image(X1,X2)),X3) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,set_intersection2(relation_image(X0,relation_image(X1,X2)),X3))))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,set_intersection2(relation_image(X0,relation_image(X1,X2)),X3))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370081,c_369672]) ).
tcf(c_424308,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(sK15(sK5),X0),X1,set_intersection2(sK15(sK5),X0)),sK5)
| ( set_intersection2(set_intersection2(sK15(sK5),X0),X1) = set_intersection2(sK15(sK5),X0) ) ),
inference(superposition,[status(thm)],[c_370081,c_412536]) ).
tcf(c_424309,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(sK15(sK8),X0),X1,set_intersection2(sK15(sK8),X0)),sK8)
| ( set_intersection2(set_intersection2(sK15(sK8),X0),X1) = set_intersection2(sK15(sK8),X0) ) ),
inference(superposition,[status(thm)],[c_370081,c_413867]) ).
tcf(c_424424,plain,
! [X0: $i,X1: $i] :
( in(apply(empty_set,sK2(empty_set,X1,empty_set)),X0)
| ( set_intersection2(relation_inverse_image(empty_set,X0),X1) = relation_inverse_image(empty_set,X0) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370082]) ).
tcf(c_424426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X2,sK2(relation_inverse_image(X2,X0),X3,relation_inverse_image(X2,X0))),X1)
| ( set_intersection2(relation_inverse_image(X2,X0),X3) = relation_inverse_image(X2,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370082,c_321]) ).
tcf(c_424427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_inverse_image(X2,X0),X3) = relation_inverse_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370082,c_320]) ).
tcf(c_424428,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_inverse_image(X1,X0),X2) = relation_inverse_image(X1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK2(relation_inverse_image(X1,X0),X2,relation_inverse_image(X1,X0)))) ),
inference(superposition,[status(thm)],[c_370082,c_97]) ).
tcf(c_424429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK2(relation_inverse_image(X2,X0),X3,relation_inverse_image(X2,X0))),X1)
| ( set_intersection2(relation_inverse_image(X2,X0),X3) = relation_inverse_image(X2,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370082,c_96]) ).
tcf(c_424430,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(X0,sK2(relation_inverse_image(X0,X1),X2,relation_inverse_image(X0,X1))),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370082,c_93]) ).
tcf(c_424431,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_inverse_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370082,c_91]) ).
tcf(c_424432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3,relation_inverse_image(X0,set_intersection2(X1,X2)))),X2)
| ( set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3) = relation_inverse_image(X0,set_intersection2(X1,X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370082,c_59]) ).
tcf(c_424433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3,relation_inverse_image(X0,set_intersection2(X1,X2)))),X1)
| ( set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3) = relation_inverse_image(X0,set_intersection2(X1,X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370082,c_58]) ).
tcf(c_424434,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,relation_inverse_image(X0,X1)),relation_inverse_image(X0,X1))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(relation_inverse_image(X0,X1),X2,relation_inverse_image(X0,X1)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370082,c_86]) ).
tcf(c_424435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,apply(X0,sK2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3,relation_inverse_image(X0,relation_inverse_image(X1,X2))))),X2)
| ( set_intersection2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3) = relation_inverse_image(X0,relation_inverse_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370082,c_88]) ).
tcf(c_424436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3,relation_inverse_image(X0,relation_inverse_image(X1,X2)))),relation_dom(X1))
| ( set_intersection2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3) = relation_inverse_image(X0,relation_inverse_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370082,c_87]) ).
tcf(c_424437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_inverse_image(X0,relation_dom(X1)),X2) = relation_inverse_image(X0,relation_dom(X1)) )
| ( apply(X1,sK13(X1,X3,apply(X1,apply(X0,sK2(relation_inverse_image(X0,relation_dom(X1)),X2,relation_inverse_image(X0,relation_dom(X1))))))) = apply(X1,apply(X0,sK2(relation_inverse_image(X0,relation_dom(X1)),X2,relation_inverse_image(X0,relation_dom(X1))))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK2(relation_inverse_image(X0,relation_dom(X1)),X2,relation_inverse_image(X0,relation_dom(X1)))),X3) ),
inference(superposition,[status(thm)],[c_370082,c_369671]) ).
tcf(c_424438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_inverse_image(X2,relation_image(X3,X0)),X4) = relation_inverse_image(X2,relation_image(X3,X0)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370082,c_369799]) ).
tcf(c_424439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_inverse_image(X2,relation_image(X0,X3)),X4) = relation_inverse_image(X2,relation_image(X0,X3)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370082,c_369798]) ).
tcf(c_424440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_inverse_image(X0,relation_image(X1,X2)),X3) = relation_inverse_image(X0,relation_image(X1,X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370082,c_369596]) ).
tcf(c_424441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_inverse_image(X1,relation_image(X0,X2)),X3) = relation_inverse_image(X1,relation_image(X0,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370082,c_369558]) ).
tcf(c_424442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_inverse_image(X0,relation_image(X1,X2)),X3) = relation_inverse_image(X0,relation_image(X1,X2)) )
| ( apply(X1,sK13(X1,X2,apply(X0,sK2(relation_inverse_image(X0,relation_image(X1,X2)),X3,relation_inverse_image(X0,relation_image(X1,X2)))))) = apply(X0,sK2(relation_inverse_image(X0,relation_image(X1,X2)),X3,relation_inverse_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370082,c_112]) ).
tcf(c_424443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_inverse_image(X0,relation_dom(X1)),X2) = relation_inverse_image(X0,relation_dom(X1)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X3))
| ~ in(apply(X0,sK2(relation_inverse_image(X0,relation_dom(X1)),X2,relation_inverse_image(X0,relation_dom(X1)))),X3) ),
inference(superposition,[status(thm)],[c_370082,c_369501]) ).
tcf(c_424444,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_inverse_image(X0,empty_set),X1) = relation_inverse_image(X0,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370082,c_372426]) ).
tcf(c_424445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X4) = relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK2(relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X4,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK2(relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X4,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370082,c_369672]) ).
tcf(c_424446,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,sK15(sK5)),X1,relation_inverse_image(X0,sK15(sK5)))),sK5)
| ( set_intersection2(relation_inverse_image(X0,sK15(sK5)),X1) = relation_inverse_image(X0,sK15(sK5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370082,c_412536]) ).
tcf(c_424447,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,sK15(sK8)),X1,relation_inverse_image(X0,sK15(sK8)))),sK8)
| ( set_intersection2(relation_inverse_image(X0,sK15(sK8)),X1) = relation_inverse_image(X0,sK15(sK8)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370082,c_413867]) ).
tcf(c_424460,plain,
! [X0: $i,X1: $i] :
( in(apply(empty_set,sK2(empty_set,X0,empty_set)),X1)
| ( set_intersection2(empty_set,X0) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_424424,c_373747]) ).
tcf(c_424611,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,empty_set),relation_dom(empty_set))
| ( set_intersection2(relation_inverse_image(empty_set,X0),X1) = relation_inverse_image(empty_set,X0) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370083]) ).
tcf(c_424613,plain,
! [X0: $i,X1: $i] :
( in(sK2(relation_inverse_image(empty_set,X0),X1,relation_inverse_image(empty_set,X0)),empty_set)
| ( set_intersection2(relation_inverse_image(empty_set,X0),X1) = relation_inverse_image(empty_set,X0) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_370083]) ).
tcf(c_424614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(relation_inverse_image(X0,X2),X3,relation_inverse_image(X0,X2)),X1)
| ( set_intersection2(relation_inverse_image(X0,X2),X3) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370083,c_321]) ).
tcf(c_424615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_inverse_image(X0,X2),X3) = relation_inverse_image(X0,X2) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370083,c_320]) ).
tcf(c_424616,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK2(relation_inverse_image(X0,X1),X2,relation_inverse_image(X0,X1))) ),
inference(superposition,[status(thm)],[c_370083,c_97]) ).
tcf(c_424617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X2),X3,relation_inverse_image(X0,X2)),X1)
| ( set_intersection2(relation_inverse_image(X0,X2),X3) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370083,c_96]) ).
tcf(c_424618,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(relation_inverse_image(X0,X1),X2,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370083,c_93]) ).
tcf(c_424619,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370083,c_91]) ).
tcf(c_424620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_inverse_image(X0,X1) )
| ( apply(X0,sK13(X0,X3,apply(X0,sK2(relation_inverse_image(X0,X1),X2,relation_inverse_image(X0,X1))))) = apply(X0,sK2(relation_inverse_image(X0,X1),X2,relation_inverse_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(relation_inverse_image(X0,X1),X2,relation_inverse_image(X0,X1)),X3) ),
inference(superposition,[status(thm)],[c_370083,c_369671]) ).
tcf(c_424621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_inverse_image(X0,X1),X2) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X3))
| ~ in(sK2(relation_inverse_image(X0,X1),X2,relation_inverse_image(X0,X1)),X3) ),
inference(superposition,[status(thm)],[c_370083,c_369501]) ).
tcf(c_424622,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_inverse_image(X0,X1),relation_dom(X0)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370083,c_423425]) ).
tcf(c_424630,plain,
! [X0: $i] :
( in(sK2(empty_set,X0,empty_set),empty_set)
| ( set_intersection2(empty_set,X0) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_424611,c_373108,c_373747]) ).
tcf(c_424711,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_image(sK1,X0),X1) = relation_image(sK1,X0) )
| ( apply(sK1,sK13(sK1,X0,sK2(relation_image(sK1,X0),X1,relation_image(sK1,X0)))) = sK2(relation_image(sK1,X0),X1,relation_image(sK1,X0)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_51,c_370084]) ).
tcf(c_424712,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_image(sK4,X0),X1) = relation_image(sK4,X0) )
| ( apply(sK4,sK13(sK4,X0,sK2(relation_image(sK4,X0),X1,relation_image(sK4,X0)))) = sK2(relation_image(sK4,X0),X1,relation_image(sK4,X0)) )
| ~ relation(sK4) ),
inference(superposition,[status(thm)],[c_76,c_370084]) ).
tcf(c_424713,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_image(empty_set,X0),X1) = relation_image(empty_set,X0) )
| ( apply(empty_set,sK13(empty_set,X0,sK2(relation_image(empty_set,X0),X1,relation_image(empty_set,X0)))) = sK2(relation_image(empty_set,X0),X1,relation_image(empty_set,X0)) )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_368630,c_370084]) ).
tcf(c_424714,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_image(relation_dom(X0),X1),X2) = relation_image(relation_dom(X0),X1) )
| ( apply(relation_dom(X0),sK13(relation_dom(X0),X1,sK2(relation_image(relation_dom(X0),X1),X2,relation_image(relation_dom(X0),X1)))) = sK2(relation_image(relation_dom(X0),X1),X2,relation_image(relation_dom(X0),X1)) )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368626,c_370084]) ).
tcf(c_424715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_image(set_intersection2(X0,X1),X2),X3) = relation_image(set_intersection2(X0,X1),X2) )
| ( apply(set_intersection2(X0,X1),sK13(set_intersection2(X0,X1),X2,sK2(relation_image(set_intersection2(X0,X1),X2),X3,relation_image(set_intersection2(X0,X1),X2)))) = sK2(relation_image(set_intersection2(X0,X1),X2),X3,relation_image(set_intersection2(X0,X1),X2)) )
| ~ empty(X1)
| ~ relation(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_381376,c_370084]) ).
tcf(c_424716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(relation_image(set_intersection2(X0,X1),X2),X3) = relation_image(set_intersection2(X0,X1),X2) )
| ( apply(set_intersection2(X0,X1),sK13(set_intersection2(X0,X1),X2,sK2(relation_image(set_intersection2(X0,X1),X2),X3,relation_image(set_intersection2(X0,X1),X2)))) = sK2(relation_image(set_intersection2(X0,X1),X2),X3,relation_image(set_intersection2(X0,X1),X2)) )
| ~ empty(X0)
| ~ relation(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_381430,c_370084]) ).
tcf(c_424717,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_image(sK16(powerset(X0)),X1),X2) = relation_image(sK16(powerset(X0)),X1) )
| ( apply(sK16(powerset(X0)),sK13(sK16(powerset(X0)),X1,sK2(relation_image(sK16(powerset(X0)),X1),X2,relation_image(sK16(powerset(X0)),X1)))) = sK2(relation_image(sK16(powerset(X0)),X1),X2,relation_image(sK16(powerset(X0)),X1)) )
| ~ empty(X0)
| ~ relation(sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_380417,c_370084]) ).
tcf(c_424718,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(powerset(empty_set),X0)
| ( set_intersection2(relation_image(sK10(powerset(empty_set),X0),X1),X2) = relation_image(sK10(powerset(empty_set),X0),X1) )
| ( apply(sK10(powerset(empty_set),X0),sK13(sK10(powerset(empty_set),X0),X1,sK2(relation_image(sK10(powerset(empty_set),X0),X1),X2,relation_image(sK10(powerset(empty_set),X0),X1)))) = sK2(relation_image(sK10(powerset(empty_set),X0),X1),X2,relation_image(sK10(powerset(empty_set),X0),X1)) )
| ~ relation(sK10(powerset(empty_set),X0)) ),
inference(superposition,[status(thm)],[c_390528,c_370084]) ).
tcf(c_424719,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(empty_set,X1) = empty_set )
| ( apply(empty_set,sK13(empty_set,X0,sK2(empty_set,X1,empty_set))) = sK2(empty_set,X1,empty_set) )
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_424713,c_375097]) ).
tcf(c_424720,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_image(sK4,X0),X1) = relation_image(sK4,X0) )
| ( apply(sK4,sK13(sK4,X0,sK2(relation_image(sK4,X0),X1,relation_image(sK4,X0)))) = sK2(relation_image(sK4,X0),X1,relation_image(sK4,X0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_424712,c_75]) ).
tcf(c_424723,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_image(sK1,X0),X1) = relation_image(sK1,X0) )
| ( apply(sK1,sK13(sK1,X0,sK2(relation_image(sK1,X0),X1,relation_image(sK1,X0)))) = sK2(relation_image(sK1,X0),X1,relation_image(sK1,X0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_424711,c_50]) ).
tcf(c_424752,plain,
in(sK16(sK15(sK5)),sK15(sK5)),
inference(global_subsumption_just,[status(thm)],[c_412587,c_78,c_6041,c_15228,c_15229]) ).
tcf(c_424754,plain,
! [X0: $i] :
( element(sK16(sK15(sK5)),X0)
| ~ subset(sK15(sK5),X0) ),
inference(superposition,[status(thm)],[c_424752,c_321]) ).
tcf(c_424755,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ subset(sK15(sK5),X0) ),
inference(superposition,[status(thm)],[c_424752,c_320]) ).
tcf(c_424756,plain,
~ in(sK15(sK5),sK16(sK15(sK5))),
inference(superposition,[status(thm)],[c_424752,c_97]) ).
tcf(c_424757,plain,
! [X0: $i] :
( in(sK16(sK15(sK5)),X0)
| ~ subset(sK15(sK5),X0) ),
inference(superposition,[status(thm)],[c_424752,c_96]) ).
tcf(c_424758,plain,
element(sK16(sK15(sK5)),sK15(sK5)),
inference(superposition,[status(thm)],[c_424752,c_93]) ).
tcf(c_424771,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ( set_intersection2(X1,sK10(X0,X2)) = sK10(X0,X2) )
| ~ subset(X0,sK2(X1,sK10(X0,X2),sK10(X0,X2))) ),
inference(superposition,[status(thm)],[c_369021,c_370144]) ).
tcf(c_424772,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( set_intersection2(X1,sK16(X0)) = sK16(X0) )
| ~ subset(X0,sK2(X1,sK16(X0),sK16(X0))) ),
inference(superposition,[status(thm)],[c_370747,c_370144]) ).
tcf(c_424773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X2)
| ( set_intersection2(X2,X3) = X0 )
| ( set_intersection2(X1,sK2(X2,X3,X0)) = sK2(X2,X3,X0) )
| ~ subset(X0,sK2(X1,sK2(X2,X3,X0),sK2(X2,X3,X0))) ),
inference(superposition,[status(thm)],[c_369015,c_370144]) ).
tcf(c_424774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X3)
| ( set_intersection2(X2,X3) = X0 )
| ( set_intersection2(X1,sK2(X2,X3,X0)) = sK2(X2,X3,X0) )
| ~ subset(X0,sK2(X1,sK2(X2,X3,X0),sK2(X2,X3,X0))) ),
inference(superposition,[status(thm)],[c_369014,c_370144]) ).
tcf(c_424775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X2,X3),X3)
| ( set_intersection2(X0,X2) = X3 )
| ( set_intersection2(X1,sK2(X0,X2,X3)) = sK2(X0,X2,X3) )
| ~ subset(X0,sK2(X1,sK2(X0,X2,X3),sK2(X0,X2,X3))) ),
inference(superposition,[status(thm)],[c_369012,c_370144]) ).
tcf(c_424776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X0,X3),X3)
| ( set_intersection2(X2,X0) = X3 )
| ( set_intersection2(X1,sK2(X2,X0,X3)) = sK2(X2,X0,X3) )
| ~ subset(X0,sK2(X1,sK2(X2,X0,X3),sK2(X2,X0,X3))) ),
inference(superposition,[status(thm)],[c_369013,c_370144]) ).
tcf(c_424777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,sK13(X2,X0,X3)) = sK13(X2,X0,X3) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_image(X2,X0))
| ~ subset(X0,sK2(X1,sK13(X2,X0,X3),sK13(X2,X0,X3))) ),
inference(superposition,[status(thm)],[c_369594,c_370144]) ).
tcf(c_424778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,sK13(X0,X2,X3)) = sK13(X0,X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,X2))
| ~ subset(relation_dom(X0),sK2(X1,sK13(X0,X2,X3),sK13(X0,X2,X3))) ),
inference(superposition,[status(thm)],[c_369556,c_370144]) ).
tcf(c_424779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X2,X0,X3),X3)
| ( relation_image(X2,X0) = X3 )
| ( set_intersection2(X1,sK12(X2,X0,X3)) = sK12(X2,X0,X3) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,sK12(X2,X0,X3),sK12(X2,X0,X3))) ),
inference(superposition,[status(thm)],[c_369299,c_370144]) ).
tcf(c_424780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X2,X3) = X0 )
| ( apply(X2,sK12(X2,X3,X0)) = sK11(X2,X3,X0) )
| ( set_intersection2(X1,sK11(X2,X3,X0)) = sK11(X2,X3,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,sK11(X2,X3,X0),sK11(X2,X3,X0))) ),
inference(superposition,[status(thm)],[c_369436,c_370144]) ).
tcf(c_424781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X2,X3,X0),X3)
| ( relation_image(X2,X3) = X0 )
| ( set_intersection2(X1,sK11(X2,X3,X0)) = sK11(X2,X3,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,sK11(X2,X3,X0),sK11(X2,X3,X0))) ),
inference(superposition,[status(thm)],[c_369307,c_370144]) ).
tcf(c_424782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X2,X3,X0),relation_dom(X2))
| ( relation_image(X2,X3) = X0 )
| ( set_intersection2(X1,sK11(X2,X3,X0)) = sK11(X2,X3,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,sK11(X2,X3,X0),sK11(X2,X3,X0))) ),
inference(superposition,[status(thm)],[c_369206,c_370144]) ).
tcf(c_424783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X3,X0),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = X0 )
| ( set_intersection2(X1,sK7(X2,X3,X0)) = sK7(X2,X3,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,sK7(X2,X3,X0),sK7(X2,X3,X0))) ),
inference(superposition,[status(thm)],[c_369020,c_370144]) ).
tcf(c_424784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK7(X2,X3,X0)),X3)
| ( relation_inverse_image(X2,X3) = X0 )
| ( set_intersection2(X1,sK7(X2,X3,X0)) = sK7(X2,X3,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,sK7(X2,X3,X0),sK7(X2,X3,X0))) ),
inference(superposition,[status(thm)],[c_369019,c_370144]) ).
tcf(c_424785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,X3),X3)
| ( relation_inverse_image(X0,X2) = X3 )
| ( set_intersection2(X1,sK7(X0,X2,X3)) = sK7(X0,X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(X1,sK7(X0,X2,X3),sK7(X0,X2,X3))) ),
inference(superposition,[status(thm)],[c_369017,c_370144]) ).
tcf(c_424786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X2,X3),X3)
| ( relation_image(X0,X2) = X3 )
| ( set_intersection2(X1,sK12(X0,X2,X3)) = sK12(X0,X2,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(X1,sK12(X0,X2,X3),sK12(X0,X2,X3))) ),
inference(superposition,[status(thm)],[c_369214,c_370144]) ).
tcf(c_424787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X0,X3),X3)
| ( relation_inverse_image(X2,X0) = X3 )
| ( set_intersection2(X1,apply(X2,sK7(X2,X0,X3))) = apply(X2,sK7(X2,X0,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,apply(X2,sK7(X2,X0,X3)),apply(X2,sK7(X2,X0,X3)))) ),
inference(superposition,[status(thm)],[c_369018,c_370144]) ).
tcf(c_424788,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X2) = X0 )
| ( set_intersection2(X1,sK2(X0,X2,X0)) = sK2(X0,X2,X0) )
| ~ subset(X0,sK2(X1,sK2(X0,X2,X0),sK2(X0,X2,X0))) ),
inference(superposition,[status(thm)],[c_370077,c_370144]) ).
tcf(c_424957,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = X1 )
| ~ subset(X1,X0)
| ~ in(sK2(X0,X1,X1),X1) ),
inference(superposition,[status(thm)],[c_370145,c_54]) ).
tcf(c_424958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X3,X0,X0),X2)
| ( set_intersection2(X3,X0) = X0 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370145,c_321]) ).
tcf(c_424959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,X0) = X0 )
| ~ empty(X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370145,c_320]) ).
tcf(c_424960,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X2) = X2 )
| ~ subset(X2,X0)
| ~ in(X0,sK2(X1,X2,X2)) ),
inference(superposition,[status(thm)],[c_370145,c_97]) ).
tcf(c_424961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,X0,X0),X2)
| ( set_intersection2(X3,X0) = X0 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370145,c_96]) ).
tcf(c_424964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,X0,X0),X2)
| ( set_intersection2(X3,X0) = X0 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370145,c_59]) ).
tcf(c_424965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,X0,X0),X1)
| ( set_intersection2(X3,X0) = X0 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370145,c_58]) ).
tcf(c_424966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK2(X3,X0,X0)),X2)
| ( set_intersection2(X3,X0) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370145,c_88]) ).
tcf(c_424967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,X0,X0),relation_dom(X1))
| ( set_intersection2(X3,X0) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370145,c_87]) ).
tcf(c_424968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X1) = X1 )
| ( apply(X3,sK13(X3,X2,apply(X3,sK2(X0,X1,X1)))) = apply(X3,sK2(X0,X1,X1)) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,relation_dom(X3))
| ~ in(sK2(X0,X1,X1),X2) ),
inference(superposition,[status(thm)],[c_370145,c_369671]) ).
tcf(c_424969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X4,X0) = X0 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370145,c_369799]) ).
tcf(c_424970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X4,X0) = X0 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370145,c_369798]) ).
tcf(c_424971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,X0) = X0 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370145,c_369596]) ).
tcf(c_424972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,X0) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370145,c_369558]) ).
tcf(c_424973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,X0) = X0 )
| ( apply(X1,sK13(X1,X2,sK2(X3,X0,X0))) = sK2(X3,X0,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370145,c_112]) ).
tcf(c_424974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,X1) = X1 )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,relation_dom(X3))
| ~ empty(relation_image(X3,X2))
| ~ in(sK2(X0,X1,X1),X2) ),
inference(superposition,[status(thm)],[c_370145,c_369501]) ).
tcf(c_424975,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1,X0,X0),X2)
| ( set_intersection2(X1,X0) = X0 )
| ~ subset(X0,sK10(sK2(X1,X0,X0),X2)) ),
inference(superposition,[status(thm)],[c_370145,c_369085]) ).
tcf(c_424976,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,X0) = X0 )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_370145,c_372426]) ).
tcf(c_424977,plain,
! [X0: $i,X1: $i] :
( empty(sK2(X1,X0,X0))
| ( set_intersection2(X1,X0) = X0 )
| ~ subset(X0,sK16(sK2(X1,X0,X0))) ),
inference(superposition,[status(thm)],[c_370145,c_370746]) ).
tcf(c_424978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,sK2(X3,X0,X0)),X1)
| ( set_intersection2(X3,X0) = X0 )
| ( sK2(X3,X0,X0) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X3,X0,X0))) ),
inference(superposition,[status(thm)],[c_370145,c_369079]) ).
tcf(c_424979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,sK2(X3,X0,X0)),X2)
| ( set_intersection2(X3,X0) = X0 )
| ( sK2(X3,X0,X0) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X3,X0,X0))) ),
inference(superposition,[status(thm)],[c_370145,c_369078]) ).
tcf(c_424980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK2(X1,X0,X0),X2,X3),X3)
| ( set_intersection2(X1,X0) = X0 )
| ( set_intersection2(sK2(X1,X0,X0),X2) = X3 )
| ~ subset(X0,sK2(sK2(X1,X0,X0),X2,X3)) ),
inference(superposition,[status(thm)],[c_370145,c_369076]) ).
tcf(c_424981,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X2 )
| ~ subset(X2,X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X2),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X2),X1) ),
inference(superposition,[status(thm)],[c_370145,c_368471]) ).
tcf(c_424982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,sK2(X2,X0,X0),X3),X3)
| ( set_intersection2(X2,X0) = X0 )
| ( set_intersection2(X1,sK2(X2,X0,X0)) = X3 )
| ~ subset(X0,sK2(X1,sK2(X2,X0,X0),X3)) ),
inference(superposition,[status(thm)],[c_370145,c_369077]) ).
tcf(c_424983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,X0) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X3,relation_image(X1,sK2(X2,X0,X0)))
| ~ subset(X0,sK13(X1,sK2(X2,X0,X0),X3)) ),
inference(superposition,[status(thm)],[c_370145,c_369593]) ).
tcf(c_424984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X4,X0) = X0 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,X0,X0)))) = sK13(X1,relation_image(X2,X3),sK2(X4,X0,X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_370145,c_369672]) ).
tcf(c_424985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X1,sK2(X2,X0,X0),X3),X3)
| ( set_intersection2(X2,X0) = X0 )
| ( relation_image(X1,sK2(X2,X0,X0)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK2(X2,X0,X0),X3)) ),
inference(superposition,[status(thm)],[c_370145,c_369298]) ).
tcf(c_424986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,X0) = X0 )
| ( sK2(X3,X0,X0) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK2(X3,X0,X0))) = sK11(X1,X2,sK2(X3,X0,X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,X0,X0))) ),
inference(superposition,[status(thm)],[c_370145,c_369435]) ).
tcf(c_424987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,sK2(X3,X0,X0)),X2)
| ( set_intersection2(X3,X0) = X0 )
| ( sK2(X3,X0,X0) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,X0,X0))) ),
inference(superposition,[status(thm)],[c_370145,c_369306]) ).
tcf(c_424988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X1,X2,sK2(X3,X0,X0)),relation_dom(X1))
| ( set_intersection2(X3,X0) = X0 )
| ( sK2(X3,X0,X0) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,X0,X0))) ),
inference(superposition,[status(thm)],[c_370145,c_369205]) ).
tcf(c_424989,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,X0),sK5)
| ( set_intersection2(X1,X0) = X0 )
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_370145,c_412536]) ).
tcf(c_424990,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,X0,X0),sK8)
| ( set_intersection2(X1,X0) = X0 )
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_370145,c_413867]) ).
tcf(c_424991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,X2,sK2(X3,X0,X0)),relation_dom(X1))
| ( set_intersection2(X3,X0) = X0 )
| ( sK2(X3,X0,X0) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X3,X0,X0))) ),
inference(superposition,[status(thm)],[c_370145,c_369084]) ).
tcf(c_424992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X1,X2,sK2(X3,X0,X0))),X2)
| ( set_intersection2(X3,X0) = X0 )
| ( sK2(X3,X0,X0) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X3,X0,X0))) ),
inference(superposition,[status(thm)],[c_370145,c_369083]) ).
tcf(c_424993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X1,sK2(X2,X0,X0),X3),X3)
| ( set_intersection2(X2,X0) = X0 )
| ( relation_inverse_image(X1,sK2(X2,X0,X0)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK2(X2,X0,X0),X3))) ),
inference(superposition,[status(thm)],[c_370145,c_369082]) ).
tcf(c_424995,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,X0) = X0 )
| ( set_intersection2(sK2(X1,X0,X0),X2) = sK2(X1,X0,X0) )
| ~ subset(X0,sK2(sK2(X1,X0,X0),X2,sK2(X1,X0,X0))) ),
inference(superposition,[status(thm)],[c_370145,c_370076]) ).
tcf(c_424996,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,X0) = X0 )
| ( set_intersection2(X1,sK2(X2,X0,X0)) = sK2(X2,X0,X0) )
| ~ subset(X0,sK2(X1,sK2(X2,X0,X0),sK2(X2,X0,X0))) ),
inference(superposition,[status(thm)],[c_370145,c_370144]) ).
tcf(c_425246,plain,
! [X0: $i,X1: $i] :
( subset(sK2(X0,powerset(X1),powerset(X1)),X1)
| ( set_intersection2(X0,powerset(X1)) = powerset(X1) ) ),
inference(superposition,[status(thm)],[c_370146,c_99]) ).
tcf(c_425255,plain,
! [X0: $i,X1: $i] :
( ~ subset(sK15(sK5),X1)
| ~ subset(sK15(sK5),X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_424755]) ).
tcf(c_425261,plain,
in(sK16(sK15(sK8)),sK15(sK8)),
inference(global_subsumption_just,[status(thm)],[c_413918,c_89,c_6042,c_15434,c_15435]) ).
tcf(c_425263,plain,
! [X0: $i] :
( element(sK16(sK15(sK8)),X0)
| ~ subset(sK15(sK8),X0) ),
inference(superposition,[status(thm)],[c_425261,c_321]) ).
tcf(c_425264,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ subset(sK15(sK8),X0) ),
inference(superposition,[status(thm)],[c_425261,c_320]) ).
tcf(c_425265,plain,
~ in(sK15(sK8),sK16(sK15(sK8))),
inference(superposition,[status(thm)],[c_425261,c_97]) ).
tcf(c_425266,plain,
! [X0: $i] :
( in(sK16(sK15(sK8)),X0)
| ~ subset(sK15(sK8),X0) ),
inference(superposition,[status(thm)],[c_425261,c_96]) ).
tcf(c_425267,plain,
element(sK16(sK15(sK8)),sK15(sK8)),
inference(superposition,[status(thm)],[c_425261,c_93]) ).
tcf(c_425287,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,X1),X1)
| ( set_intersection2(X0,set_intersection2(X1,X1)) = set_intersection2(X1,X1) ) ),
inference(superposition,[status(thm)],[c_53,c_370148]) ).
tcf(c_425288,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X2,X1),set_intersection2(X2,X1)),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_63,c_370148]) ).
tcf(c_425291,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,empty_set,empty_set),X1)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = set_intersection2(empty_set,X1) ) ),
inference(superposition,[status(thm)],[c_368545,c_370148]) ).
tcf(c_425292,plain,
! [X0: $i] :
( in(sK2(X0,sK15(sK5),sK15(sK5)),sK15(sK5))
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = set_intersection2(sK5,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_411955,c_370148]) ).
tcf(c_425293,plain,
! [X0: $i] :
( in(sK2(X0,sK15(sK8),sK15(sK8)),sK15(sK8))
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = set_intersection2(sK8,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_411956,c_370148]) ).
tcf(c_425295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,set_intersection2(X3,X0),set_intersection2(X3,X0)),X1)
| ( set_intersection2(X2,set_intersection2(X3,X0)) = set_intersection2(X3,X0) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370148,c_321]) ).
tcf(c_425296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,set_intersection2(X3,X0)) = set_intersection2(X3,X0) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370148,c_320]) ).
tcf(c_425297,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X2,X0)) = set_intersection2(X2,X0) )
| ~ in(X0,sK2(X1,set_intersection2(X2,X0),set_intersection2(X2,X0))) ),
inference(superposition,[status(thm)],[c_370148,c_97]) ).
tcf(c_425298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,set_intersection2(X3,X0),set_intersection2(X3,X0)),X1)
| ( set_intersection2(X2,set_intersection2(X3,X0)) = set_intersection2(X3,X0) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370148,c_96]) ).
tcf(c_425299,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_370148,c_93]) ).
tcf(c_425301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X3)),set_intersection2(X1,set_intersection2(X2,X3))),X3)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X3))) = set_intersection2(X1,set_intersection2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_370148,c_59]) ).
tcf(c_425302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X3)),set_intersection2(X1,set_intersection2(X2,X3))),X2)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X3))) = set_intersection2(X1,set_intersection2(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_370148,c_58]) ).
tcf(c_425303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(X1,set_intersection2(X2,relation_inverse_image(X0,X3)),set_intersection2(X2,relation_inverse_image(X0,X3)))),X3)
| ( set_intersection2(X1,set_intersection2(X2,relation_inverse_image(X0,X3))) = set_intersection2(X2,relation_inverse_image(X0,X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370148,c_88]) ).
tcf(c_425304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,relation_inverse_image(X0,X3)),set_intersection2(X2,relation_inverse_image(X0,X3))),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,relation_inverse_image(X0,X3))) = set_intersection2(X2,relation_inverse_image(X0,X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370148,c_87]) ).
tcf(c_425305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,set_intersection2(X1,relation_dom(X2))) = set_intersection2(X1,relation_dom(X2)) )
| ( apply(X2,sK13(X2,X3,apply(X2,sK2(X0,set_intersection2(X1,relation_dom(X2)),set_intersection2(X1,relation_dom(X2)))))) = apply(X2,sK2(X0,set_intersection2(X1,relation_dom(X2)),set_intersection2(X1,relation_dom(X2)))) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,set_intersection2(X1,relation_dom(X2)),set_intersection2(X1,relation_dom(X2))),X3) ),
inference(superposition,[status(thm)],[c_370148,c_369671]) ).
tcf(c_425306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,set_intersection2(X4,relation_image(X2,X0))) = set_intersection2(X4,relation_image(X2,X0)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370148,c_369799]) ).
tcf(c_425307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X2,set_intersection2(X3,relation_image(X0,X4))) = set_intersection2(X3,relation_image(X0,X4)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370148,c_369798]) ).
tcf(c_425308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,set_intersection2(X3,relation_image(X0,X1))) = set_intersection2(X3,relation_image(X0,X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370148,c_369596]) ).
tcf(c_425309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(X2,relation_image(X0,X3))) = set_intersection2(X2,relation_image(X0,X3)) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370148,c_369558]) ).
tcf(c_425310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,set_intersection2(X3,relation_image(X0,X1))) = set_intersection2(X3,relation_image(X0,X1)) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,relation_image(X0,X1)),set_intersection2(X3,relation_image(X0,X1))))) = sK2(X2,set_intersection2(X3,relation_image(X0,X1)),set_intersection2(X3,relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370148,c_112]) ).
tcf(c_425311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,set_intersection2(X1,relation_dom(X2))) = set_intersection2(X1,relation_dom(X2)) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_image(X2,X3))
| ~ in(sK2(X0,set_intersection2(X1,relation_dom(X2)),set_intersection2(X1,relation_dom(X2))),X3) ),
inference(superposition,[status(thm)],[c_370148,c_369501]) ).
tcf(c_425312,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,set_intersection2(X1,empty_set)) = set_intersection2(X1,empty_set),
inference(superposition,[status(thm)],[c_370148,c_372426]) ).
tcf(c_425313,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X0)) = set_intersection2(X2,X0) )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X0),set_intersection2(X2,X0)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X0),set_intersection2(X2,X0)),set_intersection2(X2,X0)) ),
inference(superposition,[status(thm)],[c_370148,c_368471]) ).
tcf(c_425314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,set_intersection2(X4,relation_image(X0,relation_image(X1,X2)))) = set_intersection2(X4,relation_image(X0,relation_image(X1,X2))) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,relation_image(X0,relation_image(X1,X2))),set_intersection2(X4,relation_image(X0,relation_image(X1,X2))))))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,relation_image(X0,relation_image(X1,X2))),set_intersection2(X4,relation_image(X0,relation_image(X1,X2))))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370148,c_369672]) ).
tcf(c_425315,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,set_intersection2(X1,sK15(sK5)),set_intersection2(X1,sK15(sK5))),sK5)
| ( set_intersection2(X0,set_intersection2(X1,sK15(sK5))) = set_intersection2(X1,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_370148,c_412536]) ).
tcf(c_425316,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,set_intersection2(X1,sK15(sK8)),set_intersection2(X1,sK15(sK8))),sK8)
| ( set_intersection2(X0,set_intersection2(X1,sK15(sK8))) = set_intersection2(X1,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_370148,c_413867]) ).
tcf(c_425330,plain,
! [X0: $i] :
( in(sK2(X0,sK15(sK8),sK15(sK8)),sK15(sK8))
| ( set_intersection2(X0,sK15(sK8)) = sK15(sK8) ) ),
inference(light_normalisation,[status(thm)],[c_425293,c_411956]) ).
tcf(c_425333,plain,
! [X0: $i] :
( in(sK2(X0,sK15(sK5),sK15(sK5)),sK15(sK5))
| ( set_intersection2(X0,sK15(sK5)) = sK15(sK5) ) ),
inference(light_normalisation,[status(thm)],[c_425292,c_411955]) ).
tcf(c_425522,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X2,X1),set_intersection2(X2,X1)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_63,c_370149]) ).
tcf(c_425526,plain,
! [X0: $i] :
( in(sK2(X0,sK15(sK5),sK15(sK5)),sK5)
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = set_intersection2(sK5,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_411955,c_370149]) ).
tcf(c_425527,plain,
! [X0: $i] :
( in(sK2(X0,sK15(sK8),sK15(sK8)),sK8)
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = set_intersection2(sK8,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_411956,c_370149]) ).
tcf(c_425529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,set_intersection2(X0,X3),set_intersection2(X0,X3)),X1)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = set_intersection2(X0,X3) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370149,c_321]) ).
tcf(c_425530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,set_intersection2(X0,X3)) = set_intersection2(X0,X3) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370149,c_320]) ).
tcf(c_425531,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X0,X2)) = set_intersection2(X0,X2) )
| ~ in(X0,sK2(X1,set_intersection2(X0,X2),set_intersection2(X0,X2))) ),
inference(superposition,[status(thm)],[c_370149,c_97]) ).
tcf(c_425532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,set_intersection2(X0,X3),set_intersection2(X0,X3)),X1)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = set_intersection2(X0,X3) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370149,c_96]) ).
tcf(c_425533,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_370149,c_93]) ).
tcf(c_425535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),set_intersection2(set_intersection2(X1,X2),X3)),X2)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X3)) = set_intersection2(set_intersection2(X1,X2),X3) ) ),
inference(superposition,[status(thm)],[c_370149,c_59]) ).
tcf(c_425536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),set_intersection2(set_intersection2(X1,X2),X3)),X1)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X3)) = set_intersection2(set_intersection2(X1,X2),X3) ) ),
inference(superposition,[status(thm)],[c_370149,c_58]) ).
tcf(c_425537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),set_intersection2(relation_inverse_image(X0,X2),X3))),X2)
| ( set_intersection2(X1,set_intersection2(relation_inverse_image(X0,X2),X3)) = set_intersection2(relation_inverse_image(X0,X2),X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370149,c_88]) ).
tcf(c_425538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),set_intersection2(relation_inverse_image(X0,X2),X3)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(relation_inverse_image(X0,X2),X3)) = set_intersection2(relation_inverse_image(X0,X2),X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370149,c_87]) ).
tcf(c_425539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = set_intersection2(relation_dom(X1),X2) )
| ( apply(X1,sK13(X1,X3,apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(relation_dom(X1),X2))))) = apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(relation_dom(X1),X2))) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(relation_dom(X1),X2)),X3) ),
inference(superposition,[status(thm)],[c_370149,c_369671]) ).
tcf(c_425540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,set_intersection2(relation_image(X2,X0),X4)) = set_intersection2(relation_image(X2,X0),X4) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370149,c_369799]) ).
tcf(c_425541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X2,set_intersection2(relation_image(X0,X3),X4)) = set_intersection2(relation_image(X0,X3),X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370149,c_369798]) ).
tcf(c_425542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,set_intersection2(relation_image(X0,X1),X3)) = set_intersection2(relation_image(X0,X1),X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370149,c_369596]) ).
tcf(c_425543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(relation_image(X0,X2),X3)) = set_intersection2(relation_image(X0,X2),X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370149,c_369558]) ).
tcf(c_425544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,set_intersection2(relation_image(X0,X1),X3)) = set_intersection2(relation_image(X0,X1),X3) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(relation_image(X0,X1),X3),set_intersection2(relation_image(X0,X1),X3)))) = sK2(X2,set_intersection2(relation_image(X0,X1),X3),set_intersection2(relation_image(X0,X1),X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370149,c_112]) ).
tcf(c_425545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = set_intersection2(relation_dom(X1),X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X3))
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(relation_dom(X1),X2)),X3) ),
inference(superposition,[status(thm)],[c_370149,c_369501]) ).
tcf(c_425546,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,set_intersection2(empty_set,X1)) = set_intersection2(empty_set,X1),
inference(superposition,[status(thm)],[c_370149,c_372426]) ).
tcf(c_425547,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X2)) = set_intersection2(X0,X2) )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),set_intersection2(X0,X2)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),set_intersection2(X0,X2)),set_intersection2(X0,X2)) ),
inference(superposition,[status(thm)],[c_370149,c_368471]) ).
tcf(c_425548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4)) = set_intersection2(relation_image(X0,relation_image(X1,X2)),X4) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),set_intersection2(relation_image(X0,relation_image(X1,X2)),X4))))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),set_intersection2(relation_image(X0,relation_image(X1,X2)),X4))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370149,c_369672]) ).
tcf(c_425549,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,set_intersection2(sK15(sK5),X1),set_intersection2(sK15(sK5),X1)),sK5)
| ( set_intersection2(X0,set_intersection2(sK15(sK5),X1)) = set_intersection2(sK15(sK5),X1) ) ),
inference(superposition,[status(thm)],[c_370149,c_412536]) ).
tcf(c_425550,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,set_intersection2(sK15(sK8),X1),set_intersection2(sK15(sK8),X1)),sK8)
| ( set_intersection2(X0,set_intersection2(sK15(sK8),X1)) = set_intersection2(sK15(sK8),X1) ) ),
inference(superposition,[status(thm)],[c_370149,c_413867]) ).
tcf(c_425664,plain,
! [X0: $i,X1: $i] :
( in(apply(empty_set,sK2(X0,empty_set,empty_set)),X1)
| ( set_intersection2(X0,relation_inverse_image(empty_set,X1)) = relation_inverse_image(empty_set,X1) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370150]) ).
tcf(c_425666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X2,sK2(X3,relation_inverse_image(X2,X0),relation_inverse_image(X2,X0))),X1)
| ( set_intersection2(X3,relation_inverse_image(X2,X0)) = relation_inverse_image(X2,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370150,c_321]) ).
tcf(c_425667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,relation_inverse_image(X2,X0)) = relation_inverse_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370150,c_320]) ).
tcf(c_425668,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,relation_inverse_image(X1,X0)) = relation_inverse_image(X1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK2(X2,relation_inverse_image(X1,X0),relation_inverse_image(X1,X0)))) ),
inference(superposition,[status(thm)],[c_370150,c_97]) ).
tcf(c_425669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK2(X3,relation_inverse_image(X2,X0),relation_inverse_image(X2,X0))),X1)
| ( set_intersection2(X3,relation_inverse_image(X2,X0)) = relation_inverse_image(X2,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370150,c_96]) ).
tcf(c_425670,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(apply(X0,sK2(X1,relation_inverse_image(X0,X2),relation_inverse_image(X0,X2))),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370150,c_93]) ).
tcf(c_425671,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,relation_inverse_image(X0,X1)) = relation_inverse_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370150,c_91]) ).
tcf(c_425672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(X1,relation_inverse_image(X0,set_intersection2(X2,X3)),relation_inverse_image(X0,set_intersection2(X2,X3)))),X3)
| ( set_intersection2(X1,relation_inverse_image(X0,set_intersection2(X2,X3))) = relation_inverse_image(X0,set_intersection2(X2,X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370150,c_59]) ).
tcf(c_425673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(X1,relation_inverse_image(X0,set_intersection2(X2,X3)),relation_inverse_image(X0,set_intersection2(X2,X3)))),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,set_intersection2(X2,X3))) = relation_inverse_image(X0,set_intersection2(X2,X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370150,c_58]) ).
tcf(c_425674,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,relation_inverse_image(X1,X2),relation_inverse_image(X1,X2)),relation_inverse_image(X1,X2))
| ( set_intersection2(X0,relation_inverse_image(X1,X2)) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,relation_inverse_image(X1,X2),relation_inverse_image(X1,X2)),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_370150,c_86]) ).
tcf(c_425675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,apply(X0,sK2(X2,relation_inverse_image(X0,relation_inverse_image(X1,X3)),relation_inverse_image(X0,relation_inverse_image(X1,X3))))),X3)
| ( set_intersection2(X2,relation_inverse_image(X0,relation_inverse_image(X1,X3))) = relation_inverse_image(X0,relation_inverse_image(X1,X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370150,c_88]) ).
tcf(c_425676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(X2,relation_inverse_image(X0,relation_inverse_image(X1,X3)),relation_inverse_image(X0,relation_inverse_image(X1,X3)))),relation_dom(X1))
| ( set_intersection2(X2,relation_inverse_image(X0,relation_inverse_image(X1,X3))) = relation_inverse_image(X0,relation_inverse_image(X1,X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370150,c_87]) ).
tcf(c_425677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,relation_inverse_image(X0,relation_dom(X2))) = relation_inverse_image(X0,relation_dom(X2)) )
| ( apply(X2,sK13(X2,X3,apply(X2,apply(X0,sK2(X1,relation_inverse_image(X0,relation_dom(X2)),relation_inverse_image(X0,relation_dom(X2))))))) = apply(X2,apply(X0,sK2(X1,relation_inverse_image(X0,relation_dom(X2)),relation_inverse_image(X0,relation_dom(X2))))) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(apply(X0,sK2(X1,relation_inverse_image(X0,relation_dom(X2)),relation_inverse_image(X0,relation_dom(X2)))),X3) ),
inference(superposition,[status(thm)],[c_370150,c_369671]) ).
tcf(c_425678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X4,relation_inverse_image(X2,relation_image(X3,X0))) = relation_inverse_image(X2,relation_image(X3,X0)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370150,c_369799]) ).
tcf(c_425679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,relation_inverse_image(X2,relation_image(X0,X4))) = relation_inverse_image(X2,relation_image(X0,X4)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370150,c_369798]) ).
tcf(c_425680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,relation_inverse_image(X0,relation_image(X1,X2))) = relation_inverse_image(X0,relation_image(X1,X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370150,c_369596]) ).
tcf(c_425681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,relation_inverse_image(X1,relation_image(X0,X3))) = relation_inverse_image(X1,relation_image(X0,X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370150,c_369558]) ).
tcf(c_425682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,relation_inverse_image(X0,relation_image(X1,X2))) = relation_inverse_image(X0,relation_image(X1,X2)) )
| ( apply(X1,sK13(X1,X2,apply(X0,sK2(X3,relation_inverse_image(X0,relation_image(X1,X2)),relation_inverse_image(X0,relation_image(X1,X2)))))) = apply(X0,sK2(X3,relation_inverse_image(X0,relation_image(X1,X2)),relation_inverse_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370150,c_112]) ).
tcf(c_425683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,relation_inverse_image(X0,relation_dom(X2))) = relation_inverse_image(X0,relation_dom(X2)) )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ empty(relation_image(X2,X3))
| ~ in(apply(X0,sK2(X1,relation_inverse_image(X0,relation_dom(X2)),relation_inverse_image(X0,relation_dom(X2)))),X3) ),
inference(superposition,[status(thm)],[c_370150,c_369501]) ).
tcf(c_425684,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_inverse_image(X0,empty_set)) = relation_inverse_image(X0,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370150,c_372426]) ).
tcf(c_425685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X4,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))) = relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK2(X4,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK2(X4,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370150,c_369672]) ).
tcf(c_425686,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK2(X1,relation_inverse_image(X0,sK15(sK5)),relation_inverse_image(X0,sK15(sK5)))),sK5)
| ( set_intersection2(X1,relation_inverse_image(X0,sK15(sK5))) = relation_inverse_image(X0,sK15(sK5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370150,c_412536]) ).
tcf(c_425687,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK2(X1,relation_inverse_image(X0,sK15(sK8)),relation_inverse_image(X0,sK15(sK8)))),sK8)
| ( set_intersection2(X1,relation_inverse_image(X0,sK15(sK8))) = relation_inverse_image(X0,sK15(sK8)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370150,c_413867]) ).
tcf(c_425700,plain,
! [X0: $i,X1: $i] :
( in(apply(empty_set,sK2(X0,empty_set,empty_set)),X1)
| ( set_intersection2(X0,relation_inverse_image(empty_set,X1)) = relation_inverse_image(empty_set,X1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_425664,c_368630,c_103]) ).
tcf(c_425903,plain,
! [X0: $i,X1: $i] :
( ~ subset(sK15(sK8),X1)
| ~ subset(sK15(sK8),X0)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_65,c_425264]) ).
tcf(c_425917,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,empty_set,empty_set),relation_dom(empty_set))
| ( set_intersection2(X0,relation_inverse_image(empty_set,X1)) = relation_inverse_image(empty_set,X1) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370151]) ).
tcf(c_425920,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_dom(X0),relation_inverse_image(X0,X1)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(relation_dom(X0),relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),relation_inverse_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_370151,c_54]) ).
tcf(c_425921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,relation_inverse_image(X0,X3),relation_inverse_image(X0,X3)),X1)
| ( set_intersection2(X2,relation_inverse_image(X0,X3)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370151,c_321]) ).
tcf(c_425922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,relation_inverse_image(X0,X3)) = relation_inverse_image(X0,X3) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370151,c_320]) ).
tcf(c_425923,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_inverse_image(X0,X2)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK2(X1,relation_inverse_image(X0,X2),relation_inverse_image(X0,X2))) ),
inference(superposition,[status(thm)],[c_370151,c_97]) ).
tcf(c_425924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,relation_inverse_image(X0,X3),relation_inverse_image(X0,X3)),X1)
| ( set_intersection2(X2,relation_inverse_image(X0,X3)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370151,c_96]) ).
tcf(c_425925,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,relation_inverse_image(X0,X2),relation_inverse_image(X0,X2)),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370151,c_93]) ).
tcf(c_425926,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,relation_inverse_image(X0,X2)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370151,c_91]) ).
tcf(c_425927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,relation_inverse_image(X1,X2)) = relation_inverse_image(X1,X2) )
| ( apply(X1,sK13(X1,X3,apply(X1,sK2(X0,relation_inverse_image(X1,X2),relation_inverse_image(X1,X2))))) = apply(X1,sK2(X0,relation_inverse_image(X1,X2),relation_inverse_image(X1,X2))) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,relation_inverse_image(X1,X2),relation_inverse_image(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_370151,c_369671]) ).
tcf(c_425928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,relation_inverse_image(X1,X2)) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X3))
| ~ in(sK2(X0,relation_inverse_image(X1,X2),relation_inverse_image(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_370151,c_369501]) ).
tcf(c_425929,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(relation_dom(X0),X1),relation_inverse_image(X0,X2)) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),relation_inverse_image(X0,X2),relation_inverse_image(X0,X2)),X1)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),relation_inverse_image(X0,X2),relation_inverse_image(X0,X2)),relation_inverse_image(X0,X2)) ),
inference(superposition,[status(thm)],[c_370151,c_368471]) ).
tcf(c_425934,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,empty_set,empty_set),empty_set)
| ( set_intersection2(X0,relation_inverse_image(empty_set,X1)) = relation_inverse_image(empty_set,X1) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_425917,c_373108]) ).
tcf(c_425935,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,relation_inverse_image(empty_set,X1)) = relation_inverse_image(empty_set,X1),
inference(forward_subsumption_resolution,[status(thm)],[c_425934,c_372426,c_368630,c_103]) ).
tcf(c_425996,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_image(sK1,X0)) = relation_image(sK1,X0) )
| ( apply(sK1,sK13(sK1,X0,sK2(X1,relation_image(sK1,X0),relation_image(sK1,X0)))) = sK2(X1,relation_image(sK1,X0),relation_image(sK1,X0)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_51,c_370152]) ).
tcf(c_425997,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_image(sK4,X0)) = relation_image(sK4,X0) )
| ( apply(sK4,sK13(sK4,X0,sK2(X1,relation_image(sK4,X0),relation_image(sK4,X0)))) = sK2(X1,relation_image(sK4,X0),relation_image(sK4,X0)) )
| ~ relation(sK4) ),
inference(superposition,[status(thm)],[c_76,c_370152]) ).
tcf(c_425998,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_image(empty_set,X0)) = relation_image(empty_set,X0) )
| ( apply(empty_set,sK13(empty_set,X0,sK2(X1,relation_image(empty_set,X0),relation_image(empty_set,X0)))) = sK2(X1,relation_image(empty_set,X0),relation_image(empty_set,X0)) )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_368630,c_370152]) ).
tcf(c_425999,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,relation_image(relation_dom(X0),X1)) = relation_image(relation_dom(X0),X1) )
| ( apply(relation_dom(X0),sK13(relation_dom(X0),X1,sK2(X2,relation_image(relation_dom(X0),X1),relation_image(relation_dom(X0),X1)))) = sK2(X2,relation_image(relation_dom(X0),X1),relation_image(relation_dom(X0),X1)) )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_368626,c_370152]) ).
tcf(c_426000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,relation_image(set_intersection2(X0,X1),X2)) = relation_image(set_intersection2(X0,X1),X2) )
| ( apply(set_intersection2(X0,X1),sK13(set_intersection2(X0,X1),X2,sK2(X3,relation_image(set_intersection2(X0,X1),X2),relation_image(set_intersection2(X0,X1),X2)))) = sK2(X3,relation_image(set_intersection2(X0,X1),X2),relation_image(set_intersection2(X0,X1),X2)) )
| ~ empty(X1)
| ~ relation(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_381376,c_370152]) ).
tcf(c_426001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X3,relation_image(set_intersection2(X0,X1),X2)) = relation_image(set_intersection2(X0,X1),X2) )
| ( apply(set_intersection2(X0,X1),sK13(set_intersection2(X0,X1),X2,sK2(X3,relation_image(set_intersection2(X0,X1),X2),relation_image(set_intersection2(X0,X1),X2)))) = sK2(X3,relation_image(set_intersection2(X0,X1),X2),relation_image(set_intersection2(X0,X1),X2)) )
| ~ empty(X0)
| ~ relation(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_381430,c_370152]) ).
tcf(c_426002,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X2,relation_image(sK16(powerset(X0)),X1)) = relation_image(sK16(powerset(X0)),X1) )
| ( apply(sK16(powerset(X0)),sK13(sK16(powerset(X0)),X1,sK2(X2,relation_image(sK16(powerset(X0)),X1),relation_image(sK16(powerset(X0)),X1)))) = sK2(X2,relation_image(sK16(powerset(X0)),X1),relation_image(sK16(powerset(X0)),X1)) )
| ~ empty(X0)
| ~ relation(sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_380417,c_370152]) ).
tcf(c_426003,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(powerset(empty_set),X0)
| ( set_intersection2(X2,relation_image(sK10(powerset(empty_set),X0),X1)) = relation_image(sK10(powerset(empty_set),X0),X1) )
| ( apply(sK10(powerset(empty_set),X0),sK13(sK10(powerset(empty_set),X0),X1,sK2(X2,relation_image(sK10(powerset(empty_set),X0),X1),relation_image(sK10(powerset(empty_set),X0),X1)))) = sK2(X2,relation_image(sK10(powerset(empty_set),X0),X1),relation_image(sK10(powerset(empty_set),X0),X1)) )
| ~ relation(sK10(powerset(empty_set),X0)) ),
inference(superposition,[status(thm)],[c_390528,c_370152]) ).
tcf(c_426004,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,empty_set) = empty_set )
| ( apply(empty_set,sK13(empty_set,X0,sK2(X1,empty_set,empty_set))) = sK2(X1,empty_set,empty_set) )
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_425998,c_375097]) ).
tcf(c_426005,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_image(sK4,X0)) = relation_image(sK4,X0) )
| ( apply(sK4,sK13(sK4,X0,sK2(X1,relation_image(sK4,X0),relation_image(sK4,X0)))) = sK2(X1,relation_image(sK4,X0),relation_image(sK4,X0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_425997,c_75]) ).
tcf(c_426008,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X1,relation_image(sK1,X0)) = relation_image(sK1,X0) )
| ( apply(sK1,sK13(sK1,X0,sK2(X1,relation_image(sK1,X0),relation_image(sK1,X0)))) = sK2(X1,relation_image(sK1,X0),relation_image(sK1,X0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_425996,c_50]) ).
tcf(c_426065,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_370216,c_370216,c_370295]) ).
tcf(c_426075,plain,
! [X0: $i,X1: $i] :
( element(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),X0),X0)
| in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),X0),X1) ),
inference(superposition,[status(thm)],[c_368927,c_426065]) ).
tcf(c_426076,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),X0),X0)
| in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),X0),X1) ),
inference(superposition,[status(thm)],[c_55,c_426065]) ).
tcf(c_426077,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X0),X0)
| in(sK2(set_intersection2(X0,X1),X2,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1) ),
inference(superposition,[status(thm)],[c_368926,c_426065]) ).
tcf(c_426078,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),X0)
| in(sK2(set_intersection2(X0,X1),X2,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1) ),
inference(superposition,[status(thm)],[c_56,c_426065]) ).
tcf(c_426079,plain,
! [X0: $i,X1: $i] :
( element(sK2(set_intersection2(X0,X1),X0,X0),X0)
| in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X0) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(superposition,[status(thm)],[c_368925,c_426065]) ).
tcf(c_426080,plain,
! [X0: $i,X1: $i] :
( element(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X0) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(superposition,[status(thm)],[c_368924,c_426065]) ).
tcf(c_426081,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X0) = X0 )
| ~ empty(set_intersection2(X0,X1))
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(superposition,[status(thm)],[c_368865,c_426065]) ).
tcf(c_426084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X3)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X1) ),
inference(superposition,[status(thm)],[c_57,c_426065]) ).
tcf(c_426085,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),powerset(X2),X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),powerset(X2)) = X0 )
| ~ subset(sK2(set_intersection2(X0,X1),powerset(X2),X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),powerset(X2),X0),X1) ),
inference(superposition,[status(thm)],[c_369138,c_426065]) ).
tcf(c_426086,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),X0),X2)
| in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)) = X0 )
| ~ subset(X0,X2)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),X0),X1) ),
inference(superposition,[status(thm)],[c_369929,c_426065]) ).
tcf(c_426087,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),X0),X2)
| in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)) = X0 )
| ~ subset(X0,X2)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),X0),X1) ),
inference(superposition,[status(thm)],[c_369015,c_426065]) ).
tcf(c_426088,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ subset(X0,X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1) ),
inference(superposition,[status(thm)],[c_369015,c_426065]) ).
tcf(c_426090,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)) = X0 )
| ~ empty(X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),X0),X1) ),
inference(superposition,[status(thm)],[c_368868,c_426065]) ).
tcf(c_426091,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)),X1)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(set_intersection2(X0,X1),X2)) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368506,c_426065]) ).
tcf(c_426092,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)),X0)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(set_intersection2(X0,X1),X2)) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368484,c_426065]) ).
tcf(c_426093,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X1,set_intersection2(X0,X1)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X1) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X1,set_intersection2(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368506,c_426065]) ).
tcf(c_426095,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,set_intersection2(X0,X1)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X0) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,set_intersection2(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368484,c_426065]) ).
tcf(c_426097,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),set_intersection2(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1))),X1)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),set_intersection2(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1)),set_intersection2(relation_inverse_image(X0,X1),X2))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),set_intersection2(relation_inverse_image(X0,X1),X2)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),set_intersection2(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368816,c_426065]) ).
tcf(c_426098,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),set_intersection2(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1)),relation_dom(X0))
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),set_intersection2(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1)),set_intersection2(relation_inverse_image(X0,X1),X2))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),set_intersection2(relation_inverse_image(X0,X1),X2)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),set_intersection2(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368760,c_426065]) ).
tcf(c_426099,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),relation_dom(X0),relation_inverse_image(X0,X1)),set_intersection2(relation_inverse_image(X0,X1),X2))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),relation_dom(X0)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),relation_dom(X0),relation_inverse_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368760,c_426065]) ).
tcf(c_426101,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(X0,X1),X0,X0),X2)
| in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X0) = X0 )
| ~ subset(set_intersection2(X0,X1),X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(superposition,[status(thm)],[c_369926,c_426065]) ).
tcf(c_426102,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X0,X0),X2)
| in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X0) = X0 )
| ~ subset(set_intersection2(X0,X1),X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(superposition,[status(thm)],[c_369012,c_426065]) ).
tcf(c_426103,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),X0)
| in(sK2(set_intersection2(X0,X1),X2,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ subset(set_intersection2(X0,X1),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1) ),
inference(superposition,[status(thm)],[c_369012,c_426065]) ).
tcf(c_426106,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),X1,X0),X0)
| in(sK2(set_intersection2(X0,X1),X1,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X1) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X1,X0),X1) ),
inference(superposition,[status(thm)],[c_368503,c_426065]) ).
tcf(c_426107,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),X0,X0),X0)
| in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X0) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(superposition,[status(thm)],[c_368481,c_426065]) ).
tcf(c_426108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X0),X3)
| in(sK2(set_intersection2(X0,X1),X2,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ subset(X0,X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1) ),
inference(superposition,[status(thm)],[c_369928,c_426065]) ).
tcf(c_426109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),X3)
| in(sK2(set_intersection2(X0,X1),X2,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ subset(X0,X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1) ),
inference(superposition,[status(thm)],[c_369014,c_426065]) ).
tcf(c_426110,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ empty(X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1) ),
inference(superposition,[status(thm)],[c_368867,c_426065]) ).
tcf(c_426111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X1)),X1)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X1)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368505,c_426065]) ).
tcf(c_426112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X1)),X0)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X1)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368483,c_426065]) ).
tcf(c_426113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_inverse_image(X0,X1))),X1)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_inverse_image(X0,X1)),set_intersection2(relation_inverse_image(X0,X1),X2))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_inverse_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368815,c_426065]) ).
tcf(c_426114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_inverse_image(X0,X1)),relation_dom(X0))
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_inverse_image(X0,X1)),set_intersection2(relation_inverse_image(X0,X1),X2))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_inverse_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368759,c_426065]) ).
tcf(c_426115,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(X0,X1),X0,X0),X2)
| in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X0) = X0 )
| ~ subset(X0,X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(superposition,[status(thm)],[c_369927,c_426065]) ).
tcf(c_426116,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X0,X0),X2)
| in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X0) = X0 )
| ~ subset(X0,X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(superposition,[status(thm)],[c_369013,c_426065]) ).
tcf(c_426117,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),X0)
| in(sK2(set_intersection2(X0,X1),X2,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ subset(X2,X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1) ),
inference(superposition,[status(thm)],[c_369013,c_426065]) ).
tcf(c_426118,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X0) = X0 )
| ~ empty(X0)
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(superposition,[status(thm)],[c_368866,c_426065]) ).
tcf(c_426119,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1),set_intersection2(X0,X1)),X1)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1),set_intersection2(X0,X1)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1),set_intersection2(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368504,c_426065]) ).
tcf(c_426120,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1),set_intersection2(X0,X1)),X0)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1),set_intersection2(X0,X1)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1),set_intersection2(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368482,c_426065]) ).
tcf(c_426121,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1),relation_inverse_image(X0,X1))),X1)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),set_intersection2(relation_inverse_image(X0,X1),X2))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368814,c_426065]) ).
tcf(c_426122,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),relation_dom(X0))
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),set_intersection2(relation_inverse_image(X0,X1),X2))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1)) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368758,c_426065]) ).
tcf(c_426123,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X0) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(superposition,[status(thm)],[c_368460,c_426065]) ).
tcf(c_426125,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),relation_image(X0,X1),relation_image(X0,X1)),set_intersection2(relation_image(X0,X1),X2))
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),relation_image(X0,X1)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),relation_image(X0,X1),relation_image(X0,X1)))) = sK2(set_intersection2(relation_image(X0,X1),X2),relation_image(X0,X1),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_image(X0,X1),X2),relation_image(X0,X1),relation_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_369660,c_426065]) ).
tcf(c_426126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_image(X0,X1)),set_intersection2(relation_image(X0,X1),X2))
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_image(X0,X1)))) = sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_369661,c_426065]) ).
tcf(c_426127,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),set_intersection2(relation_image(X0,X1),X2),relation_image(X0,X1)),set_intersection2(relation_image(X0,X1),X2))
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),set_intersection2(relation_image(X0,X1),X2)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),set_intersection2(relation_image(X0,X1),X2),relation_image(X0,X1)))) = sK2(set_intersection2(relation_image(X0,X1),X2),set_intersection2(relation_image(X0,X1),X2),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_image(X0,X1),X2),set_intersection2(relation_image(X0,X1),X2),relation_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_369662,c_426065]) ).
tcf(c_426128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),relation_inverse_image(X0,set_intersection2(X3,X4)),X1),set_intersection2(X1,X2))
| ( set_intersection2(set_intersection2(X1,X2),relation_inverse_image(X0,set_intersection2(X3,X4))) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(X1,X2),relation_inverse_image(X0,set_intersection2(X3,X4)),X1),X2)
| ~ in(sK2(set_intersection2(X1,X2),relation_inverse_image(X0,set_intersection2(X3,X4)),X1),relation_dom(X0))
| ~ in(apply(X0,sK2(set_intersection2(X1,X2),relation_inverse_image(X0,set_intersection2(X3,X4)),X1)),X4)
| ~ in(apply(X0,sK2(set_intersection2(X1,X2),relation_inverse_image(X0,set_intersection2(X3,X4)),X1)),X3) ),
inference(superposition,[status(thm)],[c_368735,c_426065]) ).
tcf(c_426129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,relation_image(X2,X3)),X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),relation_inverse_image(X2,relation_image(X2,X3))) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,relation_image(X2,X3)),X0),X3)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,relation_image(X2,X3)),X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,relation_image(X2,X3)),X0),relation_dom(X2)) ),
inference(superposition,[status(thm)],[c_369503,c_426065]) ).
tcf(c_426130,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X0) = X0 )
| ~ subset(X0,X0)
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(superposition,[status(thm)],[c_370145,c_426065]) ).
tcf(c_426131,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X0),X1,X0),set_intersection2(X0,X0))
| ( set_intersection2(set_intersection2(X0,X0),X1) = X0 )
| ~ in(sK2(X0,X1,X0),X1)
| ~ in(sK2(set_intersection2(X0,X0),X1,X0),X0) ),
inference(superposition,[status(thm)],[c_53,c_426065]) ).
tcf(c_426132,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1) ),
inference(superposition,[status(thm)],[c_63,c_426065]) ).
tcf(c_426134,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,empty_set),X1,X0),set_intersection2(X0,empty_set))
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = X0 )
| ~ in(sK2(empty_set,X1,X0),X1)
| ~ in(sK2(set_intersection2(X0,empty_set),X1,X0),empty_set) ),
inference(superposition,[status(thm)],[c_64,c_426065]) ).
tcf(c_426135,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(empty_set,X0),X1,empty_set),set_intersection2(empty_set,X0))
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = empty_set )
| ~ in(sK2(empty_set,X1,empty_set),X1)
| ~ in(sK2(set_intersection2(empty_set,X0),X1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_368545,c_426065]) ).
tcf(c_426136,plain,
! [X0: $i] :
( in(sK2(set_intersection2(sK5,sK15(sK5)),X0,sK5),set_intersection2(sK5,sK15(sK5)))
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = sK5 )
| ~ in(sK2(sK15(sK5),X0,sK5),X0)
| ~ in(sK2(set_intersection2(sK5,sK15(sK5)),X0,sK5),sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_426065]) ).
tcf(c_426137,plain,
! [X0: $i] :
( in(sK2(set_intersection2(sK8,sK15(sK8)),X0,sK8),set_intersection2(sK8,sK15(sK8)))
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = sK8 )
| ~ in(sK2(sK15(sK8),X0,sK8),X0)
| ~ in(sK2(set_intersection2(sK8,sK15(sK8)),X0,sK8),sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_426065]) ).
tcf(c_426138,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(X0,X1) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_426123,c_397166]) ).
tcf(c_426147,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,X0)
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_426130,c_397166]) ).
tcf(c_426153,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(X0,X1) = X0 )
| ~ empty(set_intersection2(X0,X1))
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_426081,c_397166]) ).
tcf(c_426158,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X0,empty_set),empty_set)
| ( set_intersection2(empty_set,X0) = empty_set )
| ~ in(sK2(empty_set,X0,empty_set),X1)
| ~ in(sK2(empty_set,X0,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_426135,c_368545]) ).
tcf(c_426162,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),X1,X0),X0)
| in(sK2(set_intersection2(X0,X1),X1,X0),set_intersection2(X0,X1))
| ( set_intersection2(X0,X1) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_426106,c_397167]) ).
tcf(c_426186,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X0,X0),X2)
| in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_426116,c_397166]) ).
tcf(c_426192,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(X0,X1),X0,X0),X2)
| in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(X0,X1) = X0 )
| ~ subset(X0,X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_426115,c_397166]) ).
tcf(c_426219,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X0,X0),X2)
| in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(X0,X1) = X0 )
| ~ subset(set_intersection2(X0,X1),X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_426102,c_397166]) ).
tcf(c_426225,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(X0,X1),X0,X0),X2)
| in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(X0,X1) = X0 )
| ~ subset(set_intersection2(X0,X1),X2)
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_426101,c_397166]) ).
tcf(c_426508,plain,
! [X0: $i] :
( subset(sK16(sK15(sK5)),X0)
| ~ subset(sK5,powerset(X0)) ),
inference(superposition,[status(thm)],[c_420693,c_99]) ).
tcf(c_426524,plain,
! [X0: $i,X1: $i] :
( element(sK16(sK15(sK5)),X1)
| ~ subset(sK5,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_420696,c_321]) ).
tcf(c_426525,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ subset(sK5,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_420696,c_320]) ).
tcf(c_426526,plain,
! [X0: $i] :
( ~ subset(sK5,X0)
| ~ in(X0,sK16(sK15(sK5))) ),
inference(superposition,[status(thm)],[c_420696,c_97]) ).
tcf(c_426527,plain,
! [X0: $i,X1: $i] :
( in(sK16(sK15(sK5)),X1)
| ~ subset(sK5,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_420696,c_96]) ).
tcf(c_426530,plain,
! [X0: $i,X1: $i] :
( in(sK16(sK15(sK5)),X1)
| ~ subset(sK5,set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_420696,c_59]) ).
tcf(c_426531,plain,
! [X0: $i,X1: $i] :
( in(sK16(sK15(sK5)),X0)
| ~ subset(sK5,set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_420696,c_58]) ).
tcf(c_426532,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK16(sK15(sK5))),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK5,relation_inverse_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_420696,c_88]) ).
tcf(c_426533,plain,
! [X0: $i,X1: $i] :
( in(sK16(sK15(sK5)),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK5,relation_inverse_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_420696,c_87]) ).
tcf(c_426534,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,sK13(X1,X0,apply(X1,sK16(sK15(sK5))))) = apply(X1,sK16(sK15(sK5))) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(sK5,relation_dom(X1))
| ~ in(sK16(sK15(sK5)),X0) ),
inference(superposition,[status(thm)],[c_420696,c_369671]) ).
tcf(c_426535,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X1,X2)
| ~ subset(sK5,relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_420696,c_369799]) ).
tcf(c_426536,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X2)
| ~ subset(sK5,relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_420696,c_369798]) ).
tcf(c_426537,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK5,relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_420696,c_369596]) ).
tcf(c_426538,plain,
! [X0: $i,X1: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0))
| ~ subset(sK5,relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_420696,c_369558]) ).
tcf(c_426539,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,sK13(X0,X1,sK16(sK15(sK5)))) = sK16(sK15(sK5)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK5,relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_420696,c_112]) ).
tcf(c_426540,plain,
! [X0: $i,X1: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(sK5,relation_dom(X1))
| ~ empty(relation_image(X1,X0))
| ~ in(sK16(sK15(sK5)),X0) ),
inference(superposition,[status(thm)],[c_420696,c_369501]) ).
tcf(c_426541,plain,
! [X0: $i] :
( subset(sK16(sK15(sK5)),X0)
| ~ subset(sK5,sK10(sK16(sK15(sK5)),X0)) ),
inference(superposition,[status(thm)],[c_420696,c_369085]) ).
tcf(c_426542,plain,
~ subset(sK5,empty_set),
inference(superposition,[status(thm)],[c_420696,c_372426]) ).
tcf(c_426543,plain,
( empty(sK16(sK15(sK5)))
| ~ subset(sK5,sK16(sK16(sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_420696,c_370746]) ).
tcf(c_426544,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK16(sK15(sK5))),X0)
| ( set_intersection2(X0,X1) = sK16(sK15(sK5)) )
| ~ subset(sK5,sK2(X0,X1,sK16(sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_420696,c_369079]) ).
tcf(c_426545,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK16(sK15(sK5))),X1)
| ( set_intersection2(X0,X1) = sK16(sK15(sK5)) )
| ~ subset(sK5,sK2(X0,X1,sK16(sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_420696,c_369078]) ).
tcf(c_426546,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK16(sK15(sK5)),X0,X1),X1)
| ( set_intersection2(sK16(sK15(sK5)),X0) = X1 )
| ~ subset(sK5,sK2(sK16(sK15(sK5)),X0,X1)) ),
inference(superposition,[status(thm)],[c_420696,c_369076]) ).
tcf(c_426547,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK16(sK15(sK5)),X1),X1)
| ( set_intersection2(X0,sK16(sK15(sK5))) = X1 )
| ~ subset(sK5,sK2(X0,sK16(sK15(sK5)),X1)) ),
inference(superposition,[status(thm)],[c_420696,c_369077]) ).
tcf(c_426548,plain,
! [X0: $i,X1: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_image(X0,sK16(sK15(sK5))))
| ~ subset(sK5,sK13(X0,sK16(sK15(sK5)),X1)) ),
inference(superposition,[status(thm)],[c_420696,c_369593]) ).
tcf(c_426549,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK16(sK15(sK5))))) = sK13(X0,relation_image(X1,X2),sK16(sK15(sK5))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(sK5,relation_image(X0,relation_image(X1,X2))) ),
inference(superposition,[status(thm)],[c_420696,c_369672]) ).
tcf(c_426550,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,sK16(sK15(sK5)),X1),X1)
| ( relation_image(X0,sK16(sK15(sK5))) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK5,sK12(X0,sK16(sK15(sK5)),X1)) ),
inference(superposition,[status(thm)],[c_420696,c_369298]) ).
tcf(c_426551,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK16(sK15(sK5)) )
| ( apply(X0,sK12(X0,X1,sK16(sK15(sK5)))) = sK11(X0,X1,sK16(sK15(sK5))) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK5,sK11(X0,X1,sK16(sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_420696,c_369435]) ).
tcf(c_426552,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,sK16(sK15(sK5))),X1)
| ( relation_image(X0,X1) = sK16(sK15(sK5)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK5,sK11(X0,X1,sK16(sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_420696,c_369306]) ).
tcf(c_426553,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,sK16(sK15(sK5))),relation_dom(X0))
| ( relation_image(X0,X1) = sK16(sK15(sK5)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK5,sK11(X0,X1,sK16(sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_420696,c_369205]) ).
tcf(c_426555,plain,
( in(sK16(sK15(sK5)),sK8)
| ~ subset(sK5,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_420696,c_413867]) ).
tcf(c_426556,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK16(sK15(sK5))),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK16(sK15(sK5)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK5,sK7(X0,X1,sK16(sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_420696,c_369084]) ).
tcf(c_426557,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK7(X0,X1,sK16(sK15(sK5)))),X1)
| ( relation_inverse_image(X0,X1) = sK16(sK15(sK5)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK5,sK7(X0,X1,sK16(sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_420696,c_369083]) ).
tcf(c_426558,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,sK16(sK15(sK5)),X1),X1)
| ( relation_inverse_image(X0,sK16(sK15(sK5))) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK5,apply(X0,sK7(X0,sK16(sK15(sK5)),X1))) ),
inference(superposition,[status(thm)],[c_420696,c_369082]) ).
tcf(c_426559,plain,
! [X0: $i] :
( ( set_intersection2(sK16(sK15(sK5)),X0) = sK16(sK15(sK5)) )
| ~ subset(sK5,sK2(sK16(sK15(sK5)),X0,sK16(sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_420696,c_370076]) ).
tcf(c_426560,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK16(sK15(sK5))) = sK16(sK15(sK5)) )
| ~ subset(sK5,sK2(X0,sK16(sK15(sK5)),sK16(sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_420696,c_370144]) ).
tcf(c_426795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X0) = X3 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X0) ),
inference(superposition,[status(thm)],[c_368926,c_370217]) ).
tcf(c_426797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_368925,c_370217]) ).
tcf(c_426798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_368924,c_370217]) ).
tcf(c_426799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ empty(set_intersection2(set_intersection2(X0,X1),X2))
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_368865,c_370217]) ).
tcf(c_426801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_55,c_370217]) ).
tcf(c_426802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),X4) = X5 )
| ~ in(sK2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),X4,X5),X5)
| ~ in(sK2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),X4,X5),X4)
| ~ in(sK2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),X4,X5),X3)
| ~ in(sK2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),X4,X5),X2)
| ~ in(sK2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),X4,X5),X1)
| ~ in(sK2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),X4,X5),X0) ),
inference(superposition,[status(thm)],[c_57,c_370217]) ).
tcf(c_426803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(powerset(X0),X1),X2),X3) = X4 )
| ~ subset(sK2(set_intersection2(set_intersection2(powerset(X0),X1),X2),X3,X4),X0)
| ~ in(sK2(set_intersection2(set_intersection2(powerset(X0),X1),X2),X3,X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(powerset(X0),X1),X2),X3,X4),X3)
| ~ in(sK2(set_intersection2(set_intersection2(powerset(X0),X1),X2),X3,X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(powerset(X0),X1),X2),X3,X4),X1) ),
inference(superposition,[status(thm)],[c_369138,c_370217]) ).
tcf(c_426804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 )
| ~ subset(X4,X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X1) ),
inference(superposition,[status(thm)],[c_369015,c_370217]) ).
tcf(c_426806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X0)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(X4,X0) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X0)),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X0)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X0)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X0)),set_intersection2(X4,X0)) ),
inference(superposition,[status(thm)],[c_368506,c_370217]) ).
tcf(c_426808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X4)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(X0,X4) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X4)),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X4)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X4)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X4)),set_intersection2(X0,X4)) ),
inference(superposition,[status(thm)],[c_368484,c_370217]) ).
tcf(c_426810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,relation_inverse_image(X0,X4)),set_intersection2(set_intersection2(relation_dom(X0),X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,relation_inverse_image(X0,X4)),X3)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,relation_inverse_image(X0,X4)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,relation_inverse_image(X0,X4)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,relation_inverse_image(X0,X4)),relation_inverse_image(X0,X4)) ),
inference(superposition,[status(thm)],[c_368760,c_370217]) ).
tcf(c_426812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ subset(set_intersection2(set_intersection2(X0,X1),X2),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_369926,c_370217]) ).
tcf(c_426813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ subset(set_intersection2(set_intersection2(X0,X1),X2),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_369012,c_370217]) ).
tcf(c_426816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_368481,c_370217]) ).
tcf(c_426818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X0) = X3 )
| ~ subset(X3,X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X0) ),
inference(superposition,[status(thm)],[c_369928,c_370217]) ).
tcf(c_426819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X0) = X3 )
| ~ subset(X3,X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X0) ),
inference(superposition,[status(thm)],[c_369014,c_370217]) ).
tcf(c_426820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X0) = X3 )
| ~ empty(X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X3),X0) ),
inference(superposition,[status(thm)],[c_368867,c_370217]) ).
tcf(c_426821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,set_intersection2(X3,X4)),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X0) = set_intersection2(X3,X4) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,set_intersection2(X3,X4)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,set_intersection2(X3,X4)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,set_intersection2(X3,X4)),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,set_intersection2(X3,X4)),set_intersection2(X3,X4)) ),
inference(superposition,[status(thm)],[c_368505,c_370217]) ).
tcf(c_426822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,set_intersection2(X3,X4)),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X0) = set_intersection2(X3,X4) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,set_intersection2(X3,X4)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,set_intersection2(X3,X4)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,set_intersection2(X3,X4)),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,set_intersection2(X3,X4)),set_intersection2(X3,X4)) ),
inference(superposition,[status(thm)],[c_368483,c_370217]) ).
tcf(c_426823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_inverse_image(X3,X4))),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X0) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_inverse_image(X3,X4)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_inverse_image(X3,X4)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_inverse_image(X3,X4)),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_inverse_image(X3,X4)),relation_inverse_image(X3,X4)) ),
inference(superposition,[status(thm)],[c_368815,c_370217]) ).
tcf(c_426824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_inverse_image(X3,X4)),relation_dom(X3))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X0) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_inverse_image(X3,X4)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_inverse_image(X3,X4)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_inverse_image(X3,X4)),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_inverse_image(X3,X4)),relation_inverse_image(X3,X4)) ),
inference(superposition,[status(thm)],[c_368759,c_370217]) ).
tcf(c_426825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ subset(X3,X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_369927,c_370217]) ).
tcf(c_426826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ subset(X3,X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_369013,c_370217]) ).
tcf(c_426828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ empty(X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_368866,c_370217]) ).
tcf(c_426829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4)) = X0 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),set_intersection2(X3,X4)) ),
inference(superposition,[status(thm)],[c_368504,c_370217]) ).
tcf(c_426830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4)) = X0 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),set_intersection2(X3,X4)) ),
inference(superposition,[status(thm)],[c_368482,c_370217]) ).
tcf(c_426833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_inverse_image(X3,X4),X0)),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),relation_inverse_image(X3,X4)) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_inverse_image(X3,X4),X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_inverse_image(X3,X4),X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_inverse_image(X3,X4),X0),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_inverse_image(X3,X4),X0),relation_inverse_image(X3,X4)) ),
inference(superposition,[status(thm)],[c_368814,c_370217]) ).
tcf(c_426834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_inverse_image(X3,X4),X0),relation_dom(X3))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),relation_inverse_image(X3,X4)) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_inverse_image(X3,X4),X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_inverse_image(X3,X4),X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_inverse_image(X3,X4),X0),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_inverse_image(X3,X4),X0),relation_inverse_image(X3,X4)) ),
inference(superposition,[status(thm)],[c_368758,c_370217]) ).
tcf(c_426836,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X0) = X0 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,X0),X0) ),
inference(superposition,[status(thm)],[c_368460,c_370217]) ).
tcf(c_426837,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),empty_set) = X0 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),empty_set,X0),empty_set)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),empty_set,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),empty_set,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),empty_set,X0),X0) ),
inference(superposition,[status(thm)],[c_372467,c_370217]) ).
tcf(c_426838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),relation_image(X3,X4)) = X0 )
| ( apply(X3,sK13(X3,X4,sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_image(X3,X4),X0))) = sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_image(X3,X4),X0) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_image(X3,X4),X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_image(X3,X4),X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_image(X3,X4),X0),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),relation_image(X3,X4),X0),relation_image(X3,X4)) ),
inference(superposition,[status(thm)],[c_369660,c_370217]) ).
tcf(c_426839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X0) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_image(X3,X4)))) = sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_image(X3,X4)) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_image(X3,X4)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_image(X3,X4)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_image(X3,X4)),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,relation_image(X3,X4)),relation_image(X3,X4)) ),
inference(superposition,[status(thm)],[c_369661,c_370217]) ).
tcf(c_426840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4),X5) = X6 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4),X5,X6),X6)
| ~ in(sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4),X5,X6),X5)
| ~ in(sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4),X5,X6),X4)
| ~ in(sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4),X5,X6),X3)
| ~ in(sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4),X5,X6),relation_dom(X0))
| ~ in(apply(X0,sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4),X5,X6)),X2)
| ~ in(apply(X0,sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4),X5,X6)),X1) ),
inference(superposition,[status(thm)],[c_368735,c_370217]) ).
tcf(c_426841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(relation_inverse_image(X0,relation_image(X0,X1)),X2),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,relation_image(X0,X1)),X2),X3),X4,X5),X5)
| ~ in(sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,relation_image(X0,X1)),X2),X3),X4,X5),X4)
| ~ in(sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,relation_image(X0,X1)),X2),X3),X4,X5),X3)
| ~ in(sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,relation_image(X0,X1)),X2),X3),X4,X5),X2)
| ~ in(sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,relation_image(X0,X1)),X2),X3),X4,X5),X1)
| ~ in(sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,relation_image(X0,X1)),X2),X3),X4,X5),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_369503,c_370217]) ).
tcf(c_426842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(set_intersection2(X0,X1),X2) )
| ~ subset(set_intersection2(set_intersection2(X0,X1),X2),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(set_intersection2(X0,X1),X2)),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(set_intersection2(X0,X1),X2)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(set_intersection2(X0,X1),X2)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(set_intersection2(X0,X1),X2)),set_intersection2(set_intersection2(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_370077,c_370217]) ).
tcf(c_426843,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X0),X2) = set_intersection2(set_intersection2(X0,X1),X0) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X0),X2,set_intersection2(set_intersection2(X0,X1),X0)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X0),X2,set_intersection2(set_intersection2(X0,X1),X0)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X0),X2,set_intersection2(set_intersection2(X0,X1),X0)),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X0),X2,set_intersection2(set_intersection2(X0,X1),X0)),set_intersection2(set_intersection2(X0,X1),X0)) ),
inference(superposition,[status(thm)],[c_370080,c_370217]) ).
tcf(c_426844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X3 )
| ~ subset(X3,X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X3),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X3),X1) ),
inference(superposition,[status(thm)],[c_370145,c_370217]) ).
tcf(c_426845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X0)) = set_intersection2(X3,X0) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X0),set_intersection2(X3,X0)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X0),set_intersection2(X3,X0)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X0),set_intersection2(X3,X0)),set_intersection2(X3,X0)) ),
inference(superposition,[status(thm)],[c_370148,c_370217]) ).
tcf(c_426846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3)) = set_intersection2(X0,X3) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),set_intersection2(X0,X3)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),set_intersection2(X0,X3)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),set_intersection2(X0,X3)),set_intersection2(X0,X3)) ),
inference(superposition,[status(thm)],[c_370149,c_370217]) ).
tcf(c_426847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),relation_inverse_image(X0,X3)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),relation_inverse_image(X0,X3),relation_inverse_image(X0,X3)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),relation_inverse_image(X0,X3),relation_inverse_image(X0,X3)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),relation_inverse_image(X0,X3),relation_inverse_image(X0,X3)),relation_inverse_image(X0,X3)) ),
inference(superposition,[status(thm)],[c_370151,c_370217]) ).
tcf(c_426848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)),X2) = X3 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)),X2,X3),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)),X2,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)),X2,X3),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)),X2,X3),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_53,c_370217]) ).
tcf(c_426849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 )
| ~ in(sK2(set_intersection2(X2,set_intersection2(X0,X1)),X3,X4),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X1) ),
inference(superposition,[status(thm)],[c_63,c_370217]) ).
tcf(c_426851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),empty_set),X2) = X3 )
| ~ in(sK2(empty_set,X2,X3),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),empty_set),X2,X3),empty_set)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),empty_set),X2,X3),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),empty_set),X2,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),empty_set),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_64,c_370217]) ).
tcf(c_426852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X0),X1),X2) = X3 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X0),X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X0),X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X0),X1),X2,X3),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X0),X1),X2,X3),X0) ),
inference(superposition,[status(thm)],[c_53,c_370217]) ).
tcf(c_426853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 )
| ~ in(sK2(set_intersection2(set_intersection2(X1,X0),X2),X3,X4),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X1) ),
inference(superposition,[status(thm)],[c_63,c_370217]) ).
tcf(c_426855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,empty_set),X1),X2) = X3 )
| ~ in(sK2(set_intersection2(empty_set,X1),X2,X3),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,empty_set),X1),X2,X3),empty_set)
| ~ in(sK2(set_intersection2(set_intersection2(X0,empty_set),X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,empty_set),X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,empty_set),X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_64,c_370217]) ).
tcf(c_426856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(empty_set,X0),X1),X2) = X3 )
| ~ in(sK2(set_intersection2(empty_set,X1),X2,X3),empty_set)
| ~ in(sK2(set_intersection2(set_intersection2(empty_set,X0),X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(set_intersection2(empty_set,X0),X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(empty_set,X0),X1),X2,X3),X1)
| ~ in(sK2(set_intersection2(set_intersection2(empty_set,X0),X1),X2,X3),X0) ),
inference(superposition,[status(thm)],[c_368545,c_370217]) ).
tcf(c_426857,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(sK5,sK15(sK5)),X0),X1) = X2 )
| ~ in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),sK5)
| ~ in(sK2(set_intersection2(set_intersection2(sK5,sK15(sK5)),X0),X1,X2),X2)
| ~ in(sK2(set_intersection2(set_intersection2(sK5,sK15(sK5)),X0),X1,X2),X1)
| ~ in(sK2(set_intersection2(set_intersection2(sK5,sK15(sK5)),X0),X1,X2),X0)
| ~ in(sK2(set_intersection2(set_intersection2(sK5,sK15(sK5)),X0),X1,X2),sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_370217]) ).
tcf(c_426858,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(sK8,sK15(sK8)),X0),X1) = X2 )
| ~ in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),sK8)
| ~ in(sK2(set_intersection2(set_intersection2(sK8,sK15(sK8)),X0),X1,X2),X2)
| ~ in(sK2(set_intersection2(set_intersection2(sK8,sK15(sK8)),X0),X1,X2),X1)
| ~ in(sK2(set_intersection2(set_intersection2(sK8,sK15(sK8)),X0),X1,X2),X0)
| ~ in(sK2(set_intersection2(set_intersection2(sK8,sK15(sK8)),X0),X1,X2),sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_370217]) ).
tcf(c_426894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 )
| ~ in(sK2(set_intersection2(empty_set,X0),X1,X2),empty_set)
| ~ in(sK2(set_intersection2(empty_set,X0),X1,X2),X3)
| ~ in(sK2(set_intersection2(empty_set,X0),X1,X2),X2)
| ~ in(sK2(set_intersection2(empty_set,X0),X1,X2),X1)
| ~ in(sK2(set_intersection2(empty_set,X0),X1,X2),X0) ),
inference(light_normalisation,[status(thm)],[c_426856,c_368545]) ).
tcf(c_426895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(empty_set,X0) = X1 )
| ~ in(sK2(empty_set,X0,X1),empty_set)
| ~ in(sK2(empty_set,X0,X1),X3)
| ~ in(sK2(empty_set,X0,X1),X2)
| ~ in(sK2(empty_set,X0,X1),X1)
| ~ in(sK2(empty_set,X0,X1),X0) ),
inference(light_normalisation,[status(thm)],[c_426894,c_368545]) ).
tcf(c_426896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = empty_set )
| ~ in(sK2(empty_set,X0,X1),empty_set)
| ~ in(sK2(empty_set,X0,X1),X3)
| ~ in(sK2(empty_set,X0,X1),X2)
| ~ in(sK2(empty_set,X0,X1),X1)
| ~ in(sK2(empty_set,X0,X1),X0) ),
inference(light_normalisation,[status(thm)],[c_426895,c_368545]) ).
tcf(c_426971,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(sK15(sK8),X0),X1) = X2 )
| ~ in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),sK8)
| ~ in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),X2)
| ~ in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),X1)
| ~ in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),X0)
| ~ in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),sK15(sK8)) ),
inference(light_normalisation,[status(thm)],[c_426858,c_411956]) ).
tcf(c_426978,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(sK15(sK5),X0),X1) = X2 )
| ~ in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),sK5)
| ~ in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),X2)
| ~ in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),X1)
| ~ in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),X0)
| ~ in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),sK15(sK5)) ),
inference(light_normalisation,[status(thm)],[c_426857,c_411955]) ).
tcf(c_427024,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_426843,c_397166]) ).
tcf(c_427313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_368925,c_370220]) ).
tcf(c_427314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_368924,c_370220]) ).
tcf(c_427315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ empty(set_intersection2(X0,X1))
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_368865,c_370220]) ).
tcf(c_427317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_55,c_370220]) ).
tcf(c_427318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X3,X4)),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X4)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X1) ),
inference(superposition,[status(thm)],[c_57,c_370220]) ).
tcf(c_427319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = powerset(X3) )
| ~ subset(sK2(set_intersection2(X0,X1),X2,powerset(X3)),X3)
| ~ in(sK2(set_intersection2(X1,X0),X2,powerset(X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,powerset(X3)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,powerset(X3)),X1) ),
inference(superposition,[status(thm)],[c_369138,c_370220]) ).
tcf(c_427320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ subset(set_intersection2(X0,X1),X3)
| ~ in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X0,X1)),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_369929,c_370220]) ).
tcf(c_427321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ subset(set_intersection2(X0,X1),X3)
| ~ in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X0,X1)),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_369015,c_370220]) ).
tcf(c_427322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(X3,X3)
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_369015,c_370220]) ).
tcf(c_427324,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ empty(set_intersection2(X0,X1))
| ~ in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X0,X1)),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_368868,c_370220]) ).
tcf(c_427327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(set_intersection2(X0,X1),X4)
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_369926,c_370220]) ).
tcf(c_427328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(set_intersection2(X0,X1),X4)
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_369012,c_370220]) ).
tcf(c_427331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_368481,c_370220]) ).
tcf(c_427334,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X0,X1)),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_368448,c_370220]) ).
tcf(c_427335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X2),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X2 )
| ~ subset(X2,X3)
| ~ in(sK2(set_intersection2(X1,X0),X2,X2),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X2),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X2),X1) ),
inference(superposition,[status(thm)],[c_369928,c_370220]) ).
tcf(c_427336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X2),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X2 )
| ~ subset(X2,X3)
| ~ in(sK2(set_intersection2(X1,X0),X2,X2),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X2),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X2),X1) ),
inference(superposition,[status(thm)],[c_369014,c_370220]) ).
tcf(c_427337,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X2 )
| ~ empty(X2)
| ~ in(sK2(set_intersection2(X1,X0),X2,X2),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X2),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X2),X1) ),
inference(superposition,[status(thm)],[c_368867,c_370220]) ).
tcf(c_427338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),set_intersection2(X2,X3)),X3)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(X2,X3) )
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(X2,X3),set_intersection2(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),set_intersection2(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),set_intersection2(X2,X3)),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_368505,c_370220]) ).
tcf(c_427339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),set_intersection2(X2,X3)),X2)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(X2,X3) )
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(X2,X3),set_intersection2(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),set_intersection2(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),set_intersection2(X2,X3)),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_368483,c_370220]) ).
tcf(c_427340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),relation_inverse_image(X2,X3))),X3)
| ( set_intersection2(set_intersection2(X0,X1),relation_inverse_image(X2,X3)) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X1,X0),relation_inverse_image(X2,X3),relation_inverse_image(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),relation_inverse_image(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368815,c_370220]) ).
tcf(c_427341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),relation_inverse_image(X2,X3)),relation_dom(X2))
| ( set_intersection2(set_intersection2(X0,X1),relation_inverse_image(X2,X3)) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X1,X0),relation_inverse_image(X2,X3),relation_inverse_image(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),relation_inverse_image(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368759,c_370220]) ).
tcf(c_427342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(X2,X4)
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_369927,c_370220]) ).
tcf(c_427343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(X2,X4)
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_369013,c_370220]) ).
tcf(c_427345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ empty(X2)
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_368866,c_370220]) ).
tcf(c_427346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),X3)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X4 )
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(X2,X3),X4),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_368504,c_370220]) ).
tcf(c_427347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),X2)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X4 )
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(X2,X3),X4),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_368482,c_370220]) ).
tcf(c_427350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),X4)),X3)
| ( set_intersection2(set_intersection2(X0,X1),relation_inverse_image(X2,X3)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X1,X0),relation_inverse_image(X2,X3),X4),X0)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),X4),X1)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),X4),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368814,c_370220]) ).
tcf(c_427351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),X4),relation_dom(X2))
| ( set_intersection2(set_intersection2(X0,X1),relation_inverse_image(X2,X3)) = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X1,X0),relation_inverse_image(X2,X3),X4),X0)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),X4),X1)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),X4),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368758,c_370220]) ).
tcf(c_427352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),relation_dom(X2)),relation_dom(X2))
| ( set_intersection2(set_intersection2(X0,X1),relation_inverse_image(X2,X3)) = relation_dom(X2) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X1,X0),relation_inverse_image(X2,X3),relation_dom(X2)),X0)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),relation_dom(X2)),X1)
| ~ in(sK2(set_intersection2(X0,X1),relation_inverse_image(X2,X3),relation_dom(X2)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_368758,c_370220]) ).
tcf(c_427353,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X2 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X2),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X2),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X2),X1) ),
inference(superposition,[status(thm)],[c_368460,c_370220]) ).
tcf(c_427354,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = empty_set )
| ( set_intersection2(set_intersection2(X0,X1),empty_set) = X2 )
| ~ in(sK2(set_intersection2(X0,X1),empty_set,X2),empty_set)
| ~ in(sK2(set_intersection2(X1,X0),empty_set,X2),X0)
| ~ in(sK2(set_intersection2(X0,X1),empty_set,X2),X1) ),
inference(superposition,[status(thm)],[c_372467,c_370220]) ).
tcf(c_427355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X0,X1),relation_image(X2,X3)) = X4 )
| ( apply(X2,sK13(X2,X3,sK2(set_intersection2(X0,X1),relation_image(X2,X3),X4))) = sK2(set_intersection2(X0,X1),relation_image(X2,X3),X4) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X1,X0),relation_image(X2,X3),X4),X0)
| ~ in(sK2(set_intersection2(X0,X1),relation_image(X2,X3),X4),X1)
| ~ in(sK2(set_intersection2(X0,X1),relation_image(X2,X3),X4),relation_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_369660,c_370220]) ).
tcf(c_427356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),relation_image(X2,X3)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(set_intersection2(X0,X1),relation_image(X2,X3),relation_image(X2,X3)))) = sK2(set_intersection2(X0,X1),relation_image(X2,X3),relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X1,X0),relation_image(X2,X3),relation_image(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),relation_image(X2,X3),relation_image(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),relation_image(X2,X3),relation_image(X2,X3)),relation_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_369661,c_370220]) ).
tcf(c_427357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_inverse_image(X0,set_intersection2(X4,X5)) = set_intersection2(set_intersection2(X1,X2),X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(X2,X1),X3,relation_inverse_image(X0,set_intersection2(X4,X5))),X1)
| ~ in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,set_intersection2(X4,X5))),X3)
| ~ in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,set_intersection2(X4,X5))),X2)
| ~ in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,set_intersection2(X4,X5))),relation_dom(X0))
| ~ in(apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,set_intersection2(X4,X5)))),X5)
| ~ in(apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,set_intersection2(X4,X5)))),X4) ),
inference(superposition,[status(thm)],[c_368735,c_370220]) ).
tcf(c_427358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( relation_inverse_image(X3,relation_image(X3,X4)) = set_intersection2(set_intersection2(X0,X1),X2) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X1,X0),X2,relation_inverse_image(X3,relation_image(X3,X4))),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,relation_image(X3,X4))),X4)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,relation_image(X3,X4))),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,relation_image(X3,X4))),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,relation_image(X3,X4))),relation_dom(X3)) ),
inference(superposition,[status(thm)],[c_369503,c_370220]) ).
tcf(c_427359,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ subset(set_intersection2(X0,X1),set_intersection2(X0,X1))
| ~ in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X0,X1)),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_370077,c_370220]) ).
tcf(c_427360,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X2 )
| ~ subset(X2,X2)
| ~ in(sK2(set_intersection2(X1,X0),X2,X2),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X2),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X2),X1) ),
inference(superposition,[status(thm)],[c_370145,c_370220]) ).
tcf(c_427361,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X0),X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(set_intersection2(X0,X0),X1,X2),X1)
| ~ in(sK2(set_intersection2(X0,X0),X1,X2),X0) ),
inference(superposition,[status(thm)],[c_53,c_370220]) ).
tcf(c_427362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_63,c_370220]) ).
tcf(c_427364,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 )
| ~ in(sK2(empty_set,X1,X2),X2)
| ~ in(sK2(set_intersection2(X0,empty_set),X1,X2),empty_set)
| ~ in(sK2(set_intersection2(empty_set,X0),X1,X2),X0)
| ~ in(sK2(set_intersection2(X0,empty_set),X1,X2),X1) ),
inference(superposition,[status(thm)],[c_64,c_370220]) ).
tcf(c_427365,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 )
| ~ in(sK2(empty_set,X1,X2),X2)
| ~ in(sK2(set_intersection2(X0,empty_set),X1,X2),empty_set)
| ~ in(sK2(set_intersection2(empty_set,X0),X1,X2),X1)
| ~ in(sK2(set_intersection2(empty_set,X0),X1,X2),X0) ),
inference(superposition,[status(thm)],[c_368545,c_370220]) ).
tcf(c_427366,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = X1 )
| ~ in(sK2(sK15(sK5),X0,X1),X1)
| ~ in(sK2(set_intersection2(sK15(sK5),sK5),X0,X1),sK5)
| ~ in(sK2(set_intersection2(sK5,sK15(sK5)),X0,X1),X0)
| ~ in(sK2(set_intersection2(sK5,sK15(sK5)),X0,X1),sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_370220]) ).
tcf(c_427367,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = X1 )
| ~ in(sK2(sK15(sK8),X0,X1),X1)
| ~ in(sK2(set_intersection2(sK15(sK8),sK8),X0,X1),sK8)
| ~ in(sK2(set_intersection2(sK8,sK15(sK8)),X0,X1),X0)
| ~ in(sK2(set_intersection2(sK8,sK15(sK8)),X0,X1),sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_370220]) ).
tcf(c_427452,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK15(sK8),X0) = X1 )
| ~ in(sK2(sK15(sK8),X0,X1),X1)
| ~ in(sK2(sK15(sK8),X0,X1),X0)
| ~ in(sK2(sK15(sK8),X0,X1),sK15(sK8))
| ~ in(sK2(set_intersection2(sK15(sK8),sK8),X0,X1),sK8) ),
inference(light_normalisation,[status(thm)],[c_427367,c_411956]) ).
tcf(c_427458,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(sK15(sK5),X0) = X1 )
| ~ in(sK2(sK15(sK5),X0,X1),X1)
| ~ in(sK2(sK15(sK5),X0,X1),X0)
| ~ in(sK2(sK15(sK5),X0,X1),sK15(sK5))
| ~ in(sK2(set_intersection2(sK15(sK5),sK5),X0,X1),sK5) ),
inference(light_normalisation,[status(thm)],[c_427366,c_411955]) ).
tcf(c_427721,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),X1)
| in(sK2(set_intersection2(sK15(sK5),sK5),X0,X1),sK15(sK5))
| ( set_intersection2(set_intersection2(sK15(sK5),sK5),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_370261]) ).
tcf(c_427722,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),X1)
| in(sK2(set_intersection2(sK15(sK8),sK8),X0,X1),sK15(sK8))
| ( set_intersection2(set_intersection2(sK15(sK8),sK8),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_370261]) ).
tcf(c_427724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_63,c_370261]) ).
tcf(c_427726,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X0)
| in(sK2(set_intersection2(empty_set,X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_370261]) ).
tcf(c_427727,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),empty_set)
| in(sK2(set_intersection2(X0,empty_set),X1,X2),X2)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_370261]) ).
tcf(c_427728,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),sK5)
| in(sK2(set_intersection2(sK15(sK5),sK5),X0,X1),X1)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_370261]) ).
tcf(c_427729,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),sK8)
| in(sK2(set_intersection2(sK15(sK8),sK8),X0,X1),X1)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_370261]) ).
tcf(c_427730,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(set_intersection2(X1,X0),X2) = set_intersection2(X0,X1) )
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_370261,c_54]) ).
tcf(c_427731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X3,X2),X4,X0),X1)
| in(sK2(set_intersection2(X2,X3),X4,X0),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370261,c_321]) ).
tcf(c_427733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X2,X1),X3,X0),X2)
| ( set_intersection2(set_intersection2(X2,X1),X3) = X0 )
| ~ in(X0,sK2(set_intersection2(X1,X2),X3,X0)) ),
inference(superposition,[status(thm)],[c_370261,c_97]) ).
tcf(c_427734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X3,X2),X4,X0),X1)
| in(sK2(set_intersection2(X2,X3),X4,X0),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370261,c_96]) ).
tcf(c_427735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X1,X0),X2,X3),X3)
| in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370261,c_93]) ).
tcf(c_427737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X3,X4)),X4)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370261,c_59]) ).
tcf(c_427738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X3,X4)),X3)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370261,c_58]) ).
tcf(c_427739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),X1)
| in(apply(X0,sK2(set_intersection2(X2,X1),X3,relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370261,c_88]) ).
tcf(c_427740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),X1)
| in(sK2(set_intersection2(X2,X1),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370261,c_87]) ).
tcf(c_427741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X0),X2,relation_dom(X3)),X1)
| ( set_intersection2(set_intersection2(X1,X0),X2) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(set_intersection2(X0,X1),X2,relation_dom(X3))))) = apply(X3,sK2(set_intersection2(X0,X1),X2,relation_dom(X3))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370261,c_369671]) ).
tcf(c_427746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X3,X2),X4,relation_image(X0,X1)),X3)
| ( set_intersection2(set_intersection2(X3,X2),X4) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)))) = sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370261,c_112]) ).
tcf(c_427747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X0),X2,relation_dom(X3)),X1)
| ( set_intersection2(set_intersection2(X1,X0),X2) = relation_dom(X3) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370261,c_369501]) ).
tcf(c_427749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(X1,X0),X2) = X3 )
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X2)
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_370261,c_370220]) ).
tcf(c_427750,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X0),X1)
| ( set_intersection2(set_intersection2(X1,X0),X2) = X0 )
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_370261,c_368471]) ).
tcf(c_427751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X4,X3),X5,relation_image(X0,relation_image(X1,X2))),X4)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(set_intersection2(X4,X3),X5) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,X4),X5,relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,X4),X5,relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370261,c_369672]) ).
tcf(c_427752,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X1,X0),X2,sK15(sK5)),sK5)
| in(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_370261,c_412536]) ).
tcf(c_427753,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X1,X0),X2,sK15(sK8)),sK8)
| in(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_370261,c_413867]) ).
tcf(c_427754,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X1,X0),set_intersection2(X1,X0)),X0)
| ( set_intersection2(set_intersection2(X1,X0),set_intersection2(X1,X0)) = set_intersection2(X1,X0) )
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X1,X0)) = set_intersection2(X1,X0) ) ),
inference(superposition,[status(thm)],[c_370261,c_423425]) ).
tcf(c_427755,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X1,X0),X0,X0),X1)
| in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X1,X0),X0) = X0 )
| ( set_intersection2(set_intersection2(X0,X1),X0) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(superposition,[status(thm)],[c_370261,c_426065]) ).
tcf(c_427756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X2,set_intersection2(X0,X1)),X3,X0),X2)
| ( set_intersection2(set_intersection2(X2,set_intersection2(X0,X1)),X3) = X0 )
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_370261,c_370217]) ).
tcf(c_427757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X0,X2),X3,X4),X1)
| in(sK2(set_intersection2(X2,X0),X3,X4),X4)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370261,c_321]) ).
tcf(c_427758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X0),X3,X4),X4)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370261,c_320]) ).
tcf(c_427759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(X0,sK2(set_intersection2(X0,X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_370261,c_97]) ).
tcf(c_427760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X0),X3,X4),X4)
| in(sK2(set_intersection2(X0,X2),X3,X4),X1)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370261,c_96]) ).
tcf(c_427761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X0)
| in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370261,c_93]) ).
tcf(c_427762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370261,c_91]) ).
tcf(c_427763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,set_intersection2(X0,X1)),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_370261,c_59]) ).
tcf(c_427764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,set_intersection2(X0,X1)),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_370261,c_58]) ).
tcf(c_427765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,relation_inverse_image(X0,X1)),X3,X4),X4)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370261,c_88]) ).
tcf(c_427766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,relation_inverse_image(X0,X1)),X3,X4),X4)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370261,c_87]) ).
tcf(c_427767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,relation_dom(X0)),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = X3 )
| ( apply(X0,sK13(X0,X4,apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,X3)))) = apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,X3)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_370261,c_369671]) ).
tcf(c_427768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,relation_image(X2,X0)),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_image(X2,X0),X3),X4) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370261,c_369799]) ).
tcf(c_427769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,relation_image(X0,X2)),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4) = X5 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370261,c_369798]) ).
tcf(c_427770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,relation_image(X0,X1)),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370261,c_369596]) ).
tcf(c_427771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,relation_image(X0,X1)),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370261,c_369558]) ).
tcf(c_427772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,relation_image(X0,X1)),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = X4 )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),X3,X4))) = sK2(set_intersection2(relation_image(X0,X1),X2),X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370261,c_112]) ).
tcf(c_427773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,relation_dom(X0)),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_370261,c_369501]) ).
tcf(c_427774,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,empty_set),X1,X2),X2)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_370261,c_372426]) ).
tcf(c_427776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_370261,c_368471]) ).
tcf(c_427777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4) = X5 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,X5)))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370261,c_369672]) ).
tcf(c_427778,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),sK5)
| in(sK2(set_intersection2(X0,sK15(sK5)),X1,X2),X2)
| ( set_intersection2(set_intersection2(sK15(sK5),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_370261,c_412536]) ).
tcf(c_427779,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),sK8)
| in(sK2(set_intersection2(X0,sK15(sK8)),X1,X2),X2)
| ( set_intersection2(set_intersection2(sK15(sK8),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_370261,c_413867]) ).
tcf(c_427781,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X1,X0),X0,X0),X0)
| in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X0) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(superposition,[status(thm)],[c_370261,c_426065]) ).
tcf(c_427782,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X0),X1,X0),X0)
| ( set_intersection2(set_intersection2(X0,X0),X1) = X0 ) ),
inference(equality_factoring,[status(thm)],[c_370261]) ).
tcf(c_427814,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),sK8)
| in(sK2(set_intersection2(sK15(sK8),sK8),X0,X1),X1)
| ( set_intersection2(sK15(sK8),X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_427729,c_411956]) ).
tcf(c_427818,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),sK5)
| in(sK2(set_intersection2(sK15(sK5),sK5),X0,X1),X1)
| ( set_intersection2(sK15(sK5),X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_427728,c_411955]) ).
tcf(c_427928,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X1,X0),X0,X0),X1)
| in(sK2(set_intersection2(X0,X1),X0,X0),set_intersection2(X0,X1))
| ( set_intersection2(X0,X1) = X0 )
| ( set_intersection2(set_intersection2(X1,X0),X0) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X0,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_427755,c_397166]) ).
tcf(c_428179,plain,
! [X0: $i] :
( subset(sK16(sK15(sK8)),X0)
| ~ subset(sK8,powerset(X0)) ),
inference(superposition,[status(thm)],[c_423412,c_99]) ).
tcf(c_428193,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),sK15(sK5))
| in(sK2(set_intersection2(sK15(sK5),sK5),X0,X1),X1)
| ( set_intersection2(set_intersection2(sK15(sK5),sK5),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_370266]) ).
tcf(c_428194,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),sK15(sK8))
| in(sK2(set_intersection2(sK15(sK8),sK8),X0,X1),X1)
| ( set_intersection2(set_intersection2(sK15(sK8),sK8),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_370266]) ).
tcf(c_428198,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| in(sK2(set_intersection2(empty_set,X0),X1,X2),X0)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_370266]) ).
tcf(c_428199,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| in(sK2(set_intersection2(X0,empty_set),X1,X2),empty_set)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_370266]) ).
tcf(c_428200,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),X1)
| in(sK2(set_intersection2(sK15(sK5),sK5),X0,X1),sK5)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_370266]) ).
tcf(c_428201,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),X1)
| in(sK2(set_intersection2(sK15(sK8),sK8),X0,X1),sK8)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_370266]) ).
tcf(c_428202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X2,X0),X3,X4),X1)
| in(sK2(set_intersection2(X0,X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370266,c_321]) ).
tcf(c_428204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(X0,sK2(set_intersection2(X1,X0),X2,X3)) ),
inference(superposition,[status(thm)],[c_370266,c_97]) ).
tcf(c_428205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X0),X3,X4),X1)
| in(sK2(set_intersection2(X0,X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370266,c_96]) ).
tcf(c_428206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X1,X0),X2,X3),X0)
| in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370266,c_93]) ).
tcf(c_428208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,set_intersection2(X0,X1)),X3,X4),X1)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_370266,c_59]) ).
tcf(c_428209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,set_intersection2(X0,X1)),X3,X4),X0)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_370266,c_58]) ).
tcf(c_428210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| in(apply(X0,sK2(set_intersection2(X2,relation_inverse_image(X0,X1)),X3,X4)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370266,c_88]) ).
tcf(c_428211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(X2,relation_inverse_image(X0,X1)),X3,X4),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370266,c_87]) ).
tcf(c_428212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_dom(X1),X0),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_dom(X1),X0),X2) = X3 )
| ( apply(X1,sK13(X1,X4,apply(X1,sK2(set_intersection2(X0,relation_dom(X1)),X2,X3)))) = apply(X1,sK2(set_intersection2(X0,relation_dom(X1)),X2,X3)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(set_intersection2(X0,relation_dom(X1)),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_370266,c_369671]) ).
tcf(c_428217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = X4 )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,relation_image(X0,X1)),X3,X4))) = sK2(set_intersection2(X2,relation_image(X0,X1)),X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370266,c_112]) ).
tcf(c_428218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_dom(X1),X0),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_dom(X1),X0),X2) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X4))
| ~ in(sK2(set_intersection2(X0,relation_dom(X1)),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_370266,c_369501]) ).
tcf(c_428220,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),X0)
| ( set_intersection2(set_intersection2(X1,X0),X2) = X0 )
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X0),X2)
| ~ in(sK2(set_intersection2(X1,X0),X2,X0),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1) ),
inference(superposition,[status(thm)],[c_370266,c_370220]) ).
tcf(c_428222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4) = X5 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4,X5)))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370266,c_369672]) ).
tcf(c_428223,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,sK15(sK5)),X1,X2),sK5)
| in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(sK15(sK5),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_370266,c_412536]) ).
tcf(c_428224,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,sK15(sK8)),X1,X2),sK8)
| in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(sK15(sK8),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_370266,c_413867]) ).
tcf(c_428225,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),X0,set_intersection2(X1,X0)),set_intersection2(X1,X0))
| ( set_intersection2(set_intersection2(X1,X0),X0) = set_intersection2(X1,X0) )
| ( set_intersection2(set_intersection2(X0,X1),X0) = set_intersection2(X1,X0) ) ),
inference(superposition,[status(thm)],[c_370266,c_423425]) ).
tcf(c_428226,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X1,X0),X1,X0),X0)
| in(sK2(set_intersection2(X0,X1),X1,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X1,X0),X1) = X0 )
| ( set_intersection2(set_intersection2(X0,X1),X1) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X1,X0),X1) ),
inference(superposition,[status(thm)],[c_370266,c_426065]) ).
tcf(c_428227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 )
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X0),X2) = X3 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X0),X2,X3),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X0),X2,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X0),X2,X3),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X0),X2,X3),X0) ),
inference(superposition,[status(thm)],[c_370266,c_370217]) ).
tcf(c_428228,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X0,X1)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_370266,c_54]) ).
tcf(c_428229,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X2,X3),X4,X0),X1)
| in(sK2(set_intersection2(X3,X2),X4,X0),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370266,c_321]) ).
tcf(c_428230,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X3,X2),X4,X0),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370266,c_320]) ).
tcf(c_428231,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X2,X1),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ in(X0,sK2(set_intersection2(X1,X2),X3,X0)) ),
inference(superposition,[status(thm)],[c_370266,c_97]) ).
tcf(c_428232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X3,X2),X4,X0),X2)
| in(sK2(set_intersection2(X2,X3),X4,X0),X1)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370266,c_96]) ).
tcf(c_428233,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370266,c_93]) ).
tcf(c_428234,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X2,X1),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370266,c_91]) ).
tcf(c_428235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X3,X4)),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370266,c_59]) ).
tcf(c_428236,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X3,X4)),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370266,c_58]) ).
tcf(c_428237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X1),X3,relation_inverse_image(X0,X4)),X1)
| in(apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370266,c_88]) ).
tcf(c_428238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X1),X3,relation_inverse_image(X0,X4)),X1)
| in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370266,c_87]) ).
tcf(c_428239,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X0),X2,relation_dom(X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(set_intersection2(X0,X1),X2,relation_dom(X3))))) = apply(X3,sK2(set_intersection2(X0,X1),X2,relation_dom(X3))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370266,c_369671]) ).
tcf(c_428240,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X4,X3),X5,relation_image(X2,X0)),X3)
| ( set_intersection2(set_intersection2(X3,X4),X5) = relation_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370266,c_369799]) ).
tcf(c_428241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X2),X4,relation_image(X0,X5)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370266,c_369798]) ).
tcf(c_428242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X3,X2),X4,relation_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370266,c_369596]) ).
tcf(c_428243,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X1),X3,relation_image(X0,X4)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370266,c_369558]) ).
tcf(c_428244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X3,X2),X4,relation_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)))) = sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370266,c_112]) ).
tcf(c_428245,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X0),X2,relation_dom(X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_dom(X3) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370266,c_369501]) ).
tcf(c_428246,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X1,X0),X2,empty_set),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = empty_set ) ),
inference(superposition,[status(thm)],[c_370266,c_372426]) ).
tcf(c_428248,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X0),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_370266,c_368471]) ).
tcf(c_428249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X4,X3),X5,relation_image(X0,relation_image(X1,X2))),X3)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(set_intersection2(X3,X4),X5) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,X4),X5,relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,X4),X5,relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370266,c_369672]) ).
tcf(c_428250,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),sK5)
| in(sK2(set_intersection2(X1,X0),X2,sK15(sK5)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_370266,c_412536]) ).
tcf(c_428251,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),sK8)
| in(sK2(set_intersection2(X1,X0),X2,sK15(sK8)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_370266,c_413867]) ).
tcf(c_428252,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X1,X0),set_intersection2(X0,X1),set_intersection2(X0,X1)),X0)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_370266,c_423425]) ).
tcf(c_428254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X2,set_intersection2(X0,X1)),X3,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_370266,c_370217]) ).
tcf(c_428283,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),X1)
| in(sK2(set_intersection2(sK15(sK8),sK8),X0,X1),sK8)
| ( set_intersection2(sK15(sK8),X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_428201,c_411956]) ).
tcf(c_428287,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),X1)
| in(sK2(set_intersection2(sK15(sK5),sK5),X0,X1),sK5)
| ( set_intersection2(sK15(sK5),X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_428200,c_411955]) ).
tcf(c_428347,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X1,X0),X1,set_intersection2(X0,X1)),set_intersection2(X0,X1))
| ( set_intersection2(X0,X1) = set_intersection2(X1,X0) )
| ( set_intersection2(set_intersection2(X0,X1),X1) = set_intersection2(X0,X1) ) ),
inference(light_normalisation,[status(thm)],[c_428225,c_397166]) ).
tcf(c_428397,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X1,X0),X1,X0),X0)
| in(sK2(set_intersection2(X0,X1),X1,X0),set_intersection2(X0,X1))
| ( set_intersection2(X0,X1) = X0 )
| ( set_intersection2(set_intersection2(X1,X0),X1) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_428226,c_397167]) ).
tcf(c_428536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(X0,X4)
| in(sK2(set_intersection2(X1,X2),X3,sK10(X0,X4)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK10(X0,X4) )
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK10(X0,X4))) ),
inference(superposition,[status(thm)],[c_369021,c_370273]) ).
tcf(c_428537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X0)
| in(sK2(set_intersection2(X1,X2),X3,sK16(X0)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK16(X0) )
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK16(X0))) ),
inference(superposition,[status(thm)],[c_370747,c_370273]) ).
tcf(c_428538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X0),X4)
| in(sK2(set_intersection2(X1,X2),X3,sK2(X4,X5,X0)),X1)
| ( set_intersection2(X4,X5) = X0 )
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK2(X4,X5,X0) )
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK2(X4,X5,X0))) ),
inference(superposition,[status(thm)],[c_369015,c_370273]) ).
tcf(c_428539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X0),X5)
| in(sK2(set_intersection2(X1,X2),X3,sK2(X4,X5,X0)),X1)
| ( set_intersection2(X4,X5) = X0 )
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK2(X4,X5,X0) )
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK2(X4,X5,X0))) ),
inference(superposition,[status(thm)],[c_369014,c_370273]) ).
tcf(c_428540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,X4,X5),X5)
| in(sK2(set_intersection2(X1,X2),X3,sK2(X0,X4,X5)),X1)
| ( set_intersection2(X0,X4) = X5 )
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK2(X0,X4,X5) )
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK2(X0,X4,X5))) ),
inference(superposition,[status(thm)],[c_369012,c_370273]) ).
tcf(c_428541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X0,X5),X5)
| in(sK2(set_intersection2(X1,X2),X3,sK2(X4,X0,X5)),X1)
| ( set_intersection2(X4,X0) = X5 )
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK2(X4,X0,X5) )
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK2(X4,X0,X5))) ),
inference(superposition,[status(thm)],[c_369013,c_370273]) ).
tcf(c_428542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X1,X2),X3,sK13(X4,X0,X5)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK13(X4,X0,X5) )
| ~ function(X4)
| ~ relation(X4)
| ~ in(X5,relation_image(X4,X0))
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK13(X4,X0,X5))) ),
inference(superposition,[status(thm)],[c_369594,c_370273]) ).
tcf(c_428543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X1,X2),X3,sK13(X0,X4,X5)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK13(X0,X4,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_image(X0,X4))
| ~ subset(relation_dom(X0),sK2(set_intersection2(X1,X2),X3,sK13(X0,X4,X5))) ),
inference(superposition,[status(thm)],[c_369556,c_370273]) ).
tcf(c_428544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X4,X0,X5),X5)
| in(sK2(set_intersection2(X1,X2),X3,sK12(X4,X0,X5)),X1)
| ( relation_image(X4,X0) = X5 )
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK12(X4,X0,X5) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK12(X4,X0,X5))) ),
inference(superposition,[status(thm)],[c_369299,c_370273]) ).
tcf(c_428545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X1,X2),X3,sK11(X4,X5,X0)),X1)
| ( relation_image(X4,X5) = X0 )
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK11(X4,X5,X0) )
| ( apply(X4,sK12(X4,X5,X0)) = sK11(X4,X5,X0) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK11(X4,X5,X0))) ),
inference(superposition,[status(thm)],[c_369436,c_370273]) ).
tcf(c_428546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X4,X5,X0),X5)
| in(sK2(set_intersection2(X1,X2),X3,sK11(X4,X5,X0)),X1)
| ( relation_image(X4,X5) = X0 )
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK11(X4,X5,X0) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK11(X4,X5,X0))) ),
inference(superposition,[status(thm)],[c_369307,c_370273]) ).
tcf(c_428547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X4,X5,X0),relation_dom(X4))
| in(sK2(set_intersection2(X1,X2),X3,sK11(X4,X5,X0)),X1)
| ( relation_image(X4,X5) = X0 )
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK11(X4,X5,X0) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK11(X4,X5,X0))) ),
inference(superposition,[status(thm)],[c_369206,c_370273]) ).
tcf(c_428548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X4,X5,X0),relation_dom(X4))
| in(sK2(set_intersection2(X1,X2),X3,sK7(X4,X5,X0)),X1)
| ( relation_inverse_image(X4,X5) = X0 )
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK7(X4,X5,X0) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK7(X4,X5,X0))) ),
inference(superposition,[status(thm)],[c_369020,c_370273]) ).
tcf(c_428549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X4,sK7(X4,X5,X0)),X5)
| in(sK2(set_intersection2(X1,X2),X3,sK7(X4,X5,X0)),X1)
| ( relation_inverse_image(X4,X5) = X0 )
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK7(X4,X5,X0) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK7(X4,X5,X0))) ),
inference(superposition,[status(thm)],[c_369019,c_370273]) ).
tcf(c_428550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,X4,X5),X5)
| in(sK2(set_intersection2(X1,X2),X3,sK7(X0,X4,X5)),X1)
| ( relation_inverse_image(X0,X4) = X5 )
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK7(X0,X4,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(set_intersection2(X1,X2),X3,sK7(X0,X4,X5))) ),
inference(superposition,[status(thm)],[c_369017,c_370273]) ).
tcf(c_428551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X0,X4,X5),X5)
| in(sK2(set_intersection2(X1,X2),X3,sK12(X0,X4,X5)),X1)
| ( relation_image(X0,X4) = X5 )
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK12(X0,X4,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(set_intersection2(X1,X2),X3,sK12(X0,X4,X5))) ),
inference(superposition,[status(thm)],[c_369214,c_370273]) ).
tcf(c_428552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X4,X0,X5),X5)
| in(sK2(set_intersection2(X1,X2),X3,apply(X4,sK7(X4,X0,X5))),X1)
| ( relation_inverse_image(X4,X0) = X5 )
| ( apply(X4,sK7(X4,X0,X5)) = set_intersection2(set_intersection2(X1,X2),X3) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,apply(X4,sK7(X4,X0,X5)))) ),
inference(superposition,[status(thm)],[c_369018,c_370273]) ).
tcf(c_428553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,sK2(X0,X4,X0)),X1)
| ( set_intersection2(X0,X4) = X0 )
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK2(X0,X4,X0) )
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK2(X0,X4,X0))) ),
inference(superposition,[status(thm)],[c_370077,c_370273]) ).
tcf(c_428554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,sK2(X4,X0,X0)),X1)
| ( set_intersection2(X4,X0) = X0 )
| ( set_intersection2(set_intersection2(X1,X2),X3) = sK2(X4,X0,X0) )
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK2(X4,X0,X0))) ),
inference(superposition,[status(thm)],[c_370145,c_370273]) ).
tcf(c_428555,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK16(sK15(sK5))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK16(sK15(sK5)) )
| ~ subset(sK5,sK2(set_intersection2(X0,X1),X2,sK16(sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_420696,c_370273]) ).
tcf(c_428556,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X1,X1),X2,X0),X1)
| ( set_intersection2(set_intersection2(X1,X1),X2) = X0 )
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_53,c_370273]) ).
tcf(c_428559,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X2,empty_set),X1,X0),X2)
| ( set_intersection2(set_intersection2(X2,empty_set),X1) = X0 )
| ~ in(X0,sK2(empty_set,X1,X0)) ),
inference(superposition,[status(thm)],[c_64,c_370273]) ).
tcf(c_428560,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(empty_set,X2),X1,X0),empty_set)
| ( set_intersection2(set_intersection2(empty_set,X2),X1) = X0 )
| ~ in(X0,sK2(empty_set,X1,X0)) ),
inference(superposition,[status(thm)],[c_368545,c_370273]) ).
tcf(c_428561,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(sK5,sK15(sK5)),X1,X0),sK5)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X1) = X0 )
| ~ in(X0,sK2(sK15(sK5),X1,X0)) ),
inference(superposition,[status(thm)],[c_411955,c_370273]) ).
tcf(c_428562,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(sK8,sK15(sK8)),X1,X0),sK8)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X1) = X0 )
| ~ in(X0,sK2(sK15(sK8),X1,X0)) ),
inference(superposition,[status(thm)],[c_411956,c_370273]) ).
tcf(c_428563,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(empty_set,X2),X1) = X0 )
| ~ in(X0,sK2(empty_set,X1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_428560,c_372426]) ).
tcf(c_428572,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X1,X0),sK8)
| ( set_intersection2(sK15(sK8),X1) = X0 )
| ~ in(X0,sK2(sK15(sK8),X1,X0)) ),
inference(light_normalisation,[status(thm)],[c_428562,c_411956]) ).
tcf(c_428576,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X1,X0),sK5)
| ( set_intersection2(sK15(sK5),X1) = X0 )
| ~ in(X0,sK2(sK15(sK5),X1,X0)) ),
inference(light_normalisation,[status(thm)],[c_428561,c_411955]) ).
tcf(c_428790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X2)
| in(sK2(set_intersection2(X2,X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(X2,X2),X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_370274]) ).
tcf(c_428793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X3,X0),X2)
| in(sK2(set_intersection2(X2,empty_set),X3,X0),X1)
| ( set_intersection2(set_intersection2(X2,empty_set),X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_370274]) ).
tcf(c_428795,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X2,X0),sK5)
| in(sK2(set_intersection2(sK5,sK15(sK5)),X2,X0),X1)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X2) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_411955,c_370274]) ).
tcf(c_428796,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X2,X0),sK8)
| in(sK2(set_intersection2(sK8,sK15(sK8)),X2,X0),X1)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X2) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_411956,c_370274]) ).
tcf(c_428797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X1)
| in(sK2(set_intersection2(X2,X2),X3,X0),X2)
| ( set_intersection2(set_intersection2(X2,X2),X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_370274]) ).
tcf(c_428800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X3,X0),X1)
| in(sK2(set_intersection2(X2,empty_set),X3,X0),X2)
| ( set_intersection2(set_intersection2(X2,empty_set),X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_370274]) ).
tcf(c_428801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X3,X0),X1)
| in(sK2(set_intersection2(empty_set,X2),X3,X0),empty_set)
| ( set_intersection2(set_intersection2(empty_set,X2),X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368545,c_370274]) ).
tcf(c_428802,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X2,X0),X1)
| in(sK2(set_intersection2(sK5,sK15(sK5)),X2,X0),sK5)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X2) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_411955,c_370274]) ).
tcf(c_428803,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X2,X0),X1)
| in(sK2(set_intersection2(sK8,sK15(sK8)),X2,X0),sK8)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X2) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_411956,c_370274]) ).
tcf(c_428804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X2,X4),X5,X0),X3)
| in(sK2(set_intersection2(X2,X4),X5,X0),X1)
| ( set_intersection2(set_intersection2(X2,X4),X5) = X0 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_321]) ).
tcf(c_428805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X4),X5,X0),X1)
| ( set_intersection2(set_intersection2(X2,X4),X5) = X0 )
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_320]) ).
tcf(c_428806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(X3,X4)
| ~ in(X0,sK2(set_intersection2(X0,X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_370274,c_97]) ).
tcf(c_428807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X4),X5,X0),X3)
| in(sK2(set_intersection2(X2,X4),X5,X0),X1)
| ( set_intersection2(set_intersection2(X2,X4),X5) = X0 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_96]) ).
tcf(c_428808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X2,X3),X4,X0),X2)
| in(sK2(set_intersection2(X2,X3),X4,X0),X1)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_93]) ).
tcf(c_428809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,X0),X1)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_91]) ).
tcf(c_428810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,X0),X3)
| in(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,X0),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X3),X4),X5) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_59]) ).
tcf(c_428811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,X0),X2)
| in(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,X0),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X3),X4),X5) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_58]) ).
tcf(c_428812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X2,X3),X4),X5,X0),X1)
| in(apply(X2,sK2(set_intersection2(relation_inverse_image(X2,X3),X4),X5,X0)),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,X3),X4),X5) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_88]) ).
tcf(c_428813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X2,X3),X4),X5,X0),X1)
| in(sK2(set_intersection2(relation_inverse_image(X2,X3),X4),X5,X0),relation_dom(X2))
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,X3),X4),X5) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_87]) ).
tcf(c_428814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X5)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = X3 )
| ( apply(X0,sK13(X0,X4,apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,X3)))) = apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,X3)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X3,X5)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_370274,c_369671]) ).
tcf(c_428815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_image(X4,X2),X5),X6,X0),X1)
| ( set_intersection2(set_intersection2(relation_image(X4,X2),X5),X6) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_369799]) ).
tcf(c_428816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_image(X0,X4),X5),X6,X2),X3)
| ( set_intersection2(set_intersection2(relation_image(X0,X4),X5),X6) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370274,c_369798]) ).
tcf(c_428817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X2,X3),X4),X5,X0),X1)
| ( set_intersection2(set_intersection2(relation_image(X2,X3),X4),X5) = X0 )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_369596]) ).
tcf(c_428818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X2,X3),X4),X5,X0),X1)
| ( set_intersection2(set_intersection2(relation_image(X2,X3),X4),X5) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_369558]) ).
tcf(c_428819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X2,X3),X4),X5,X0),X1)
| ( set_intersection2(set_intersection2(relation_image(X2,X3),X4),X5) = X0 )
| ( apply(X2,sK13(X2,X3,sK2(set_intersection2(relation_image(X2,X3),X4),X5,X0))) = sK2(set_intersection2(relation_image(X2,X3),X4),X5,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_112]) ).
tcf(c_428820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X5)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X3,X5)
| ~ empty(relation_image(X0,X4))
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_370274,c_369501]) ).
tcf(c_428821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(empty_set,X2),X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_372426]) ).
tcf(c_428822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ subset(X0,X3)
| ~ in(sK2(set_intersection2(X1,X0),X2,X0),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1) ),
inference(superposition,[status(thm)],[c_370274,c_370220]) ).
tcf(c_428823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(X3,X4)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_370274,c_368471]) ).
tcf(c_428824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_image(X2,relation_image(X3,X4)),X5),X6,X0),X1)
| ( set_intersection2(set_intersection2(relation_image(X2,relation_image(X3,X4)),X5),X6) = X0 )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK2(set_intersection2(relation_image(X2,relation_image(X3,X4)),X5),X6,X0)))) = sK13(X2,relation_image(X3,X4),sK2(set_intersection2(relation_image(X2,relation_image(X3,X4)),X5),X6,X0)) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_369672]) ).
tcf(c_428825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK15(sK5),X2),X3,X0),sK5)
| in(sK2(set_intersection2(sK15(sK5),X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(sK15(sK5),X2),X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_412536]) ).
tcf(c_428826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK15(sK8),X2),X3,X0),sK8)
| in(sK2(set_intersection2(sK15(sK8),X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(sK15(sK8),X2),X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_413867]) ).
tcf(c_428829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(X3,set_intersection2(X0,X1))
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2) ),
inference(superposition,[status(thm)],[c_370274,c_54]) ).
tcf(c_428830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X3,X4),X5,X0),X2)
| in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_321]) ).
tcf(c_428831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ~ empty(X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_320]) ).
tcf(c_428832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X4),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X4 )
| ~ subset(X4,X0)
| ~ in(X0,sK2(set_intersection2(X1,X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_370274,c_97]) ).
tcf(c_428833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| in(sK2(set_intersection2(X3,X4),X5,X0),X2)
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_96]) ).
tcf(c_428836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| in(sK2(set_intersection2(X3,X4),X5,X0),X2)
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370274,c_59]) ).
tcf(c_428837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| in(sK2(set_intersection2(X3,X4),X5,X0),X1)
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370274,c_58]) ).
tcf(c_428838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| in(apply(X1,sK2(set_intersection2(X3,X4),X5,X0)),X2)
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370274,c_88]) ).
tcf(c_428839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| in(sK2(set_intersection2(X3,X4),X5,X0),relation_dom(X1))
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370274,c_87]) ).
tcf(c_428840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ( apply(X5,sK13(X5,X4,apply(X5,sK2(set_intersection2(X0,X1),X2,X3)))) = apply(X5,sK2(set_intersection2(X0,X1),X2,X3)) )
| ~ function(X5)
| ~ relation(X5)
| ~ subset(X3,relation_dom(X5))
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_370274,c_369671]) ).
tcf(c_428841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X4,X5),X6,X0),X4)
| ( set_intersection2(set_intersection2(X4,X5),X6) = X0 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370274,c_369799]) ).
tcf(c_428842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X4,X5),X6,X0),X4)
| ( set_intersection2(set_intersection2(X4,X5),X6) = X0 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370274,c_369798]) ).
tcf(c_428843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370274,c_369596]) ).
tcf(c_428844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370274,c_369558]) ).
tcf(c_428845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ( apply(X1,sK13(X1,X2,sK2(set_intersection2(X3,X4),X5,X0))) = sK2(set_intersection2(X3,X4),X5,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370274,c_112]) ).
tcf(c_428846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ function(X5)
| ~ relation(X5)
| ~ subset(X3,relation_dom(X5))
| ~ empty(relation_image(X5,X4))
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_370274,c_369501]) ).
tcf(c_428847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(set_intersection2(X1,X2),X3,X0),X4)
| in(sK2(set_intersection2(X1,X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ subset(X0,sK10(sK2(set_intersection2(X1,X2),X3,X0),X4)) ),
inference(superposition,[status(thm)],[c_370274,c_369085]) ).
tcf(c_428848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_370274,c_372426]) ).
tcf(c_428849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(sK2(set_intersection2(X1,X2),X3,X0))
| in(sK2(set_intersection2(X1,X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ subset(X0,sK16(sK2(set_intersection2(X1,X2),X3,X0))) ),
inference(superposition,[status(thm)],[c_370274,c_370746]) ).
tcf(c_428850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| in(sK2(X1,X2,sK2(set_intersection2(X3,X4),X5,X0)),X1)
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ( sK2(set_intersection2(X3,X4),X5,X0) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(set_intersection2(X3,X4),X5,X0))) ),
inference(superposition,[status(thm)],[c_370274,c_369079]) ).
tcf(c_428851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| in(sK2(X1,X2,sK2(set_intersection2(X3,X4),X5,X0)),X2)
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ( sK2(set_intersection2(X3,X4),X5,X0) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(set_intersection2(X3,X4),X5,X0))) ),
inference(superposition,[status(thm)],[c_370274,c_369078]) ).
tcf(c_428852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X0),X1)
| in(sK2(sK2(set_intersection2(X1,X2),X3,X0),X4,X5),X5)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ( set_intersection2(sK2(set_intersection2(X1,X2),X3,X0),X4) = X5 )
| ~ subset(X0,sK2(sK2(set_intersection2(X1,X2),X3,X0),X4,X5)) ),
inference(superposition,[status(thm)],[c_370274,c_369076]) ).
tcf(c_428853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(X3,X3)
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_370274,c_370220]) ).
tcf(c_428855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,X0),X2)
| in(sK2(X1,sK2(set_intersection2(X2,X3),X4,X0),X5),X5)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ( set_intersection2(X1,sK2(set_intersection2(X2,X3),X4,X0)) = X5 )
| ~ subset(X0,sK2(X1,sK2(set_intersection2(X2,X3),X4,X0),X5)) ),
inference(superposition,[status(thm)],[c_370274,c_369077]) ).
tcf(c_428856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,X0),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X5,relation_image(X1,sK2(set_intersection2(X2,X3),X4,X0)))
| ~ subset(X0,sK13(X1,sK2(set_intersection2(X2,X3),X4,X0),X5)) ),
inference(superposition,[status(thm)],[c_370274,c_369593]) ).
tcf(c_428857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X4,X5),X6,X0),X4)
| ( set_intersection2(set_intersection2(X4,X5),X6) = X0 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(set_intersection2(X4,X5),X6,X0)))) = sK13(X1,relation_image(X2,X3),sK2(set_intersection2(X4,X5),X6,X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_370274,c_369672]) ).
tcf(c_428858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,X0),X2)
| in(sK11(X1,sK2(set_intersection2(X2,X3),X4,X0),X5),X5)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ( relation_image(X1,sK2(set_intersection2(X2,X3),X4,X0)) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK2(set_intersection2(X2,X3),X4,X0),X5)) ),
inference(superposition,[status(thm)],[c_370274,c_369298]) ).
tcf(c_428859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ( sK2(set_intersection2(X3,X4),X5,X0) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK2(set_intersection2(X3,X4),X5,X0))) = sK11(X1,X2,sK2(set_intersection2(X3,X4),X5,X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(set_intersection2(X3,X4),X5,X0))) ),
inference(superposition,[status(thm)],[c_370274,c_369435]) ).
tcf(c_428860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| in(sK12(X1,X2,sK2(set_intersection2(X3,X4),X5,X0)),X2)
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ( sK2(set_intersection2(X3,X4),X5,X0) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(set_intersection2(X3,X4),X5,X0))) ),
inference(superposition,[status(thm)],[c_370274,c_369306]) ).
tcf(c_428861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| in(sK12(X1,X2,sK2(set_intersection2(X3,X4),X5,X0)),relation_dom(X1))
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ( sK2(set_intersection2(X3,X4),X5,X0) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(set_intersection2(X3,X4),X5,X0))) ),
inference(superposition,[status(thm)],[c_370274,c_369205]) ).
tcf(c_428862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X0),sK5)
| in(sK2(set_intersection2(X1,X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_370274,c_412536]) ).
tcf(c_428863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X0),sK8)
| in(sK2(set_intersection2(X1,X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_370274,c_413867]) ).
tcf(c_428864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| in(sK7(X1,X2,sK2(set_intersection2(X3,X4),X5,X0)),relation_dom(X1))
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ( sK2(set_intersection2(X3,X4),X5,X0) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(set_intersection2(X3,X4),X5,X0))) ),
inference(superposition,[status(thm)],[c_370274,c_369084]) ).
tcf(c_428865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,X0),X3)
| in(apply(X1,sK7(X1,X2,sK2(set_intersection2(X3,X4),X5,X0))),X2)
| ( set_intersection2(set_intersection2(X3,X4),X5) = X0 )
| ( sK2(set_intersection2(X3,X4),X5,X0) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(set_intersection2(X3,X4),X5,X0))) ),
inference(superposition,[status(thm)],[c_370274,c_369083]) ).
tcf(c_428866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,X0),X2)
| in(sK7(X1,sK2(set_intersection2(X2,X3),X4,X0),X5),X5)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ( relation_inverse_image(X1,sK2(set_intersection2(X2,X3),X4,X0)) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK2(set_intersection2(X2,X3),X4,X0),X5))) ),
inference(superposition,[status(thm)],[c_370274,c_369082]) ).
tcf(c_428868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ( set_intersection2(sK2(set_intersection2(X1,X2),X3,X0),X4) = sK2(set_intersection2(X1,X2),X3,X0) )
| ~ subset(X0,sK2(sK2(set_intersection2(X1,X2),X3,X0),X4,sK2(set_intersection2(X1,X2),X3,X0))) ),
inference(superposition,[status(thm)],[c_370274,c_370076]) ).
tcf(c_428869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,X0),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ( set_intersection2(X1,sK2(set_intersection2(X2,X3),X4,X0)) = sK2(set_intersection2(X2,X3),X4,X0) )
| ~ subset(X0,sK2(X1,sK2(set_intersection2(X2,X3),X4,X0),sK2(set_intersection2(X2,X3),X4,X0))) ),
inference(superposition,[status(thm)],[c_370274,c_370144]) ).
tcf(c_428871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 )
| ~ subset(X4,X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X1) ),
inference(superposition,[status(thm)],[c_370274,c_370217]) ).
tcf(c_428872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X4,X5),X6,X0),X4)
| in(sK2(set_intersection2(X1,X2),X3,sK2(set_intersection2(X4,X5),X6,X0)),X1)
| ( set_intersection2(set_intersection2(X4,X5),X6) = X0 )
| ( sK2(set_intersection2(X4,X5),X6,X0) = set_intersection2(set_intersection2(X1,X2),X3) )
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK2(set_intersection2(X4,X5),X6,X0))) ),
inference(superposition,[status(thm)],[c_370274,c_370273]) ).
tcf(c_428873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ subset(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_370274]) ).
tcf(c_428888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X3,X0),X1)
| ( set_intersection2(set_intersection2(empty_set,X2),X3) = X0 )
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_428801,c_372426]) ).
tcf(c_429441,plain,
! [X0: $i,X1: $i] :
( element(sK16(sK15(sK8)),X1)
| ~ subset(sK8,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_423415,c_321]) ).
tcf(c_429442,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ subset(sK8,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_423415,c_320]) ).
tcf(c_429443,plain,
! [X0: $i] :
( ~ subset(sK8,X0)
| ~ in(X0,sK16(sK15(sK8))) ),
inference(superposition,[status(thm)],[c_423415,c_97]) ).
tcf(c_429444,plain,
! [X0: $i,X1: $i] :
( in(sK16(sK15(sK8)),X1)
| ~ subset(sK8,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_423415,c_96]) ).
tcf(c_429447,plain,
! [X0: $i,X1: $i] :
( in(sK16(sK15(sK8)),X1)
| ~ subset(sK8,set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_423415,c_59]) ).
tcf(c_429448,plain,
! [X0: $i,X1: $i] :
( in(sK16(sK15(sK8)),X0)
| ~ subset(sK8,set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_423415,c_58]) ).
tcf(c_429449,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK16(sK15(sK8))),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK8,relation_inverse_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_423415,c_88]) ).
tcf(c_429450,plain,
! [X0: $i,X1: $i] :
( in(sK16(sK15(sK8)),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK8,relation_inverse_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_423415,c_87]) ).
tcf(c_429451,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,sK13(X1,X0,apply(X1,sK16(sK15(sK8))))) = apply(X1,sK16(sK15(sK8))) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(sK8,relation_dom(X1))
| ~ in(sK16(sK15(sK8)),X0) ),
inference(superposition,[status(thm)],[c_423415,c_369671]) ).
tcf(c_429452,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X1,X2)
| ~ subset(sK8,relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_423415,c_369799]) ).
tcf(c_429453,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X2)
| ~ subset(sK8,relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_423415,c_369798]) ).
tcf(c_429454,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK8,relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_423415,c_369596]) ).
tcf(c_429455,plain,
! [X0: $i,X1: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0))
| ~ subset(sK8,relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_423415,c_369558]) ).
tcf(c_429456,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,sK13(X0,X1,sK16(sK15(sK8)))) = sK16(sK15(sK8)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK8,relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_423415,c_112]) ).
tcf(c_429457,plain,
! [X0: $i,X1: $i] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(sK8,relation_dom(X1))
| ~ empty(relation_image(X1,X0))
| ~ in(sK16(sK15(sK8)),X0) ),
inference(superposition,[status(thm)],[c_423415,c_369501]) ).
tcf(c_429458,plain,
! [X0: $i] :
( subset(sK16(sK15(sK8)),X0)
| ~ subset(sK8,sK10(sK16(sK15(sK8)),X0)) ),
inference(superposition,[status(thm)],[c_423415,c_369085]) ).
tcf(c_429459,plain,
~ subset(sK8,empty_set),
inference(superposition,[status(thm)],[c_423415,c_372426]) ).
tcf(c_429460,plain,
( empty(sK16(sK15(sK8)))
| ~ subset(sK8,sK16(sK16(sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_423415,c_370746]) ).
tcf(c_429461,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK16(sK15(sK8))),X0)
| ( set_intersection2(X0,X1) = sK16(sK15(sK8)) )
| ~ subset(sK8,sK2(X0,X1,sK16(sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_423415,c_369079]) ).
tcf(c_429462,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1,sK16(sK15(sK8))),X1)
| ( set_intersection2(X0,X1) = sK16(sK15(sK8)) )
| ~ subset(sK8,sK2(X0,X1,sK16(sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_423415,c_369078]) ).
tcf(c_429463,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK16(sK15(sK8)),X0,X1),X1)
| ( set_intersection2(sK16(sK15(sK8)),X0) = X1 )
| ~ subset(sK8,sK2(sK16(sK15(sK8)),X0,X1)) ),
inference(superposition,[status(thm)],[c_423415,c_369076]) ).
tcf(c_429464,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK16(sK15(sK8)),X1),X1)
| ( set_intersection2(X0,sK16(sK15(sK8))) = X1 )
| ~ subset(sK8,sK2(X0,sK16(sK15(sK8)),X1)) ),
inference(superposition,[status(thm)],[c_423415,c_369077]) ).
tcf(c_429465,plain,
! [X0: $i,X1: $i] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_image(X0,sK16(sK15(sK8))))
| ~ subset(sK8,sK13(X0,sK16(sK15(sK8)),X1)) ),
inference(superposition,[status(thm)],[c_423415,c_369593]) ).
tcf(c_429466,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK16(sK15(sK8))))) = sK13(X0,relation_image(X1,X2),sK16(sK15(sK8))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(sK8,relation_image(X0,relation_image(X1,X2))) ),
inference(superposition,[status(thm)],[c_423415,c_369672]) ).
tcf(c_429467,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,sK16(sK15(sK8)),X1),X1)
| ( relation_image(X0,sK16(sK15(sK8))) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK8,sK12(X0,sK16(sK15(sK8)),X1)) ),
inference(superposition,[status(thm)],[c_423415,c_369298]) ).
tcf(c_429468,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = sK16(sK15(sK8)) )
| ( apply(X0,sK12(X0,X1,sK16(sK15(sK8)))) = sK11(X0,X1,sK16(sK15(sK8))) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK8,sK11(X0,X1,sK16(sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_423415,c_369435]) ).
tcf(c_429469,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,sK16(sK15(sK8))),X1)
| ( relation_image(X0,X1) = sK16(sK15(sK8)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK8,sK11(X0,X1,sK16(sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_423415,c_369306]) ).
tcf(c_429470,plain,
! [X0: $i,X1: $i] :
( in(sK12(X0,X1,sK16(sK15(sK8))),relation_dom(X0))
| ( relation_image(X0,X1) = sK16(sK15(sK8)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK8,sK11(X0,X1,sK16(sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_423415,c_369205]) ).
tcf(c_429471,plain,
( in(sK16(sK15(sK8)),sK5)
| ~ subset(sK8,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_423415,c_412536]) ).
tcf(c_429473,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1,sK16(sK15(sK8))),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK16(sK15(sK8)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK8,sK7(X0,X1,sK16(sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_423415,c_369084]) ).
tcf(c_429474,plain,
! [X0: $i,X1: $i] :
( in(apply(X0,sK7(X0,X1,sK16(sK15(sK8)))),X1)
| ( relation_inverse_image(X0,X1) = sK16(sK15(sK8)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK8,sK7(X0,X1,sK16(sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_423415,c_369083]) ).
tcf(c_429475,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,sK16(sK15(sK8)),X1),X1)
| ( relation_inverse_image(X0,sK16(sK15(sK8))) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(sK8,apply(X0,sK7(X0,sK16(sK15(sK8)),X1))) ),
inference(superposition,[status(thm)],[c_423415,c_369082]) ).
tcf(c_429476,plain,
! [X0: $i] :
( ( set_intersection2(sK16(sK15(sK8)),X0) = sK16(sK15(sK8)) )
| ~ subset(sK8,sK2(sK16(sK15(sK8)),X0,sK16(sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_423415,c_370076]) ).
tcf(c_429477,plain,
! [X0: $i] :
( ( set_intersection2(X0,sK16(sK15(sK8))) = sK16(sK15(sK8)) )
| ~ subset(sK8,sK2(X0,sK16(sK15(sK8)),sK16(sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_423415,c_370144]) ).
tcf(c_429478,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK16(sK15(sK8))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK16(sK15(sK8)) )
| ~ subset(sK8,sK2(set_intersection2(X0,X1),X2,sK16(sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_423415,c_370273]) ).
tcf(c_429638,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| in(sK2(set_intersection2(X0,X0),X1,X2),X0)
| ( set_intersection2(set_intersection2(X0,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_53,c_370275]) ).
tcf(c_429641,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(empty_set,X1,X2),X2)
| in(sK2(set_intersection2(X0,empty_set),X1,X2),X0)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_370275]) ).
tcf(c_429642,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(empty_set,X1,X2),X2)
| in(sK2(set_intersection2(empty_set,X0),X1,X2),empty_set)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_370275]) ).
tcf(c_429643,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK5),X0,X1),X1)
| in(sK2(set_intersection2(sK5,sK15(sK5)),X0,X1),sK5)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_370275]) ).
tcf(c_429644,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK8),X0,X1),X1)
| in(sK2(set_intersection2(sK8,sK15(sK8)),X0,X1),sK8)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_370275]) ).
tcf(c_429645,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X0)
| element(sK2(set_intersection2(X0,X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_53,c_370275]) ).
tcf(c_429648,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X0)
| element(sK2(set_intersection2(X0,empty_set),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_370275]) ).
tcf(c_429649,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),empty_set)
| element(sK2(set_intersection2(empty_set,X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_370275]) ).
tcf(c_429650,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),sK5)
| element(sK2(set_intersection2(sK5,sK15(sK5)),X0,X1),X1)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_370275]) ).
tcf(c_429651,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),sK8)
| element(sK2(set_intersection2(sK8,sK15(sK8)),X0,X1),X1)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_370275]) ).
tcf(c_429653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_intersection2(X0,X1),X2,powerset(X3)),X3)
| in(sK2(set_intersection2(X0,X1),X2,powerset(X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = powerset(X3) ) ),
inference(superposition,[status(thm)],[c_370275,c_99]) ).
tcf(c_429654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X0,X2),X3,X4),X4)
| element(sK2(set_intersection2(X0,X2),X3,X4),X1)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370275,c_321]) ).
tcf(c_429655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X0,X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370275,c_320]) ).
tcf(c_429656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(X0,sK2(set_intersection2(X0,X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_370275,c_97]) ).
tcf(c_429657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X0,X2),X3,X4),X4)
| in(sK2(set_intersection2(X0,X2),X3,X4),X1)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370275,c_96]) ).
tcf(c_429658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X3)
| element(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370275,c_93]) ).
tcf(c_429659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370275,c_91]) ).
tcf(c_429660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_370275,c_59]) ).
tcf(c_429661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_370275,c_58]) ).
tcf(c_429662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370275,c_88]) ).
tcf(c_429663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370275,c_87]) ).
tcf(c_429664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = X3 )
| ( apply(X0,sK13(X0,X4,apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,X3)))) = apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,X3)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_370275,c_369671]) ).
tcf(c_429665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(relation_image(X2,X0),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_image(X2,X0),X3),X4) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370275,c_369799]) ).
tcf(c_429666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(relation_image(X0,X2),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4) = X5 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370275,c_369798]) ).
tcf(c_429667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(relation_image(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370275,c_369596]) ).
tcf(c_429668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(relation_image(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370275,c_369558]) ).
tcf(c_429669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(relation_image(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = X4 )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),X3,X4))) = sK2(set_intersection2(relation_image(X0,X1),X2),X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370275,c_112]) ).
tcf(c_429670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_370275,c_369501]) ).
tcf(c_429671,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(empty_set,X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_370275,c_372426]) ).
tcf(c_429672,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X0),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X0),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1) ),
inference(superposition,[status(thm)],[c_370275,c_370220]) ).
tcf(c_429673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_370275,c_368471]) ).
tcf(c_429674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4) = X5 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,X5)))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370275,c_369672]) ).
tcf(c_429675,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),sK5)
| element(sK2(set_intersection2(sK15(sK5),X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(sK15(sK5),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_370275,c_412536]) ).
tcf(c_429676,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),sK8)
| element(sK2(set_intersection2(sK15(sK8),X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(sK15(sK8),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_370275,c_413867]) ).
tcf(c_429684,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X0,X1),empty_set)
| element(sK2(empty_set,X0,X1),X1)
| ( set_intersection2(empty_set,X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_429649,c_368545]) ).
tcf(c_429685,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,X0),empty_set)
| element(sK2(empty_set,X1,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_429684,c_368545]) ).
tcf(c_429687,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(empty_set,X0,X1),X1)
| in(sK2(empty_set,X0,X1),X2)
| ( set_intersection2(empty_set,X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_429648,c_64]) ).
tcf(c_429688,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(empty_set,X1,X0),X0)
| in(sK2(empty_set,X1,X0),X2)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_429687,c_368545]) ).
tcf(c_429886,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X1)
| ( set_intersection2(set_intersection2(X1,X1),X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53,c_370276]) ).
tcf(c_429889,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,X0),X1)
| ( set_intersection2(set_intersection2(X1,empty_set),X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_64,c_370276]) ).
tcf(c_429891,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X1,X0),sK5)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_411955,c_370276]) ).
tcf(c_429892,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X1,X0),sK8)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_411956,c_370276]) ).
tcf(c_429893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X0,X3),X4,X2),X1)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X2 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370276,c_321]) ).
tcf(c_429894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X0,X3),X4) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370276,c_320]) ).
tcf(c_429895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ empty(X3)
| ~ in(X0,sK2(set_intersection2(X0,X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_370276,c_97]) ).
tcf(c_429896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X2),X1)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X2 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370276,c_96]) ).
tcf(c_429897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X1,X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370276,c_93]) ).
tcf(c_429898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370276,c_91]) ).
tcf(c_429899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,X0),X2)
| ( set_intersection2(set_intersection2(set_intersection2(X1,X2),X3),X4) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370276,c_59]) ).
tcf(c_429900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,X0),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X1,X2),X3),X4) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370276,c_58]) ).
tcf(c_429901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,X1)),X2)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X2),X3),X4) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370276,c_88]) ).
tcf(c_429902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,X1),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X2),X3),X4) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370276,c_87]) ).
tcf(c_429903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = X3 )
| ( apply(X0,sK13(X0,X4,apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,X3)))) = apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,X3)) )
| ~ empty(X3)
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_370276,c_369671]) ).
tcf(c_429904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_image(X2,X0),X4),X5) = X3 )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370276,c_369799]) ).
tcf(c_429905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X3),X4),X5) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370276,c_369798]) ).
tcf(c_429906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4) = X1 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370276,c_369596]) ).
tcf(c_429907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370276,c_369558]) ).
tcf(c_429908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4) = X1 )
| ( apply(X0,sK13(X0,X2,sK2(set_intersection2(relation_image(X0,X2),X3),X4,X1))) = sK2(set_intersection2(relation_image(X0,X2),X3),X4,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370276,c_112]) ).
tcf(c_429909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = X3 )
| ~ empty(X3)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X4))
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_370276,c_369501]) ).
tcf(c_429910,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(empty_set,X1),X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370276,c_372426]) ).
tcf(c_429911,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ empty(X0)
| ~ in(sK2(set_intersection2(X1,X0),X2,X0),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1) ),
inference(superposition,[status(thm)],[c_370276,c_370220]) ).
tcf(c_429912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ empty(X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_370276,c_368471]) ).
tcf(c_429913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,relation_image(X1,X3)),X4),X5) = X2 )
| ( apply(X1,sK13(X1,X3,sK13(X0,relation_image(X1,X3),sK2(set_intersection2(relation_image(X0,relation_image(X1,X3)),X4),X5,X2)))) = sK13(X0,relation_image(X1,X3),sK2(set_intersection2(relation_image(X0,relation_image(X1,X3)),X4),X5,X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370276,c_369672]) ).
tcf(c_429914,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK5),X1),X2,X0),sK5)
| ( set_intersection2(set_intersection2(sK15(sK5),X1),X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370276,c_412536]) ).
tcf(c_429915,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK8),X1),X2,X0),sK8)
| ( set_intersection2(set_intersection2(sK15(sK8),X1),X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370276,c_413867]) ).
tcf(c_430132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK2(set_intersection2(X0,X0),X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(set_intersection2(X0,X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_53,c_370277]) ).
tcf(c_430135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X1,set_intersection2(X2,X3)),X3)
| in(sK2(set_intersection2(X0,empty_set),X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_64,c_370277]) ).
tcf(c_430136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X1,set_intersection2(X2,X3)),X3)
| in(sK2(set_intersection2(empty_set,X0),X1,set_intersection2(X2,X3)),empty_set)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368545,c_370277]) ).
tcf(c_430137,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X0,set_intersection2(X1,X2)),X2)
| in(sK2(set_intersection2(sK5,sK15(sK5)),X0,set_intersection2(X1,X2)),sK5)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411955,c_370277]) ).
tcf(c_430138,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X0,set_intersection2(X1,X2)),X2)
| in(sK2(set_intersection2(sK8,sK15(sK8)),X0,set_intersection2(X1,X2)),sK8)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411956,c_370277]) ).
tcf(c_430139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X3) ) ),
inference(superposition,[status(thm)],[c_53,c_370277]) ).
tcf(c_430140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X4,X3)),X4)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_63,c_370277]) ).
tcf(c_430143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),X3)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(empty_set,X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(empty_set,X3) ) ),
inference(superposition,[status(thm)],[c_368545,c_370277]) ).
tcf(c_430144,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),sK15(sK5))
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(sK5,sK15(sK5))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(sK5,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_411955,c_370277]) ).
tcf(c_430145,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),sK15(sK8))
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(sK8,sK15(sK8))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(sK8,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_411956,c_370277]) ).
tcf(c_430146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X0)
| in(sK2(set_intersection2(X0,X0),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(set_intersection2(X0,X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_53,c_370277]) ).
tcf(c_430149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X1,set_intersection2(X2,X3)),X0)
| in(sK2(set_intersection2(X0,empty_set),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_64,c_370277]) ).
tcf(c_430150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X1,set_intersection2(X2,X3)),empty_set)
| in(sK2(set_intersection2(empty_set,X0),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368545,c_370277]) ).
tcf(c_430151,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X0,set_intersection2(X1,X2)),sK5)
| in(sK2(set_intersection2(sK5,sK15(sK5)),X0,set_intersection2(X1,X2)),X2)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411955,c_370277]) ).
tcf(c_430152,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X0,set_intersection2(X1,X2)),sK8)
| in(sK2(set_intersection2(sK8,sK15(sK8)),X0,set_intersection2(X1,X2)),X2)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411956,c_370277]) ).
tcf(c_430153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X3)),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X3) ) ),
inference(superposition,[status(thm)],[c_53,c_370277]) ).
tcf(c_430154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X4,X3)),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_63,c_370277]) ).
tcf(c_430156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,empty_set)),empty_set)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,empty_set) ) ),
inference(superposition,[status(thm)],[c_64,c_370277]) ).
tcf(c_430157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(empty_set,X3)),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(empty_set,X3) ) ),
inference(superposition,[status(thm)],[c_368545,c_370277]) ).
tcf(c_430158,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(sK5,sK15(sK5))),sK15(sK5))
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(sK5,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_411955,c_370277]) ).
tcf(c_430159,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(sK8,sK15(sK8))),sK15(sK8))
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(sK8,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_411956,c_370277]) ).
tcf(c_430160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X0,X1))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,set_intersection2(X0,X1)) )
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X0,X1))),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X0,X1))),set_intersection2(X3,set_intersection2(X0,X1))) ),
inference(superposition,[status(thm)],[c_370277,c_54]) ).
tcf(c_430161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X2,X3),X4,set_intersection2(X5,X0)),X1)
| in(sK2(set_intersection2(X2,X3),X4,set_intersection2(X5,X0)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = set_intersection2(X5,X0) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370277,c_321]) ).
tcf(c_430162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,set_intersection2(X5,X0)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = set_intersection2(X5,X0) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370277,c_320]) ).
tcf(c_430163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,set_intersection2(X4,X0)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = set_intersection2(X4,X0) )
| ~ in(X0,sK2(set_intersection2(X1,X2),X3,set_intersection2(X4,X0))) ),
inference(superposition,[status(thm)],[c_370277,c_97]) ).
tcf(c_430164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,set_intersection2(X5,X0)),X2)
| in(sK2(set_intersection2(X2,X3),X4,set_intersection2(X5,X0)),X1)
| ( set_intersection2(set_intersection2(X2,X3),X4) = set_intersection2(X5,X0) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370277,c_96]) ).
tcf(c_430165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X4)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370277,c_93]) ).
tcf(c_430166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,set_intersection2(X4,X0)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = set_intersection2(X4,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370277,c_91]) ).
tcf(c_430167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X4,X5))),X5)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X4,X5))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,set_intersection2(X4,X5)) ) ),
inference(superposition,[status(thm)],[c_370277,c_59]) ).
tcf(c_430168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X4,X5))),X4)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X4,X5))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,set_intersection2(X4,X5)) ) ),
inference(superposition,[status(thm)],[c_370277,c_58]) ).
tcf(c_430169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X1,X2),X3,set_intersection2(X4,relation_inverse_image(X0,X5))),X1)
| in(apply(X0,sK2(set_intersection2(X1,X2),X3,set_intersection2(X4,relation_inverse_image(X0,X5)))),X5)
| ( set_intersection2(set_intersection2(X1,X2),X3) = set_intersection2(X4,relation_inverse_image(X0,X5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370277,c_88]) ).
tcf(c_430170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X1,X2),X3,set_intersection2(X4,relation_inverse_image(X0,X5))),X1)
| in(sK2(set_intersection2(X1,X2),X3,set_intersection2(X4,relation_inverse_image(X0,X5))),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,X2),X3) = set_intersection2(X4,relation_inverse_image(X0,X5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370277,c_87]) ).
tcf(c_430171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,relation_dom(X4))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,relation_dom(X4)) )
| ( apply(X4,sK13(X4,X5,apply(X4,sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,relation_dom(X4)))))) = apply(X4,sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,relation_dom(X4)))) )
| ~ function(X4)
| ~ relation(X4)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,relation_dom(X4))),X5) ),
inference(superposition,[status(thm)],[c_370277,c_369671]) ).
tcf(c_430172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X3,X4),X5,set_intersection2(X6,relation_image(X2,X0))),X3)
| ( set_intersection2(set_intersection2(X3,X4),X5) = set_intersection2(X6,relation_image(X2,X0)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370277,c_369799]) ).
tcf(c_430173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X2,X3),X4,set_intersection2(X5,relation_image(X0,X6))),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = set_intersection2(X5,relation_image(X0,X6)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370277,c_369798]) ).
tcf(c_430174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,set_intersection2(X5,relation_image(X0,X1))),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = set_intersection2(X5,relation_image(X0,X1)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370277,c_369596]) ).
tcf(c_430175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X1,X2),X3,set_intersection2(X4,relation_image(X0,X5))),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = set_intersection2(X4,relation_image(X0,X5)) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370277,c_369558]) ).
tcf(c_430176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,set_intersection2(X5,relation_image(X0,X1))),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = set_intersection2(X5,relation_image(X0,X1)) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,X3),X4,set_intersection2(X5,relation_image(X0,X1))))) = sK2(set_intersection2(X2,X3),X4,set_intersection2(X5,relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370277,c_112]) ).
tcf(c_430177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,relation_dom(X4))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,relation_dom(X4)) )
| ~ function(X4)
| ~ relation(X4)
| ~ empty(relation_image(X4,X5))
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,relation_dom(X4))),X5) ),
inference(superposition,[status(thm)],[c_370277,c_369501]) ).
tcf(c_430178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,empty_set)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,empty_set) ) ),
inference(superposition,[status(thm)],[c_370277,c_372426]) ).
tcf(c_430180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X3,X4),X5,set_intersection2(X6,relation_image(X0,relation_image(X1,X2)))),X3)
| ( set_intersection2(X6,relation_image(X0,relation_image(X1,X2))) = set_intersection2(set_intersection2(X3,X4),X5) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,X4),X5,set_intersection2(X6,relation_image(X0,relation_image(X1,X2))))))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,X4),X5,set_intersection2(X6,relation_image(X0,relation_image(X1,X2))))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370277,c_369672]) ).
tcf(c_430181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,sK15(sK5))),sK5)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,sK15(sK5))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_370277,c_412536]) ).
tcf(c_430182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,sK15(sK8))),sK8)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,sK15(sK8))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_370277,c_413867]) ).
tcf(c_430185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X0)),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(X4,X0) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X0)),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X0)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X0)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X0)),set_intersection2(X4,X0)) ),
inference(superposition,[status(thm)],[c_370277,c_370217]) ).
tcf(c_430186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X0,X2),X3,set_intersection2(X4,X5)),X1)
| in(sK2(set_intersection2(X0,X2),X3,set_intersection2(X4,X5)),X5)
| ( set_intersection2(set_intersection2(X0,X2),X3) = set_intersection2(X4,X5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370277,c_321]) ).
tcf(c_430187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X2),X3,set_intersection2(X4,X5)),X5)
| ( set_intersection2(set_intersection2(X0,X2),X3) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370277,c_320]) ).
tcf(c_430188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ in(X0,sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4))) ),
inference(superposition,[status(thm)],[c_370277,c_97]) ).
tcf(c_430189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X2),X3,set_intersection2(X4,X5)),X5)
| in(sK2(set_intersection2(X0,X2),X3,set_intersection2(X4,X5)),X1)
| ( set_intersection2(set_intersection2(X0,X2),X3) = set_intersection2(X4,X5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370277,c_96]) ).
tcf(c_430190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370277,c_93]) ).
tcf(c_430191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370277,c_91]) ).
tcf(c_430192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X5)),X5)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X5)),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(X4,X5) ) ),
inference(superposition,[status(thm)],[c_370277,c_59]) ).
tcf(c_430193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X5)),X5)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X5)),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(X4,X5) ) ),
inference(superposition,[status(thm)],[c_370277,c_58]) ).
tcf(c_430194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,set_intersection2(X4,X5)),X5)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,set_intersection2(X4,X5))),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = set_intersection2(X4,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370277,c_88]) ).
tcf(c_430195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,set_intersection2(X4,X5)),X5)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,set_intersection2(X4,X5)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = set_intersection2(X4,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370277,c_87]) ).
tcf(c_430196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = set_intersection2(X3,X4) )
| ( apply(X0,sK13(X0,X5,apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(X3,X4))))) = apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(X3,X4))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370277,c_369671]) ).
tcf(c_430197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_image(X2,X0),X3),X4,set_intersection2(X5,X6)),X6)
| ( set_intersection2(set_intersection2(relation_image(X2,X0),X3),X4) = set_intersection2(X5,X6) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370277,c_369799]) ).
tcf(c_430198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_image(X0,X2),X3),X4,set_intersection2(X5,X6)),X6)
| ( set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4) = set_intersection2(X5,X6) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370277,c_369798]) ).
tcf(c_430199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,set_intersection2(X4,X5)),X5)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370277,c_369596]) ).
tcf(c_430200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,set_intersection2(X4,X5)),X5)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = set_intersection2(X4,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370277,c_369558]) ).
tcf(c_430201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,set_intersection2(X4,X5)),X5)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = set_intersection2(X4,X5) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),X3,set_intersection2(X4,X5)))) = sK2(set_intersection2(relation_image(X0,X1),X2),X3,set_intersection2(X4,X5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370277,c_112]) ).
tcf(c_430202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X5))
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370277,c_369501]) ).
tcf(c_430203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X0),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_370277,c_372426]) ).
tcf(c_430204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X2),X0),X3,set_intersection2(X1,X2)),X2)
| ( set_intersection2(set_intersection2(set_intersection2(X1,X2),X0),X3) = set_intersection2(X1,X2) )
| ~ in(sK2(set_intersection2(set_intersection2(X1,X2),X0),X3,set_intersection2(X1,X2)),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X1,X2),X0),X3,set_intersection2(X1,X2)),X0)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X1,X2)),X3,set_intersection2(X1,X2)),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370277,c_370220]) ).
tcf(c_430205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),set_intersection2(X3,X4)) ),
inference(superposition,[status(thm)],[c_370277,c_368471]) ).
tcf(c_430206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,set_intersection2(X5,X6)),X6)
| ( set_intersection2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4) = set_intersection2(X5,X6) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,set_intersection2(X5,X6))))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,set_intersection2(X5,X6))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370277,c_369672]) ).
tcf(c_430207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK15(sK5),X0),X1,set_intersection2(X2,X3)),sK5)
| in(sK2(set_intersection2(sK15(sK5),X0),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(set_intersection2(sK15(sK5),X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_370277,c_412536]) ).
tcf(c_430208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK15(sK8),X0),X1,set_intersection2(X2,X3)),sK8)
| in(sK2(set_intersection2(sK15(sK8),X0),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(set_intersection2(sK15(sK8),X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_370277,c_413867]) ).
tcf(c_430211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X0)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X0) ) ),
inference(equality_factoring,[status(thm)],[c_370277]) ).
tcf(c_430235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_430156,c_372426]) ).
tcf(c_430241,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,set_intersection2(X0,X1)),empty_set)
| in(sK2(empty_set,X2,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(light_normalisation,[status(thm)],[c_430150,c_368545]) ).
tcf(c_430277,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),X0)
| in(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),sK15(sK8))
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK15(sK8) ) ),
inference(light_normalisation,[status(thm)],[c_430159,c_411956]) ).
tcf(c_430281,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),X0)
| in(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),sK15(sK5))
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK15(sK5) ) ),
inference(light_normalisation,[status(thm)],[c_430158,c_411955]) ).
tcf(c_430671,plain,
set_intersection2(empty_set,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_378043,c_397130]) ).
tcf(c_430672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X0)),X1,set_intersection2(X2,X3)),X0)
| in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,set_intersection2(X2,X3)),X3)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397130,c_370277]) ).
tcf(c_430673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X0)),X1,set_intersection2(X2,X3)),X3)
| in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397130,c_370277]) ).
tcf(c_430674,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),X0)
| element(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_370275]) ).
tcf(c_430675,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(sK16(powerset(X0)),X1,X2),X2)
| in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X2),X0)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_370275]) ).
tcf(c_430676,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),X2)
| in(sK2(set_intersection2(sK16(powerset(X0)),X0),X1,X2),X0)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_370266]) ).
tcf(c_430677,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),X0)
| in(sK2(set_intersection2(sK16(powerset(X0)),X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_370261]) ).
tcf(c_430678,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X2 )
| ~ in(sK2(sK16(powerset(X0)),X1,X2),X2)
| ~ in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X2),X1)
| ~ in(sK2(set_intersection2(sK16(powerset(X0)),X0),X1,X2),X0)
| ~ in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X2),sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_397130,c_370220]) ).
tcf(c_430679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1),X2) = X3 )
| ~ in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1),X2,X3),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1),X2,X3),sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_397130,c_370217]) ).
tcf(c_430680,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X0),set_intersection2(X0,sK16(powerset(X0))))
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X0 )
| ~ in(sK2(sK16(powerset(X0)),X1,X0),X1)
| ~ in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X0),sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_397130,c_426065]) ).
tcf(c_430681,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK16(powerset(X0)),X1,sK16(powerset(X0))),X0)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = set_intersection2(X0,sK16(powerset(X0))) ) ),
inference(superposition,[status(thm)],[c_397130,c_370081]) ).
tcf(c_430682,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK16(powerset(X0)),X1,sK16(powerset(X0))),sK16(powerset(X0)))
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = set_intersection2(X0,sK16(powerset(X0))) ) ),
inference(superposition,[status(thm)],[c_397130,c_370080]) ).
tcf(c_430683,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ subset(sK16(powerset(X1)),X2)
| ~ in(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_397130,c_369930]) ).
tcf(c_430684,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ in(X0,X1)
| ~ subset(sK16(powerset(X1)),X2)
| ~ in(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_397130,c_369786]) ).
tcf(c_430685,plain,
! [X0: $i] :
( element(sK16(sK16(powerset(X0))),X0)
| empty(set_intersection2(X0,sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_397130,c_389068]) ).
tcf(c_430686,plain,
! [X0: $i] :
( empty(set_intersection2(sK16(powerset(X0)),X0))
| in(sK16(sK16(powerset(X0))),sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_397130,c_389060]) ).
tcf(c_430687,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK16(powerset(X0))))
| element(sK16(sK16(powerset(X0))),sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_397130,c_388051]) ).
tcf(c_430688,plain,
! [X0: $i] :
( in(sK16(sK16(powerset(X0))),X0)
| empty(set_intersection2(sK16(powerset(X0)),X0)) ),
inference(superposition,[status(thm)],[c_397130,c_388043]) ).
tcf(c_430689,plain,
! [X0: $i] :
( in(sK16(sK16(powerset(X0))),X0)
| empty(set_intersection2(X0,sK16(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_397130,c_370751]) ).
tcf(c_430690,plain,
! [X0: $i] :
( empty(set_intersection2(X0,sK16(powerset(X0))))
| in(sK16(sK16(powerset(X0))),sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_397130,c_370750]) ).
tcf(c_430691,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X1,sK16(powerset(X0)))
| ~ in(sK16(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_397130,c_369080]) ).
tcf(c_430695,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,X1)
| ~ subset(sK16(powerset(X1)),X2)
| ~ in(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_397130,c_369016]) ).
tcf(c_430697,plain,
! [X0: $i,X1: $i] :
( subset(set_intersection2(X0,sK16(powerset(X0))),X1)
| in(sK10(sK16(powerset(X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_397130,c_368986]) ).
tcf(c_430699,plain,
! [X0: $i] : subset(sK16(powerset(X0)),sK16(powerset(X0))),
inference(superposition,[status(thm)],[c_397130,c_380850]) ).
tcf(c_430700,plain,
! [X0: $i,X1: $i] :
( subset(set_intersection2(X0,sK16(powerset(X0))),X1)
| in(sK10(sK16(powerset(X0)),X1),sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_397130,c_368985]) ).
tcf(c_430701,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ~ empty(sK16(powerset(X1)))
| ~ in(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_397130,c_368869]) ).
tcf(c_430702,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,sK16(powerset(X0))) = X1 )
| ~ subset(X1,X0)
| ~ subset(X1,sK16(powerset(X0)))
| ~ subset(sK16(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_397130,c_368558]) ).
tcf(c_430703,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),sK16(powerset(X0)))
| in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_368503]) ).
tcf(c_430704,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),X2)
| in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X2),sK16(powerset(X0)))
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_368503]) ).
tcf(c_430705,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),X0)
| in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_368481]) ).
tcf(c_430706,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),X2)
| in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X2),X0)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_368481]) ).
tcf(c_430707,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X2 )
| ~ in(sK2(sK16(powerset(X0)),X1,X2),X0)
| ~ in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X2),X2)
| ~ in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X2),X1)
| ~ in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X2),sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_397130,c_368471]) ).
tcf(c_430709,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X1)),X2,X0),X1)
| ( set_intersection2(set_intersection2(X1,sK16(powerset(X1))),X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370276]) ).
tcf(c_430710,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X1,sK16(powerset(X1))),X2,X0),X1)
| ( set_intersection2(set_intersection2(X1,sK16(powerset(X1))),X2) = X0 )
| ~ in(X0,sK2(sK16(powerset(X1)),X2,X0)) ),
inference(superposition,[status(thm)],[c_397130,c_370273]) ).
tcf(c_430711,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK16(powerset(X1)),sK16(powerset(X1))),X1)
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X1)))) = set_intersection2(X1,sK16(powerset(X1))) ) ),
inference(superposition,[status(thm)],[c_397130,c_370149]) ).
tcf(c_430712,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK16(powerset(X1)),sK16(powerset(X1))),sK16(powerset(X1)))
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X1)))) = set_intersection2(X1,sK16(powerset(X1))) ) ),
inference(superposition,[status(thm)],[c_397130,c_370148]) ).
tcf(c_430713,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,sK16(powerset(X1)),X2),X2)
| in(sK12(X0,set_intersection2(X1,sK16(powerset(X1))),X2),X1)
| ( relation_image(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_369303]) ).
tcf(c_430714,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,sK16(powerset(X1)),X2),X1)
| in(sK11(X0,set_intersection2(X1,sK16(powerset(X1))),X2),X2)
| ( relation_image(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_369303]) ).
tcf(c_430715,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,sK16(powerset(X1)),X2),X2)
| in(sK12(X0,set_intersection2(X1,sK16(powerset(X1))),X2),sK16(powerset(X1)))
| ( relation_image(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_369302]) ).
tcf(c_430716,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,sK16(powerset(X1)),X2),sK16(powerset(X1)))
| in(sK11(X0,set_intersection2(X1,sK16(powerset(X1))),X2),X2)
| ( relation_image(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_369302]) ).
tcf(c_430717,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_intersection2(X1,sK16(powerset(X1))))
| ~ in(sK10(X0,sK16(powerset(X1))),X1)
| ~ in(sK10(X0,set_intersection2(X1,sK16(powerset(X1)))),sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_397130,c_368972]) ).
tcf(c_430718,plain,
! [X0: $i,X1: $i] :
( element(X0,sK16(powerset(X1)))
| ~ in(X0,X1)
| ~ in(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_397130,c_368928]) ).
tcf(c_430719,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,sK16(powerset(X1)),X2)),X1)
| in(sK7(X0,set_intersection2(X1,sK16(powerset(X1))),X2),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_368703]) ).
tcf(c_430720,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK16(powerset(X1)),X2),X2)
| in(apply(X0,sK7(X0,set_intersection2(X1,sK16(powerset(X1))),X2)),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_368703]) ).
tcf(c_430721,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,set_intersection2(X1,sK16(powerset(X1))),X2),X2)
| in(apply(X0,sK7(X0,sK16(powerset(X1)),X2)),sK16(powerset(X1)))
| ( relation_inverse_image(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_368702]) ).
tcf(c_430722,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK16(powerset(X1)),X2),X2)
| in(apply(X0,sK7(X0,set_intersection2(X1,sK16(powerset(X1))),X2)),sK16(powerset(X1)))
| ( relation_inverse_image(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_368702]) ).
tcf(c_430723,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,sK16(powerset(X1)),X2)),X1)
| ~ in(sK7(X0,set_intersection2(X1,sK16(powerset(X1))),X2),X2)
| ~ in(sK7(X0,set_intersection2(X1,sK16(powerset(X1))),X2),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,set_intersection2(X1,sK16(powerset(X1))),X2)),sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_397130,c_368654]) ).
tcf(c_430724,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK16(powerset(X1)),X2),sK16(powerset(X1)))
| in(sK2(X0,set_intersection2(X1,sK16(powerset(X1))),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_368504]) ).
tcf(c_430725,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK16(powerset(X1)),X2),X2)
| in(sK2(X0,set_intersection2(X1,sK16(powerset(X1))),X2),sK16(powerset(X1)))
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_368504]) ).
tcf(c_430726,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK16(powerset(X1)),X2),X1)
| in(sK2(X0,set_intersection2(X1,sK16(powerset(X1))),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_368482]) ).
tcf(c_430727,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK16(powerset(X1)),X2),X2)
| in(sK2(X0,set_intersection2(X1,sK16(powerset(X1))),X2),X1)
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_368482]) ).
tcf(c_430730,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_397130,c_58]) ).
tcf(c_430732,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),sK16(powerset(X0)))
| in(sK2(set_intersection2(sK16(powerset(X0)),X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(sK16(powerset(X0)),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_370266]) ).
tcf(c_430733,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),X2)
| in(sK2(set_intersection2(sK16(powerset(X0)),X0),X1,X2),sK16(powerset(X0)))
| ( set_intersection2(set_intersection2(sK16(powerset(X0)),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_370261]) ).
tcf(c_430734,plain,
! [X0: $i,X1: $i] :
( subset(sK16(powerset(X0)),X1)
| ~ empty(sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_397130,c_380845]) ).
tcf(c_430735,plain,
! [X0: $i] :
( function(sK16(powerset(X0)))
| ~ empty(sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_397130,c_381376]) ).
tcf(c_430736,plain,
! [X0: $i] :
( relation(sK16(powerset(X0)))
| ~ empty(sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_397130,c_381375]) ).
tcf(c_430739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),sK16(powerset(set_intersection2(X0,X1)))),X2) = X3 )
| ~ in(sK2(sK16(powerset(set_intersection2(X0,X1))),X2,X3),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),sK16(powerset(set_intersection2(X0,X1)))),X2,X3),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),sK16(powerset(set_intersection2(X0,X1)))),X2,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),sK16(powerset(set_intersection2(X0,X1)))),X2,X3),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),sK16(powerset(set_intersection2(X0,X1)))),X2,X3),sK16(powerset(set_intersection2(X0,X1)))) ),
inference(superposition,[status(thm)],[c_397130,c_370217]) ).
tcf(c_430740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X2)),X3,X0),X1)
| in(sK2(set_intersection2(X2,sK16(powerset(X2))),X3,X0),X2)
| ( set_intersection2(set_intersection2(X2,sK16(powerset(X2))),X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397130,c_370274]) ).
tcf(c_430741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X2)),X3,X0),X2)
| in(sK2(set_intersection2(X2,sK16(powerset(X2))),X3,X0),X1)
| ( set_intersection2(set_intersection2(X2,sK16(powerset(X2))),X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397130,c_370274]) ).
tcf(c_430742,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,sK16(powerset(X2)),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,sK16(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_397130,c_369598]) ).
tcf(c_430743,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,sK16(powerset(X2)),X0),sK16(powerset(X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,sK16(powerset(X2))))) ),
inference(superposition,[status(thm)],[c_397130,c_369597]) ).
tcf(c_430744,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,sK16(powerset(X2))),X2)
| ( set_intersection2(X2,sK16(powerset(X2))) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,sK16(powerset(X2))))) = sK11(X0,X1,set_intersection2(X2,sK16(powerset(X2)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_369440]) ).
tcf(c_430745,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,sK16(powerset(X2))),sK16(powerset(X2)))
| ( set_intersection2(X2,sK16(powerset(X2))) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,sK16(powerset(X2))))) = sK11(X0,X1,set_intersection2(X2,sK16(powerset(X2)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_369439]) ).
tcf(c_430746,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,sK16(powerset(X1))),X1)
| in(sK12(X0,X2,set_intersection2(X1,sK16(powerset(X1)))),X2)
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_369311]) ).
tcf(c_430747,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,sK16(powerset(X1))),X2)
| in(sK11(X0,X2,set_intersection2(X1,sK16(powerset(X1)))),X1)
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_369311]) ).
tcf(c_430748,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,sK16(powerset(X1))),sK16(powerset(X1)))
| in(sK12(X0,X2,set_intersection2(X1,sK16(powerset(X1)))),X2)
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_369310]) ).
tcf(c_430749,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,sK16(powerset(X1))),X2)
| in(sK11(X0,X2,set_intersection2(X1,sK16(powerset(X1)))),sK16(powerset(X1)))
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_369310]) ).
tcf(c_430750,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,sK16(powerset(X1))),relation_dom(X0))
| in(sK11(X0,X2,set_intersection2(X1,sK16(powerset(X1)))),X1)
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_369210]) ).
tcf(c_430751,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,sK16(powerset(X1))),X1)
| in(sK12(X0,X2,set_intersection2(X1,sK16(powerset(X1)))),relation_dom(X0))
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_369210]) ).
tcf(c_430752,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X2,sK16(powerset(X1))),relation_dom(X0))
| in(sK11(X0,X2,set_intersection2(X1,sK16(powerset(X1)))),sK16(powerset(X1)))
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_369209]) ).
tcf(c_430753,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X2,sK16(powerset(X1))),sK16(powerset(X1)))
| in(sK12(X0,X2,set_intersection2(X1,sK16(powerset(X1)))),relation_dom(X0))
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_369209]) ).
tcf(c_430754,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_inverse_image(X0,sK16(powerset(X2))))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X2)
| ~ in(apply(X0,X1),sK16(powerset(X2))) ),
inference(superposition,[status(thm)],[c_397130,c_368735]) ).
tcf(c_430755,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X2,sK16(powerset(X1)))),X2)
| in(sK7(X0,X2,set_intersection2(X1,sK16(powerset(X1)))),X1)
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_368701]) ).
tcf(c_430756,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK16(powerset(X1))),X1)
| in(apply(X0,sK7(X0,X2,set_intersection2(X1,sK16(powerset(X1))))),X2)
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_368701]) ).
tcf(c_430757,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,X2,sK16(powerset(X1)))),X2)
| in(sK7(X0,X2,set_intersection2(X1,sK16(powerset(X1)))),sK16(powerset(X1)))
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_368700]) ).
tcf(c_430758,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK16(powerset(X1))),sK16(powerset(X1)))
| in(apply(X0,sK7(X0,X2,set_intersection2(X1,sK16(powerset(X1))))),X2)
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_368700]) ).
tcf(c_430759,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK16(powerset(X1))),relation_dom(X0))
| in(sK7(X0,X2,set_intersection2(X1,sK16(powerset(X1)))),X1)
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_368673]) ).
tcf(c_430760,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK16(powerset(X1))),X1)
| in(sK7(X0,X2,set_intersection2(X1,sK16(powerset(X1)))),relation_dom(X0))
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_368673]) ).
tcf(c_430761,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK16(powerset(X1))),relation_dom(X0))
| in(sK7(X0,X2,set_intersection2(X1,sK16(powerset(X1)))),sK16(powerset(X1)))
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_368672]) ).
tcf(c_430762,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X2,sK16(powerset(X1))),sK16(powerset(X1)))
| in(sK7(X0,X2,set_intersection2(X1,sK16(powerset(X1)))),relation_dom(X0))
| ( set_intersection2(X1,sK16(powerset(X1))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_368672]) ).
tcf(c_430763,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,sK16(powerset(X0))),X1)
| in(sK2(X1,X2,set_intersection2(X0,sK16(powerset(X0)))),sK16(powerset(X0)))
| ( set_intersection2(X0,sK16(powerset(X0))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_397130,c_368506]) ).
tcf(c_430764,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,sK16(powerset(X0))),sK16(powerset(X0)))
| in(sK2(X1,X2,set_intersection2(X0,sK16(powerset(X0)))),X1)
| ( set_intersection2(X0,sK16(powerset(X0))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_397130,c_368506]) ).
tcf(c_430765,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,sK16(powerset(X0))),X2)
| in(sK2(X1,X2,set_intersection2(X0,sK16(powerset(X0)))),sK16(powerset(X0)))
| ( set_intersection2(X0,sK16(powerset(X0))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_397130,c_368505]) ).
tcf(c_430766,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,sK16(powerset(X0))),sK16(powerset(X0)))
| in(sK2(X1,X2,set_intersection2(X0,sK16(powerset(X0)))),X2)
| ( set_intersection2(X0,sK16(powerset(X0))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_397130,c_368505]) ).
tcf(c_430767,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,sK16(powerset(X0))),X1)
| in(sK2(X1,X2,set_intersection2(X0,sK16(powerset(X0)))),X0)
| ( set_intersection2(X0,sK16(powerset(X0))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_397130,c_368484]) ).
tcf(c_430768,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,sK16(powerset(X0))),X0)
| in(sK2(X1,X2,set_intersection2(X0,sK16(powerset(X0)))),X1)
| ( set_intersection2(X0,sK16(powerset(X0))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_397130,c_368484]) ).
tcf(c_430769,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,sK16(powerset(X0))),X2)
| in(sK2(X1,X2,set_intersection2(X0,sK16(powerset(X0)))),X0)
| ( set_intersection2(X0,sK16(powerset(X0))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_397130,c_368483]) ).
tcf(c_430770,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,sK16(powerset(X0))),X0)
| in(sK2(X1,X2,set_intersection2(X0,sK16(powerset(X0)))),X2)
| ( set_intersection2(X0,sK16(powerset(X0))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_397130,c_368483]) ).
tcf(c_430771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK16(powerset(X3))),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,sK16(powerset(X3)))),sK16(powerset(X3)))
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,sK16(powerset(X3))) ) ),
inference(superposition,[status(thm)],[c_397130,c_370277]) ).
tcf(c_430772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK16(powerset(X3))),sK16(powerset(X3)))
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,sK16(powerset(X3)))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,sK16(powerset(X3))) ) ),
inference(superposition,[status(thm)],[c_397130,c_370277]) ).
tcf(c_430781,plain,
! [X0: $i] :
( empty(sK16(powerset(X0)))
| in(sK16(sK16(powerset(X0))),X0) ),
inference(light_normalisation,[status(thm)],[c_430689,c_397130]) ).
tcf(c_430785,plain,
! [X0: $i] :
( empty(sK16(powerset(X0)))
| element(sK16(sK16(powerset(X0))),X0) ),
inference(light_normalisation,[status(thm)],[c_430685,c_397130]) ).
tcf(c_430788,plain,
! [X0: $i,X1: $i] :
( subset(sK16(powerset(X0)),X1)
| in(sK10(sK16(powerset(X0)),X1),X0) ),
inference(light_normalisation,[status(thm)],[c_430697,c_397130]) ).
tcf(c_430791,plain,
! [X0: $i] :
( empty(sK16(powerset(X0)))
| in(sK16(sK16(powerset(X0))),sK16(powerset(X0))) ),
inference(light_normalisation,[status(thm)],[c_430690,c_397130]) ).
tcf(c_430794,plain,
! [X0: $i] :
( empty(sK16(powerset(X0)))
| element(sK16(sK16(powerset(X0))),sK16(powerset(X0))) ),
inference(light_normalisation,[status(thm)],[c_430687,c_397130]) ).
tcf(c_430802,plain,
! [X0: $i,X1: $i] :
( subset(sK16(powerset(X0)),X1)
| in(sK10(sK16(powerset(X0)),X1),sK16(powerset(X0))) ),
inference(light_normalisation,[status(thm)],[c_430700,c_397130]) ).
tcf(c_430829,plain,
! [X0: $i,X1: $i] :
( ( sK16(powerset(X0)) = X1 )
| ~ subset(X1,X0)
| ~ subset(X1,sK16(powerset(X0)))
| ~ subset(sK16(powerset(X0)),X1) ),
inference(light_normalisation,[status(thm)],[c_430702,c_397130]) ).
tcf(c_430834,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK16(powerset(X0)),X1,sK16(powerset(X0))),X0)
| ( set_intersection2(sK16(powerset(X0)),X1) = sK16(powerset(X0)) ) ),
inference(light_normalisation,[status(thm)],[c_430681,c_397130]) ).
tcf(c_430843,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK16(powerset(X0)),X1,sK16(powerset(X0))),sK16(powerset(X0)))
| ( set_intersection2(sK16(powerset(X0)),X1) = sK16(powerset(X0)) ) ),
inference(light_normalisation,[status(thm)],[c_430682,c_397130]) ).
tcf(c_430849,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,sK16(powerset(X2))),X2)
| in(sK2(X0,X1,sK16(powerset(X2))),X1)
| ( set_intersection2(X0,X1) = sK16(powerset(X2)) ) ),
inference(light_normalisation,[status(thm)],[c_430770,c_397130]) ).
tcf(c_430854,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,sK16(powerset(X2))),X2)
| in(sK2(X0,X1,sK16(powerset(X2))),X0)
| ( set_intersection2(X0,X1) = sK16(powerset(X2)) ) ),
inference(light_normalisation,[status(thm)],[c_430768,c_397130]) ).
tcf(c_430865,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),X2)
| in(sK2(sK16(powerset(X0)),X1,X2),X0)
| ( set_intersection2(sK16(powerset(X0)),X1) = X2 ) ),
inference(light_normalisation,[status(thm)],[c_430706,c_397130]) ).
tcf(c_430872,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(sK16(powerset(X0)),X1,X2),X2)
| in(sK2(sK16(powerset(X0)),X1,X2),X0)
| ( set_intersection2(sK16(powerset(X0)),X1) = X2 ) ),
inference(light_normalisation,[status(thm)],[c_430675,c_397130]) ).
tcf(c_430880,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,sK16(powerset(X2))),X1)
| in(sK2(X0,X1,sK16(powerset(X2))),sK16(powerset(X2)))
| ( set_intersection2(X0,X1) = sK16(powerset(X2)) ) ),
inference(light_normalisation,[status(thm)],[c_430766,c_397130]) ).
tcf(c_430885,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,sK16(powerset(X2))),X0)
| in(sK2(X0,X1,sK16(powerset(X2))),sK16(powerset(X2)))
| ( set_intersection2(X0,X1) = sK16(powerset(X2)) ) ),
inference(light_normalisation,[status(thm)],[c_430764,c_397130]) ).
tcf(c_430890,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),X2)
| in(sK2(sK16(powerset(X0)),X1,X2),sK16(powerset(X0)))
| ( set_intersection2(sK16(powerset(X0)),X1) = X2 ) ),
inference(light_normalisation,[status(thm)],[c_430733,c_397160]) ).
tcf(c_430937,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X0)),X1,set_intersection2(X2,X3)),X3)
| in(sK2(sK16(powerset(X0)),X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(sK16(powerset(X0)),X1) = set_intersection2(X2,X3) ) ),
inference(light_normalisation,[status(thm)],[c_430673,c_397130]) ).
tcf(c_431059,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(sK16(powerset(X0)),X1) = X2 )
| ~ in(sK2(sK16(powerset(X0)),X1,X2),X2)
| ~ in(sK2(sK16(powerset(X0)),X1,X2),X1)
| ~ in(sK2(sK16(powerset(X0)),X1,X2),X0)
| ~ in(sK2(sK16(powerset(X0)),X1,X2),sK16(powerset(X0))) ),
inference(light_normalisation,[status(thm)],[c_430707,c_397130]) ).
tcf(c_431073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(sK16(powerset(X0)),X1),X2) = X3 )
| ~ in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X1)
| ~ in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X0)
| ~ in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),sK16(powerset(X0))) ),
inference(light_normalisation,[status(thm)],[c_430679,c_397130]) ).
tcf(c_431309,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,sK16(powerset(X1)),X2),X2)
| in(sK2(X0,sK16(powerset(X1)),X2),X1)
| ( set_intersection2(X0,sK16(powerset(X1))) = X2 ) ),
inference(superposition,[status(thm)],[c_368926,c_430730]) ).
tcf(c_431310,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK16(powerset(X1)),X2),X2)
| in(sK2(X0,sK16(powerset(X1)),X2),X1)
| ( set_intersection2(X0,sK16(powerset(X1))) = X2 ) ),
inference(superposition,[status(thm)],[c_56,c_430730]) ).
tcf(c_431311,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK16(powerset(X2))),X1)
| in(sK2(X0,X1,sK16(powerset(X2))),X2)
| ( set_intersection2(X0,X1) = sK16(powerset(X2)) ) ),
inference(superposition,[status(thm)],[c_368925,c_430730]) ).
tcf(c_431312,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,sK16(powerset(X2))),X0)
| in(sK2(X0,X1,sK16(powerset(X2))),X2)
| ( set_intersection2(X0,X1) = sK16(powerset(X2)) ) ),
inference(superposition,[status(thm)],[c_368924,c_430730]) ).
tcf(c_431313,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,sK16(powerset(X2))),X2)
| ( set_intersection2(X0,X1) = sK16(powerset(X2)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368865,c_430730]) ).
tcf(c_431316,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK7(X0,sK16(powerset(X1)),X2),X2)
| in(apply(X0,sK7(X0,sK16(powerset(X1)),X2)),X1)
| ( relation_inverse_image(X0,sK16(powerset(X1))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368931,c_430730]) ).
tcf(c_431317,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,sK16(powerset(X1)),X2),X2)
| in(apply(X0,sK7(X0,sK16(powerset(X1)),X2)),X1)
| ( relation_inverse_image(X0,sK16(powerset(X1))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_430730]) ).
tcf(c_431318,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,sK16(powerset(X2))),X2)
| element(apply(X0,sK7(X0,X1,sK16(powerset(X2)))),X1)
| ( relation_inverse_image(X0,X1) = sK16(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368930,c_430730]) ).
tcf(c_431319,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,sK16(powerset(X2))),X2)
| element(sK7(X0,X1,sK16(powerset(X2))),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK16(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368929,c_430730]) ).
tcf(c_431320,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,sK16(powerset(X2))),X2)
| ( relation_inverse_image(X0,X1) = sK16(powerset(X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368871,c_430730]) ).
tcf(c_431321,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,sK16(powerset(X2))),X2)
| ( relation_inverse_image(X0,X1) = sK16(powerset(X2)) )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_379483,c_430730]) ).
tcf(c_431322,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,sK16(powerset(X2))),X2)
| in(sK7(X0,X1,sK16(powerset(X2))),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = sK16(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_375319,c_430730]) ).
tcf(c_431323,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,sK16(powerset(X2))),X2)
| in(apply(X0,sK7(X0,X1,sK16(powerset(X2)))),X1)
| ( relation_inverse_image(X0,X1) = sK16(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_85,c_430730]) ).
tcf(c_431324,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK7(X0,X1,sK16(powerset(X2))),X2)
| in(sK7(X0,X1,sK16(powerset(X2))),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = sK16(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_84,c_430730]) ).
tcf(c_431326,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,sK16(powerset(X2))),X2)
| ( relation_image(X0,X1) = sK16(powerset(X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369301,c_430730]) ).
tcf(c_431327,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK12(X0,X1,sK16(powerset(X2))),X1)
| in(sK11(X0,X1,sK16(powerset(X2))),X2)
| ( relation_image(X0,X1) = sK16(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369300,c_430730]) ).
tcf(c_431328,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,sK16(powerset(X2))),X2)
| ( relation_image(X0,X1) = sK16(powerset(X2)) )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_386602,c_430730]) ).
tcf(c_431329,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,sK16(powerset(X2))),X2)
| element(sK12(X0,X1,sK16(powerset(X2))),relation_dom(X0))
| ( relation_image(X0,X1) = sK16(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369215,c_430730]) ).
tcf(c_431330,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,sK16(powerset(X2))),X2)
| ( relation_image(X0,X1) = sK16(powerset(X2)) )
| ( apply(X0,sK12(X0,X1,sK16(powerset(X2)))) = sK11(X0,X1,sK16(powerset(X2))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_430730]) ).
tcf(c_431331,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,X1,sK16(powerset(X2))),X1)
| in(sK11(X0,X1,sK16(powerset(X2))),X2)
| ( relation_image(X0,X1) = sK16(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_430730]) ).
tcf(c_431332,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK11(X0,X1,sK16(powerset(X2))),X2)
| in(sK12(X0,X1,sK16(powerset(X2))),relation_dom(X0))
| ( relation_image(X0,X1) = sK16(powerset(X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_106,c_430730]) ).
tcf(c_431333,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK11(X0,sK16(powerset(X1)),X2),X2)
| in(sK12(X0,sK16(powerset(X1)),X2),X1)
| ( relation_image(X0,sK16(powerset(X1))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369308,c_430730]) ).
tcf(c_431334,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,sK16(powerset(X1)),X2),X1)
| in(sK11(X0,sK16(powerset(X1)),X2),X2)
| ( relation_image(X0,sK16(powerset(X1))) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_107,c_430730]) ).
tcf(c_431335,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK13(X1,sK16(powerset(X2)),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,sK16(powerset(X2)))) ),
inference(superposition,[status(thm)],[c_111,c_430730]) ).
tcf(c_431337,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(sK16(powerset(X0)),X1),X2)
| in(sK10(set_intersection2(sK16(powerset(X0)),X1),X2),X0) ),
inference(superposition,[status(thm)],[c_368986,c_430730]) ).
tcf(c_431338,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X0,sK16(powerset(X1))),X2)
| in(sK10(set_intersection2(X0,sK16(powerset(X1))),X2),X1) ),
inference(superposition,[status(thm)],[c_368985,c_430730]) ).
tcf(c_431339,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK16(powerset(X1)),X0))
| in(sK16(set_intersection2(X0,sK16(powerset(X1)))),X1) ),
inference(superposition,[status(thm)],[c_389060,c_430730]) ).
tcf(c_431340,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,sK16(powerset(X1))))
| in(sK16(set_intersection2(X0,sK16(powerset(X1)))),X1) ),
inference(superposition,[status(thm)],[c_370750,c_430730]) ).
tcf(c_431341,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,sK16(powerset(X0))))
| in(sK16(set_intersection2(sK16(powerset(X0)),X1)),X0) ),
inference(superposition,[status(thm)],[c_388043,c_430730]) ).
tcf(c_431342,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(sK16(powerset(X0)),X1))
| in(sK16(set_intersection2(sK16(powerset(X0)),X1)),X0) ),
inference(superposition,[status(thm)],[c_370751,c_430730]) ).
tcf(c_431343,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK10(X0,X2),X1)
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369021,c_430730]) ).
tcf(c_431344,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK16(X0),X1)
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_370747,c_430730]) ).
tcf(c_431345,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X0,sK16(powerset(X1))),X2)
| in(apply(X0,sK10(relation_inverse_image(X0,sK16(powerset(X1))),X2)),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368987,c_430730]) ).
tcf(c_431346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(sK16(powerset(X2)),X3,X0),X1)
| in(sK2(sK16(powerset(X2)),X3,X0),X2)
| ( set_intersection2(sK16(powerset(X2)),X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369929,c_430730]) ).
tcf(c_431347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X2)),X3,X0),X2)
| in(sK2(sK16(powerset(X2)),X3,X0),X1)
| ( set_intersection2(sK16(powerset(X2)),X3) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369015,c_430730]) ).
tcf(c_431348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X2)
| in(sK2(X2,X3,X0),X1)
| ( set_intersection2(X2,X3) = X0 )
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369015,c_430730]) ).
tcf(c_431349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X3)
| in(sK2(X2,X3,X0),X1)
| ( set_intersection2(X2,X3) = X0 )
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369014,c_430730]) ).
tcf(c_431350,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X1)),X2,X0),X1)
| ( set_intersection2(sK16(powerset(X1)),X2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368868,c_430730]) ).
tcf(c_431352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X0)),X1,set_intersection2(X2,X3)),X2)
| in(sK2(sK16(powerset(X0)),X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(sK16(powerset(X0)),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368484,c_430730]) ).
tcf(c_431353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,sK16(powerset(X1)))),X2)
| in(sK2(X2,X3,set_intersection2(X0,sK16(powerset(X1)))),X1)
| ( set_intersection2(X0,sK16(powerset(X1))) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368506,c_430730]) ).
tcf(c_431354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,sK16(powerset(X1)))),X3)
| in(sK2(X2,X3,set_intersection2(X0,sK16(powerset(X1)))),X1)
| ( set_intersection2(X0,sK16(powerset(X1))) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368505,c_430730]) ).
tcf(c_431355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(sK16(powerset(X0)),X1)),X2)
| in(sK2(X2,X3,set_intersection2(sK16(powerset(X0)),X1)),X0)
| ( set_intersection2(sK16(powerset(X0)),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368484,c_430730]) ).
tcf(c_431356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(sK16(powerset(X0)),X1)),X3)
| in(sK2(X2,X3,set_intersection2(sK16(powerset(X0)),X1)),X0)
| ( set_intersection2(sK16(powerset(X0)),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368483,c_430730]) ).
tcf(c_431357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X0,sK16(powerset(X1)))),X2)
| in(apply(X0,sK2(X2,X3,relation_inverse_image(X0,sK16(powerset(X1))))),X1)
| ( relation_inverse_image(X0,sK16(powerset(X1))) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_430730]) ).
tcf(c_431358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_inverse_image(X0,sK16(powerset(X1)))),X3)
| in(apply(X0,sK2(X2,X3,relation_inverse_image(X0,sK16(powerset(X1))))),X1)
| ( relation_inverse_image(X0,sK16(powerset(X1))) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_430730]) ).
tcf(c_431359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X1)),X2,relation_inverse_image(X0,X3)),X1)
| in(apply(X0,sK2(sK16(powerset(X1)),X2,relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(sK16(powerset(X1)),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368816,c_430730]) ).
tcf(c_431360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X1)),X2,relation_inverse_image(X0,X3)),X1)
| in(sK2(sK16(powerset(X1)),X2,relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(sK16(powerset(X1)),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368760,c_430730]) ).
tcf(c_431361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,X2,sK16(powerset(X3))),X1)
| in(sK2(X0,X2,sK16(powerset(X3))),X3)
| ( set_intersection2(X0,X2) = sK16(powerset(X3)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369926,c_430730]) ).
tcf(c_431362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X2,sK16(powerset(X3))),X3)
| in(sK2(X0,X2,sK16(powerset(X3))),X1)
| ( set_intersection2(X0,X2) = sK16(powerset(X3)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369012,c_430730]) ).
tcf(c_431363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X2,X3),X3)
| in(sK2(X0,X2,X3),X1)
| ( set_intersection2(X0,X2) = X3 )
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369012,c_430730]) ).
tcf(c_431364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,sK16(powerset(X3))),X0)
| in(sK2(set_intersection2(X0,X1),X2,sK16(powerset(X3))),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK16(powerset(X3)) ) ),
inference(superposition,[status(thm)],[c_370266,c_430730]) ).
tcf(c_431365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK16(powerset(X3))),X3)
| in(sK2(set_intersection2(X0,X1),X2,sK16(powerset(X3))),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK16(powerset(X3)) ) ),
inference(superposition,[status(thm)],[c_368503,c_430730]) ).
tcf(c_431366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK16(powerset(X3))),X3)
| in(sK2(set_intersection2(X0,X1),X2,sK16(powerset(X3))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK16(powerset(X3)) ) ),
inference(superposition,[status(thm)],[c_368481,c_430730]) ).
tcf(c_431367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,sK16(powerset(X1))),X2,X3),X3)
| in(sK2(set_intersection2(X0,sK16(powerset(X1))),X2,X3),X1)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X1))),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_368503,c_430730]) ).
tcf(c_431368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X3)
| in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(sK16(powerset(X0)),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370275,c_430730]) ).
tcf(c_431369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,sK16(powerset(X0))),X2,X3),X3)
| in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(sK16(powerset(X0)),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370261,c_430730]) ).
tcf(c_431370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X3)
| in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(sK16(powerset(X0)),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_368481,c_430730]) ).
tcf(c_431371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,sK16(powerset(X3))),X3)
| in(apply(X0,sK2(relation_inverse_image(X0,X1),X2,sK16(powerset(X3)))),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = sK16(powerset(X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_430730]) ).
tcf(c_431372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,sK16(powerset(X3))),X3)
| in(sK2(relation_inverse_image(X0,X1),X2,sK16(powerset(X3))),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = sK16(powerset(X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368757,c_430730]) ).
tcf(c_431373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,sK16(powerset(X1))),X2,X3),X3)
| in(apply(X0,sK2(relation_inverse_image(X0,sK16(powerset(X1))),X2,X3)),X1)
| ( set_intersection2(relation_inverse_image(X0,sK16(powerset(X1))),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368813,c_430730]) ).
tcf(c_431375,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,sK16(powerset(X0))),X0)
| ( sK16(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_372470,c_430730]) ).
tcf(c_431376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,sK16(powerset(X3)),X0),X1)
| in(sK2(X2,sK16(powerset(X3)),X0),X3)
| ( set_intersection2(X2,sK16(powerset(X3))) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369928,c_430730]) ).
tcf(c_431377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,sK16(powerset(X3)),X0),X3)
| in(sK2(X2,sK16(powerset(X3)),X0),X1)
| ( set_intersection2(X2,sK16(powerset(X3))) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369014,c_430730]) ).
tcf(c_431378,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK16(powerset(X2)),X0),X2)
| ( set_intersection2(X1,sK16(powerset(X2))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368867,c_430730]) ).
tcf(c_431379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,sK16(powerset(X1)),set_intersection2(X2,X3)),X3)
| in(sK2(X0,sK16(powerset(X1)),set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,sK16(powerset(X1))) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368505,c_430730]) ).
tcf(c_431380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,sK16(powerset(X1)),set_intersection2(X2,X3)),X2)
| in(sK2(X0,sK16(powerset(X1)),set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,sK16(powerset(X1))) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368483,c_430730]) ).
tcf(c_431381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,sK16(powerset(X2)),relation_inverse_image(X0,X3)),X2)
| in(apply(X0,sK2(X1,sK16(powerset(X2)),relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(X1,sK16(powerset(X2))) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368815,c_430730]) ).
tcf(c_431382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,sK16(powerset(X2)),relation_inverse_image(X0,X3)),X2)
| in(sK2(X1,sK16(powerset(X2)),relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(X1,sK16(powerset(X2))) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368759,c_430730]) ).
tcf(c_431383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X2,X0,sK16(powerset(X3))),X1)
| in(sK2(X2,X0,sK16(powerset(X3))),X3)
| ( set_intersection2(X2,X0) = sK16(powerset(X3)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369927,c_430730]) ).
tcf(c_431384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X0,sK16(powerset(X3))),X3)
| in(sK2(X2,X0,sK16(powerset(X3))),X1)
| ( set_intersection2(X2,X0) = sK16(powerset(X3)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369013,c_430730]) ).
tcf(c_431385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X0,X3),X3)
| in(sK2(X2,X0,X3),X1)
| ( set_intersection2(X2,X0) = X3 )
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369013,c_430730]) ).
tcf(c_431386,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X0,sK16(powerset(X2))),X2)
| ( set_intersection2(X1,X0) = sK16(powerset(X2)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_368866,c_430730]) ).
tcf(c_431387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X3)
| in(sK2(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X2)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK16(powerset(X3)) ) ),
inference(superposition,[status(thm)],[c_368504,c_430730]) ).
tcf(c_431388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X3)
| in(sK2(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK16(powerset(X3)) ) ),
inference(superposition,[status(thm)],[c_368482,c_430730]) ).
tcf(c_431389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,sK16(powerset(X2))),X3),X3)
| in(sK2(X0,set_intersection2(X1,sK16(powerset(X2))),X3),X2)
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X2)))) = X3 ) ),
inference(superposition,[status(thm)],[c_368504,c_430730]) ).
tcf(c_431390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(sK16(powerset(X1)),X2),X3),X3)
| in(sK2(X0,set_intersection2(sK16(powerset(X1)),X2),X3),X1)
| ( set_intersection2(X0,set_intersection2(sK16(powerset(X1)),X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_368482,c_430730]) ).
tcf(c_431391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,relation_inverse_image(X0,sK16(powerset(X2))),X3),X3)
| in(apply(X0,sK2(X1,relation_inverse_image(X0,sK16(powerset(X2))),X3)),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,sK16(powerset(X2)))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_430730]) ).
tcf(c_431392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),sK16(powerset(X3))),X3)
| in(apply(X0,sK2(X1,relation_inverse_image(X0,X2),sK16(powerset(X3)))),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = sK16(powerset(X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368814,c_430730]) ).
tcf(c_431393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,relation_inverse_image(X0,X2),sK16(powerset(X3))),X3)
| in(sK2(X1,relation_inverse_image(X0,X2),sK16(powerset(X3))),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = sK16(powerset(X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368758,c_430730]) ).
tcf(c_431394,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK16(powerset(X1)),sK16(powerset(X1))),X1)
| ( set_intersection2(X0,sK16(powerset(X1))) = sK16(powerset(X1)) ) ),
inference(superposition,[status(thm)],[c_368460,c_430730]) ).
tcf(c_431395,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,empty_set,sK16(powerset(X0))),X0)
| ( sK16(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_372467,c_430730]) ).
tcf(c_431396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X1,X2,X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,sK16(powerset(X3)))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_369594,c_430730]) ).
tcf(c_431397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X0,X3,X2),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_image(X0,X3))
| ~ subset(relation_dom(X0),sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369556,c_430730]) ).
tcf(c_431398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X1,set_intersection2(X2,sK16(powerset(X3))),X0),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,sK16(powerset(X3))))) ),
inference(superposition,[status(thm)],[c_369597,c_430730]) ).
tcf(c_431399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X1,set_intersection2(sK16(powerset(X2)),X3),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(sK16(powerset(X2)),X3))) ),
inference(superposition,[status(thm)],[c_369598,c_430730]) ).
tcf(c_431400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK13(X1,relation_inverse_image(X2,sK16(powerset(X3))),X0)),X3)
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_inverse_image(X2,sK16(powerset(X3))))) ),
inference(superposition,[status(thm)],[c_369599,c_430730]) ).
tcf(c_431401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_image(X0,X1),X2,sK16(powerset(X3))),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = sK16(powerset(X3)) )
| ( apply(X0,sK13(X0,X1,sK2(relation_image(X0,X1),X2,sK16(powerset(X3))))) = sK2(relation_image(X0,X1),X2,sK16(powerset(X3))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369659,c_430730]) ).
tcf(c_431402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,relation_image(X0,X1),sK16(powerset(X3))),X3)
| ( set_intersection2(X2,relation_image(X0,X1)) = sK16(powerset(X3)) )
| ( apply(X0,sK13(X0,X1,sK2(X2,relation_image(X0,X1),sK16(powerset(X3))))) = sK2(X2,relation_image(X0,X1),sK16(powerset(X3))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369660,c_430730]) ).
tcf(c_431403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,sK16(powerset(X3)),relation_image(X0,X1)),X3)
| ( set_intersection2(X2,sK16(powerset(X3))) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,sK16(powerset(X3)),relation_image(X0,X1)))) = sK2(X2,sK16(powerset(X3)),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369661,c_430730]) ).
tcf(c_431404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X2)),X3,relation_image(X0,X1)),X2)
| ( set_intersection2(sK16(powerset(X2)),X3) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(sK16(powerset(X2)),X3,relation_image(X0,X1)))) = sK2(sK16(powerset(X2)),X3,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369662,c_430730]) ).
tcf(c_431405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X2,X0,sK16(powerset(X3))),X1)
| in(sK11(X2,X0,sK16(powerset(X3))),X3)
| ( relation_image(X2,X0) = sK16(powerset(X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369940,c_430730]) ).
tcf(c_431406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X2,X0,sK16(powerset(X3))),X1)
| in(sK11(X2,X0,sK16(powerset(X3))),X3)
| ( relation_image(X2,X0) = sK16(powerset(X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369299,c_430730]) ).
tcf(c_431407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X2,X0,X3),X1)
| in(sK11(X2,X0,X3),X3)
| ( relation_image(X2,X0) = X3 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369299,c_430730]) ).
tcf(c_431408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X1)
| in(sK11(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X3)
| ( relation_image(X0,set_intersection2(X1,X2)) = sK16(powerset(X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_430730]) ).
tcf(c_431409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X2)
| in(sK11(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X3)
| ( relation_image(X0,set_intersection2(X1,X2)) = sK16(powerset(X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_430730]) ).
tcf(c_431410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X1,sK16(powerset(X2))),X3),X2)
| in(sK11(X0,set_intersection2(X1,sK16(powerset(X2))),X3),X3)
| ( relation_image(X0,set_intersection2(X1,sK16(powerset(X2)))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369302,c_430730]) ).
tcf(c_431411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(sK16(powerset(X1)),X2),X3),X1)
| in(sK11(X0,set_intersection2(sK16(powerset(X1)),X2),X3),X3)
| ( relation_image(X0,set_intersection2(sK16(powerset(X1)),X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369303,c_430730]) ).
tcf(c_431412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),sK16(powerset(X3))),X3)
| in(sK12(X0,relation_inverse_image(X1,X2),sK16(powerset(X3))),relation_dom(X1))
| ( relation_image(X0,relation_inverse_image(X1,X2)) = sK16(powerset(X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369305,c_430730]) ).
tcf(c_431413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,relation_inverse_image(X1,X2),sK16(powerset(X3))),X3)
| in(apply(X1,sK12(X0,relation_inverse_image(X1,X2),sK16(powerset(X3)))),X2)
| ( relation_image(X0,relation_inverse_image(X1,X2)) = sK16(powerset(X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_430730]) ).
tcf(c_431414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,relation_inverse_image(X1,sK16(powerset(X2))),X3),X3)
| in(apply(X1,sK12(X0,relation_inverse_image(X1,sK16(powerset(X2))),X3)),X2)
| ( relation_image(X0,relation_inverse_image(X1,sK16(powerset(X2)))) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369304,c_430730]) ).
tcf(c_431415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,relation_image(X1,X2),sK16(powerset(X3))),X3)
| ( relation_image(X0,relation_image(X1,X2)) = sK16(powerset(X3)) )
| ( apply(X1,sK13(X1,X2,sK12(X0,relation_image(X1,X2),sK16(powerset(X3))))) = sK12(X0,relation_image(X1,X2),sK16(powerset(X3))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369670,c_430730]) ).
tcf(c_431416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X2,X3,X0),X1)
| ( relation_image(X2,X3) = X0 )
| ( apply(X2,sK12(X2,X3,X0)) = sK11(X2,X3,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369436,c_430730]) ).
tcf(c_431417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X2,X3,X0),X3)
| in(sK11(X2,X3,X0),X1)
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369307,c_430730]) ).
tcf(c_431418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X2,X3,X0),X1)
| in(sK12(X2,X3,X0),relation_dom(X2))
| ( relation_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369206,c_430730]) ).
tcf(c_431419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK11(X2,sK16(powerset(X3)),X0),X1)
| in(sK12(X2,sK16(powerset(X3)),X0),X3)
| ( relation_image(X2,sK16(powerset(X3))) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369937,c_430730]) ).
tcf(c_431420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X2,sK16(powerset(X3)),X0),X3)
| in(sK11(X2,sK16(powerset(X3)),X0),X1)
| ( relation_image(X2,sK16(powerset(X3))) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369307,c_430730]) ).
tcf(c_431421,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK12(X0,sK16(powerset(X2)),X1),X2)
| ( relation_image(X0,sK16(powerset(X2))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369309,c_430730]) ).
tcf(c_431422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,sK16(powerset(X1)),set_intersection2(X2,X3)),X1)
| in(sK11(X0,sK16(powerset(X1)),set_intersection2(X2,X3)),X2)
| ( relation_image(X0,sK16(powerset(X1))) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_430730]) ).
tcf(c_431423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,sK16(powerset(X1)),set_intersection2(X2,X3)),X1)
| in(sK11(X0,sK16(powerset(X1)),set_intersection2(X2,X3)),X3)
| ( relation_image(X0,sK16(powerset(X1))) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_430730]) ).
tcf(c_431424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,sK16(powerset(X3)))),X3)
| ( set_intersection2(X2,sK16(powerset(X3))) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,sK16(powerset(X3))))) = sK11(X0,X1,set_intersection2(X2,sK16(powerset(X3)))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369439,c_430730]) ).
tcf(c_431425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,set_intersection2(X1,sK16(powerset(X2)))),X3)
| in(sK11(X0,X3,set_intersection2(X1,sK16(powerset(X2)))),X2)
| ( set_intersection2(X1,sK16(powerset(X2))) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369310,c_430730]) ).
tcf(c_431426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X3,set_intersection2(X1,sK16(powerset(X2)))),X2)
| in(sK12(X0,X3,set_intersection2(X1,sK16(powerset(X2)))),relation_dom(X0))
| ( set_intersection2(X1,sK16(powerset(X2))) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369209,c_430730]) ).
tcf(c_431427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(sK16(powerset(X2)),X3)),X2)
| ( set_intersection2(sK16(powerset(X2)),X3) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(sK16(powerset(X2)),X3))) = sK11(X0,X1,set_intersection2(sK16(powerset(X2)),X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369440,c_430730]) ).
tcf(c_431428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,set_intersection2(sK16(powerset(X1)),X2)),X3)
| in(sK11(X0,X3,set_intersection2(sK16(powerset(X1)),X2)),X1)
| ( set_intersection2(sK16(powerset(X1)),X2) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369311,c_430730]) ).
tcf(c_431429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X3,set_intersection2(sK16(powerset(X1)),X2)),X1)
| in(sK12(X0,X3,set_intersection2(sK16(powerset(X1)),X2)),relation_dom(X0))
| ( set_intersection2(sK16(powerset(X1)),X2) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369210,c_430730]) ).
tcf(c_431430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_inverse_image(X1,sK16(powerset(X2)))),X3)
| in(apply(X1,sK11(X0,X3,relation_inverse_image(X1,sK16(powerset(X2))))),X2)
| ( relation_inverse_image(X1,sK16(powerset(X2))) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_430730]) ).
tcf(c_431431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,relation_inverse_image(X1,sK16(powerset(X2)))),relation_dom(X0))
| in(apply(X1,sK11(X0,X3,relation_inverse_image(X1,sK16(powerset(X2))))),X2)
| ( relation_inverse_image(X1,sK16(powerset(X2))) = relation_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369211,c_430730]) ).
tcf(c_431432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,sK16(powerset(X2)),relation_inverse_image(X1,X3)),X2)
| in(sK11(X0,sK16(powerset(X2)),relation_inverse_image(X1,X3)),relation_dom(X1))
| ( relation_image(X0,sK16(powerset(X2))) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369313,c_430730]) ).
tcf(c_431433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,sK16(powerset(X2)),relation_inverse_image(X1,X3)),X2)
| in(apply(X1,sK11(X0,sK16(powerset(X2)),relation_inverse_image(X1,X3))),X3)
| ( relation_image(X0,sK16(powerset(X2))) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369312,c_430730]) ).
tcf(c_431434,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,sK16(powerset(X3)),relation_image(X1,X2)),X3)
| ( relation_image(X0,sK16(powerset(X3))) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK11(X0,sK16(powerset(X3)),relation_image(X1,X2)))) = sK11(X0,sK16(powerset(X3)),relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369668,c_430730]) ).
tcf(c_431435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X3,X0),X1)
| in(sK7(X2,X3,X0),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369020,c_430730]) ).
tcf(c_431436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X3,X0),X1)
| in(apply(X2,sK7(X2,X3,X0)),X3)
| ( relation_inverse_image(X2,X3) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369019,c_430730]) ).
tcf(c_431437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X1,sK16(powerset(X2)))),X2)
| in(apply(X0,sK7(X0,X3,set_intersection2(X1,sK16(powerset(X2))))),X3)
| ( set_intersection2(X1,sK16(powerset(X2))) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_430730]) ).
tcf(c_431438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X1,sK16(powerset(X2)))),X2)
| in(sK7(X0,X3,set_intersection2(X1,sK16(powerset(X2)))),relation_dom(X0))
| ( set_intersection2(X1,sK16(powerset(X2))) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368672,c_430730]) ).
tcf(c_431439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(sK16(powerset(X1)),X2)),X1)
| in(apply(X0,sK7(X0,X3,set_intersection2(sK16(powerset(X1)),X2))),X3)
| ( set_intersection2(sK16(powerset(X1)),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_430730]) ).
tcf(c_431440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(sK16(powerset(X1)),X2)),X1)
| in(sK7(X0,X3,set_intersection2(sK16(powerset(X1)),X2)),relation_dom(X0))
| ( set_intersection2(sK16(powerset(X1)),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368673,c_430730]) ).
tcf(c_431441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,relation_inverse_image(X1,sK16(powerset(X2)))),relation_dom(X0))
| in(apply(X1,sK7(X0,X3,relation_inverse_image(X1,sK16(powerset(X2))))),X2)
| ( relation_inverse_image(X1,sK16(powerset(X2))) = relation_inverse_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368819,c_430730]) ).
tcf(c_431442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X0,X3,relation_inverse_image(X1,sK16(powerset(X2))))),X2)
| in(apply(X0,sK7(X0,X3,relation_inverse_image(X1,sK16(powerset(X2))))),X3)
| ( relation_inverse_image(X1,sK16(powerset(X2))) = relation_inverse_image(X0,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_430730]) ).
tcf(c_431443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X0,X2,sK16(powerset(X3))),X1)
| in(sK7(X0,X2,sK16(powerset(X3))),X3)
| ( relation_inverse_image(X0,X2) = sK16(powerset(X3)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369931,c_430730]) ).
tcf(c_431444,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,sK16(powerset(X3))),X3)
| in(sK7(X0,X2,sK16(powerset(X3))),X1)
| ( relation_inverse_image(X0,X2) = sK16(powerset(X3)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369017,c_430730]) ).
tcf(c_431445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X2,X3),X3)
| in(sK7(X0,X2,X3),X1)
| ( relation_inverse_image(X0,X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369017,c_430730]) ).
tcf(c_431446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK12(X0,X2,sK16(powerset(X3))),X1)
| in(sK11(X0,X2,sK16(powerset(X3))),X3)
| ( relation_image(X0,X2) = sK16(powerset(X3)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369939,c_430730]) ).
tcf(c_431447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X2,sK16(powerset(X3))),X1)
| in(sK11(X0,X2,sK16(powerset(X3))),X3)
| ( relation_image(X0,X2) = sK16(powerset(X3)) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_369214,c_430730]) ).
tcf(c_431448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X2,X3),X1)
| in(sK11(X0,X2,X3),X3)
| ( relation_image(X0,X2) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369214,c_430730]) ).
tcf(c_431449,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK7(X2,sK16(powerset(X3)),X0),X1)
| in(apply(X2,sK7(X2,sK16(powerset(X3)),X0)),X3)
| ( relation_inverse_image(X2,sK16(powerset(X3))) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369933,c_430730]) ).
tcf(c_431450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,sK16(powerset(X3)),X0),X1)
| in(apply(X2,sK7(X2,sK16(powerset(X3)),X0)),X3)
| ( relation_inverse_image(X2,sK16(powerset(X3))) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369019,c_430730]) ).
tcf(c_431451,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK7(X0,sK16(powerset(X2)),X1)),X2)
| ( relation_inverse_image(X0,sK16(powerset(X2))) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368872,c_430730]) ).
tcf(c_431452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,sK16(powerset(X1)),set_intersection2(X2,X3)),X2)
| in(apply(X0,sK7(X0,sK16(powerset(X1)),set_intersection2(X2,X3))),X1)
| ( relation_inverse_image(X0,sK16(powerset(X1))) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368701,c_430730]) ).
tcf(c_431453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,sK16(powerset(X1)),set_intersection2(X2,X3)),X3)
| in(apply(X0,sK7(X0,sK16(powerset(X1)),set_intersection2(X2,X3))),X1)
| ( relation_inverse_image(X0,sK16(powerset(X1))) = set_intersection2(X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368700,c_430730]) ).
tcf(c_431454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK7(X0,sK16(powerset(X2)),relation_inverse_image(X1,X3))),X3)
| in(apply(X0,sK7(X0,sK16(powerset(X2)),relation_inverse_image(X1,X3))),X2)
| ( relation_inverse_image(X0,sK16(powerset(X2))) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368818,c_430730]) ).
tcf(c_431455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,sK16(powerset(X2)),relation_inverse_image(X1,X3)),relation_dom(X1))
| in(apply(X0,sK7(X0,sK16(powerset(X2)),relation_inverse_image(X1,X3))),X2)
| ( relation_inverse_image(X0,sK16(powerset(X2))) = relation_inverse_image(X1,X3) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368762,c_430730]) ).
tcf(c_431456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,sK16(powerset(X3)),relation_image(X1,X2))),X3)
| ( relation_inverse_image(X0,sK16(powerset(X3))) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK7(X0,sK16(powerset(X3)),relation_image(X1,X2)))) = sK7(X0,sK16(powerset(X3)),relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369664,c_430730]) ).
tcf(c_431457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X0,X3),X3)
| in(apply(X2,sK7(X2,X0,X3)),X1)
| ( relation_inverse_image(X2,X0) = X3 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_369018,c_430730]) ).
tcf(c_431458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X0,sK16(powerset(X3))),X3)
| element(apply(X2,sK7(X2,X0,sK16(powerset(X3)))),X1)
| ( relation_inverse_image(X2,X0) = sK16(powerset(X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369932,c_430730]) ).
tcf(c_431459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X2,X0,sK16(powerset(X3))),X3)
| in(apply(X2,sK7(X2,X0,sK16(powerset(X3)))),X1)
| ( relation_inverse_image(X2,X0) = sK16(powerset(X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_369018,c_430730]) ).
tcf(c_431460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),sK16(powerset(X3)))),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = sK16(powerset(X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_430730]) ).
tcf(c_431461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),sK16(powerset(X3)))),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = sK16(powerset(X3)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_430730]) ).
tcf(c_431462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,sK16(powerset(X2))),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,sK16(powerset(X2))),X3)),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,sK16(powerset(X2)))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368702,c_430730]) ).
tcf(c_431463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(sK16(powerset(X1)),X2),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(sK16(powerset(X1)),X2),X3)),X1)
| ( relation_inverse_image(X0,set_intersection2(sK16(powerset(X1)),X2)) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368703,c_430730]) ).
tcf(c_431464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),sK16(powerset(X3))),X3)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,X2),sK16(powerset(X3))))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = sK16(powerset(X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_430730]) ).
tcf(c_431465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_inverse_image(X1,X2),sK16(powerset(X3))),X3)
| in(apply(X0,sK7(X0,relation_inverse_image(X1,X2),sK16(powerset(X3)))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = sK16(powerset(X3)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368761,c_430730]) ).
tcf(c_431466,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_inverse_image(X1,sK16(powerset(X2))),X3),X3)
| in(apply(X1,apply(X0,sK7(X0,relation_inverse_image(X1,sK16(powerset(X2))),X3))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,sK16(powerset(X2)))) = X3 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368817,c_430730]) ).
tcf(c_431467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,relation_image(X1,X2),sK16(powerset(X3))),X3)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = sK16(powerset(X3)) )
| ( apply(X1,sK13(X1,X2,apply(X0,sK7(X0,relation_image(X1,X2),sK16(powerset(X3)))))) = apply(X0,sK7(X0,relation_image(X1,X2),sK16(powerset(X3)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369663,c_430730]) ).
tcf(c_431468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK11(X0,X2,relation_inverse_image(X1,sK16(powerset(X3))))),X3)
| ( relation_inverse_image(X1,sK16(powerset(X3))) = relation_image(X0,X2) )
| ( apply(X0,sK12(X0,X2,relation_inverse_image(X1,sK16(powerset(X3))))) = sK11(X0,X2,relation_inverse_image(X1,sK16(powerset(X3)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_369441,c_430730]) ).
tcf(c_431469,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X2,X0),X1)
| ( set_intersection2(X0,X2) = X0 )
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_370077,c_430730]) ).
tcf(c_431470,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,sK16(powerset(X1))),X2,set_intersection2(X0,sK16(powerset(X1)))),X1)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X1))),X2) = set_intersection2(X0,sK16(powerset(X1))) ) ),
inference(superposition,[status(thm)],[c_370080,c_430730]) ).
tcf(c_431471,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,set_intersection2(sK16(powerset(X0)),X1)),X0)
| ( set_intersection2(set_intersection2(sK16(powerset(X0)),X1),X2) = set_intersection2(sK16(powerset(X0)),X1) ) ),
inference(superposition,[status(thm)],[c_370081,c_430730]) ).
tcf(c_431472,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,sK16(powerset(X1))),X2,relation_inverse_image(X0,sK16(powerset(X1))))),X1)
| ( set_intersection2(relation_inverse_image(X0,sK16(powerset(X1))),X2) = relation_inverse_image(X0,sK16(powerset(X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370082,c_430730]) ).
tcf(c_431473,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,X0,X0),X1)
| ( set_intersection2(X2,X0) = X0 )
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_370145,c_430730]) ).
tcf(c_431474,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,sK16(powerset(X2))),set_intersection2(X1,sK16(powerset(X2)))),X2)
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X2)))) = set_intersection2(X1,sK16(powerset(X2))) ) ),
inference(superposition,[status(thm)],[c_370148,c_430730]) ).
tcf(c_431475,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(sK16(powerset(X1)),X2),set_intersection2(sK16(powerset(X1)),X2)),X1)
| ( set_intersection2(X0,set_intersection2(sK16(powerset(X1)),X2)) = set_intersection2(sK16(powerset(X1)),X2) ) ),
inference(superposition,[status(thm)],[c_370149,c_430730]) ).
tcf(c_431476,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK2(X1,relation_inverse_image(X0,sK16(powerset(X2))),relation_inverse_image(X0,sK16(powerset(X2))))),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,sK16(powerset(X2)))) = relation_inverse_image(X0,sK16(powerset(X2))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370150,c_430730]) ).
tcf(c_431477,plain,
! [X0: $i] :
( in(sK16(sK15(sK5)),X0)
| ~ subset(sK5,sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_420696,c_430730]) ).
tcf(c_431478,plain,
! [X0: $i] :
( in(sK16(sK15(sK8)),X0)
| ~ subset(sK8,sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_423415,c_430730]) ).
tcf(c_431479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK16(powerset(X1)),X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(sK16(powerset(X1)),X2),X3) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370276,c_430730]) ).
tcf(c_431480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,X0),X2)
| in(sK2(set_intersection2(X2,X3),X4,X0),X1)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_370274,c_430730]) ).
tcf(c_431481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(sK16(powerset(X2)),X3),X4,X0),X2)
| in(sK2(set_intersection2(sK16(powerset(X2)),X3),X4,X0),X1)
| ( set_intersection2(set_intersection2(sK16(powerset(X2)),X3),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370274,c_430730]) ).
tcf(c_431482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,sK16(powerset(X0))),X2,X3),X0)
| in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(sK16(powerset(X0)),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370266,c_430730]) ).
tcf(c_431483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,sK16(powerset(X3))),X3)
| in(sK2(set_intersection2(X0,X1),X2,sK16(powerset(X3))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK16(powerset(X3)) ) ),
inference(superposition,[status(thm)],[c_370261,c_430730]) ).
tcf(c_431484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,set_intersection2(X3,X4)),X4)
| in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(sK16(powerset(X0)),X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370277,c_430730]) ).
tcf(c_431485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,sK16(powerset(X4)))),X4)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,sK16(powerset(X4)))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,sK16(powerset(X4))) ) ),
inference(superposition,[status(thm)],[c_370277,c_430730]) ).
tcf(c_432903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK2(set_intersection2(X0,X0),X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(set_intersection2(X0,X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_53,c_370278]) ).
tcf(c_432906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X1,set_intersection2(X2,X3)),X2)
| in(sK2(set_intersection2(X0,empty_set),X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_64,c_370278]) ).
tcf(c_432907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X1,set_intersection2(X2,X3)),X2)
| in(sK2(set_intersection2(empty_set,X0),X1,set_intersection2(X2,X3)),empty_set)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368545,c_370278]) ).
tcf(c_432908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X0)),X1,set_intersection2(X2,X3)),X2)
| in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,set_intersection2(X2,X3)),X0)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397130,c_370278]) ).
tcf(c_432909,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X0,set_intersection2(X1,X2)),X1)
| in(sK2(set_intersection2(sK5,sK15(sK5)),X0,set_intersection2(X1,X2)),sK5)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411955,c_370278]) ).
tcf(c_432910,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X0,set_intersection2(X1,X2)),X1)
| in(sK2(set_intersection2(sK8,sK15(sK8)),X0,set_intersection2(X1,X2)),sK8)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411956,c_370278]) ).
tcf(c_432912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X4,X3)),X3)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_63,c_370278]) ).
tcf(c_432916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK16(powerset(X3))),X3)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,sK16(powerset(X3)))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,sK16(powerset(X3))) ) ),
inference(superposition,[status(thm)],[c_397130,c_370278]) ).
tcf(c_432917,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),sK5)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(sK5,sK15(sK5))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(sK5,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_411955,c_370278]) ).
tcf(c_432918,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),sK8)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(sK8,sK15(sK8))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(sK8,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_411956,c_370278]) ).
tcf(c_432919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X0)
| in(sK2(set_intersection2(X0,X0),X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(set_intersection2(X0,X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_53,c_370278]) ).
tcf(c_432922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X1,set_intersection2(X2,X3)),X0)
| in(sK2(set_intersection2(X0,empty_set),X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_64,c_370278]) ).
tcf(c_432923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X1,set_intersection2(X2,X3)),empty_set)
| in(sK2(set_intersection2(empty_set,X0),X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368545,c_370278]) ).
tcf(c_432924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X0)),X1,set_intersection2(X2,X3)),X0)
| in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397130,c_370278]) ).
tcf(c_432925,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X0,set_intersection2(X1,X2)),sK5)
| in(sK2(set_intersection2(sK5,sK15(sK5)),X0,set_intersection2(X1,X2)),X1)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411955,c_370278]) ).
tcf(c_432926,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X0,set_intersection2(X1,X2)),sK8)
| in(sK2(set_intersection2(sK8,sK15(sK8)),X0,set_intersection2(X1,X2)),X1)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411956,c_370278]) ).
tcf(c_432928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X4,X3)),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_63,c_370278]) ).
tcf(c_432930,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,empty_set)),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,empty_set) ) ),
inference(superposition,[status(thm)],[c_64,c_370278]) ).
tcf(c_432931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(empty_set,X3)),empty_set)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(empty_set,X3) ) ),
inference(superposition,[status(thm)],[c_368545,c_370278]) ).
tcf(c_432932,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK16(powerset(X3))),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,sK16(powerset(X3)))),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,sK16(powerset(X3))) ) ),
inference(superposition,[status(thm)],[c_397130,c_370278]) ).
tcf(c_432933,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(sK5,sK15(sK5))),sK5)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(sK5,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_411955,c_370278]) ).
tcf(c_432934,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(sK8,sK15(sK8))),sK8)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(sK8,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_411956,c_370278]) ).
tcf(c_432935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(set_intersection2(X0,X1),X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(set_intersection2(X0,X1),X3) )
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(set_intersection2(X0,X1),X3)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(set_intersection2(X0,X1),X3)),set_intersection2(set_intersection2(X0,X1),X3)) ),
inference(superposition,[status(thm)],[c_370278,c_54]) ).
tcf(c_432936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X2,X3),X4,set_intersection2(X0,X5)),X1)
| in(sK2(set_intersection2(X2,X3),X4,set_intersection2(X0,X5)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = set_intersection2(X0,X5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370278,c_321]) ).
tcf(c_432937,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,set_intersection2(X0,X5)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = set_intersection2(X0,X5) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370278,c_320]) ).
tcf(c_432938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,set_intersection2(X0,X4)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = set_intersection2(X0,X4) )
| ~ in(X0,sK2(set_intersection2(X1,X2),X3,set_intersection2(X0,X4))) ),
inference(superposition,[status(thm)],[c_370278,c_97]) ).
tcf(c_432939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,set_intersection2(X0,X5)),X2)
| in(sK2(set_intersection2(X2,X3),X4,set_intersection2(X0,X5)),X1)
| ( set_intersection2(set_intersection2(X2,X3),X4) = set_intersection2(X0,X5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370278,c_96]) ).
tcf(c_432940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X3)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370278,c_93]) ).
tcf(c_432941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,set_intersection2(X0,X4)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = set_intersection2(X0,X4) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370278,c_91]) ).
tcf(c_432942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(set_intersection2(X3,X4),X5)),X4)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(set_intersection2(X3,X4),X5)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(set_intersection2(X3,X4),X5) ) ),
inference(superposition,[status(thm)],[c_370278,c_59]) ).
tcf(c_432943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(set_intersection2(X3,X4),X5)),X3)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(set_intersection2(X3,X4),X5)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(set_intersection2(X3,X4),X5) ) ),
inference(superposition,[status(thm)],[c_370278,c_58]) ).
tcf(c_432944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,set_intersection2(relation_inverse_image(X0,X1),X2)),X3)
| in(apply(X0,sK2(set_intersection2(X3,X4),X5,set_intersection2(relation_inverse_image(X0,X1),X2))),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = set_intersection2(set_intersection2(X3,X4),X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370278,c_88]) ).
tcf(c_432945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,set_intersection2(relation_inverse_image(X0,X1),X2)),X3)
| in(sK2(set_intersection2(X3,X4),X5,set_intersection2(relation_inverse_image(X0,X1),X2)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = set_intersection2(set_intersection2(X3,X4),X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370278,c_87]) ).
tcf(c_432946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(relation_dom(X3),X4)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(relation_dom(X3),X4) )
| ( apply(X3,sK13(X3,X5,apply(X3,sK2(set_intersection2(X0,X1),X2,set_intersection2(relation_dom(X3),X4))))) = apply(X3,sK2(set_intersection2(X0,X1),X2,set_intersection2(relation_dom(X3),X4))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(relation_dom(X3),X4)),X5) ),
inference(superposition,[status(thm)],[c_370278,c_369671]) ).
tcf(c_432947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X4,X5),X6,set_intersection2(relation_image(X2,X0),X3)),X4)
| ( set_intersection2(relation_image(X2,X0),X3) = set_intersection2(set_intersection2(X4,X5),X6) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370278,c_369799]) ).
tcf(c_432948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X4,X5),X6,set_intersection2(relation_image(X0,X2),X3)),X4)
| ( set_intersection2(relation_image(X0,X2),X3) = set_intersection2(set_intersection2(X4,X5),X6) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370278,c_369798]) ).
tcf(c_432949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,set_intersection2(relation_image(X0,X1),X2)),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = set_intersection2(set_intersection2(X3,X4),X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370278,c_369596]) ).
tcf(c_432950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,set_intersection2(relation_image(X0,X1),X2)),X3)
| ( set_intersection2(relation_image(X0,X1),X2) = set_intersection2(set_intersection2(X3,X4),X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370278,c_369558]) ).
tcf(c_432951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,set_intersection2(relation_image(X0,X1),X5)),X2)
| ( set_intersection2(relation_image(X0,X1),X5) = set_intersection2(set_intersection2(X2,X3),X4) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,X3),X4,set_intersection2(relation_image(X0,X1),X5)))) = sK2(set_intersection2(X2,X3),X4,set_intersection2(relation_image(X0,X1),X5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370278,c_112]) ).
tcf(c_432952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(relation_dom(X3),X4)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(relation_dom(X3),X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X5))
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(relation_dom(X3),X4)),X5) ),
inference(superposition,[status(thm)],[c_370278,c_369501]) ).
tcf(c_432953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(empty_set,X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(empty_set,X3) ) ),
inference(superposition,[status(thm)],[c_370278,c_372426]) ).
tcf(c_432955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X3,X4),X5,set_intersection2(relation_image(X0,relation_image(X1,X2)),X6)),X3)
| ( set_intersection2(relation_image(X0,relation_image(X1,X2)),X6) = set_intersection2(set_intersection2(X3,X4),X5) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,X4),X5,set_intersection2(relation_image(X0,relation_image(X1,X2)),X6))))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,X4),X5,set_intersection2(relation_image(X0,relation_image(X1,X2)),X6))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370278,c_369672]) ).
tcf(c_432956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(sK15(sK5),X3)),sK5)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(sK15(sK5),X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(sK15(sK5),X3) ) ),
inference(superposition,[status(thm)],[c_370278,c_412536]) ).
tcf(c_432957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(sK15(sK8),X3)),sK8)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(sK15(sK8),X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(sK15(sK8),X3) ) ),
inference(superposition,[status(thm)],[c_370278,c_413867]) ).
tcf(c_432959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(sK16(powerset(X3)),X4)),X3)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(sK16(powerset(X3)),X4)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(sK16(powerset(X3)),X4) ) ),
inference(superposition,[status(thm)],[c_370278,c_430730]) ).
tcf(c_432961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X4)),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(X0,X4) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X4)),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X4)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X4)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X4)),set_intersection2(X0,X4)) ),
inference(superposition,[status(thm)],[c_370278,c_370217]) ).
tcf(c_432962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X0,X2),X3,set_intersection2(X4,X5)),X1)
| in(sK2(set_intersection2(X0,X2),X3,set_intersection2(X4,X5)),X4)
| ( set_intersection2(set_intersection2(X0,X2),X3) = set_intersection2(X4,X5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370278,c_321]) ).
tcf(c_432963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X2),X3,set_intersection2(X4,X5)),X4)
| ( set_intersection2(set_intersection2(X0,X2),X3) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370278,c_320]) ).
tcf(c_432964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ in(X0,sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4))) ),
inference(superposition,[status(thm)],[c_370278,c_97]) ).
tcf(c_432965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X2),X3,set_intersection2(X4,X5)),X4)
| in(sK2(set_intersection2(X0,X2),X3,set_intersection2(X4,X5)),X1)
| ( set_intersection2(set_intersection2(X0,X2),X3) = set_intersection2(X4,X5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370278,c_96]) ).
tcf(c_432966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370278,c_93]) ).
tcf(c_432967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370278,c_91]) ).
tcf(c_432968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X5)),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X5)),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(X4,X5) ) ),
inference(superposition,[status(thm)],[c_370278,c_59]) ).
tcf(c_432969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X5)),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X4,X5)),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(X4,X5) ) ),
inference(superposition,[status(thm)],[c_370278,c_58]) ).
tcf(c_432970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,set_intersection2(X4,X5)),X4)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,set_intersection2(X4,X5))),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = set_intersection2(X4,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370278,c_88]) ).
tcf(c_432971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,set_intersection2(X4,X5)),X4)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,set_intersection2(X4,X5)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = set_intersection2(X4,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370278,c_87]) ).
tcf(c_432972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = set_intersection2(X3,X4) )
| ( apply(X0,sK13(X0,X5,apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(X3,X4))))) = apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(X3,X4))) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370278,c_369671]) ).
tcf(c_432973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_image(X2,X0),X3),X4,set_intersection2(X5,X6)),X5)
| ( set_intersection2(set_intersection2(relation_image(X2,X0),X3),X4) = set_intersection2(X5,X6) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370278,c_369799]) ).
tcf(c_432974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_image(X0,X2),X3),X4,set_intersection2(X5,X6)),X5)
| ( set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4) = set_intersection2(X5,X6) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370278,c_369798]) ).
tcf(c_432975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,set_intersection2(X4,X5)),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370278,c_369596]) ).
tcf(c_432976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,set_intersection2(X4,X5)),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = set_intersection2(X4,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370278,c_369558]) ).
tcf(c_432977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,set_intersection2(X4,X5)),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = set_intersection2(X4,X5) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),X3,set_intersection2(X4,X5)))) = sK2(set_intersection2(relation_image(X0,X1),X2),X3,set_intersection2(X4,X5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370278,c_112]) ).
tcf(c_432978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = set_intersection2(X3,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X5))
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,set_intersection2(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370278,c_369501]) ).
tcf(c_432979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X0),X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_370278,c_372426]) ).
tcf(c_432980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X2),X0),X3,set_intersection2(X1,X2)),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X1,X2),X0),X3) = set_intersection2(X1,X2) )
| ~ in(sK2(set_intersection2(set_intersection2(X1,X2),X0),X3,set_intersection2(X1,X2)),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X1,X2),X0),X3,set_intersection2(X1,X2)),X0)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X1,X2)),X3,set_intersection2(X1,X2)),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370278,c_370220]) ).
tcf(c_432981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,X4) )
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),set_intersection2(X3,X4)) ),
inference(superposition,[status(thm)],[c_370278,c_368471]) ).
tcf(c_432982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,set_intersection2(X5,X6)),X5)
| ( set_intersection2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4) = set_intersection2(X5,X6) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,set_intersection2(X5,X6))))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4,set_intersection2(X5,X6))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370278,c_369672]) ).
tcf(c_432983,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK15(sK5),X0),X1,set_intersection2(X2,X3)),sK5)
| in(sK2(set_intersection2(sK15(sK5),X0),X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(set_intersection2(sK15(sK5),X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_370278,c_412536]) ).
tcf(c_432984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK15(sK8),X0),X1,set_intersection2(X2,X3)),sK8)
| in(sK2(set_intersection2(sK15(sK8),X0),X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(set_intersection2(sK15(sK8),X0),X1) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_370278,c_413867]) ).
tcf(c_432986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,set_intersection2(X3,X4)),X3)
| in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(sK16(powerset(X0)),X1),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370278,c_430730]) ).
tcf(c_432988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X3) ) ),
inference(equality_factoring,[status(thm)],[c_370278]) ).
tcf(c_433009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(empty_set,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_432931,c_372426]) ).
tcf(c_433015,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X2,set_intersection2(X0,X1)),empty_set)
| in(sK2(empty_set,X2,set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(light_normalisation,[status(thm)],[c_432923,c_368545]) ).
tcf(c_433549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,X3)),X1)
| in(apply(X0,sK2(set_intersection2(X1,X1),X2,relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(set_intersection2(X1,X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370279]) ).
tcf(c_433552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,relation_inverse_image(X0,X3)),X1)
| in(apply(X0,sK2(set_intersection2(X1,empty_set),X2,relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(set_intersection2(X1,empty_set),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370279]) ).
tcf(c_433554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X1)),X2,relation_inverse_image(X0,X3)),X1)
| in(apply(X0,sK2(set_intersection2(X1,sK16(powerset(X1))),X2,relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(set_intersection2(X1,sK16(powerset(X1))),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370279]) ).
tcf(c_433555,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X1,relation_inverse_image(X0,X2)),sK5)
| in(apply(X0,sK2(set_intersection2(sK5,sK15(sK5)),X1,relation_inverse_image(X0,X2))),X2)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_370279]) ).
tcf(c_433556,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X1,relation_inverse_image(X0,X2)),sK8)
| in(apply(X0,sK2(set_intersection2(sK8,sK15(sK8)),X1,relation_inverse_image(X0,X2))),X2)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_370279]) ).
tcf(c_433557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),X0)
| in(apply(empty_set,sK2(set_intersection2(X0,X1),X2,relation_inverse_image(empty_set,X3))),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(empty_set,X3) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370279]) ).
tcf(c_433558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(X1,X2,relation_inverse_image(X0,X3))),X3)
| in(sK2(set_intersection2(X1,X1),X2,relation_inverse_image(X0,X3)),X1)
| ( set_intersection2(set_intersection2(X1,X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370279]) ).
tcf(c_433561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(empty_set,X2,relation_inverse_image(X0,X3))),X3)
| in(sK2(set_intersection2(X1,empty_set),X2,relation_inverse_image(X0,X3)),X1)
| ( set_intersection2(set_intersection2(X1,empty_set),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370279]) ).
tcf(c_433562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,relation_inverse_image(X0,X3)),empty_set)
| in(apply(X0,sK2(empty_set,X2,relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(set_intersection2(empty_set,X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_370279]) ).
tcf(c_433563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(sK16(powerset(X1)),X2,relation_inverse_image(X0,X3))),X3)
| in(sK2(set_intersection2(X1,sK16(powerset(X1))),X2,relation_inverse_image(X0,X3)),X1)
| ( set_intersection2(set_intersection2(X1,sK16(powerset(X1))),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370279]) ).
tcf(c_433564,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK5,sK15(sK5)),X1,relation_inverse_image(X0,X2)),sK5)
| in(apply(X0,sK2(sK15(sK5),X1,relation_inverse_image(X0,X2))),X2)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_370279]) ).
tcf(c_433565,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK8,sK15(sK8)),X1,relation_inverse_image(X0,X2)),sK8)
| in(apply(X0,sK2(sK15(sK8),X1,relation_inverse_image(X0,X2))),X2)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_370279]) ).
tcf(c_433566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(empty_set,sK2(set_intersection2(X0,X1),X2,empty_set)),X3)
| in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(empty_set,X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(empty_set,X3) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370279]) ).
tcf(c_433567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X0,X3),X4,relation_inverse_image(X2,X5)),X1)
| in(apply(X2,sK2(set_intersection2(X0,X3),X4,relation_inverse_image(X2,X5))),X5)
| ( set_intersection2(set_intersection2(X0,X3),X4) = relation_inverse_image(X2,X5) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370279,c_321]) ).
tcf(c_433568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK2(set_intersection2(X0,X3),X4,relation_inverse_image(X2,X5))),X5)
| ( set_intersection2(set_intersection2(X0,X3),X4) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370279,c_320]) ).
tcf(c_433569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4))),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(X0,sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4))) ),
inference(superposition,[status(thm)],[c_370279,c_97]) ).
tcf(c_433570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,relation_inverse_image(X2,X5)),X1)
| in(apply(X2,sK2(set_intersection2(X0,X3),X4,relation_inverse_image(X2,X5))),X5)
| ( set_intersection2(set_intersection2(X0,X3),X4) = relation_inverse_image(X2,X5) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370279,c_96]) ).
tcf(c_433571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),X1)
| in(apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_93]) ).
tcf(c_433572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_91]) ).
tcf(c_433573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,relation_inverse_image(X0,X5)),X2)
| in(apply(X0,sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,relation_inverse_image(X0,X5))),X5)
| ( set_intersection2(set_intersection2(set_intersection2(X1,X2),X3),X4) = relation_inverse_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_59]) ).
tcf(c_433574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,relation_inverse_image(X0,X5)),X1)
| in(apply(X0,sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,relation_inverse_image(X0,X5))),X5)
| ( set_intersection2(set_intersection2(set_intersection2(X1,X2),X3),X4) = relation_inverse_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_58]) ).
tcf(c_433575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X1,sK2(set_intersection2(relation_inverse_image(X1,X2),X3),X4,relation_inverse_image(X0,X5))),X2)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X1,X2),X3),X4,relation_inverse_image(X0,X5))),X5)
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X2),X3),X4) = relation_inverse_image(X0,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_88]) ).
tcf(c_433576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X1,X2),X3),X4,relation_inverse_image(X0,X5)),relation_dom(X1))
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X1,X2),X3),X4,relation_inverse_image(X0,X5))),X5)
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X2),X3),X4) = relation_inverse_image(X0,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_87]) ).
tcf(c_433577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X3,sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X3,X4))),X4)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = relation_inverse_image(X3,X4) )
| ( apply(X0,sK13(X0,X5,apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X3,X4))))) = apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X3,X4))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370279,c_369671]) ).
tcf(c_433578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(apply(X2,sK2(set_intersection2(relation_image(X3,X0),X4),X5,relation_inverse_image(X2,X6))),X6)
| ( set_intersection2(set_intersection2(relation_image(X3,X0),X4),X5) = relation_inverse_image(X2,X6) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370279,c_369799]) ).
tcf(c_433579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(apply(X2,sK2(set_intersection2(relation_image(X0,X3),X4),X5,relation_inverse_image(X2,X6))),X6)
| ( set_intersection2(set_intersection2(relation_image(X0,X3),X4),X5) = relation_inverse_image(X2,X6) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370279,c_369798]) ).
tcf(c_433580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK2(set_intersection2(relation_image(X1,X2),X3),X4,relation_inverse_image(X0,X5))),X5)
| ( set_intersection2(set_intersection2(relation_image(X1,X2),X3),X4) = relation_inverse_image(X0,X5) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_369596]) ).
tcf(c_433581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X1,sK2(set_intersection2(relation_image(X0,X2),X3),X4,relation_inverse_image(X1,X5))),X5)
| ( set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4) = relation_inverse_image(X1,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370279,c_369558]) ).
tcf(c_433582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK2(set_intersection2(relation_image(X1,X2),X3),X4,relation_inverse_image(X0,X5))),X5)
| ( set_intersection2(set_intersection2(relation_image(X1,X2),X3),X4) = relation_inverse_image(X0,X5) )
| ( apply(X1,sK13(X1,X2,sK2(set_intersection2(relation_image(X1,X2),X3),X4,relation_inverse_image(X0,X5)))) = sK2(set_intersection2(relation_image(X1,X2),X3),X4,relation_inverse_image(X0,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_112]) ).
tcf(c_433583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X3,sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X3,X4))),X4)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X0,X5))
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370279,c_369501]) ).
tcf(c_433584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(set_intersection2(empty_set,X1),X2,relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(set_intersection2(empty_set,X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_372426]) ).
tcf(c_433585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X1,sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,relation_inverse_image(X1,X2))),X2)
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X2),X0),X3) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,relation_inverse_image(X1,X2)),X3)
| ~ in(sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,relation_inverse_image(X1,X2)),X0)
| ~ in(sK2(set_intersection2(X0,relation_inverse_image(X1,X2)),X3,relation_inverse_image(X1,X2)),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370279,c_370220]) ).
tcf(c_433586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4))),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),relation_inverse_image(X3,X4)) ),
inference(superposition,[status(thm)],[c_370279,c_368471]) ).
tcf(c_433587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(apply(X0,sK2(set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5,relation_inverse_image(X0,X6))),X6)
| ( set_intersection2(set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5) = relation_inverse_image(X0,X6) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5,relation_inverse_image(X0,X6))))) = sK13(X1,relation_image(X2,X3),sK2(set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5,relation_inverse_image(X0,X6))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_369672]) ).
tcf(c_433588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK15(sK5),X1),X2,relation_inverse_image(X0,X3)),sK5)
| in(apply(X0,sK2(set_intersection2(sK15(sK5),X1),X2,relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(set_intersection2(sK15(sK5),X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_412536]) ).
tcf(c_433589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK15(sK8),X1),X2,relation_inverse_image(X0,X3)),sK8)
| in(apply(X0,sK2(set_intersection2(sK15(sK8),X1),X2,relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(set_intersection2(sK15(sK8),X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_413867]) ).
tcf(c_433590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(sK16(powerset(X1)),X2),X3,relation_inverse_image(X0,X4)),X1)
| in(apply(X0,sK2(set_intersection2(sK16(powerset(X1)),X2),X3,relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(set_intersection2(sK16(powerset(X1)),X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_430730]) ).
tcf(c_433592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X2,X0)),X3)
| element(apply(X2,sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X2,X0))),X1)
| ( set_intersection2(set_intersection2(X3,X4),X5) = relation_inverse_image(X2,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370279,c_321]) ).
tcf(c_433593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X2,X0)),X3)
| ( set_intersection2(set_intersection2(X3,X4),X5) = relation_inverse_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370279,c_320]) ).
tcf(c_433594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,relation_inverse_image(X1,X0)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_inverse_image(X1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK2(set_intersection2(X2,X3),X4,relation_inverse_image(X1,X0)))) ),
inference(superposition,[status(thm)],[c_370279,c_97]) ).
tcf(c_433595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X2,X0)),X3)
| in(apply(X2,sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X2,X0))),X1)
| ( set_intersection2(set_intersection2(X3,X4),X5) = relation_inverse_image(X2,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370279,c_96]) ).
tcf(c_433596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),X1)
| element(apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_93]) ).
tcf(c_433597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,relation_inverse_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_inverse_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_91]) ).
tcf(c_433598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X0,set_intersection2(X1,X2))),X3)
| in(apply(X0,sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X0,set_intersection2(X1,X2)))),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = set_intersection2(set_intersection2(X3,X4),X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_59]) ).
tcf(c_433599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X0,set_intersection2(X1,X2))),X3)
| in(apply(X0,sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X0,set_intersection2(X1,X2)))),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = set_intersection2(set_intersection2(X3,X4),X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_58]) ).
tcf(c_433600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),X0)
| in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),relation_inverse_image(X3,X4))
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),relation_dom(X3)) ),
inference(superposition,[status(thm)],[c_370279,c_86]) ).
tcf(c_433601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X0,relation_inverse_image(X1,X2))),X3)
| in(apply(X1,apply(X0,sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X0,relation_inverse_image(X1,X2))))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(set_intersection2(X3,X4),X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_88]) ).
tcf(c_433602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X0,relation_inverse_image(X1,X2))),X3)
| in(apply(X0,sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X0,relation_inverse_image(X1,X2)))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(set_intersection2(X3,X4),X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_87]) ).
tcf(c_433603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,relation_dom(X4))),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,relation_dom(X4)) )
| ( apply(X4,sK13(X4,X5,apply(X4,apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,relation_dom(X4))))))) = apply(X4,apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,relation_dom(X4))))) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ in(apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,relation_dom(X4)))),X5) ),
inference(superposition,[status(thm)],[c_370279,c_369671]) ).
tcf(c_433604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X4,X5),X6,relation_inverse_image(X2,relation_image(X3,X0))),X4)
| ( relation_inverse_image(X2,relation_image(X3,X0)) = set_intersection2(set_intersection2(X4,X5),X6) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370279,c_369799]) ).
tcf(c_433605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X4,X5),X6,relation_inverse_image(X2,relation_image(X0,X3))),X4)
| ( relation_inverse_image(X2,relation_image(X0,X3)) = set_intersection2(set_intersection2(X4,X5),X6) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370279,c_369798]) ).
tcf(c_433606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X0,relation_image(X1,X2))),X3)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = set_intersection2(set_intersection2(X3,X4),X5) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_369596]) ).
tcf(c_433607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X1,relation_image(X0,X2))),X3)
| ( relation_inverse_image(X1,relation_image(X0,X2)) = set_intersection2(set_intersection2(X3,X4),X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370279,c_369558]) ).
tcf(c_433608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X0,relation_image(X1,X2))),X3)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = set_intersection2(set_intersection2(X3,X4),X5) )
| ( apply(X1,sK13(X1,X2,apply(X0,sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X0,relation_image(X1,X2)))))) = apply(X0,sK2(set_intersection2(X3,X4),X5,relation_inverse_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_112]) ).
tcf(c_433609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,relation_dom(X4))),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,relation_dom(X4)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ empty(relation_image(X4,X5))
| ~ in(apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,relation_dom(X4)))),X5) ),
inference(superposition,[status(thm)],[c_370279,c_369501]) ).
tcf(c_433610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,empty_set)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_372426]) ).
tcf(c_433611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X4,X5),X6,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))),X4)
| ( relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))) = set_intersection2(set_intersection2(X4,X5),X6) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK2(set_intersection2(X4,X5),X6,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK2(set_intersection2(X4,X5),X6,relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_369672]) ).
tcf(c_433612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,sK15(sK5))),X1)
| in(apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,sK15(sK5)))),sK5)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,sK15(sK5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_412536]) ).
tcf(c_433613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,sK15(sK8))),X1)
| in(apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,sK15(sK8)))),sK8)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,sK15(sK8)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_413867]) ).
tcf(c_433614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,sK16(powerset(X4)))),X1)
| in(apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,sK16(powerset(X4))))),X4)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,sK16(powerset(X4))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370279,c_430730]) ).
tcf(c_433645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(empty_set,sK2(set_intersection2(X0,X1),X2,empty_set)),X3)
| in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(empty_set,X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(empty_set,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_433566,c_368630,c_103]) ).
tcf(c_433649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(empty_set,X2,relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(set_intersection2(empty_set,X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_433562,c_372426]) ).
tcf(c_433664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),X0)
| in(apply(empty_set,sK2(set_intersection2(X0,X1),X2,relation_inverse_image(empty_set,X3))),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(empty_set,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_433557,c_368630,c_103]) ).
tcf(c_434301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,X3)),X1)
| in(sK2(set_intersection2(X1,X1),X2,relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370280]) ).
tcf(c_434304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,relation_inverse_image(X0,X3)),X1)
| in(sK2(set_intersection2(X1,empty_set),X2,relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,empty_set),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370280]) ).
tcf(c_434306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X1)),X2,relation_inverse_image(X0,X3)),X1)
| in(sK2(set_intersection2(X1,sK16(powerset(X1))),X2,relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,sK16(powerset(X1))),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370280]) ).
tcf(c_434307,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X1,relation_inverse_image(X0,X2)),sK5)
| in(sK2(set_intersection2(sK5,sK15(sK5)),X1,relation_inverse_image(X0,X2)),relation_dom(X0))
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_370280]) ).
tcf(c_434308,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X1,relation_inverse_image(X0,X2)),sK8)
| in(sK2(set_intersection2(sK8,sK15(sK8)),X1,relation_inverse_image(X0,X2)),relation_dom(X0))
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_370280]) ).
tcf(c_434309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),X0)
| in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(empty_set,X3)),relation_dom(empty_set))
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(empty_set,X3) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370280]) ).
tcf(c_434310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,X3)),relation_dom(X0))
| in(sK2(set_intersection2(X1,X1),X2,relation_inverse_image(X0,X3)),X1)
| ( set_intersection2(set_intersection2(X1,X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370280]) ).
tcf(c_434313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,relation_inverse_image(X0,X3)),relation_dom(X0))
| in(sK2(set_intersection2(X1,empty_set),X2,relation_inverse_image(X0,X3)),X1)
| ( set_intersection2(set_intersection2(X1,empty_set),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370280]) ).
tcf(c_434314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,relation_inverse_image(X0,X3)),relation_dom(X0))
| in(sK2(set_intersection2(empty_set,X1),X2,relation_inverse_image(X0,X3)),empty_set)
| ( set_intersection2(set_intersection2(empty_set,X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_370280]) ).
tcf(c_434315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X1)),X2,relation_inverse_image(X0,X3)),relation_dom(X0))
| in(sK2(set_intersection2(X1,sK16(powerset(X1))),X2,relation_inverse_image(X0,X3)),X1)
| ( set_intersection2(set_intersection2(X1,sK16(powerset(X1))),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370280]) ).
tcf(c_434316,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X1,relation_inverse_image(X0,X2)),relation_dom(X0))
| in(sK2(set_intersection2(sK5,sK15(sK5)),X1,relation_inverse_image(X0,X2)),sK5)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_370280]) ).
tcf(c_434317,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X1,relation_inverse_image(X0,X2)),relation_dom(X0))
| in(sK2(set_intersection2(sK8,sK15(sK8)),X1,relation_inverse_image(X0,X2)),sK8)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X1) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_370280]) ).
tcf(c_434318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),relation_dom(empty_set))
| in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(empty_set,X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(empty_set,X3) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370280]) ).
tcf(c_434320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X0,X3),X4,relation_inverse_image(X2,X5)),X1)
| in(sK2(set_intersection2(X0,X3),X4,relation_inverse_image(X2,X5)),relation_dom(X2))
| ( set_intersection2(set_intersection2(X0,X3),X4) = relation_inverse_image(X2,X5) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370280,c_321]) ).
tcf(c_434321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,relation_inverse_image(X2,X5)),relation_dom(X2))
| ( set_intersection2(set_intersection2(X0,X3),X4) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370280,c_320]) ).
tcf(c_434322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),relation_dom(X3))
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(X0,sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4))) ),
inference(superposition,[status(thm)],[c_370280,c_97]) ).
tcf(c_434323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,relation_inverse_image(X2,X5)),X1)
| in(sK2(set_intersection2(X0,X3),X4,relation_inverse_image(X2,X5)),relation_dom(X2))
| ( set_intersection2(set_intersection2(X0,X3),X4) = relation_inverse_image(X2,X5) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370280,c_96]) ).
tcf(c_434324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),X1)
| in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370280,c_93]) ).
tcf(c_434325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370280,c_91]) ).
tcf(c_434326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,relation_inverse_image(X0,X5)),X2)
| in(sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,relation_inverse_image(X0,X5)),relation_dom(X0))
| ( set_intersection2(set_intersection2(set_intersection2(X1,X2),X3),X4) = relation_inverse_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370280,c_59]) ).
tcf(c_434327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,relation_inverse_image(X0,X5)),X1)
| in(sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,relation_inverse_image(X0,X5)),relation_dom(X0))
| ( set_intersection2(set_intersection2(set_intersection2(X1,X2),X3),X4) = relation_inverse_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370280,c_58]) ).
tcf(c_434328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X1,X2),X3),X4,relation_inverse_image(X0,X5)),relation_dom(X0))
| in(apply(X1,sK2(set_intersection2(relation_inverse_image(X1,X2),X3),X4,relation_inverse_image(X0,X5))),X2)
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X2),X3),X4) = relation_inverse_image(X0,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370280,c_88]) ).
tcf(c_434329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X1,X2),X3),X4,relation_inverse_image(X0,X5)),relation_dom(X1))
| in(sK2(set_intersection2(relation_inverse_image(X1,X2),X3),X4,relation_inverse_image(X0,X5)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X2),X3),X4) = relation_inverse_image(X0,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370280,c_87]) ).
tcf(c_434330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X3,X4)),relation_dom(X3))
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = relation_inverse_image(X3,X4) )
| ( apply(X0,sK13(X0,X5,apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X3,X4))))) = apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X3,X4))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370280,c_369671]) ).
tcf(c_434331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_image(X3,X0),X4),X5,relation_inverse_image(X2,X6)),relation_dom(X2))
| ( set_intersection2(set_intersection2(relation_image(X3,X0),X4),X5) = relation_inverse_image(X2,X6) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370280,c_369799]) ).
tcf(c_434332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_image(X0,X3),X4),X5,relation_inverse_image(X2,X6)),relation_dom(X2))
| ( set_intersection2(set_intersection2(relation_image(X0,X3),X4),X5) = relation_inverse_image(X2,X6) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370280,c_369798]) ).
tcf(c_434333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X1,X2),X3),X4,relation_inverse_image(X0,X5)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_image(X1,X2),X3),X4) = relation_inverse_image(X0,X5) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370280,c_369596]) ).
tcf(c_434334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X0,X2),X3),X4,relation_inverse_image(X1,X5)),relation_dom(X1))
| ( set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4) = relation_inverse_image(X1,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370280,c_369558]) ).
tcf(c_434335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X1,X2),X3),X4,relation_inverse_image(X0,X5)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_image(X1,X2),X3),X4) = relation_inverse_image(X0,X5) )
| ( apply(X1,sK13(X1,X2,sK2(set_intersection2(relation_image(X1,X2),X3),X4,relation_inverse_image(X0,X5)))) = sK2(set_intersection2(relation_image(X1,X2),X3),X4,relation_inverse_image(X0,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370280,c_112]) ).
tcf(c_434336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X3,X4)),relation_dom(X3))
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X0,X5))
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370280,c_369501]) ).
tcf(c_434337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(set_intersection2(empty_set,X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370280,c_372426]) ).
tcf(c_434338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,relation_inverse_image(X1,X2)),relation_dom(X1))
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X2),X0),X3) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,relation_inverse_image(X1,X2)),X3)
| ~ in(sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,relation_inverse_image(X1,X2)),X0)
| ~ in(sK2(set_intersection2(X0,relation_inverse_image(X1,X2)),X3,relation_inverse_image(X1,X2)),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370280,c_370220]) ).
tcf(c_434339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),relation_dom(X3))
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),relation_inverse_image(X3,X4)) ),
inference(superposition,[status(thm)],[c_370280,c_368471]) ).
tcf(c_434340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5,relation_inverse_image(X0,X6)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5) = relation_inverse_image(X0,X6) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5,relation_inverse_image(X0,X6))))) = sK13(X1,relation_image(X2,X3),sK2(set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5,relation_inverse_image(X0,X6))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370280,c_369672]) ).
tcf(c_434341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK15(sK5),X1),X2,relation_inverse_image(X0,X3)),sK5)
| in(sK2(set_intersection2(sK15(sK5),X1),X2,relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(set_intersection2(sK15(sK5),X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370280,c_412536]) ).
tcf(c_434342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK15(sK8),X1),X2,relation_inverse_image(X0,X3)),sK8)
| in(sK2(set_intersection2(sK15(sK8),X1),X2,relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(set_intersection2(sK15(sK8),X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370280,c_413867]) ).
tcf(c_434343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(sK16(powerset(X1)),X2),X3,relation_inverse_image(X0,X4)),X1)
| in(sK2(set_intersection2(sK16(powerset(X1)),X2),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(set_intersection2(sK16(powerset(X1)),X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370280,c_430730]) ).
tcf(c_434345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X2,X3),X4,relation_inverse_image(X0,X5)),X1)
| in(sK2(set_intersection2(X2,X3),X4,relation_inverse_image(X0,X5)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_inverse_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370280,c_321]) ).
tcf(c_434346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,relation_inverse_image(X0,X5)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_inverse_image(X0,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370280,c_320]) ).
tcf(c_434347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4))) ),
inference(superposition,[status(thm)],[c_370280,c_97]) ).
tcf(c_434348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X2,X3),X4,relation_inverse_image(X0,X5)),X2)
| in(sK2(set_intersection2(X2,X3),X4,relation_inverse_image(X0,X5)),X1)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_inverse_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370280,c_96]) ).
tcf(c_434349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),X1)
| element(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370280,c_93]) ).
tcf(c_434350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370280,c_91]) ).
tcf(c_434351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(X3,X4) )
| ( apply(X3,sK13(X3,X5,apply(X3,sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4))))) = apply(X3,sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370280,c_369671]) ).
tcf(c_434352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X5))
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370280,c_369501]) ).
tcf(c_434355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,relation_inverse_image(X0,X4)),set_intersection2(relation_dom(X0),X1))
| ( set_intersection2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,relation_inverse_image(X0,X4)),X3)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,relation_inverse_image(X0,X4)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,relation_inverse_image(X0,X4)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,relation_inverse_image(X0,X4)),relation_inverse_image(X0,X4)) ),
inference(superposition,[status(thm)],[c_370280,c_370217]) ).
tcf(c_434356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_dom(X0),X1),X2,relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_factoring,[status(thm)],[c_370280]) ).
tcf(c_434388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),empty_set)
| in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(empty_set,X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(empty_set,X3) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_434318,c_373108]) ).
tcf(c_434389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(empty_set,X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(empty_set,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_434388,c_372426,c_368630,c_103]) ).
tcf(c_434392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(set_intersection2(empty_set,X1),X2) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_434314,c_372426]) ).
tcf(c_434407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),X0)
| in(sK2(set_intersection2(X0,X1),X2,relation_inverse_image(empty_set,X3)),empty_set)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(empty_set,X3) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_434309,c_373108]) ).
tcf(c_434408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,empty_set),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_inverse_image(empty_set,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_434407,c_372426,c_368630,c_103]) ).
tcf(c_434867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(X2,X2),X3) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,X2),X3,relation_image(X0,X1)))) = sK2(set_intersection2(X2,X2),X3,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370281]) ).
tcf(c_434870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X3,relation_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(X2,empty_set),X3) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,empty_set),X3,relation_image(X0,X1)))) = sK2(set_intersection2(X2,empty_set),X3,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370281]) ).
tcf(c_434872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X2)),X3,relation_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(X2,sK16(powerset(X2))),X3) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,sK16(powerset(X2))),X3,relation_image(X0,X1)))) = sK2(set_intersection2(X2,sK16(powerset(X2))),X3,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370281]) ).
tcf(c_434873,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X2,relation_image(X0,X1)),sK5)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X2) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(sK5,sK15(sK5)),X2,relation_image(X0,X1)))) = sK2(set_intersection2(sK5,sK15(sK5)),X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_370281]) ).
tcf(c_434874,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X2,relation_image(X0,X1)),sK8)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X2) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(sK8,sK15(sK8)),X2,relation_image(X0,X1)))) = sK2(set_intersection2(sK8,sK15(sK8)),X2,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_370281]) ).
tcf(c_434875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,empty_set),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_image(empty_set,X0) )
| ( apply(empty_set,sK13(empty_set,X0,sK2(set_intersection2(X1,X2),X3,relation_image(empty_set,X0)))) = sK2(set_intersection2(X1,X2),X3,relation_image(empty_set,X0)) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_375097,c_370281]) ).
tcf(c_434876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X0,X4),X5,relation_image(X2,X3)),X1)
| ( set_intersection2(set_intersection2(X0,X4),X5) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(set_intersection2(X0,X4),X5,relation_image(X2,X3)))) = sK2(set_intersection2(X0,X4),X5,relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370281,c_321]) ).
tcf(c_434877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(X0,X4),X5) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(set_intersection2(X0,X4),X5,relation_image(X2,X3)))) = sK2(set_intersection2(X0,X4),X5,relation_image(X2,X3)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370281,c_320]) ).
tcf(c_434878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK2(set_intersection2(X0,X1),X2,relation_image(X3,X4)))) = sK2(set_intersection2(X0,X1),X2,relation_image(X3,X4)) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(X0,sK2(set_intersection2(X0,X1),X2,relation_image(X3,X4))) ),
inference(superposition,[status(thm)],[c_370281,c_97]) ).
tcf(c_434879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X4),X5,relation_image(X2,X3)),X1)
| ( set_intersection2(set_intersection2(X0,X4),X5) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(set_intersection2(X0,X4),X5,relation_image(X2,X3)))) = sK2(set_intersection2(X0,X4),X5,relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370281,c_96]) ).
tcf(c_434880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)))) = sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370281,c_93]) ).
tcf(c_434881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X1,X3),X4) = relation_image(X0,X2) )
| ( apply(X0,sK13(X0,X2,sK2(set_intersection2(X1,X3),X4,relation_image(X0,X2)))) = sK2(set_intersection2(X1,X3),X4,relation_image(X0,X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370281,c_91]) ).
tcf(c_434882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,relation_image(X0,X1)),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X3),X4),X5) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,relation_image(X0,X1)))) = sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370281,c_59]) ).
tcf(c_434883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,relation_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X3),X4),X5) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,relation_image(X0,X1)))) = sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370281,c_58]) ).
tcf(c_434884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X1,sK2(set_intersection2(relation_inverse_image(X1,X3),X4),X5,relation_image(X0,X2))),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X3),X4),X5) = relation_image(X0,X2) )
| ( apply(X0,sK13(X0,X2,sK2(set_intersection2(relation_inverse_image(X1,X3),X4),X5,relation_image(X0,X2)))) = sK2(set_intersection2(relation_inverse_image(X1,X3),X4),X5,relation_image(X0,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370281,c_88]) ).
tcf(c_434885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X1,X3),X4),X5,relation_image(X0,X2)),relation_dom(X1))
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X3),X4),X5) = relation_image(X0,X2) )
| ( apply(X0,sK13(X0,X2,sK2(set_intersection2(relation_inverse_image(X1,X3),X4),X5,relation_image(X0,X2)))) = sK2(set_intersection2(relation_inverse_image(X1,X3),X4),X5,relation_image(X0,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370281,c_87]) ).
tcf(c_434886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK2(set_intersection2(relation_dom(X0),X1),X2,relation_image(X3,X4)))) = sK2(set_intersection2(relation_dom(X0),X1),X2,relation_image(X3,X4)) )
| ( apply(X0,sK13(X0,X5,apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,relation_image(X3,X4))))) = apply(X0,sK2(set_intersection2(relation_dom(X0),X1),X2,relation_image(X3,X4))) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,relation_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370281,c_369671]) ).
tcf(c_434887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( set_intersection2(set_intersection2(relation_image(X3,X0),X5),X6) = relation_image(X2,X4) )
| ( apply(X2,sK13(X2,X4,sK2(set_intersection2(relation_image(X3,X0),X5),X6,relation_image(X2,X4)))) = sK2(set_intersection2(relation_image(X3,X0),X5),X6,relation_image(X2,X4)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370281,c_369799]) ).
tcf(c_434888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X4),X5),X6) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(set_intersection2(relation_image(X0,X4),X5),X6,relation_image(X2,X3)))) = sK2(set_intersection2(relation_image(X0,X4),X5),X6,relation_image(X2,X3)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370281,c_369798]) ).
tcf(c_434889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_image(X1,X2),X4),X5) = relation_image(X0,X3) )
| ( apply(X0,sK13(X0,X3,sK2(set_intersection2(relation_image(X1,X2),X4),X5,relation_image(X0,X3)))) = sK2(set_intersection2(relation_image(X1,X2),X4),X5,relation_image(X0,X3)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370281,c_369596]) ).
tcf(c_434890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X3),X4),X5) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK2(set_intersection2(relation_image(X0,X3),X4),X5,relation_image(X1,X2)))) = sK2(set_intersection2(relation_image(X0,X3),X4),X5,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370281,c_369558]) ).
tcf(c_434891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_image(X1,X3),X4),X5) = relation_image(X0,X2) )
| ( apply(X1,sK13(X1,X3,sK2(set_intersection2(relation_image(X1,X3),X4),X5,relation_image(X0,X2)))) = sK2(set_intersection2(relation_image(X1,X3),X4),X5,relation_image(X0,X2)) )
| ( apply(X0,sK13(X0,X2,sK2(set_intersection2(relation_image(X1,X3),X4),X5,relation_image(X0,X2)))) = sK2(set_intersection2(relation_image(X1,X3),X4),X5,relation_image(X0,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370281,c_112]) ).
tcf(c_434892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_dom(X0),X1),X2) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK2(set_intersection2(relation_dom(X0),X1),X2,relation_image(X3,X4)))) = sK2(set_intersection2(relation_dom(X0),X1),X2,relation_image(X3,X4)) )
| ~ function(X3)
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ empty(relation_image(X0,X5))
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),X2,relation_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370281,c_369501]) ).
tcf(c_434893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(empty_set,X2),X3) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(empty_set,X2),X3,relation_image(X0,X1)))) = sK2(set_intersection2(empty_set,X2),X3,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370281,c_372426]) ).
tcf(c_434894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(relation_image(X1,X2),X0),X3) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK2(set_intersection2(relation_image(X1,X2),X0),X3,relation_image(X1,X2)))) = sK2(set_intersection2(relation_image(X1,X2),X0),X3,relation_image(X1,X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(set_intersection2(relation_image(X1,X2),X0),X3,relation_image(X1,X2)),X3)
| ~ in(sK2(set_intersection2(relation_image(X1,X2),X0),X3,relation_image(X1,X2)),X0)
| ~ in(sK2(set_intersection2(X0,relation_image(X1,X2)),X3,relation_image(X1,X2)),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370281,c_370220]) ).
tcf(c_434895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK2(set_intersection2(X0,X1),X2,relation_image(X3,X4)))) = sK2(set_intersection2(X0,X1),X2,relation_image(X3,X4)) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_image(X3,X4)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_image(X3,X4)),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_image(X3,X4)),relation_image(X3,X4)) ),
inference(superposition,[status(thm)],[c_370281,c_368471]) ).
tcf(c_434896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( set_intersection2(set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5) = relation_image(X0,X6) )
| ( apply(X0,sK13(X0,X6,sK2(set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5,relation_image(X0,X6)))) = sK2(set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5,relation_image(X0,X6)) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5,relation_image(X0,X6))))) = sK13(X1,relation_image(X2,X3),sK2(set_intersection2(relation_image(X1,relation_image(X2,X3)),X4),X5,relation_image(X0,X6))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370281,c_369672]) ).
tcf(c_434897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK15(sK5),X2),X3,relation_image(X0,X1)),sK5)
| ( set_intersection2(set_intersection2(sK15(sK5),X2),X3) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(sK15(sK5),X2),X3,relation_image(X0,X1)))) = sK2(set_intersection2(sK15(sK5),X2),X3,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370281,c_412536]) ).
tcf(c_434898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK15(sK8),X2),X3,relation_image(X0,X1)),sK8)
| ( set_intersection2(set_intersection2(sK15(sK8),X2),X3) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(sK15(sK8),X2),X3,relation_image(X0,X1)))) = sK2(set_intersection2(sK15(sK8),X2),X3,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370281,c_413867]) ).
tcf(c_434899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(sK16(powerset(X2)),X3),X4,relation_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(sK16(powerset(X2)),X3),X4) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(sK16(powerset(X2)),X3),X4,relation_image(X0,X1)))) = sK2(set_intersection2(sK16(powerset(X2)),X3),X4,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370281,c_430730]) ).
tcf(c_434916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,empty_set),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = empty_set )
| ( apply(empty_set,sK13(empty_set,X0,sK2(set_intersection2(X1,X2),X3,empty_set))) = sK2(set_intersection2(X1,X2),X3,empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_434875,c_375097]) ).
tcf(c_434917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,empty_set),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = empty_set )
| ( apply(empty_set,sK13(empty_set,X0,sK2(set_intersection2(X1,X2),X3,empty_set))) = sK2(set_intersection2(X1,X2),X3,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_434916,c_368630,c_103]) ).
tcf(c_435381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(X0,X1)
| in(sK2(set_intersection2(sK10(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(sK10(X0,X1),X2),X3) = X4 )
| ~ subset(X0,sK2(set_intersection2(sK10(X0,X1),X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_369021,c_370285]) ).
tcf(c_435382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X0)
| in(sK2(set_intersection2(sK16(X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(sK16(X0),X1),X2) = X3 )
| ~ subset(X0,sK2(set_intersection2(sK16(X0),X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_370747,c_370285]) ).
tcf(c_435383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,X2,X0),X1)
| in(sK2(set_intersection2(sK2(X1,X2,X0),X3),X4,X5),X5)
| ( set_intersection2(X1,X2) = X0 )
| ( set_intersection2(set_intersection2(sK2(X1,X2,X0),X3),X4) = X5 )
| ~ subset(X0,sK2(set_intersection2(sK2(X1,X2,X0),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369015,c_370285]) ).
tcf(c_435384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,X2,X0),X2)
| in(sK2(set_intersection2(sK2(X1,X2,X0),X3),X4,X5),X5)
| ( set_intersection2(X1,X2) = X0 )
| ( set_intersection2(set_intersection2(sK2(X1,X2,X0),X3),X4) = X5 )
| ~ subset(X0,sK2(set_intersection2(sK2(X1,X2,X0),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369014,c_370285]) ).
tcf(c_435385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(set_intersection2(sK2(X0,X1,X2),X3),X4,X5),X5)
| ( set_intersection2(X0,X1) = X2 )
| ( set_intersection2(set_intersection2(sK2(X0,X1,X2),X3),X4) = X5 )
| ~ subset(X0,sK2(set_intersection2(sK2(X0,X1,X2),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369012,c_370285]) ).
tcf(c_435386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,X0,X2),X2)
| in(sK2(set_intersection2(sK2(X1,X0,X2),X3),X4,X5),X5)
| ( set_intersection2(X1,X0) = X2 )
| ( set_intersection2(set_intersection2(sK2(X1,X0,X2),X3),X4) = X5 )
| ~ subset(X0,sK2(set_intersection2(sK2(X1,X0,X2),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369013,c_370285]) ).
tcf(c_435387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(sK13(X1,X0,X2),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(sK13(X1,X0,X2),X3),X4) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_image(X1,X0))
| ~ subset(X0,sK2(set_intersection2(sK13(X1,X0,X2),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369594,c_370285]) ).
tcf(c_435388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(sK13(X0,X1,X2),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(sK13(X0,X1,X2),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_image(X0,X1))
| ~ subset(relation_dom(X0),sK2(set_intersection2(sK13(X0,X1,X2),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369556,c_370285]) ).
tcf(c_435389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X1,X0,X2),X2)
| in(sK2(set_intersection2(sK12(X1,X0,X2),X3),X4,X5),X5)
| ( relation_image(X1,X0) = X2 )
| ( set_intersection2(set_intersection2(sK12(X1,X0,X2),X3),X4) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(set_intersection2(sK12(X1,X0,X2),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369299,c_370285]) ).
tcf(c_435390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(sK11(X1,X2,X0),X3),X4,X5),X5)
| ( relation_image(X1,X2) = X0 )
| ( apply(X1,sK12(X1,X2,X0)) = sK11(X1,X2,X0) )
| ( set_intersection2(set_intersection2(sK11(X1,X2,X0),X3),X4) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(set_intersection2(sK11(X1,X2,X0),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369436,c_370285]) ).
tcf(c_435391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X1,X2,X0),X2)
| in(sK2(set_intersection2(sK11(X1,X2,X0),X3),X4,X5),X5)
| ( relation_image(X1,X2) = X0 )
| ( set_intersection2(set_intersection2(sK11(X1,X2,X0),X3),X4) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(set_intersection2(sK11(X1,X2,X0),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369307,c_370285]) ).
tcf(c_435392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X1,X2,X0),relation_dom(X1))
| in(sK2(set_intersection2(sK11(X1,X2,X0),X3),X4,X5),X5)
| ( relation_image(X1,X2) = X0 )
| ( set_intersection2(set_intersection2(sK11(X1,X2,X0),X3),X4) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(set_intersection2(sK11(X1,X2,X0),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369206,c_370285]) ).
tcf(c_435393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X1,X2,X0),relation_dom(X1))
| in(sK2(set_intersection2(sK7(X1,X2,X0),X3),X4,X5),X5)
| ( relation_inverse_image(X1,X2) = X0 )
| ( set_intersection2(set_intersection2(sK7(X1,X2,X0),X3),X4) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(set_intersection2(sK7(X1,X2,X0),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369020,c_370285]) ).
tcf(c_435394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X1,sK7(X1,X2,X0)),X2)
| in(sK2(set_intersection2(sK7(X1,X2,X0),X3),X4,X5),X5)
| ( relation_inverse_image(X1,X2) = X0 )
| ( set_intersection2(set_intersection2(sK7(X1,X2,X0),X3),X4) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(set_intersection2(sK7(X1,X2,X0),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369019,c_370285]) ).
tcf(c_435395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,X1,X2),X2)
| in(sK2(set_intersection2(sK7(X0,X1,X2),X3),X4,X5),X5)
| ( relation_inverse_image(X0,X1) = X2 )
| ( set_intersection2(set_intersection2(sK7(X0,X1,X2),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(set_intersection2(sK7(X0,X1,X2),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369017,c_370285]) ).
tcf(c_435396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X0,X1,X2),X2)
| in(sK2(set_intersection2(sK12(X0,X1,X2),X3),X4,X5),X5)
| ( relation_image(X0,X1) = X2 )
| ( set_intersection2(set_intersection2(sK12(X0,X1,X2),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(set_intersection2(sK12(X0,X1,X2),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369214,c_370285]) ).
tcf(c_435397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X1,X0,X2),X2)
| in(sK2(set_intersection2(apply(X1,sK7(X1,X0,X2)),X3),X4,X5),X5)
| ( relation_inverse_image(X1,X0) = X2 )
| ( set_intersection2(set_intersection2(apply(X1,sK7(X1,X0,X2)),X3),X4) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK2(set_intersection2(apply(X1,sK7(X1,X0,X2)),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_369018,c_370285]) ).
tcf(c_435398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(sK2(X0,X1,X0),X2),X3,X4),X4)
| ( set_intersection2(X0,X1) = X0 )
| ( set_intersection2(set_intersection2(sK2(X0,X1,X0),X2),X3) = X4 )
| ~ subset(X0,sK2(set_intersection2(sK2(X0,X1,X0),X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_370077,c_370285]) ).
tcf(c_435399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(sK2(X1,X0,X0),X2),X3,X4),X4)
| ( set_intersection2(X1,X0) = X0 )
| ( set_intersection2(set_intersection2(sK2(X1,X0,X0),X2),X3) = X4 )
| ~ subset(X0,sK2(set_intersection2(sK2(X1,X0,X0),X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_370145,c_370285]) ).
tcf(c_435400,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK16(sK15(sK5)),X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(sK16(sK15(sK5)),X0),X1) = X2 )
| ~ subset(sK5,sK2(set_intersection2(sK16(sK15(sK5)),X0),X1,X2)) ),
inference(superposition,[status(thm)],[c_420696,c_370285]) ).
tcf(c_435401,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK16(sK15(sK8)),X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(sK16(sK15(sK8)),X0),X1) = X2 )
| ~ subset(sK8,sK2(set_intersection2(sK16(sK15(sK8)),X0),X1,X2)) ),
inference(superposition,[status(thm)],[c_423415,c_370285]) ).
tcf(c_435402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X0),X1)
| in(sK2(set_intersection2(sK2(set_intersection2(X1,X2),X3,X0),X4),X5,X6),X6)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ( set_intersection2(set_intersection2(sK2(set_intersection2(X1,X2),X3,X0),X4),X5) = X6 )
| ~ subset(X0,sK2(set_intersection2(sK2(set_intersection2(X1,X2),X3,X0),X4),X5,X6)) ),
inference(superposition,[status(thm)],[c_370274,c_370285]) ).
tcf(c_435403,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,X0),X1) = X2 )
| ~ in(X0,sK2(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_53,c_370285]) ).
tcf(c_435406,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,empty_set),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 )
| ~ in(X0,sK2(empty_set,X1,X2)) ),
inference(superposition,[status(thm)],[c_64,c_370285]) ).
tcf(c_435407,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(empty_set,X2),X0,X1),X1)
| ( set_intersection2(set_intersection2(empty_set,X2),X0) = X1 )
| ~ in(empty_set,sK2(empty_set,X0,X1)) ),
inference(superposition,[status(thm)],[c_368545,c_370285]) ).
tcf(c_435408,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X2 )
| ~ in(X0,sK2(sK16(powerset(X0)),X1,X2)) ),
inference(superposition,[status(thm)],[c_397130,c_370285]) ).
tcf(c_435409,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(sK5,sK15(sK5)),X0,X1),X1)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = X1 )
| ~ in(sK5,sK2(sK15(sK5),X0,X1)) ),
inference(superposition,[status(thm)],[c_411955,c_370285]) ).
tcf(c_435410,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(sK8,sK15(sK8)),X0,X1),X1)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = X1 )
| ~ in(sK8,sK2(sK15(sK8),X0,X1)) ),
inference(superposition,[status(thm)],[c_411956,c_370285]) ).
tcf(c_435414,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| ( set_intersection2(empty_set,X1) = X2 )
| ~ in(X0,sK2(empty_set,X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_435406,c_64]) ).
tcf(c_435419,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),X1)
| ( set_intersection2(sK15(sK8),X0) = X1 )
| ~ in(sK8,sK2(sK15(sK8),X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_435410,c_411956]) ).
tcf(c_435423,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),X1)
| ( set_intersection2(sK15(sK5),X0) = X1 )
| ~ in(sK5,sK2(sK15(sK5),X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_435409,c_411955]) ).
tcf(c_435427,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),X2)
| ( set_intersection2(sK16(powerset(X0)),X1) = X2 )
| ~ in(X0,sK2(sK16(powerset(X0)),X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_435408,c_397130]) ).
tcf(c_435640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X2,X3),X3)
| in(sK2(set_intersection2(X0,X0),X2,X3),X1)
| ( set_intersection2(set_intersection2(X0,X0),X2) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_370286]) ).
tcf(c_435643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,X3),X3)
| in(sK2(set_intersection2(X0,empty_set),X2,X3),X1)
| ( set_intersection2(set_intersection2(X0,empty_set),X2) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_370286]) ).
tcf(c_435644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,X3),X3)
| in(sK2(set_intersection2(empty_set,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(empty_set,X1),X2) = X3 )
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_368545,c_370286]) ).
tcf(c_435645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X0)),X2,X3),X3)
| in(sK2(set_intersection2(X0,sK16(powerset(X0))),X2,X3),X1)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X2) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397130,c_370286]) ).
tcf(c_435646,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X1,X2),X2)
| in(sK2(set_intersection2(sK5,sK15(sK5)),X1,X2),X0)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X1) = X2 )
| ~ subset(sK5,X0) ),
inference(superposition,[status(thm)],[c_411955,c_370286]) ).
tcf(c_435647,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X1,X2),X2)
| in(sK2(set_intersection2(sK8,sK15(sK8)),X1,X2),X0)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X1) = X2 )
| ~ subset(sK8,X0) ),
inference(superposition,[status(thm)],[c_411956,c_370286]) ).
tcf(c_435648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X2,X3),X1)
| in(sK2(set_intersection2(X0,X0),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X0),X2) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_370286]) ).
tcf(c_435651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,X3),X1)
| in(sK2(set_intersection2(X0,empty_set),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,empty_set),X2) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_370286]) ).
tcf(c_435652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,X3),X0)
| in(sK2(set_intersection2(empty_set,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(empty_set,X1),X2) = X3 )
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_368545,c_370286]) ).
tcf(c_435653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X0)),X2,X3),X1)
| in(sK2(set_intersection2(X0,sK16(powerset(X0))),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X2) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397130,c_370286]) ).
tcf(c_435654,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X1,X2),X0)
| in(sK2(set_intersection2(sK5,sK15(sK5)),X1,X2),X2)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X1) = X2 )
| ~ subset(sK5,X0) ),
inference(superposition,[status(thm)],[c_411955,c_370286]) ).
tcf(c_435655,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X1,X2),X0)
| in(sK2(set_intersection2(sK8,sK15(sK8)),X1,X2),X2)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X1) = X2 )
| ~ subset(sK8,X0) ),
inference(superposition,[status(thm)],[c_411956,c_370286]) ).
tcf(c_435656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) )
| ~ subset(X0,X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_370286,c_54]) ).
tcf(c_435657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X0,X4),X5,X2),X3)
| in(sK2(set_intersection2(X0,X4),X5,X2),X1)
| ( set_intersection2(set_intersection2(X0,X4),X5) = X2 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_321]) ).
tcf(c_435658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X4),X5,X2),X1)
| ( set_intersection2(set_intersection2(X0,X4),X5) = X2 )
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_320]) ).
tcf(c_435659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X0),X4)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ subset(X1,X4)
| ~ in(X0,sK2(set_intersection2(X1,X2),X3,X0)) ),
inference(superposition,[status(thm)],[c_370286,c_97]) ).
tcf(c_435660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X4),X5,X2),X3)
| in(sK2(set_intersection2(X0,X4),X5,X2),X1)
| ( set_intersection2(set_intersection2(X0,X4),X5) = X2 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_96]) ).
tcf(c_435667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X5)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(set_intersection2(X0,X1),X2,relation_dom(X3))))) = apply(X3,sK2(set_intersection2(X0,X1),X2,relation_dom(X3))) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,X5)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370286,c_369671]) ).
tcf(c_435668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X0,X5),X6,relation_image(X4,X2)),X1)
| ( set_intersection2(set_intersection2(X0,X5),X6) = relation_image(X4,X2) )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_369799]) ).
tcf(c_435669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X2,X4),X5,relation_image(X0,X6)),X3)
| ( set_intersection2(set_intersection2(X2,X4),X5) = relation_image(X0,X6) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370286,c_369798]) ).
tcf(c_435670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X4),X5,relation_image(X2,X3)),X1)
| ( set_intersection2(set_intersection2(X0,X4),X5) = relation_image(X2,X3) )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_369596]) ).
tcf(c_435671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,relation_image(X2,X5)),X1)
| ( set_intersection2(set_intersection2(X0,X3),X4) = relation_image(X2,X5) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_369558]) ).
tcf(c_435673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X5)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_dom(X3) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X0,X5)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370286,c_369501]) ).
tcf(c_435674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X2),X3,empty_set),X1)
| ( set_intersection2(set_intersection2(X0,X2),X3) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_372426]) ).
tcf(c_435675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X4)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(X0,X4)
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_370286,c_370220]) ).
tcf(c_435676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X0),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ subset(X0,X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_370286,c_368471]) ).
tcf(c_435677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X0,X5),X6,relation_image(X2,relation_image(X3,X4))),X1)
| ( relation_image(X2,relation_image(X3,X4)) = set_intersection2(set_intersection2(X0,X5),X6) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK2(set_intersection2(X0,X5),X6,relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK2(set_intersection2(X0,X5),X6,relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_369672]) ).
tcf(c_435678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X2),X3,sK15(sK5)),sK5)
| in(sK2(set_intersection2(X0,X2),X3,sK15(sK5)),X1)
| ( set_intersection2(set_intersection2(X0,X2),X3) = sK15(sK5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_412536]) ).
tcf(c_435679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X2),X3,sK15(sK8)),sK8)
| in(sK2(set_intersection2(X0,X2),X3,sK15(sK8)),X1)
| ( set_intersection2(set_intersection2(X0,X2),X3) = sK15(sK8) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_413867]) ).
tcf(c_435680,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X2),set_intersection2(X0,X2),set_intersection2(X0,X2)),X1)
| ( set_intersection2(set_intersection2(X0,X2),set_intersection2(X0,X2)) = set_intersection2(X0,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_423425]) ).
tcf(c_435681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X2),X3,sK16(powerset(X4))),X4)
| in(sK2(set_intersection2(X0,X2),X3,sK16(powerset(X4))),X1)
| ( set_intersection2(set_intersection2(X0,X2),X3) = sK16(powerset(X4)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_430730]) ).
tcf(c_435683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ subset(set_intersection2(X0,X1),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_370286,c_370217]) ).
tcf(c_435685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X0,X3),X4,X5),X2)
| in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_321]) ).
tcf(c_435686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ~ empty(X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_320]) ).
tcf(c_435687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X4 )
| ~ subset(X1,X0)
| ~ in(X0,sK2(set_intersection2(X1,X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_370286,c_97]) ).
tcf(c_435688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| in(sK2(set_intersection2(X0,X3),X4,X5),X2)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_96]) ).
tcf(c_435691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| in(sK2(set_intersection2(X0,X3),X4,X5),X2)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370286,c_59]) ).
tcf(c_435692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| in(sK2(set_intersection2(X0,X3),X4,X5),X1)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370286,c_58]) ).
tcf(c_435693,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| in(apply(X1,sK2(set_intersection2(X0,X3),X4,X5)),X2)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370286,c_88]) ).
tcf(c_435694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| in(sK2(set_intersection2(X0,X3),X4,X5),relation_dom(X1))
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370286,c_87]) ).
tcf(c_435695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ( apply(X5,sK13(X5,X4,apply(X5,sK2(set_intersection2(X0,X1),X2,X3)))) = apply(X5,sK2(set_intersection2(X0,X1),X2,X3)) )
| ~ function(X5)
| ~ relation(X5)
| ~ subset(X0,relation_dom(X5))
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_370286,c_369671]) ).
tcf(c_435696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X0,X4),X5,X6),X6)
| ( set_intersection2(set_intersection2(X0,X4),X5) = X6 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370286,c_369799]) ).
tcf(c_435697,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X0,X4),X5,X6),X6)
| ( set_intersection2(set_intersection2(X0,X4),X5) = X6 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370286,c_369798]) ).
tcf(c_435698,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370286,c_369596]) ).
tcf(c_435699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370286,c_369558]) ).
tcf(c_435700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ( apply(X1,sK13(X1,X2,sK2(set_intersection2(X0,X3),X4,X5))) = sK2(set_intersection2(X0,X3),X4,X5) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370286,c_112]) ).
tcf(c_435701,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ function(X5)
| ~ relation(X5)
| ~ subset(X0,relation_dom(X5))
| ~ empty(relation_image(X5,X4))
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X4) ),
inference(superposition,[status(thm)],[c_370286,c_369501]) ).
tcf(c_435702,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(set_intersection2(X0,X1),X2,X3),X4)
| in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(X0,sK10(sK2(set_intersection2(X0,X1),X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_370286,c_369085]) ).
tcf(c_435703,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_370286,c_372426]) ).
tcf(c_435704,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(sK2(set_intersection2(X0,X1),X2,X3))
| in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(X0,sK16(sK2(set_intersection2(X0,X1),X2,X3))) ),
inference(superposition,[status(thm)],[c_370286,c_370746]) ).
tcf(c_435705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| in(sK2(X1,X2,sK2(set_intersection2(X0,X3),X4,X5)),X1)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ( sK2(set_intersection2(X0,X3),X4,X5) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(set_intersection2(X0,X3),X4,X5))) ),
inference(superposition,[status(thm)],[c_370286,c_369079]) ).
tcf(c_435706,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| in(sK2(X1,X2,sK2(set_intersection2(X0,X3),X4,X5)),X2)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ( sK2(set_intersection2(X0,X3),X4,X5) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(set_intersection2(X0,X3),X4,X5))) ),
inference(superposition,[status(thm)],[c_370286,c_369078]) ).
tcf(c_435707,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(sK2(set_intersection2(X0,X1),X2,X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ( set_intersection2(sK2(set_intersection2(X0,X1),X2,X3),X4) = X5 )
| ~ subset(X0,sK2(sK2(set_intersection2(X0,X1),X2,X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_370286,c_369076]) ).
tcf(c_435710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X2),X3,X4),X4)
| in(sK2(X1,sK2(set_intersection2(X0,X2),X3,X4),X5),X5)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ( set_intersection2(X1,sK2(set_intersection2(X0,X2),X3,X4)) = X5 )
| ~ subset(X0,sK2(X1,sK2(set_intersection2(X0,X2),X3,X4),X5)) ),
inference(superposition,[status(thm)],[c_370286,c_369077]) ).
tcf(c_435711,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X5,relation_image(X1,sK2(set_intersection2(X0,X2),X3,X4)))
| ~ subset(X0,sK13(X1,sK2(set_intersection2(X0,X2),X3,X4),X5)) ),
inference(superposition,[status(thm)],[c_370286,c_369593]) ).
tcf(c_435712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X0,X4),X5,X6),X6)
| ( set_intersection2(set_intersection2(X0,X4),X5) = X6 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(set_intersection2(X0,X4),X5,X6)))) = sK13(X1,relation_image(X2,X3),sK2(set_intersection2(X0,X4),X5,X6)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_370286,c_369672]) ).
tcf(c_435713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X2),X3,X4),X4)
| in(sK11(X1,sK2(set_intersection2(X0,X2),X3,X4),X5),X5)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ( relation_image(X1,sK2(set_intersection2(X0,X2),X3,X4)) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK2(set_intersection2(X0,X2),X3,X4),X5)) ),
inference(superposition,[status(thm)],[c_370286,c_369298]) ).
tcf(c_435714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ( sK2(set_intersection2(X0,X3),X4,X5) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK2(set_intersection2(X0,X3),X4,X5))) = sK11(X1,X2,sK2(set_intersection2(X0,X3),X4,X5)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(set_intersection2(X0,X3),X4,X5))) ),
inference(superposition,[status(thm)],[c_370286,c_369435]) ).
tcf(c_435715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| in(sK12(X1,X2,sK2(set_intersection2(X0,X3),X4,X5)),X2)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ( sK2(set_intersection2(X0,X3),X4,X5) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(set_intersection2(X0,X3),X4,X5))) ),
inference(superposition,[status(thm)],[c_370286,c_369306]) ).
tcf(c_435716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| in(sK12(X1,X2,sK2(set_intersection2(X0,X3),X4,X5)),relation_dom(X1))
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ( sK2(set_intersection2(X0,X3),X4,X5) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(set_intersection2(X0,X3),X4,X5))) ),
inference(superposition,[status(thm)],[c_370286,c_369205]) ).
tcf(c_435717,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),sK5)
| in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_370286,c_412536]) ).
tcf(c_435718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),sK8)
| in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_370286,c_413867]) ).
tcf(c_435719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| in(sK7(X1,X2,sK2(set_intersection2(X0,X3),X4,X5)),relation_dom(X1))
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ( sK2(set_intersection2(X0,X3),X4,X5) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(set_intersection2(X0,X3),X4,X5))) ),
inference(superposition,[status(thm)],[c_370286,c_369084]) ).
tcf(c_435720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X3),X4,X5),X5)
| in(apply(X1,sK7(X1,X2,sK2(set_intersection2(X0,X3),X4,X5))),X2)
| ( set_intersection2(set_intersection2(X0,X3),X4) = X5 )
| ( sK2(set_intersection2(X0,X3),X4,X5) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(set_intersection2(X0,X3),X4,X5))) ),
inference(superposition,[status(thm)],[c_370286,c_369083]) ).
tcf(c_435721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X2),X3,X4),X4)
| in(sK7(X1,sK2(set_intersection2(X0,X2),X3,X4),X5),X5)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ( relation_inverse_image(X1,sK2(set_intersection2(X0,X2),X3,X4)) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK2(set_intersection2(X0,X2),X3,X4),X5))) ),
inference(superposition,[status(thm)],[c_370286,c_369082]) ).
tcf(c_435722,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X2),X1,set_intersection2(X0,X2)),set_intersection2(X0,X2))
| ( set_intersection2(set_intersection2(X0,X2),X1) = set_intersection2(X0,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370286,c_423425]) ).
tcf(c_435723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ( set_intersection2(sK2(set_intersection2(X0,X1),X2,X3),X4) = sK2(set_intersection2(X0,X1),X2,X3) )
| ~ subset(X0,sK2(sK2(set_intersection2(X0,X1),X2,X3),X4,sK2(set_intersection2(X0,X1),X2,X3))) ),
inference(superposition,[status(thm)],[c_370286,c_370076]) ).
tcf(c_435724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ( set_intersection2(X1,sK2(set_intersection2(X0,X2),X3,X4)) = sK2(set_intersection2(X0,X2),X3,X4) )
| ~ subset(X0,sK2(X1,sK2(set_intersection2(X0,X2),X3,X4),sK2(set_intersection2(X0,X2),X3,X4))) ),
inference(superposition,[status(thm)],[c_370286,c_370144]) ).
tcf(c_435725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X2),X3,X4),X4)
| in(sK2(set_intersection2(X0,X2),X3,X4),X1)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_370286,c_430730]) ).
tcf(c_435728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X0,X4),X5,X6),X6)
| in(sK2(set_intersection2(X1,X2),X3,sK2(set_intersection2(X0,X4),X5,X6)),X1)
| ( set_intersection2(set_intersection2(X0,X4),X5) = X6 )
| ( sK2(set_intersection2(X0,X4),X5,X6) = set_intersection2(set_intersection2(X1,X2),X3) )
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK2(set_intersection2(X0,X4),X5,X6))) ),
inference(superposition,[status(thm)],[c_370286,c_370273]) ).
tcf(c_435729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(sK2(set_intersection2(X0,X1),X2,X3),X4),X5,X6),X6)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ( set_intersection2(set_intersection2(sK2(set_intersection2(X0,X1),X2,X3),X4),X5) = X6 )
| ~ subset(X0,sK2(set_intersection2(sK2(set_intersection2(X0,X1),X2,X3),X4),X5,X6)) ),
inference(superposition,[status(thm)],[c_370286,c_370285]) ).
tcf(c_435730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X2),X3,X1),X1)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X1 )
| ~ subset(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_370286]) ).
tcf(c_435744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X1,X2),X3)
| in(sK2(set_intersection2(empty_set,X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_435652,c_369177]) ).
tcf(c_435747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,X3),X3)
| in(sK2(empty_set,X2,X3),X1)
| ( set_intersection2(empty_set,X2) = X3 )
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_435651,c_64]) ).
tcf(c_435753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X1,X2),X2)
| in(sK2(set_intersection2(empty_set,X0),X1,X2),X3)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_435644,c_369177]) ).
tcf(c_435784,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK8),X1,X2),X2)
| in(sK2(sK15(sK8),X1,X2),X0)
| ( set_intersection2(sK15(sK8),X1) = X2 )
| ~ subset(sK8,X0) ),
inference(light_normalisation,[status(thm)],[c_435655,c_411956]) ).
tcf(c_435789,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK15(sK5),X1,X2),X2)
| in(sK2(sK15(sK5),X1,X2),X0)
| ( set_intersection2(sK15(sK5),X1) = X2 )
| ~ subset(sK5,X0) ),
inference(light_normalisation,[status(thm)],[c_435654,c_411955]) ).
tcf(c_435848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(X0)),X2,X3),X3)
| in(sK2(sK16(powerset(X0)),X2,X3),X1)
| ( set_intersection2(sK16(powerset(X0)),X2) = X3 )
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_435653,c_397130]) ).
tcf(c_436284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 )
| ~ in(X0,sK2(set_intersection2(X0,X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_397136,c_370285]) ).
tcf(c_436285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397136,c_370278]) ).
tcf(c_436286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X3)
| in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397136,c_370278]) ).
tcf(c_436287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397136,c_370277]) ).
tcf(c_436288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X4)
| in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397136,c_370277]) ).
tcf(c_436289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| element(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_370275]) ).
tcf(c_436290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_370275]) ).
tcf(c_436291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X0),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_370266]) ).
tcf(c_436292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X0),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_370261]) ).
tcf(c_436293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397136,c_370220]) ).
tcf(c_436294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2),X3) = X4 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2),X3,X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2),X3,X4),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2),X3,X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2),X3,X4),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397136,c_370217]) ).
tcf(c_436295,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X0),set_intersection2(X0,set_intersection2(X0,X1)))
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X0),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397136,c_426065]) ).
tcf(c_436296,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X0)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = set_intersection2(X0,set_intersection2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_397136,c_370081]) ).
tcf(c_436297,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = set_intersection2(X0,set_intersection2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_397136,c_370080]) ).
tcf(c_436298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X0,X3)
| ~ in(X0,X1)
| ~ subset(set_intersection2(X1,X2),X3)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_397136,c_369930]) ).
tcf(c_436299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ in(X0,X1)
| ~ subset(set_intersection2(X1,X2),X3)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_397136,c_369786]) ).
tcf(c_436300,plain,
! [X0: $i,X1: $i] :
( element(sK16(set_intersection2(X0,X1)),X0)
| empty(set_intersection2(X0,set_intersection2(X0,X1))) ),
inference(superposition,[status(thm)],[c_397136,c_389068]) ).
tcf(c_436301,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),X0))
| in(sK16(set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397136,c_389060]) ).
tcf(c_436302,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,set_intersection2(X0,X1)))
| element(sK16(set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397136,c_388051]) ).
tcf(c_436303,plain,
! [X0: $i,X1: $i] :
( in(sK16(set_intersection2(X0,X1)),X0)
| empty(set_intersection2(set_intersection2(X0,X1),X0)) ),
inference(superposition,[status(thm)],[c_397136,c_388043]) ).
tcf(c_436304,plain,
! [X0: $i,X1: $i] :
( in(sK16(set_intersection2(X0,X1)),X0)
| empty(set_intersection2(X0,set_intersection2(X0,X1))) ),
inference(superposition,[status(thm)],[c_397136,c_370751]) ).
tcf(c_436305,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,set_intersection2(X0,X1)))
| in(sK16(set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397136,c_370750]) ).
tcf(c_436306,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ in(X2,set_intersection2(X0,X1))
| ~ in(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_397136,c_369080]) ).
tcf(c_436310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ in(X0,X1)
| ~ subset(set_intersection2(X1,X2),X3)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_397136,c_369016]) ).
tcf(c_436312,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X0,set_intersection2(X0,X1)),X2)
| in(sK10(set_intersection2(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_397136,c_368986]) ).
tcf(c_436314,plain,
! [X0: $i,X1: $i] : subset(set_intersection2(X0,X1),set_intersection2(X0,X1)),
inference(superposition,[status(thm)],[c_397136,c_380850]) ).
tcf(c_436315,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X0,set_intersection2(X0,X1)),X2)
| in(sK10(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397136,c_368985]) ).
tcf(c_436316,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X1)
| ~ empty(set_intersection2(X1,X2))
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_397136,c_368869]) ).
tcf(c_436317,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,set_intersection2(X0,X1)) = X2 )
| ~ subset(X2,X0)
| ~ subset(X2,set_intersection2(X0,X1))
| ~ subset(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_397136,c_368558]) ).
tcf(c_436318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),set_intersection2(X0,X1))
| in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_368503]) ).
tcf(c_436319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_368503]) ).
tcf(c_436320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_368481]) ).
tcf(c_436321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_368481]) ).
tcf(c_436322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),X3)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397136,c_368471]) ).
tcf(c_436324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| in(sK2(set_intersection2(X1,set_intersection2(X1,X2)),X3,relation_inverse_image(X0,X4)),X1)
| ( set_intersection2(set_intersection2(X1,set_intersection2(X1,X2)),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370280]) ).
tcf(c_436325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),X1)
| in(sK2(set_intersection2(X1,set_intersection2(X1,X2)),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,set_intersection2(X1,X2)),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370280]) ).
tcf(c_436326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4))),X4)
| in(sK2(set_intersection2(X1,set_intersection2(X1,X2)),X3,relation_inverse_image(X0,X4)),X1)
| ( set_intersection2(set_intersection2(X1,set_intersection2(X1,X2)),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370279]) ).
tcf(c_436327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X2),X3,relation_inverse_image(X0,X4)),X1)
| in(apply(X0,sK2(set_intersection2(X1,set_intersection2(X1,X2)),X3,relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(set_intersection2(X1,set_intersection2(X1,X2)),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370279]) ).
tcf(c_436328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,set_intersection2(X1,X2)),X3) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370276]) ).
tcf(c_436329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,set_intersection2(X1,X2)),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,set_intersection2(X1,X2)),X3) = X0 )
| ~ in(X0,sK2(set_intersection2(X1,X2),X3,X0)) ),
inference(superposition,[status(thm)],[c_397136,c_370273]) ).
tcf(c_436330,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X1)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X1,X2))) = set_intersection2(X1,set_intersection2(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_397136,c_370149]) ).
tcf(c_436331,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),set_intersection2(X1,X2))
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X1,X2))) = set_intersection2(X1,set_intersection2(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_397136,c_370148]) ).
tcf(c_436332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,set_intersection2(X1,X2),X3),X3)
| in(sK12(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3),X1)
| ( relation_image(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_369303]) ).
tcf(c_436333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X1,X2),X3),X1)
| in(sK11(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3),X3)
| ( relation_image(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_369303]) ).
tcf(c_436334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,set_intersection2(X1,X2),X3),X3)
| in(sK12(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3),set_intersection2(X1,X2))
| ( relation_image(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_369302]) ).
tcf(c_436335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X1,X2),X3),set_intersection2(X1,X2))
| in(sK11(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3),X3)
| ( relation_image(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_369302]) ).
tcf(c_436336,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_intersection2(X1,set_intersection2(X1,X2)))
| ~ in(sK10(X0,set_intersection2(X1,X2)),X1)
| ~ in(sK10(X0,set_intersection2(X1,set_intersection2(X1,X2))),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_397136,c_368972]) ).
tcf(c_436337,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_intersection2(X1,X2))
| ~ in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_397136,c_368928]) ).
tcf(c_436338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X1,X2),X3)),X1)
| in(sK7(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3),X3)
| ( relation_inverse_image(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_368703]) ).
tcf(c_436339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3)),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_368703]) ).
tcf(c_436340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,X2),X3)),set_intersection2(X1,X2))
| ( relation_inverse_image(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_368702]) ).
tcf(c_436341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3)),set_intersection2(X1,X2))
| ( relation_inverse_image(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_368702]) ).
tcf(c_436342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,set_intersection2(X1,X2),X3)),X1)
| ~ in(sK7(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3),X3)
| ~ in(sK7(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3)),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_397136,c_368654]) ).
tcf(c_436343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),set_intersection2(X1,X2))
| in(sK2(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_368504]) ).
tcf(c_436344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3),set_intersection2(X1,X2))
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_368504]) ).
tcf(c_436345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X1)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_368482]) ).
tcf(c_436346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_368482]) ).
tcf(c_436351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),set_intersection2(X0,X1))
| in(sK2(set_intersection2(set_intersection2(X0,X1),X0),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X0),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_370266]) ).
tcf(c_436352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X0),X2,X3),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X0),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_370261]) ).
tcf(c_436353,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X0,X1),X2)
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397136,c_380845]) ).
tcf(c_436354,plain,
! [X0: $i,X1: $i] :
( function(set_intersection2(X0,X1))
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397136,c_381376]) ).
tcf(c_436355,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X0,X1))
| ~ empty(set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397136,c_381375]) ).
tcf(c_436358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X2),X3,X4),X1)
| in(sK2(set_intersection2(X0,set_intersection2(X0,X2)),X3,X4),X4)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X2)),X3) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397136,c_370286]) ).
tcf(c_436359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X2),X3,X4),X4)
| in(sK2(set_intersection2(X0,set_intersection2(X0,X2)),X3,X4),X1)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X2)),X3) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397136,c_370286]) ).
tcf(c_436360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X3) = X4 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X3,X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X3,X4),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X3,X4),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X3,X4),set_intersection2(set_intersection2(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_397136,c_370217]) ).
tcf(c_436361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(X2,set_intersection2(X2,X3)),X4) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,set_intersection2(X2,X3)),X4,relation_image(X0,X1)))) = sK2(set_intersection2(X2,set_intersection2(X2,X3)),X4,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370281]) ).
tcf(c_436362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,X0),X1)
| in(sK2(set_intersection2(X2,set_intersection2(X2,X3)),X4,X0),X2)
| ( set_intersection2(set_intersection2(X2,set_intersection2(X2,X3)),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397136,c_370274]) ).
tcf(c_436363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X3),X4,X0),X2)
| in(sK2(set_intersection2(X2,set_intersection2(X2,X3)),X4,X0),X1)
| ( set_intersection2(set_intersection2(X2,set_intersection2(X2,X3)),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397136,c_370274]) ).
tcf(c_436364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X1,set_intersection2(X2,X3),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,set_intersection2(X2,X3)))) ),
inference(superposition,[status(thm)],[c_397136,c_369598]) ).
tcf(c_436365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X1,set_intersection2(X2,X3),X0),set_intersection2(X2,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,set_intersection2(X2,X3)))) ),
inference(superposition,[status(thm)],[c_397136,c_369597]) ).
tcf(c_436366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),X2)
| ( set_intersection2(X2,set_intersection2(X2,X3)) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,set_intersection2(X2,X3)))) = sK11(X0,X1,set_intersection2(X2,set_intersection2(X2,X3))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_369440]) ).
tcf(c_436367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X2,X3)),set_intersection2(X2,X3))
| ( set_intersection2(X2,set_intersection2(X2,X3)) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,set_intersection2(X2,X3)))) = sK11(X0,X1,set_intersection2(X2,set_intersection2(X2,X3))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_369439]) ).
tcf(c_436368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X3,set_intersection2(X1,X2)),X1)
| in(sK12(X0,X3,set_intersection2(X1,set_intersection2(X1,X2))),X3)
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_369311]) ).
tcf(c_436369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,set_intersection2(X1,X2)),X3)
| in(sK11(X0,X3,set_intersection2(X1,set_intersection2(X1,X2))),X1)
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_369311]) ).
tcf(c_436370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X3,set_intersection2(X1,X2)),set_intersection2(X1,X2))
| in(sK12(X0,X3,set_intersection2(X1,set_intersection2(X1,X2))),X3)
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_369310]) ).
tcf(c_436371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,set_intersection2(X1,X2)),X3)
| in(sK11(X0,X3,set_intersection2(X1,set_intersection2(X1,X2))),set_intersection2(X1,X2))
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_369310]) ).
tcf(c_436372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,set_intersection2(X1,X2)),relation_dom(X0))
| in(sK11(X0,X3,set_intersection2(X1,set_intersection2(X1,X2))),X1)
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_369210]) ).
tcf(c_436373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X3,set_intersection2(X1,X2)),X1)
| in(sK12(X0,X3,set_intersection2(X1,set_intersection2(X1,X2))),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_369210]) ).
tcf(c_436374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,set_intersection2(X1,X2)),relation_dom(X0))
| in(sK11(X0,X3,set_intersection2(X1,set_intersection2(X1,X2))),set_intersection2(X1,X2))
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_369209]) ).
tcf(c_436375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X3,set_intersection2(X1,X2)),set_intersection2(X1,X2))
| in(sK12(X0,X3,set_intersection2(X1,set_intersection2(X1,X2))),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_369209]) ).
tcf(c_436376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_inverse_image(X0,set_intersection2(X2,X3)))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X2)
| ~ in(apply(X0,X1),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_397136,c_368735]) ).
tcf(c_436377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X3,set_intersection2(X1,X2))),X3)
| in(sK7(X0,X3,set_intersection2(X1,set_intersection2(X1,X2))),X1)
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_368701]) ).
tcf(c_436378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X1,X2)),X1)
| in(apply(X0,sK7(X0,X3,set_intersection2(X1,set_intersection2(X1,X2)))),X3)
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_368701]) ).
tcf(c_436379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X3,set_intersection2(X1,X2))),X3)
| in(sK7(X0,X3,set_intersection2(X1,set_intersection2(X1,X2))),set_intersection2(X1,X2))
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_368700]) ).
tcf(c_436380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X1,X2)),set_intersection2(X1,X2))
| in(apply(X0,sK7(X0,X3,set_intersection2(X1,set_intersection2(X1,X2)))),X3)
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_368700]) ).
tcf(c_436381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X1,X2)),relation_dom(X0))
| in(sK7(X0,X3,set_intersection2(X1,set_intersection2(X1,X2))),X1)
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_368673]) ).
tcf(c_436382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X1,X2)),X1)
| in(sK7(X0,X3,set_intersection2(X1,set_intersection2(X1,X2))),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_368673]) ).
tcf(c_436383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X1,X2)),relation_dom(X0))
| in(sK7(X0,X3,set_intersection2(X1,set_intersection2(X1,X2))),set_intersection2(X1,X2))
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_368672]) ).
tcf(c_436384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X1,X2)),set_intersection2(X1,X2))
| in(sK7(X0,X3,set_intersection2(X1,set_intersection2(X1,X2))),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X1,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_368672]) ).
tcf(c_436385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),X2)
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X0,X1))),set_intersection2(X0,X1))
| ( set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397136,c_368506]) ).
tcf(c_436386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),set_intersection2(X0,X1))
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X0,X1))),X2)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397136,c_368506]) ).
tcf(c_436387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),X3)
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X0,X1))),set_intersection2(X0,X1))
| ( set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397136,c_368505]) ).
tcf(c_436388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),set_intersection2(X0,X1))
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X0,X1))),X3)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397136,c_368505]) ).
tcf(c_436389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),X2)
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X0,X1))),X0)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397136,c_368484]) ).
tcf(c_436390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),X0)
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X0,X1))),X2)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397136,c_368484]) ).
tcf(c_436391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),X3)
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X0,X1))),X0)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397136,c_368483]) ).
tcf(c_436392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),X0)
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X0,X1))),X3)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397136,c_368483]) ).
tcf(c_436393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X3,X4))),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,set_intersection2(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_397136,c_370278]) ).
tcf(c_436394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X3)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X3,X4))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,set_intersection2(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_397136,c_370278]) ).
tcf(c_436395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X3,X4))),set_intersection2(X3,X4))
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,set_intersection2(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_397136,c_370277]) ).
tcf(c_436396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,X4)),set_intersection2(X3,X4))
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X3,X4))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,set_intersection2(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_397136,c_370277]) ).
tcf(c_436407,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| in(sK16(set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_436305,c_397136]) ).
tcf(c_436410,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X0,X1))
| element(sK16(set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_436302,c_397136]) ).
tcf(c_436418,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X0,X1),X2)
| in(sK10(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_436315,c_397136]) ).
tcf(c_436445,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ subset(X2,X0)
| ~ subset(X2,set_intersection2(X0,X1))
| ~ subset(set_intersection2(X0,X1),X2) ),
inference(light_normalisation,[status(thm)],[c_436317,c_397136]) ).
tcf(c_436457,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X0,X1) ) ),
inference(light_normalisation,[status(thm)],[c_436297,c_397136]) ).
tcf(c_436463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),X3)
| in(sK2(X2,X3,set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(light_normalisation,[status(thm)],[c_436392,c_397136]) ).
tcf(c_436468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),X2)
| in(sK2(X2,X3,set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(light_normalisation,[status(thm)],[c_436390,c_397136]) ).
tcf(c_436489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),X3)
| in(sK2(X2,X3,set_intersection2(X0,X1)),set_intersection2(X0,X1))
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(light_normalisation,[status(thm)],[c_436388,c_397136]) ).
tcf(c_436494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),X2)
| in(sK2(X2,X3,set_intersection2(X0,X1)),set_intersection2(X0,X1))
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(light_normalisation,[status(thm)],[c_436386,c_397136]) ).
tcf(c_436499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(X0,X1),X2,X3),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 ) ),
inference(light_normalisation,[status(thm)],[c_436352,c_397166]) ).
tcf(c_436701,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),set_intersection2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_436322,c_397136]) ).
tcf(c_436720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),set_intersection2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_436294,c_397136]) ).
tcf(c_436904,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X0)
| in(sK2(set_intersection2(X0,X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_53,c_370287]) ).
tcf(c_436907,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(empty_set,X1,X2),X0)
| in(sK2(set_intersection2(X0,empty_set),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_370287]) ).
tcf(c_436908,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(empty_set,X1,X2),empty_set)
| in(sK2(set_intersection2(empty_set,X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_370287]) ).
tcf(c_436909,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(sK16(powerset(X0)),X1,X2),X0)
| in(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_370287]) ).
tcf(c_436910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X0)
| in(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_370287]) ).
tcf(c_436911,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK5),X0,X1),sK5)
| in(sK2(set_intersection2(sK5,sK15(sK5)),X0,X1),X1)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_370287]) ).
tcf(c_436912,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK8),X0,X1),sK8)
| in(sK2(set_intersection2(sK8,sK15(sK8)),X0,X1),X1)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_370287]) ).
tcf(c_436913,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| element(sK2(set_intersection2(X0,X0),X1,X2),X0)
| ( set_intersection2(set_intersection2(X0,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_53,c_370287]) ).
tcf(c_436916,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| element(sK2(set_intersection2(X0,empty_set),X1,X2),X0)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_370287]) ).
tcf(c_436917,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| element(sK2(set_intersection2(empty_set,X0),X1,X2),empty_set)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_370287]) ).
tcf(c_436918,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),X2)
| element(sK2(set_intersection2(X0,sK16(powerset(X0))),X1,X2),X0)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_370287]) ).
tcf(c_436919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| element(sK2(set_intersection2(X0,set_intersection2(X0,X1)),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_370287]) ).
tcf(c_436920,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK5),X0,X1),X1)
| element(sK2(set_intersection2(sK5,sK15(sK5)),X0,X1),sK5)
| ( set_intersection2(set_intersection2(sK5,sK15(sK5)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_370287]) ).
tcf(c_436921,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK15(sK8),X0,X1),X1)
| element(sK2(set_intersection2(sK8,sK15(sK8)),X0,X1),sK8)
| ( set_intersection2(set_intersection2(sK8,sK15(sK8)),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_370287]) ).
tcf(c_436923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(set_intersection2(powerset(X0),X1),X2,X3),X0)
| in(sK2(set_intersection2(powerset(X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(powerset(X0),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370287,c_99]) ).
tcf(c_436925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X2,X3),X4,X0),X2)
| element(sK2(set_intersection2(X2,X3),X4,X0),X1)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370287,c_321]) ).
tcf(c_436926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X2,X3),X4,X0),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370287,c_320]) ).
tcf(c_436927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X1,X2),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ in(X0,sK2(set_intersection2(X1,X2),X3,X0)) ),
inference(superposition,[status(thm)],[c_370287,c_97]) ).
tcf(c_436935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(set_intersection2(X0,X1),X2,relation_dom(X3))))) = apply(X3,sK2(set_intersection2(X0,X1),X2,relation_dom(X3))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370287,c_369671]) ).
tcf(c_436936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X3,X4),X5,relation_image(X2,X0)),X3)
| ( set_intersection2(set_intersection2(X3,X4),X5) = relation_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370287,c_369799]) ).
tcf(c_436937,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X2,X3),X4,relation_image(X0,X5)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370287,c_369798]) ).
tcf(c_436938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X2,X3),X4,relation_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370287,c_369596]) ).
tcf(c_436939,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X1,X2),X3,relation_image(X0,X4)),X1)
| ( set_intersection2(set_intersection2(X1,X2),X3) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370287,c_369558]) ).
tcf(c_436941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = relation_dom(X3) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370287,c_369501]) ).
tcf(c_436942,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(X0,X1),X2,empty_set),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = empty_set ) ),
inference(superposition,[status(thm)],[c_370287,c_372426]) ).
tcf(c_436943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_370287,c_370220]) ).
tcf(c_436944,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(set_intersection2(X0,X1),X2,X0),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_370287,c_368471]) ).
tcf(c_436945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(X3,X4),X5,relation_image(X0,relation_image(X1,X2))),X3)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(set_intersection2(X3,X4),X5) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,X4),X5,relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(X3,X4),X5,relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370287,c_369672]) ).
tcf(c_436946,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),sK5)
| element(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_370287,c_412536]) ).
tcf(c_436947,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),sK8)
| element(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_370287,c_413867]) ).
tcf(c_436948,plain,
! [X0: $i,X1: $i] :
( element(sK2(set_intersection2(X0,X1),set_intersection2(X0,X1),set_intersection2(X0,X1)),X0)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_370287,c_423425]) ).
tcf(c_436949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),X2,sK16(powerset(X3))),X0)
| in(sK2(set_intersection2(X0,X1),X2,sK16(powerset(X3))),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK16(powerset(X3)) ) ),
inference(superposition,[status(thm)],[c_370287,c_430730]) ).
tcf(c_436951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_370287,c_370217]) ).
tcf(c_436971,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK8),X0,X1),sK8)
| in(sK2(sK15(sK8),X0,X1),X1)
| ( set_intersection2(sK15(sK8),X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_436921,c_411956]) ).
tcf(c_436975,plain,
! [X0: $i,X1: $i] :
( element(sK2(sK15(sK5),X0,X1),sK5)
| in(sK2(sK15(sK5),X0,X1),X1)
| ( set_intersection2(sK15(sK5),X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_436920,c_411955]) ).
tcf(c_436995,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(sK16(powerset(X0)),X1,X2),X0)
| in(sK2(sK16(powerset(X0)),X1,X2),X2)
| ( set_intersection2(sK16(powerset(X0)),X1) = X2 ) ),
inference(light_normalisation,[status(thm)],[c_436918,c_397130]) ).
tcf(c_437230,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,X0),X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53,c_370288]) ).
tcf(c_437233,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,empty_set),X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_64,c_370288]) ).
tcf(c_437234,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(empty_set,X1,X2),X2)
| ( set_intersection2(set_intersection2(empty_set,X0),X1) = X2 )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_368545,c_370288]) ).
tcf(c_437235,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(sK16(powerset(X0)),X1,X2),X2)
| ( set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1) = X2 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370288]) ).
tcf(c_437236,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2) = X3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370288]) ).
tcf(c_437240,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(X2,X3),X4,X0),X1)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370288,c_321]) ).
tcf(c_437241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ~ empty(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370288,c_320]) ).
tcf(c_437242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X1,X2),X3) = X0 )
| ~ empty(X1)
| ~ in(X0,sK2(set_intersection2(X1,X2),X3,X0)) ),
inference(superposition,[status(thm)],[c_370288,c_97]) ).
tcf(c_437245,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X2),X3) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370288,c_91]) ).
tcf(c_437250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(set_intersection2(X0,X1),X2,relation_dom(X3))))) = apply(X3,sK2(set_intersection2(X0,X1),X2,relation_dom(X3))) )
| ~ empty(X0)
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370288,c_369671]) ).
tcf(c_437251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(X3,X4),X5) = relation_image(X2,X0) )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370288,c_369799]) ).
tcf(c_437252,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(X2,X3),X4) = relation_image(X0,X5) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370288,c_369798]) ).
tcf(c_437253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X1,X3),X4) = relation_image(X0,X2) )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370288,c_369596]) ).
tcf(c_437254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X1,X2),X3) = relation_image(X0,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370288,c_369558]) ).
tcf(c_437256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = relation_dom(X3) )
| ~ empty(X0)
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(set_intersection2(X0,X1),X2,relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370288,c_369501]) ).
tcf(c_437258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ empty(X0)
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_370288,c_370220]) ).
tcf(c_437259,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X0 )
| ~ empty(X0)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X0),X0) ),
inference(superposition,[status(thm)],[c_370288,c_368471]) ).
tcf(c_437260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( relation_image(X0,relation_image(X1,X3)) = set_intersection2(set_intersection2(X2,X4),X5) )
| ( apply(X1,sK13(X1,X3,sK13(X0,relation_image(X1,X3),sK2(set_intersection2(X2,X4),X5,relation_image(X0,relation_image(X1,X3)))))) = sK13(X0,relation_image(X1,X3),sK2(set_intersection2(X2,X4),X5,relation_image(X0,relation_image(X1,X3)))) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370288,c_369672]) ).
tcf(c_437261,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK5)),sK5)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK15(sK5) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370288,c_412536]) ).
tcf(c_437262,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK15(sK8)),sK8)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK15(sK8) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370288,c_413867]) ).
tcf(c_437263,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)) = set_intersection2(X0,X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370288,c_423425]) ).
tcf(c_437264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,sK16(powerset(X3))),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = sK16(powerset(X3)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370288,c_430730]) ).
tcf(c_437266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 )
| ~ empty(set_intersection2(X0,X1))
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0) ),
inference(superposition,[status(thm)],[c_370288,c_370217]) ).
tcf(c_437270,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X0,X1),X1)
| ( set_intersection2(empty_set,X0) = X1 )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_437234,c_368545]) ).
tcf(c_437271,plain,
! [X0: $i,X1: $i] :
( in(sK2(empty_set,X1,X0),X0)
| ( X0 = empty_set )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_437270,c_368545]) ).
tcf(c_437435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)),X2,X3),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_53,c_370289]) ).
tcf(c_437438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X0,X1),empty_set),X2,X3),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),empty_set),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_64,c_370289]) ).
tcf(c_437439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(set_intersection2(X0,X1))),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X0,X1),sK16(powerset(set_intersection2(X0,X1)))),X2,X3),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),sK16(powerset(set_intersection2(X0,X1)))),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397130,c_370289]) ).
tcf(c_437440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X3,X4),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397136,c_370289]) ).
tcf(c_437441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X0,X0),X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X0),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_53,c_370289]) ).
tcf(c_437442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X0),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_63,c_370289]) ).
tcf(c_437444,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X0,empty_set),X1),X2,X3),empty_set)
| ( set_intersection2(set_intersection2(set_intersection2(X0,empty_set),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_64,c_370289]) ).
tcf(c_437445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(empty_set,X0),X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(set_intersection2(empty_set,X0),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_368545,c_370289]) ).
tcf(c_437446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1),X2,X3),sK16(powerset(X0)))
| ( set_intersection2(set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397130,c_370289]) ).
tcf(c_437447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2),X3,X4),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397136,c_370289]) ).
tcf(c_437448,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),X2)
| in(sK2(set_intersection2(set_intersection2(sK5,sK15(sK5)),X0),X1,X2),sK15(sK5))
| ( set_intersection2(set_intersection2(set_intersection2(sK5,sK15(sK5)),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_411955,c_370289]) ).
tcf(c_437449,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),X2)
| in(sK2(set_intersection2(set_intersection2(sK8,sK15(sK8)),X0),X1,X2),sK15(sK8))
| ( set_intersection2(set_intersection2(set_intersection2(sK8,sK15(sK8)),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_411956,c_370289]) ).
tcf(c_437450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X1)
| in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_53,c_370289]) ).
tcf(c_437453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,X3),X1)
| in(sK2(set_intersection2(set_intersection2(X0,X1),empty_set),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),empty_set),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_64,c_370289]) ).
tcf(c_437454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(set_intersection2(X0,X1))),X2,X3),X1)
| in(sK2(set_intersection2(set_intersection2(X0,X1),sK16(powerset(set_intersection2(X0,X1)))),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),sK16(powerset(set_intersection2(X0,X1)))),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397130,c_370289]) ).
tcf(c_437455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X1)
| in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397136,c_370289]) ).
tcf(c_437456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| in(sK2(set_intersection2(set_intersection2(X0,X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X0),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_53,c_370289]) ).
tcf(c_437457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X0),X2),X3,X4),X1)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_63,c_370289]) ).
tcf(c_437459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,X3),empty_set)
| in(sK2(set_intersection2(set_intersection2(X0,empty_set),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,empty_set),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_64,c_370289]) ).
tcf(c_437460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,X3),X0)
| in(sK2(set_intersection2(set_intersection2(empty_set,X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(empty_set,X0),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_368545,c_370289]) ).
tcf(c_437461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),sK16(powerset(X0)))
| in(sK2(set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397130,c_370289]) ).
tcf(c_437462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),set_intersection2(X0,X1))
| in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397136,c_370289]) ).
tcf(c_437463,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),sK15(sK5))
| in(sK2(set_intersection2(set_intersection2(sK5,sK15(sK5)),X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(set_intersection2(sK5,sK15(sK5)),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_411955,c_370289]) ).
tcf(c_437464,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),sK15(sK8))
| in(sK2(set_intersection2(set_intersection2(sK8,sK15(sK8)),X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(set_intersection2(sK8,sK15(sK8)),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_411956,c_370289]) ).
tcf(c_437466,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,X0),X1)
| in(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,X0),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X3),X4),X5) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370289,c_321]) ).
tcf(c_437467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,X0),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X3),X4),X5) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370289,c_320]) ).
tcf(c_437468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,X0),X2)
| ( set_intersection2(set_intersection2(set_intersection2(X1,X2),X3),X4) = X0 )
| ~ in(X0,sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,X0)) ),
inference(superposition,[status(thm)],[c_370289,c_97]) ).
tcf(c_437476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,relation_dom(X4)),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = relation_dom(X4) )
| ( apply(X4,sK13(X4,X5,apply(X4,sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,relation_dom(X4))))) = apply(X4,sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,relation_dom(X4))) )
| ~ function(X4)
| ~ relation(X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,relation_dom(X4)),X5) ),
inference(superposition,[status(thm)],[c_370289,c_369671]) ).
tcf(c_437477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(set_intersection2(X3,X4),X5),X6,relation_image(X2,X0)),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X3,X4),X5),X6) = relation_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370289,c_369799]) ).
tcf(c_437478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,relation_image(X0,X6)),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X3),X4),X5) = relation_image(X0,X6) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370289,c_369798]) ).
tcf(c_437479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,relation_image(X0,X1)),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X3),X4),X5) = relation_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370289,c_369596]) ).
tcf(c_437480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,relation_image(X0,X5)),X2)
| ( set_intersection2(set_intersection2(set_intersection2(X1,X2),X3),X4) = relation_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370289,c_369558]) ).
tcf(c_437482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,relation_dom(X4)),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = relation_dom(X4) )
| ~ function(X4)
| ~ relation(X4)
| ~ empty(relation_image(X4,X5))
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,relation_dom(X4)),X5) ),
inference(superposition,[status(thm)],[c_370289,c_369501]) ).
tcf(c_437483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,empty_set),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = empty_set ) ),
inference(superposition,[status(thm)],[c_370289,c_372426]) ).
tcf(c_437484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X2),X0),X3,X4),X2)
| ( set_intersection2(set_intersection2(set_intersection2(X1,X2),X0),X3) = X4 )
| ~ in(sK2(set_intersection2(set_intersection2(X1,X2),X0),X3,X4),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X1,X2),X0),X3,X4),X0)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X1,X2)),X3,X4),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370289,c_370220]) ).
tcf(c_437485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X1)),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X1)),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X1)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_370289,c_368471]) ).
tcf(c_437486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(set_intersection2(X3,X4),X5),X6,relation_image(X0,relation_image(X1,X2))),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X3,X4),X5),X6) = relation_image(X0,relation_image(X1,X2)) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(set_intersection2(X3,X4),X5),X6,relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(set_intersection2(X3,X4),X5),X6,relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370289,c_369672]) ).
tcf(c_437487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,sK15(sK5)),sK5)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,sK15(sK5)),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_370289,c_412536]) ).
tcf(c_437488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,sK15(sK8)),sK8)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,sK15(sK8)),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_370289,c_413867]) ).
tcf(c_437489,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(set_intersection2(X0,X1),X2)),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(set_intersection2(X0,X1),X2)) = set_intersection2(set_intersection2(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_370289,c_423425]) ).
tcf(c_437490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,sK16(powerset(X4))),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,sK16(powerset(X4))),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = sK16(powerset(X4)) ) ),
inference(superposition,[status(thm)],[c_370289,c_430730]) ).
tcf(c_437493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(set_intersection2(X2,X0),X3),X4,X5),X1)
| in(sK2(set_intersection2(set_intersection2(X2,X0),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X0),X3),X4) = X5 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370289,c_321]) ).
tcf(c_437494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,X0),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X0),X3),X4) = X5 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370289,c_320]) ).
tcf(c_437495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X0),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X1,X0),X2),X3) = X4 )
| ~ in(X0,sK2(set_intersection2(set_intersection2(X1,X0),X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_370289,c_97]) ).
tcf(c_437496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,X0),X3),X4,X5),X5)
| in(sK2(set_intersection2(set_intersection2(X2,X0),X3),X4,X5),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X0),X3),X4) = X5 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370289,c_96]) ).
tcf(c_437497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X1)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_370289,c_93]) ).
tcf(c_437498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X0),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X1,X0),X2),X3) = X4 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370289,c_91]) ).
tcf(c_437499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3),X4,X5),X5)
| in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3),X4,X5),X2)
| ( set_intersection2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3),X4) = X5 ) ),
inference(superposition,[status(thm)],[c_370289,c_59]) ).
tcf(c_437500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3),X4,X5),X5)
| in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3),X4,X5),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3),X4) = X5 ) ),
inference(superposition,[status(thm)],[c_370289,c_58]) ).
tcf(c_437501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3),X4,X5),X5)
| in(apply(X0,sK2(set_intersection2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3),X4,X5)),X2)
| ( set_intersection2(set_intersection2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370289,c_88]) ).
tcf(c_437502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3),X4,X5),X5)
| in(sK2(set_intersection2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3),X4,X5),relation_dom(X0))
| ( set_intersection2(set_intersection2(set_intersection2(X1,relation_inverse_image(X0,X2)),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370289,c_87]) ).
tcf(c_437503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,relation_dom(X1)),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,relation_dom(X1)),X2),X3) = X4 )
| ( apply(X1,sK13(X1,X5,apply(X1,sK2(set_intersection2(set_intersection2(X0,relation_dom(X1)),X2),X3,X4)))) = apply(X1,sK2(set_intersection2(set_intersection2(X0,relation_dom(X1)),X2),X3,X4)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,relation_dom(X1)),X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_370289,c_369671]) ).
tcf(c_437504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(set_intersection2(X3,relation_image(X2,X0)),X4),X5,X6),X6)
| ( set_intersection2(set_intersection2(set_intersection2(X3,relation_image(X2,X0)),X4),X5) = X6 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370289,c_369799]) ).
tcf(c_437505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,relation_image(X0,X3)),X4),X5,X6),X6)
| ( set_intersection2(set_intersection2(set_intersection2(X2,relation_image(X0,X3)),X4),X5) = X6 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370289,c_369798]) ).
tcf(c_437506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,relation_image(X0,X1)),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(set_intersection2(X2,relation_image(X0,X1)),X3),X4) = X5 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370289,c_369596]) ).
tcf(c_437507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,relation_image(X0,X2)),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(set_intersection2(X1,relation_image(X0,X2)),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370289,c_369558]) ).
tcf(c_437508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,relation_image(X0,X1)),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(set_intersection2(X2,relation_image(X0,X1)),X3),X4) = X5 )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(set_intersection2(X2,relation_image(X0,X1)),X3),X4,X5))) = sK2(set_intersection2(set_intersection2(X2,relation_image(X0,X1)),X3),X4,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370289,c_112]) ).
tcf(c_437509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,relation_dom(X1)),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,relation_dom(X1)),X2),X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X5))
| ~ in(sK2(set_intersection2(set_intersection2(X0,relation_dom(X1)),X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_370289,c_369501]) ).
tcf(c_437510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,empty_set),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,empty_set),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370289,c_372426]) ).
tcf(c_437512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4),X5,X6),X6)
| ( set_intersection2(set_intersection2(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4),X5) = X6 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4),X5,X6)))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(set_intersection2(X3,relation_image(X0,relation_image(X1,X2))),X4),X5,X6)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370289,c_369672]) ).
tcf(c_437513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,sK15(sK5)),X1),X2,X3),sK5)
| in(sK2(set_intersection2(set_intersection2(X0,sK15(sK5)),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,sK15(sK5)),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370289,c_412536]) ).
tcf(c_437514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,sK15(sK8)),X1),X2,X3),sK8)
| in(sK2(set_intersection2(set_intersection2(X0,sK15(sK8)),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,sK15(sK8)),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370289,c_413867]) ).
tcf(c_437515,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X1,set_intersection2(set_intersection2(X0,X1),X2)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X1) = set_intersection2(set_intersection2(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_370289,c_423425]) ).
tcf(c_437516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,sK16(powerset(X1))),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,sK16(powerset(X1))),X2),X3,X4),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,sK16(powerset(X1))),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_370289,c_430730]) ).
tcf(c_437519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X1),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X1 ) ),
inference(equality_factoring,[status(thm)],[c_370289]) ).
tcf(c_437578,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),X2)
| in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),sK15(sK8))
| ( set_intersection2(set_intersection2(sK15(sK8),X0),X1) = X2 ) ),
inference(light_normalisation,[status(thm)],[c_437464,c_411956]) ).
tcf(c_437582,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),X2)
| in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),sK15(sK5))
| ( set_intersection2(set_intersection2(sK15(sK5),X0),X1) = X2 ) ),
inference(light_normalisation,[status(thm)],[c_437463,c_411955]) ).
tcf(c_437650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(light_normalisation,[status(thm)],[c_437462,c_397136]) ).
tcf(c_437654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X3)
| in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),sK16(powerset(X0)))
| ( set_intersection2(set_intersection2(sK16(powerset(X0)),X1),X2) = X3 ) ),
inference(light_normalisation,[status(thm)],[c_437461,c_397130]) ).
tcf(c_438002,plain,
! [X0: $i] : set_intersection2(sK16(powerset(X0)),sK16(powerset(X0))) = sK16(powerset(X0)),
inference(superposition,[status(thm)],[c_397130,c_397137]) ).
tcf(c_438005,plain,
set_intersection2(sK15(sK5),sK15(sK5)) = sK15(sK5),
inference(superposition,[status(thm)],[c_411955,c_397137]) ).
tcf(c_438006,plain,
set_intersection2(sK15(sK8),sK15(sK8)) = sK15(sK8),
inference(superposition,[status(thm)],[c_411956,c_397137]) ).
tcf(c_438007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X0),X2),X3,X4),set_intersection2(X1,X0))
| in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397137,c_370289]) ).
tcf(c_438008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X0),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2),X3,X4),set_intersection2(X1,X0))
| ( set_intersection2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397137,c_370289]) ).
tcf(c_438009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370288]) ).
tcf(c_438010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| element(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_370287]) ).
tcf(c_438011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X1,X0),X2,X3),X0)
| in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_370287]) ).
tcf(c_438012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X3 )
| ~ in(X0,sK2(set_intersection2(X1,X0),X2,X3)) ),
inference(superposition,[status(thm)],[c_397137,c_370285]) ).
tcf(c_438013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X3,X4)),X0)
| in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,set_intersection2(X3,X4)),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397137,c_370278]) ).
tcf(c_438014,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X3,X4)),X3)
| in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397137,c_370278]) ).
tcf(c_438015,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X3,X4)),X0)
| in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,set_intersection2(X3,X4)),X4)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397137,c_370277]) ).
tcf(c_438016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X3,X4)),X4)
| in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,set_intersection2(X3,X4)),X0)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397137,c_370277]) ).
tcf(c_438017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| element(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_370275]) ).
tcf(c_438018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X1,X0),X2,X3),X3)
| in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_370275]) ).
tcf(c_438019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X1,X0),X0),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_370266]) ).
tcf(c_438020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| in(sK2(set_intersection2(set_intersection2(X1,X0),X0),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_370261]) ).
tcf(c_438021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X3 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X3),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X1,X0),X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X3),set_intersection2(X1,X0)) ),
inference(superposition,[status(thm)],[c_397137,c_370220]) ).
tcf(c_438022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2),X3) = X4 )
| ~ in(sK2(set_intersection2(set_intersection2(X1,X0),X2),X3,X4),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2),X3,X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2),X3,X4),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2),X3,X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2),X3,X4),set_intersection2(X1,X0)) ),
inference(superposition,[status(thm)],[c_397137,c_370217]) ).
tcf(c_438023,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X0),set_intersection2(X0,set_intersection2(X1,X0)))
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X0 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X0),X2)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X0),set_intersection2(X1,X0)) ),
inference(superposition,[status(thm)],[c_397137,c_426065]) ).
tcf(c_438024,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X1,X0)),X0)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = set_intersection2(X0,set_intersection2(X1,X0)) ) ),
inference(superposition,[status(thm)],[c_397137,c_370081]) ).
tcf(c_438025,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X1,X0),X2,set_intersection2(X1,X0)),set_intersection2(X1,X0))
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = set_intersection2(X0,set_intersection2(X1,X0)) ) ),
inference(superposition,[status(thm)],[c_397137,c_370080]) ).
tcf(c_438026,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(X0,X3)
| ~ in(X0,X2)
| ~ subset(set_intersection2(X1,X2),X3)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_397137,c_369930]) ).
tcf(c_438027,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ empty(X3)
| ~ in(X0,X2)
| ~ subset(set_intersection2(X1,X2),X3)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_397137,c_369786]) ).
tcf(c_438028,plain,
! [X0: $i,X1: $i] :
( element(sK16(set_intersection2(X1,X0)),X0)
| empty(set_intersection2(X0,set_intersection2(X1,X0))) ),
inference(superposition,[status(thm)],[c_397137,c_389068]) ).
tcf(c_438029,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),X1))
| in(sK16(set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397137,c_389060]) ).
tcf(c_438030,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,set_intersection2(X0,X1)))
| element(sK16(set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397137,c_388051]) ).
tcf(c_438031,plain,
! [X0: $i,X1: $i] :
( in(sK16(set_intersection2(X0,X1)),X1)
| empty(set_intersection2(set_intersection2(X0,X1),X1)) ),
inference(superposition,[status(thm)],[c_397137,c_388043]) ).
tcf(c_438032,plain,
! [X0: $i,X1: $i] :
( in(sK16(set_intersection2(X1,X0)),X0)
| empty(set_intersection2(X0,set_intersection2(X1,X0))) ),
inference(superposition,[status(thm)],[c_397137,c_370751]) ).
tcf(c_438033,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,set_intersection2(X0,X1)))
| in(sK16(set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397137,c_370750]) ).
tcf(c_438034,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(X2,set_intersection2(X0,X1))
| ~ in(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_397137,c_369080]) ).
tcf(c_438038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ in(X0,X2)
| ~ subset(set_intersection2(X1,X2),X3)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_397137,c_369016]) ).
tcf(c_438040,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X1,set_intersection2(X0,X1)),X2)
| in(sK10(set_intersection2(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_397137,c_368986]) ).
tcf(c_438043,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_intersection2(X1,set_intersection2(X0,X1)),X2)
| in(sK10(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397137,c_368985]) ).
tcf(c_438044,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ empty(set_intersection2(X1,X2))
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_397137,c_368869]) ).
tcf(c_438045,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(X0,X1)) = X2 )
| ~ subset(X2,X1)
| ~ subset(X2,set_intersection2(X0,X1))
| ~ subset(set_intersection2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_397137,c_368558]) ).
tcf(c_438046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),set_intersection2(X1,X0))
| in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_368503]) ).
tcf(c_438047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X3),set_intersection2(X1,X0))
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_368503]) ).
tcf(c_438048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X3),X3)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_368481]) ).
tcf(c_438049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X1,X0),X2,X3),X3)
| in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X3),X0)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_368481]) ).
tcf(c_438050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2) = X3 )
| ~ in(sK2(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X3),X3)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X1,X0)),X2,X3),set_intersection2(X1,X0)) ),
inference(superposition,[status(thm)],[c_397137,c_368471]) ).
tcf(c_438052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X1),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| in(sK2(set_intersection2(X1,set_intersection2(X2,X1)),X3,relation_inverse_image(X0,X4)),X1)
| ( set_intersection2(set_intersection2(X1,set_intersection2(X2,X1)),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370280]) ).
tcf(c_438053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X1),X3,relation_inverse_image(X0,X4)),X1)
| in(sK2(set_intersection2(X1,set_intersection2(X2,X1)),X3,relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(set_intersection2(X1,set_intersection2(X2,X1)),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370280]) ).
tcf(c_438054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(set_intersection2(X2,X1),X3,relation_inverse_image(X0,X4))),X4)
| in(sK2(set_intersection2(X1,set_intersection2(X2,X1)),X3,relation_inverse_image(X0,X4)),X1)
| ( set_intersection2(set_intersection2(X1,set_intersection2(X2,X1)),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370279]) ).
tcf(c_438055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X1),X3,relation_inverse_image(X0,X4)),X1)
| in(apply(X0,sK2(set_intersection2(X1,set_intersection2(X2,X1)),X3,relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(set_intersection2(X1,set_intersection2(X2,X1)),X3) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370279]) ).
tcf(c_438056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X2,X1),X3,X0),X1)
| ( set_intersection2(set_intersection2(X1,set_intersection2(X2,X1)),X3) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370276]) ).
tcf(c_438057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X2,set_intersection2(X1,X2)),X3,X0),X2)
| ( set_intersection2(set_intersection2(X2,set_intersection2(X1,X2)),X3) = X0 )
| ~ in(X0,sK2(set_intersection2(X1,X2),X3,X0)) ),
inference(superposition,[status(thm)],[c_397137,c_370273]) ).
tcf(c_438058,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X2,X1),set_intersection2(X2,X1)),X1)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X1))) = set_intersection2(X1,set_intersection2(X2,X1)) ) ),
inference(superposition,[status(thm)],[c_397137,c_370149]) ).
tcf(c_438059,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X2,X1),set_intersection2(X2,X1)),set_intersection2(X2,X1))
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X1))) = set_intersection2(X1,set_intersection2(X2,X1)) ) ),
inference(superposition,[status(thm)],[c_397137,c_370148]) ).
tcf(c_438060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,set_intersection2(X2,X1),X3),X3)
| in(sK12(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3),X1)
| ( relation_image(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_369303]) ).
tcf(c_438061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X2,X1),X3),X1)
| in(sK11(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3),X3)
| ( relation_image(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_369303]) ).
tcf(c_438062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,set_intersection2(X2,X1),X3),X3)
| in(sK12(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3),set_intersection2(X2,X1))
| ( relation_image(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_369302]) ).
tcf(c_438063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,set_intersection2(X2,X1),X3),set_intersection2(X2,X1))
| in(sK11(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3),X3)
| ( relation_image(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_369302]) ).
tcf(c_438064,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_intersection2(X1,set_intersection2(X2,X1)))
| ~ in(sK10(X0,set_intersection2(X2,X1)),X1)
| ~ in(sK10(X0,set_intersection2(X1,set_intersection2(X2,X1))),set_intersection2(X2,X1)) ),
inference(superposition,[status(thm)],[c_397137,c_368972]) ).
tcf(c_438065,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_intersection2(X1,X2))
| ~ in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_397137,c_368928]) ).
tcf(c_438066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,set_intersection2(X2,X1),X3)),X1)
| in(sK7(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3),X3)
| ( relation_inverse_image(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_368703]) ).
tcf(c_438067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X2,X1),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3)),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_368703]) ).
tcf(c_438068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X2,X1),X3)),set_intersection2(X2,X1))
| ( relation_inverse_image(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_368702]) ).
tcf(c_438069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,set_intersection2(X2,X1),X3),X3)
| in(apply(X0,sK7(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3)),set_intersection2(X2,X1))
| ( relation_inverse_image(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_368702]) ).
tcf(c_438070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(apply(X0,sK7(X0,set_intersection2(X2,X1),X3)),X1)
| ~ in(sK7(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3),X3)
| ~ in(sK7(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3)),set_intersection2(X2,X1)) ),
inference(superposition,[status(thm)],[c_397137,c_368654]) ).
tcf(c_438071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,X1),X3),set_intersection2(X2,X1))
| in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_368504]) ).
tcf(c_438072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,X1),X3),X3)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3),set_intersection2(X2,X1))
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_368504]) ).
tcf(c_438073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,X1),X3),X1)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_368482]) ).
tcf(c_438074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,X1),X3),X3)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_368482]) ).
tcf(c_438079,plain,
! [X0: $i,X1: $i] : set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)) = set_intersection2(X0,X1),
inference(superposition,[status(thm)],[c_397137,c_397137]) ).
tcf(c_438080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),set_intersection2(X0,X1))
| in(sK2(set_intersection2(set_intersection2(X0,X1),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_370266]) ).
tcf(c_438081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X1),X2,X3),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_370261]) ).
tcf(c_438087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X0),X3,X4),X1)
| in(sK2(set_intersection2(X0,set_intersection2(X2,X0)),X3,X4),X4)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X2,X0)),X3) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397137,c_370286]) ).
tcf(c_438088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,X0),X3,X4),X4)
| in(sK2(set_intersection2(X0,set_intersection2(X2,X0)),X3,X4),X1)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X2,X0)),X3) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397137,c_370286]) ).
tcf(c_438089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,set_intersection2(X0,X1)),X3,X4),X1)
| in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1))),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1))),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397137,c_370289]) ).
tcf(c_438090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,set_intersection2(X0,X1)),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1))),X3,X4),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1))),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397137,c_370289]) ).
tcf(c_438091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1))),X3) = X4 )
| ~ in(sK2(set_intersection2(X2,set_intersection2(X0,X1)),X3,X4),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1))),X3,X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1))),X3,X4),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1))),X3,X4),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1))),X3,X4),set_intersection2(X2,set_intersection2(X0,X1))) ),
inference(superposition,[status(thm)],[c_397137,c_370217]) ).
tcf(c_438092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X3,X2),X4,relation_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(X2,set_intersection2(X3,X2)),X4) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(X2,set_intersection2(X3,X2)),X4,relation_image(X0,X1)))) = sK2(set_intersection2(X2,set_intersection2(X3,X2)),X4,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370281]) ).
tcf(c_438093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X3,X2),X4,X0),X1)
| in(sK2(set_intersection2(X2,set_intersection2(X3,X2)),X4,X0),X2)
| ( set_intersection2(set_intersection2(X2,set_intersection2(X3,X2)),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397137,c_370274]) ).
tcf(c_438094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X3,X2),X4,X0),X2)
| in(sK2(set_intersection2(X2,set_intersection2(X3,X2)),X4,X0),X1)
| ( set_intersection2(set_intersection2(X2,set_intersection2(X3,X2)),X4) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397137,c_370274]) ).
tcf(c_438095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X1,set_intersection2(X3,X2),X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,set_intersection2(X3,X2)))) ),
inference(superposition,[status(thm)],[c_397137,c_369598]) ).
tcf(c_438096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK13(X1,set_intersection2(X3,X2),X0),set_intersection2(X3,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_intersection2(X2,set_intersection2(X3,X2)))) ),
inference(superposition,[status(thm)],[c_397137,c_369597]) ).
tcf(c_438097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X3,X2)),X2)
| ( set_intersection2(X2,set_intersection2(X3,X2)) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,set_intersection2(X3,X2)))) = sK11(X0,X1,set_intersection2(X2,set_intersection2(X3,X2))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_369440]) ).
tcf(c_438098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X1,set_intersection2(X3,X2)),set_intersection2(X3,X2))
| ( set_intersection2(X2,set_intersection2(X3,X2)) = relation_image(X0,X1) )
| ( apply(X0,sK12(X0,X1,set_intersection2(X2,set_intersection2(X3,X2)))) = sK11(X0,X1,set_intersection2(X2,set_intersection2(X3,X2))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_369439]) ).
tcf(c_438099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X3,set_intersection2(X2,X1)),X1)
| in(sK12(X0,X3,set_intersection2(X1,set_intersection2(X2,X1))),X3)
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_369311]) ).
tcf(c_438100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,set_intersection2(X2,X1)),X3)
| in(sK11(X0,X3,set_intersection2(X1,set_intersection2(X2,X1))),X1)
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_369311]) ).
tcf(c_438101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X3,set_intersection2(X2,X1)),set_intersection2(X2,X1))
| in(sK12(X0,X3,set_intersection2(X1,set_intersection2(X2,X1))),X3)
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_369310]) ).
tcf(c_438102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,set_intersection2(X2,X1)),X3)
| in(sK11(X0,X3,set_intersection2(X1,set_intersection2(X2,X1))),set_intersection2(X2,X1))
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_369310]) ).
tcf(c_438103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,set_intersection2(X2,X1)),relation_dom(X0))
| in(sK11(X0,X3,set_intersection2(X1,set_intersection2(X2,X1))),X1)
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_369210]) ).
tcf(c_438104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X3,set_intersection2(X2,X1)),X1)
| in(sK12(X0,X3,set_intersection2(X1,set_intersection2(X2,X1))),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_369210]) ).
tcf(c_438105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK12(X0,X3,set_intersection2(X2,X1)),relation_dom(X0))
| in(sK11(X0,X3,set_intersection2(X1,set_intersection2(X2,X1))),set_intersection2(X2,X1))
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_369209]) ).
tcf(c_438106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK11(X0,X3,set_intersection2(X2,X1)),set_intersection2(X2,X1))
| in(sK12(X0,X3,set_intersection2(X1,set_intersection2(X2,X1))),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_369209]) ).
tcf(c_438107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_inverse_image(X0,set_intersection2(X2,X3)))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X3)
| ~ in(apply(X0,X1),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_397137,c_368735]) ).
tcf(c_438108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X3,set_intersection2(X2,X1))),X3)
| in(sK7(X0,X3,set_intersection2(X1,set_intersection2(X2,X1))),X1)
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_368701]) ).
tcf(c_438109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X2,X1)),X1)
| in(apply(X0,sK7(X0,X3,set_intersection2(X1,set_intersection2(X2,X1)))),X3)
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_368701]) ).
tcf(c_438110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK7(X0,X3,set_intersection2(X2,X1))),X3)
| in(sK7(X0,X3,set_intersection2(X1,set_intersection2(X2,X1))),set_intersection2(X2,X1))
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_368700]) ).
tcf(c_438111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X2,X1)),set_intersection2(X2,X1))
| in(apply(X0,sK7(X0,X3,set_intersection2(X1,set_intersection2(X2,X1)))),X3)
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_368700]) ).
tcf(c_438112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X2,X1)),relation_dom(X0))
| in(sK7(X0,X3,set_intersection2(X1,set_intersection2(X2,X1))),X1)
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_368673]) ).
tcf(c_438113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X2,X1)),X1)
| in(sK7(X0,X3,set_intersection2(X1,set_intersection2(X2,X1))),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_368673]) ).
tcf(c_438114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X2,X1)),relation_dom(X0))
| in(sK7(X0,X3,set_intersection2(X1,set_intersection2(X2,X1))),set_intersection2(X2,X1))
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_368672]) ).
tcf(c_438115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X3,set_intersection2(X2,X1)),set_intersection2(X2,X1))
| in(sK7(X0,X3,set_intersection2(X1,set_intersection2(X2,X1))),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X1)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_368672]) ).
tcf(c_438116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X1,X0)),X2)
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X1,X0))),set_intersection2(X1,X0))
| ( set_intersection2(X0,set_intersection2(X1,X0)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397137,c_368506]) ).
tcf(c_438117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X1,X0)),set_intersection2(X1,X0))
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X1,X0))),X2)
| ( set_intersection2(X0,set_intersection2(X1,X0)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397137,c_368506]) ).
tcf(c_438118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X1,X0)),X3)
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X1,X0))),set_intersection2(X1,X0))
| ( set_intersection2(X0,set_intersection2(X1,X0)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397137,c_368505]) ).
tcf(c_438119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X1,X0)),set_intersection2(X1,X0))
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X1,X0))),X3)
| ( set_intersection2(X0,set_intersection2(X1,X0)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397137,c_368505]) ).
tcf(c_438120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X1,X0)),X2)
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X1,X0))),X0)
| ( set_intersection2(X0,set_intersection2(X1,X0)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397137,c_368484]) ).
tcf(c_438121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X1,X0)),X0)
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X1,X0))),X2)
| ( set_intersection2(X0,set_intersection2(X1,X0)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397137,c_368484]) ).
tcf(c_438122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X1,X0)),X3)
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X1,X0))),X0)
| ( set_intersection2(X0,set_intersection2(X1,X0)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397137,c_368483]) ).
tcf(c_438123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X1,X0)),X0)
| in(sK2(X2,X3,set_intersection2(X0,set_intersection2(X1,X0))),X3)
| ( set_intersection2(X0,set_intersection2(X1,X0)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397137,c_368483]) ).
tcf(c_438124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X4,X3)),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X4,X3))),X3)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,set_intersection2(X4,X3)) ) ),
inference(superposition,[status(thm)],[c_397137,c_370278]) ).
tcf(c_438125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X4,X3)),X3)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X4,X3))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,set_intersection2(X4,X3)) ) ),
inference(superposition,[status(thm)],[c_397137,c_370278]) ).
tcf(c_438126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X4,X3)),X0)
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X4,X3))),set_intersection2(X4,X3))
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,set_intersection2(X4,X3)) ) ),
inference(superposition,[status(thm)],[c_397137,c_370277]) ).
tcf(c_438127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X4,X3)),set_intersection2(X4,X3))
| in(sK2(set_intersection2(X0,X1),X2,set_intersection2(X3,set_intersection2(X4,X3))),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,set_intersection2(X4,X3)) ) ),
inference(superposition,[status(thm)],[c_397137,c_370277]) ).
tcf(c_438184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),X3)
| in(sK2(X2,X3,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(light_normalisation,[status(thm)],[c_438123,c_397137]) ).
tcf(c_438189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,set_intersection2(X0,X1)),X2)
| in(sK2(X2,X3,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) ) ),
inference(light_normalisation,[status(thm)],[c_438121,c_397137]) ).
tcf(c_438425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),X2) = X3 )
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X2)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),X1)
| ~ in(sK2(set_intersection2(X0,X1),X2,X3),set_intersection2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_438050,c_397137]) ).
tcf(c_438445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),set_intersection2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_438022,c_397137]) ).
tcf(c_438560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)),X2,X3),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_53,c_370290]) ).
tcf(c_438563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X0,X1),empty_set),X2,X3),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),empty_set),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_64,c_370290]) ).
tcf(c_438564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(set_intersection2(X0,X1))),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X0,X1),sK16(powerset(set_intersection2(X0,X1)))),X2,X3),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),sK16(powerset(set_intersection2(X0,X1)))),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397130,c_370290]) ).
tcf(c_438565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X3,X4),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397136,c_370290]) ).
tcf(c_438566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,set_intersection2(X0,X1)),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1))),X3,X4),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1))),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397137,c_370290]) ).
tcf(c_438568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X0),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_63,c_370290]) ).
tcf(c_438570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X0,empty_set),X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,empty_set),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_64,c_370290]) ).
tcf(c_438571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(empty_set,X0),X1),X2,X3),empty_set)
| ( set_intersection2(set_intersection2(set_intersection2(empty_set,X0),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_368545,c_370290]) ).
tcf(c_438572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X3)
| in(sK2(set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1),X2,X3),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397130,c_370290]) ).
tcf(c_438573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2),X3,X4),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397136,c_370290]) ).
tcf(c_438574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X0),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2),X3,X4),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397137,c_370290]) ).
tcf(c_438575,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),X2)
| in(sK2(set_intersection2(set_intersection2(sK5,sK15(sK5)),X0),X1,X2),sK5)
| ( set_intersection2(set_intersection2(set_intersection2(sK5,sK15(sK5)),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_411955,c_370290]) ).
tcf(c_438576,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),X2)
| in(sK2(set_intersection2(set_intersection2(sK8,sK15(sK8)),X0),X1,X2),sK8)
| ( set_intersection2(set_intersection2(set_intersection2(sK8,sK15(sK8)),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_411956,c_370290]) ).
tcf(c_438577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),X2,X3),X0)
| in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_53,c_370290]) ).
tcf(c_438580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,X3),X0)
| in(sK2(set_intersection2(set_intersection2(X0,X1),empty_set),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),empty_set),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_64,c_370290]) ).
tcf(c_438581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(set_intersection2(X0,X1))),X2,X3),X0)
| in(sK2(set_intersection2(set_intersection2(X0,X1),sK16(powerset(set_intersection2(X0,X1)))),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),sK16(powerset(set_intersection2(X0,X1)))),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397130,c_370290]) ).
tcf(c_438582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X0)
| in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397136,c_370290]) ).
tcf(c_438583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,set_intersection2(X0,X1)),X3,X4),X0)
| in(sK2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1))),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,set_intersection2(X0,X1))),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397137,c_370290]) ).
tcf(c_438585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X0),X2),X3,X4),X0)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_63,c_370290]) ).
tcf(c_438587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,X3),X0)
| in(sK2(set_intersection2(set_intersection2(X0,empty_set),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,empty_set),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_64,c_370290]) ).
tcf(c_438588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,X3),empty_set)
| in(sK2(set_intersection2(set_intersection2(empty_set,X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(empty_set,X0),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_368545,c_370290]) ).
tcf(c_438589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(sK16(powerset(X0)),X1),X2,X3),X0)
| in(sK2(set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,sK16(powerset(X0))),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_397130,c_370290]) ).
tcf(c_438590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X0)
| in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,set_intersection2(X0,X1)),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397136,c_370290]) ).
tcf(c_438591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X0),X2),X3,X4),X0)
| in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X0)),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_397137,c_370290]) ).
tcf(c_438592,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK5),X0),X1,X2),sK5)
| in(sK2(set_intersection2(set_intersection2(sK5,sK15(sK5)),X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(set_intersection2(sK5,sK15(sK5)),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_411955,c_370290]) ).
tcf(c_438593,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(sK15(sK8),X0),X1,X2),sK8)
| in(sK2(set_intersection2(set_intersection2(sK8,sK15(sK8)),X0),X1,X2),X2)
| ( set_intersection2(set_intersection2(set_intersection2(sK8,sK15(sK8)),X0),X1) = X2 ) ),
inference(superposition,[status(thm)],[c_411956,c_370290]) ).
tcf(c_438595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,X0),X1)
| in(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,X0),X2)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X3),X4),X5) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370290,c_321]) ).
tcf(c_438596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,X0),X2)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X3),X4),X5) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370290,c_320]) ).
tcf(c_438597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,X0),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X1,X2),X3),X4) = X0 )
| ~ in(X0,sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,X0)) ),
inference(superposition,[status(thm)],[c_370290,c_97]) ).
tcf(c_438605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,relation_dom(X4)),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = relation_dom(X4) )
| ( apply(X4,sK13(X4,X5,apply(X4,sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,relation_dom(X4))))) = apply(X4,sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,relation_dom(X4))) )
| ~ function(X4)
| ~ relation(X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,relation_dom(X4)),X5) ),
inference(superposition,[status(thm)],[c_370290,c_369671]) ).
tcf(c_438606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(set_intersection2(X3,X4),X5),X6,relation_image(X2,X0)),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X3,X4),X5),X6) = relation_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370290,c_369799]) ).
tcf(c_438607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,relation_image(X0,X6)),X2)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X3),X4),X5) = relation_image(X0,X6) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370290,c_369798]) ).
tcf(c_438608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X2,X3),X4),X5,relation_image(X0,X1)),X2)
| ( set_intersection2(set_intersection2(set_intersection2(X2,X3),X4),X5) = relation_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370290,c_369596]) ).
tcf(c_438609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X2),X3),X4,relation_image(X0,X5)),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X1,X2),X3),X4) = relation_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370290,c_369558]) ).
tcf(c_438611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,relation_dom(X4)),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = relation_dom(X4) )
| ~ function(X4)
| ~ relation(X4)
| ~ empty(relation_image(X4,X5))
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,relation_dom(X4)),X5) ),
inference(superposition,[status(thm)],[c_370290,c_369501]) ).
tcf(c_438612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,empty_set),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = empty_set ) ),
inference(superposition,[status(thm)],[c_370290,c_372426]) ).
tcf(c_438613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X1,X2),X0),X3,X4),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X1,X2),X0),X3) = X4 )
| ~ in(sK2(set_intersection2(set_intersection2(X1,X2),X0),X3,X4),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X1,X2),X0),X3,X4),X0)
| ~ in(sK2(set_intersection2(X0,set_intersection2(X1,X2)),X3,X4),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370290,c_370220]) ).
tcf(c_438614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X1)),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X1)),X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X1)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_370290,c_368471]) ).
tcf(c_438615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(set_intersection2(X3,X4),X5),X6,relation_image(X0,relation_image(X1,X2))),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X3,X4),X5),X6) = relation_image(X0,relation_image(X1,X2)) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(set_intersection2(X3,X4),X5),X6,relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(set_intersection2(X3,X4),X5),X6,relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370290,c_369672]) ).
tcf(c_438616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,sK15(sK5)),sK5)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,sK15(sK5)),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_370290,c_412536]) ).
tcf(c_438617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,sK15(sK8)),sK8)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,sK15(sK8)),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_370290,c_413867]) ).
tcf(c_438618,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(set_intersection2(X0,X1),X2)),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(set_intersection2(X0,X1),X2)) = set_intersection2(set_intersection2(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_370290,c_423425]) ).
tcf(c_438619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,sK16(powerset(X4))),X4)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,sK16(powerset(X4))),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = sK16(powerset(X4)) ) ),
inference(superposition,[status(thm)],[c_370290,c_430730]) ).
tcf(c_438622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(set_intersection2(X0,X2),X3),X4,X5),X1)
| in(sK2(set_intersection2(set_intersection2(X0,X2),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X2),X3),X4) = X5 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370290,c_321]) ).
tcf(c_438623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X2),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X2),X3),X4) = X5 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370290,c_320]) ).
tcf(c_438624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 )
| ~ in(X0,sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_370290,c_97]) ).
tcf(c_438625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X2),X3),X4,X5),X5)
| in(sK2(set_intersection2(set_intersection2(X0,X2),X3),X4,X5),X1)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X2),X3),X4) = X5 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370290,c_96]) ).
tcf(c_438626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X0)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_370290,c_93]) ).
tcf(c_438627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X4 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370290,c_91]) ).
tcf(c_438628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),X4,X5),X5)
| in(sK2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),X4,X5),X1)
| ( set_intersection2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),X4) = X5 ) ),
inference(superposition,[status(thm)],[c_370290,c_59]) ).
tcf(c_438629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),X4,X5),X5)
| in(sK2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),X4,X5),X0)
| ( set_intersection2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),X4) = X5 ) ),
inference(superposition,[status(thm)],[c_370290,c_58]) ).
tcf(c_438630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3),X4,X5),X5)
| in(apply(X0,sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3),X4,X5)),X1)
| ( set_intersection2(set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370290,c_88]) ).
tcf(c_438631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3),X4,X5),X5)
| in(sK2(set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3),X4,X5),relation_dom(X0))
| ( set_intersection2(set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370290,c_87]) ).
tcf(c_438632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3) = X4 )
| ( apply(X0,sK13(X0,X5,apply(X0,sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,X4)))) = apply(X0,sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,X4)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_370290,c_369671]) ).
tcf(c_438633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(set_intersection2(relation_image(X2,X0),X3),X4),X5,X6),X6)
| ( set_intersection2(set_intersection2(set_intersection2(relation_image(X2,X0),X3),X4),X5) = X6 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370290,c_369799]) ).
tcf(c_438634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4),X5,X6),X6)
| ( set_intersection2(set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4),X5) = X6 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370290,c_369798]) ).
tcf(c_438635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3),X4) = X5 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370290,c_369596]) ).
tcf(c_438636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370290,c_369558]) ).
tcf(c_438637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3),X4) = X5 )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3),X4,X5))) = sK2(set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3),X4,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370290,c_112]) ).
tcf(c_438638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X5))
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_370290,c_369501]) ).
tcf(c_438639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(empty_set,X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(empty_set,X0),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370290,c_372426]) ).
tcf(c_438641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4),X5,X6),X6)
| ( set_intersection2(set_intersection2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4),X5) = X6 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(set_intersection2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4),X5,X6)))) = sK13(X0,relation_image(X1,X2),sK2(set_intersection2(set_intersection2(relation_image(X0,relation_image(X1,X2)),X3),X4),X5,X6)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370290,c_369672]) ).
tcf(c_438642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(sK15(sK5),X0),X1),X2,X3),sK5)
| in(sK2(set_intersection2(set_intersection2(sK15(sK5),X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(sK15(sK5),X0),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370290,c_412536]) ).
tcf(c_438643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(sK15(sK8),X0),X1),X2,X3),sK8)
| in(sK2(set_intersection2(set_intersection2(sK15(sK8),X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(set_intersection2(sK15(sK8),X0),X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_370290,c_413867]) ).
tcf(c_438644,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X0,set_intersection2(set_intersection2(X0,X1),X2)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X0) = set_intersection2(set_intersection2(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_370290,c_423425]) ).
tcf(c_438645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(sK16(powerset(X0)),X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(set_intersection2(sK16(powerset(X0)),X1),X2),X3,X4),X0)
| ( set_intersection2(set_intersection2(set_intersection2(sK16(powerset(X0)),X1),X2),X3) = X4 ) ),
inference(superposition,[status(thm)],[c_370290,c_430730]) ).
tcf(c_438648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),X3,X0),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3) = X0 ) ),
inference(equality_factoring,[status(thm)],[c_370290]) ).
tcf(c_439118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,X3),X3)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),X2,X3)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370291]) ).
tcf(c_439121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,X3),X3)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),empty_set),X2,X3)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),empty_set),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370291]) ).
tcf(c_439122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(relation_inverse_image(X0,X1))),X2,X3),X3)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),sK16(powerset(relation_inverse_image(X0,X1)))),X2,X3)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),sK16(powerset(relation_inverse_image(X0,X1)))),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370291]) ).
tcf(c_439123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(relation_inverse_image(X0,X1),X2)),X3,X4)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(relation_inverse_image(X0,X1),X2)),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370291]) ).
tcf(c_439124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,relation_inverse_image(X0,X1)),X3,X4),X4)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(X2,relation_inverse_image(X0,X1))),X3,X4)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(X2,relation_inverse_image(X0,X1))),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370291]) ).
tcf(c_439125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,X3),X3)
| in(apply(empty_set,sK2(set_intersection2(relation_inverse_image(empty_set,X0),X1),X2,X3)),X0)
| ( set_intersection2(set_intersection2(relation_inverse_image(empty_set,X0),X1),X2) = X3 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370291]) ).
tcf(c_439126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(relation_inverse_image(X0,X1),X2,X3)),X1)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370291]) ).
tcf(c_439129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(empty_set,X2,X3)),X1)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),empty_set),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),empty_set),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370291]) ).
tcf(c_439130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(sK16(powerset(relation_inverse_image(X0,X1))),X2,X3)),X1)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),sK16(powerset(relation_inverse_image(X0,X1)))),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),sK16(powerset(relation_inverse_image(X0,X1)))),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370291]) ).
tcf(c_439131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4)),X1)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(relation_inverse_image(X0,X1),X2)),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(relation_inverse_image(X0,X1),X2)),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370291]) ).
tcf(c_439132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(set_intersection2(X2,relation_inverse_image(X0,X1)),X3,X4)),X1)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(X2,relation_inverse_image(X0,X1))),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(X2,relation_inverse_image(X0,X1))),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370291]) ).
tcf(c_439133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(empty_set,sK2(set_intersection2(empty_set,X1),X2,X3)),X0)
| in(sK2(set_intersection2(relation_inverse_image(empty_set,X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(empty_set,X0),X1),X2) = X3 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370291]) ).
tcf(c_439135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(relation_inverse_image(X2,X3),X4),X5,X0),X1)
| in(apply(X2,sK2(set_intersection2(relation_inverse_image(X2,X3),X4),X5,X0)),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,X3),X4),X5) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370291,c_321]) ).
tcf(c_439136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK2(set_intersection2(relation_inverse_image(X2,X3),X4),X5,X0)),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,X3),X4),X5) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370291,c_320]) ).
tcf(c_439137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(set_intersection2(relation_inverse_image(X1,X2),X3),X4,X0)),X2)
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X2),X3),X4) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(set_intersection2(relation_inverse_image(X1,X2),X3),X4,X0)) ),
inference(superposition,[status(thm)],[c_370291,c_97]) ).
tcf(c_439143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X1,sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,relation_inverse_image(X1,X5))),X5)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,relation_inverse_image(X1,X5))),X2)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X2),X3),X4) = relation_inverse_image(X1,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_88]) ).
tcf(c_439144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,relation_inverse_image(X1,X5)),relation_dom(X1))
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,relation_inverse_image(X1,X5))),X2)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X2),X3),X4) = relation_inverse_image(X1,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_87]) ).
tcf(c_439145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_dom(X4))),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = relation_dom(X4) )
| ( apply(X4,sK13(X4,X5,apply(X4,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_dom(X4))))) = apply(X4,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_dom(X4))) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_dom(X4)),X5) ),
inference(superposition,[status(thm)],[c_370291,c_369671]) ).
tcf(c_439146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(apply(X2,sK2(set_intersection2(relation_inverse_image(X2,X4),X5),X6,relation_image(X3,X0))),X4)
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,X4),X5),X6) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370291,c_369799]) ).
tcf(c_439147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(apply(X2,sK2(set_intersection2(relation_inverse_image(X2,X3),X4),X5,relation_image(X0,X6))),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,X3),X4),X5) = relation_image(X0,X6) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370291,c_369798]) ).
tcf(c_439148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X3),X4),X5,relation_image(X1,X2))),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X3),X4),X5) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_369596]) ).
tcf(c_439149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X1,sK2(set_intersection2(relation_inverse_image(X1,X2),X3),X4,relation_image(X0,X5))),X2)
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X2),X3),X4) = relation_image(X0,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370291,c_369558]) ).
tcf(c_439150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X3),X4),X5,relation_image(X1,X2))),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X3),X4),X5) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK2(set_intersection2(relation_inverse_image(X0,X3),X4),X5,relation_image(X1,X2)))) = sK2(set_intersection2(relation_inverse_image(X0,X3),X4),X5,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_112]) ).
tcf(c_439151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_dom(X4))),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = relation_dom(X4) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ empty(relation_image(X4,X5))
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_dom(X4)),X5) ),
inference(superposition,[status(thm)],[c_370291,c_369501]) ).
tcf(c_439152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,empty_set)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_372426]) ).
tcf(c_439153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,X4)),X2)
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X2),X0),X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,X4),X3)
| ~ in(sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,X4),X0)
| ~ in(sK2(set_intersection2(X0,relation_inverse_image(X1,X2)),X3,X4),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370291,c_370220]) ).
tcf(c_439154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_inverse_image(X0,X1))),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_inverse_image(X0,X1)),X3)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_inverse_image(X0,X1)),X2)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_inverse_image(X0,X1)),relation_inverse_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_370291,c_368471]) ).
tcf(c_439155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X4),X5),X6,relation_image(X1,relation_image(X2,X3)))),X4)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X4),X5),X6) = relation_image(X1,relation_image(X2,X3)) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(set_intersection2(relation_inverse_image(X0,X4),X5),X6,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK2(set_intersection2(relation_inverse_image(X0,X4),X5),X6,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_369672]) ).
tcf(c_439156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,sK15(sK5)),sK5)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,sK15(sK5))),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_412536]) ).
tcf(c_439157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,sK15(sK8)),sK8)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,sK15(sK8))),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_413867]) ).
tcf(c_439158,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),set_intersection2(relation_inverse_image(X0,X1),X2),set_intersection2(relation_inverse_image(X0,X1),X2))),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),set_intersection2(relation_inverse_image(X0,X1),X2)) = set_intersection2(relation_inverse_image(X0,X1),X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_423425]) ).
tcf(c_439159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,sK16(powerset(X4))),X4)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,sK16(powerset(X4)))),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = sK16(powerset(X4)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_430730]) ).
tcf(c_439161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X2,X0),X3),X4,X5),X5)
| element(apply(X2,sK2(set_intersection2(relation_inverse_image(X2,X0),X3),X4,X5)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,X0),X3),X4) = X5 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370291,c_321]) ).
tcf(c_439162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X2,X0),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,X0),X3),X4) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370291,c_320]) ).
tcf(c_439163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X1,X0),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X0),X2),X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK2(set_intersection2(relation_inverse_image(X1,X0),X2),X3,X4))) ),
inference(superposition,[status(thm)],[c_370291,c_97]) ).
tcf(c_439164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X2,X0),X3),X4,X5),X5)
| in(apply(X2,sK2(set_intersection2(relation_inverse_image(X2,X0),X3),X4,X5)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,X0),X3),X4) = X5 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370291,c_96]) ).
tcf(c_439165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| element(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_93]) ).
tcf(c_439166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_91]) ).
tcf(c_439167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4,X5),X5)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4,X5)),X2)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_59]) ).
tcf(c_439168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4,X5),X5)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4,X5)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,set_intersection2(X1,X2)),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_58]) ).
tcf(c_439169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),relation_inverse_image(X0,X1))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370291,c_86]) ).
tcf(c_439170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3),X4,X5),X5)
| in(apply(X1,apply(X0,sK2(set_intersection2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3),X4,X5))),X2)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3),X4) = X5 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_88]) ).
tcf(c_439171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3),X4,X5),X5)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3),X4,X5)),relation_dom(X1))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,relation_inverse_image(X1,X2)),X3),X4) = X5 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_87]) ).
tcf(c_439172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,relation_dom(X1)),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,relation_dom(X1)),X2),X3) = X4 )
| ( apply(X1,sK13(X1,X5,apply(X1,apply(X0,sK2(set_intersection2(relation_inverse_image(X0,relation_dom(X1)),X2),X3,X4))))) = apply(X1,apply(X0,sK2(set_intersection2(relation_inverse_image(X0,relation_dom(X1)),X2),X3,X4))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,relation_dom(X1)),X2),X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370291,c_369671]) ).
tcf(c_439173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X2,relation_image(X3,X0)),X4),X5,X6),X6)
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,relation_image(X3,X0)),X4),X5) = X6 )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370291,c_369799]) ).
tcf(c_439174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X2,relation_image(X0,X3)),X4),X5,X6),X6)
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,relation_image(X0,X3)),X4),X5) = X6 )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370291,c_369798]) ).
tcf(c_439175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,relation_image(X1,X2)),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,relation_image(X1,X2)),X3),X4) = X5 )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_369596]) ).
tcf(c_439176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X1,relation_image(X0,X2)),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,relation_image(X0,X2)),X3),X4) = X5 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370291,c_369558]) ).
tcf(c_439177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,relation_image(X1,X2)),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,relation_image(X1,X2)),X3),X4) = X5 )
| ( apply(X1,sK13(X1,X2,apply(X0,sK2(set_intersection2(relation_inverse_image(X0,relation_image(X1,X2)),X3),X4,X5)))) = apply(X0,sK2(set_intersection2(relation_inverse_image(X0,relation_image(X1,X2)),X3),X4,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_112]) ).
tcf(c_439178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,relation_dom(X1)),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,relation_dom(X1)),X2),X3) = X4 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_image(X1,X5))
| ~ in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,relation_dom(X1)),X2),X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370291,c_369501]) ).
tcf(c_439179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,empty_set),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,empty_set),X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_372426]) ).
tcf(c_439180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X4),X5,X6),X6)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X4),X5) = X6 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK2(set_intersection2(relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X4),X5,X6))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK2(set_intersection2(relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))),X4),X5,X6))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_369672]) ).
tcf(c_439181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,sK15(sK5)),X1),X2,X3),X3)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,sK15(sK5)),X1),X2,X3)),sK5)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,sK15(sK5)),X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_412536]) ).
tcf(c_439182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,sK15(sK8)),X1),X2,X3),X3)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,sK15(sK8)),X1),X2,X3)),sK8)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,sK15(sK8)),X1),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_413867]) ).
tcf(c_439183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,sK16(powerset(X1))),X2),X3,X4),X4)
| in(apply(X0,sK2(set_intersection2(relation_inverse_image(X0,sK16(powerset(X1))),X2),X3,X4)),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,sK16(powerset(X1))),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370291,c_430730]) ).
tcf(c_439818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,X3),X3)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),X2,X3),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370292]) ).
tcf(c_439821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,X3),X3)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),empty_set),X2,X3),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),empty_set),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370292]) ).
tcf(c_439822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(relation_inverse_image(X0,X1))),X2,X3),X3)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),sK16(powerset(relation_inverse_image(X0,X1)))),X2,X3),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),sK16(powerset(relation_inverse_image(X0,X1)))),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370292]) ).
tcf(c_439823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(relation_inverse_image(X0,X1),X2)),X3,X4),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(relation_inverse_image(X0,X1),X2)),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370292]) ).
tcf(c_439824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,relation_inverse_image(X0,X1)),X3,X4),X4)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(X2,relation_inverse_image(X0,X1))),X3,X4),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(X2,relation_inverse_image(X0,X1))),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370292]) ).
tcf(c_439825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,X3),X3)
| in(sK2(set_intersection2(relation_inverse_image(empty_set,X0),X1),X2,X3),relation_dom(empty_set))
| ( set_intersection2(set_intersection2(relation_inverse_image(empty_set,X0),X1),X2) = X3 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370292]) ).
tcf(c_439826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_inverse_image(X0,X1),X2,X3),relation_dom(X0))
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),relation_inverse_image(X0,X1)),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370292]) ).
tcf(c_439829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,X3),relation_dom(X0))
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),empty_set),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),empty_set),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370292]) ).
tcf(c_439830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(relation_inverse_image(X0,X1))),X2,X3),relation_dom(X0))
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),sK16(powerset(relation_inverse_image(X0,X1)))),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),sK16(powerset(relation_inverse_image(X0,X1)))),X2) = X3 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370292]) ).
tcf(c_439831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),relation_dom(X0))
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(relation_inverse_image(X0,X1),X2)),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(relation_inverse_image(X0,X1),X2)),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370292]) ).
tcf(c_439832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,relation_inverse_image(X0,X1)),X3,X4),relation_dom(X0))
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(X2,relation_inverse_image(X0,X1))),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),set_intersection2(X2,relation_inverse_image(X0,X1))),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370292]) ).
tcf(c_439833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,X3),relation_dom(empty_set))
| in(sK2(set_intersection2(relation_inverse_image(empty_set,X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(empty_set,X0),X1),X2) = X3 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370292]) ).
tcf(c_439834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(empty_set,X0),X1),X2,X3),empty_set)
| in(sK2(set_intersection2(relation_inverse_image(empty_set,X0),X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_inverse_image(empty_set,X0),X1),X2) = X3 )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373108,c_370292]) ).
tcf(c_439836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(relation_inverse_image(X2,X3),X4),X5,X0),X1)
| in(sK2(set_intersection2(relation_inverse_image(X2,X3),X4),X5,X0),relation_dom(X2))
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,X3),X4),X5) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370292,c_321]) ).
tcf(c_439837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X2,X3),X4),X5,X0),relation_dom(X2))
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,X3),X4),X5) = X0 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370292,c_320]) ).
tcf(c_439838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X1,X2),X3),X4,X0),relation_dom(X1))
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X2),X3),X4) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(set_intersection2(relation_inverse_image(X1,X2),X3),X4,X0)) ),
inference(superposition,[status(thm)],[c_370292,c_97]) ).
tcf(c_439844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,relation_inverse_image(X1,X5)),relation_dom(X0))
| in(apply(X1,sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,relation_inverse_image(X1,X5))),X5)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X2),X3),X4) = relation_inverse_image(X1,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370292,c_88]) ).
tcf(c_439845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,relation_inverse_image(X1,X5)),relation_dom(X1))
| in(sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,relation_inverse_image(X1,X5)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X2),X3),X4) = relation_inverse_image(X1,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370292,c_87]) ).
tcf(c_439846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_dom(X4)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = relation_dom(X4) )
| ( apply(X4,sK13(X4,X5,apply(X4,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_dom(X4))))) = apply(X4,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_dom(X4))) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_dom(X4)),X5) ),
inference(superposition,[status(thm)],[c_370292,c_369671]) ).
tcf(c_439847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X2,X4),X5),X6,relation_image(X3,X0)),relation_dom(X2))
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,X4),X5),X6) = relation_image(X3,X0) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370292,c_369799]) ).
tcf(c_439848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X2,X3),X4),X5,relation_image(X0,X6)),relation_dom(X2))
| ( set_intersection2(set_intersection2(relation_inverse_image(X2,X3),X4),X5) = relation_image(X0,X6) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370292,c_369798]) ).
tcf(c_439849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X3),X4),X5,relation_image(X1,X2)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X3),X4),X5) = relation_image(X1,X2) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370292,c_369596]) ).
tcf(c_439850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X1,X2),X3),X4,relation_image(X0,X5)),relation_dom(X1))
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X2),X3),X4) = relation_image(X0,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370292,c_369558]) ).
tcf(c_439851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X3),X4),X5,relation_image(X1,X2)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X3),X4),X5) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK2(set_intersection2(relation_inverse_image(X0,X3),X4),X5,relation_image(X1,X2)))) = sK2(set_intersection2(relation_inverse_image(X0,X3),X4),X5,relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370292,c_112]) ).
tcf(c_439852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_dom(X4)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = relation_dom(X4) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ empty(relation_image(X4,X5))
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_dom(X4)),X5) ),
inference(superposition,[status(thm)],[c_370292,c_369501]) ).
tcf(c_439853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,empty_set),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370292,c_372426]) ).
tcf(c_439854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,X4),relation_dom(X1))
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X2),X0),X3) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,X4),X3)
| ~ in(sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,X4),X0)
| ~ in(sK2(set_intersection2(X0,relation_inverse_image(X1,X2)),X3,X4),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370292,c_370220]) ).
tcf(c_439855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_inverse_image(X0,X1)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = relation_inverse_image(X0,X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_inverse_image(X0,X1)),X3)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_inverse_image(X0,X1)),X2)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_inverse_image(X0,X1)),relation_inverse_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_370292,c_368471]) ).
tcf(c_439856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X4),X5),X6,relation_image(X1,relation_image(X2,X3))),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X4),X5),X6) = relation_image(X1,relation_image(X2,X3)) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(set_intersection2(relation_inverse_image(X0,X4),X5),X6,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK2(set_intersection2(relation_inverse_image(X0,X4),X5),X6,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370292,c_369672]) ).
tcf(c_439857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,sK15(sK5)),sK5)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,sK15(sK5)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = sK15(sK5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370292,c_412536]) ).
tcf(c_439858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,sK15(sK8)),sK8)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,sK15(sK8)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = sK15(sK8) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370292,c_413867]) ).
tcf(c_439859,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),set_intersection2(relation_inverse_image(X0,X1),X2),set_intersection2(relation_inverse_image(X0,X1),X2)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),set_intersection2(relation_inverse_image(X0,X1),X2)) = set_intersection2(relation_inverse_image(X0,X1),X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370292,c_423425]) ).
tcf(c_439860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,sK16(powerset(X4))),X4)
| in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,sK16(powerset(X4))),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = sK16(powerset(X4)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370292,c_430730]) ).
tcf(c_439862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,X5),X1)
| in(sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X2),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370292,c_321]) ).
tcf(c_439863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,X5),X5)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X2),X3),X4) = X5 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370292,c_320]) ).
tcf(c_439864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4)) ),
inference(superposition,[status(thm)],[c_370292,c_97]) ).
tcf(c_439865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,X5),X5)
| in(sK2(set_intersection2(relation_inverse_image(X0,X2),X3),X4,X5),X1)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X2),X3),X4) = X5 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370292,c_96]) ).
tcf(c_439866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| element(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370292,c_93]) ).
tcf(c_439867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370292,c_91]) ).
tcf(c_439868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ( apply(X0,sK13(X0,X5,apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4)))) = apply(X0,sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_370292,c_369671]) ).
tcf(c_439869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_image(X0,X5))
| ~ in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_370292,c_369501]) ).
tcf(c_439870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,relation_dom(X1)),relation_dom(X1))
| ( set_intersection2(set_intersection2(relation_inverse_image(X1,X2),X0),X3) = relation_dom(X1) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,relation_dom(X1)),X3)
| ~ in(sK2(set_intersection2(relation_inverse_image(X1,X2),X0),X3,relation_dom(X1)),X0)
| ~ in(sK2(set_intersection2(X0,relation_inverse_image(X1,X2)),X3,relation_dom(X1)),relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370292,c_370220]) ).
tcf(c_439871,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),relation_dom(X0),set_intersection2(relation_inverse_image(X0,X1),X2)),set_intersection2(relation_inverse_image(X0,X1),X2))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),relation_dom(X0)) = set_intersection2(relation_inverse_image(X0,X1),X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370292,c_423425]) ).
tcf(c_439873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_inverse_image(X0,X1),X2),X3,relation_dom(X0)),relation_dom(X0))
| ( set_intersection2(set_intersection2(relation_inverse_image(X0,X1),X2),X3) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_factoring,[status(thm)],[c_370292]) ).
tcf(c_440204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_image(X0,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),relation_image(X0,X1)),X2) = X3 )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),relation_image(X0,X1)),X2,X3))) = sK2(set_intersection2(relation_image(X0,X1),relation_image(X0,X1)),X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370293]) ).
tcf(c_440207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(empty_set,X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),empty_set),X2) = X3 )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),empty_set),X2,X3))) = sK2(set_intersection2(relation_image(X0,X1),empty_set),X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370293]) ).
tcf(c_440208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(sK16(powerset(relation_image(X0,X1))),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),sK16(powerset(relation_image(X0,X1)))),X2) = X3 )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),sK16(powerset(relation_image(X0,X1)))),X2,X3))) = sK2(set_intersection2(relation_image(X0,X1),sK16(powerset(relation_image(X0,X1)))),X2,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370293]) ).
tcf(c_440209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),set_intersection2(relation_image(X0,X1),X2)),X3) = X4 )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),set_intersection2(relation_image(X0,X1),X2)),X3,X4))) = sK2(set_intersection2(relation_image(X0,X1),set_intersection2(relation_image(X0,X1),X2)),X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370293]) ).
tcf(c_440210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X2,relation_image(X0,X1)),X3,X4),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),set_intersection2(X2,relation_image(X0,X1))),X3) = X4 )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),set_intersection2(X2,relation_image(X0,X1))),X3,X4))) = sK2(set_intersection2(relation_image(X0,X1),set_intersection2(X2,relation_image(X0,X1))),X3,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370293]) ).
tcf(c_440211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(relation_image(empty_set,X0),X1),X2) = X3 )
| ( apply(empty_set,sK13(empty_set,X0,sK2(set_intersection2(relation_image(empty_set,X0),X1),X2,X3))) = sK2(set_intersection2(relation_image(empty_set,X0),X1),X2,X3) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_375097,c_370293]) ).
tcf(c_440213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(set_intersection2(relation_image(X2,X3),X4),X5,X0),X1)
| ( set_intersection2(set_intersection2(relation_image(X2,X3),X4),X5) = X0 )
| ( apply(X2,sK13(X2,X3,sK2(set_intersection2(relation_image(X2,X3),X4),X5,X0))) = sK2(set_intersection2(relation_image(X2,X3),X4),X5,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370293,c_321]) ).
tcf(c_440214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_image(X2,X3),X4),X5) = X0 )
| ( apply(X2,sK13(X2,X3,sK2(set_intersection2(relation_image(X2,X3),X4),X5,X0))) = sK2(set_intersection2(relation_image(X2,X3),X4),X5,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370293,c_320]) ).
tcf(c_440215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(relation_image(X1,X2),X3),X4) = X0 )
| ( apply(X1,sK13(X1,X2,sK2(set_intersection2(relation_image(X1,X2),X3),X4,X0))) = sK2(set_intersection2(relation_image(X1,X2),X3),X4,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,sK2(set_intersection2(relation_image(X1,X2),X3),X4,X0)) ),
inference(superposition,[status(thm)],[c_370293,c_97]) ).
tcf(c_440221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X1,sK2(set_intersection2(relation_image(X0,X2),X3),X4,relation_inverse_image(X1,X5))),X5)
| ( set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4) = relation_inverse_image(X1,X5) )
| ( apply(X0,sK13(X0,X2,sK2(set_intersection2(relation_image(X0,X2),X3),X4,relation_inverse_image(X1,X5)))) = sK2(set_intersection2(relation_image(X0,X2),X3),X4,relation_inverse_image(X1,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370293,c_88]) ).
tcf(c_440222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(relation_image(X0,X2),X3),X4,relation_inverse_image(X1,X5)),relation_dom(X1))
| ( set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4) = relation_inverse_image(X1,X5) )
| ( apply(X0,sK13(X0,X2,sK2(set_intersection2(relation_image(X0,X2),X3),X4,relation_inverse_image(X1,X5)))) = sK2(set_intersection2(relation_image(X0,X2),X3),X4,relation_inverse_image(X1,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370293,c_87]) ).
tcf(c_440223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = relation_dom(X4) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_dom(X4)))) = sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_dom(X4)) )
| ( apply(X4,sK13(X4,X5,apply(X4,sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_dom(X4))))) = apply(X4,sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_dom(X4))) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_dom(X4)),X5) ),
inference(superposition,[status(thm)],[c_370293,c_369671]) ).
tcf(c_440224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( set_intersection2(set_intersection2(relation_image(X2,X4),X5),X6) = relation_image(X3,X0) )
| ( apply(X2,sK13(X2,X4,sK2(set_intersection2(relation_image(X2,X4),X5),X6,relation_image(X3,X0)))) = sK2(set_intersection2(relation_image(X2,X4),X5),X6,relation_image(X3,X0)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370293,c_369799]) ).
tcf(c_440225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( set_intersection2(set_intersection2(relation_image(X2,X3),X4),X5) = relation_image(X0,X6) )
| ( apply(X2,sK13(X2,X3,sK2(set_intersection2(relation_image(X2,X3),X4),X5,relation_image(X0,X6)))) = sK2(set_intersection2(relation_image(X2,X3),X4),X5,relation_image(X0,X6)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370293,c_369798]) ).
tcf(c_440226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X3),X4),X5) = relation_image(X1,X2) )
| ( apply(X0,sK13(X0,X3,sK2(set_intersection2(relation_image(X0,X3),X4),X5,relation_image(X1,X2)))) = sK2(set_intersection2(relation_image(X0,X3),X4),X5,relation_image(X1,X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370293,c_369596]) ).
tcf(c_440227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_image(X1,X2),X3),X4) = relation_image(X0,X5) )
| ( apply(X1,sK13(X1,X2,sK2(set_intersection2(relation_image(X1,X2),X3),X4,relation_image(X0,X5)))) = sK2(set_intersection2(relation_image(X1,X2),X3),X4,relation_image(X0,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370293,c_369558]) ).
tcf(c_440228,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X2),X3),X4) = relation_image(X1,X5) )
| ( apply(X1,sK13(X1,X5,sK2(set_intersection2(relation_image(X0,X2),X3),X4,relation_image(X1,X5)))) = sK2(set_intersection2(relation_image(X0,X2),X3),X4,relation_image(X1,X5)) )
| ( apply(X0,sK13(X0,X2,sK2(set_intersection2(relation_image(X0,X2),X3),X4,relation_image(X1,X5)))) = sK2(set_intersection2(relation_image(X0,X2),X3),X4,relation_image(X1,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370293,c_112]) ).
tcf(c_440229,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = relation_dom(X4) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_dom(X4)))) = sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_dom(X4)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ empty(relation_image(X4,X5))
| ~ in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_dom(X4)),X5) ),
inference(superposition,[status(thm)],[c_370293,c_369501]) ).
tcf(c_440230,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = empty_set )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),X3,empty_set))) = sK2(set_intersection2(relation_image(X0,X1),X2),X3,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370293,c_372426]) ).
tcf(c_440231,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(relation_image(X1,X2),X0),X3) = X4 )
| ( apply(X1,sK13(X1,X2,sK2(set_intersection2(relation_image(X1,X2),X0),X3,X4))) = sK2(set_intersection2(relation_image(X1,X2),X0),X3,X4) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(set_intersection2(relation_image(X1,X2),X0),X3,X4),X3)
| ~ in(sK2(set_intersection2(relation_image(X1,X2),X0),X3,X4),X0)
| ~ in(sK2(set_intersection2(X0,relation_image(X1,X2)),X3,X4),relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370293,c_370220]) ).
tcf(c_440232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_image(X0,X1)))) = sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_image(X0,X1)),X3)
| ~ in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_image(X0,X1)),X2)
| ~ in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,relation_image(X0,X1)),relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_370293,c_368471]) ).
tcf(c_440233,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X4),X5),X6) = relation_image(X1,relation_image(X2,X3)) )
| ( apply(X0,sK13(X0,X4,sK2(set_intersection2(relation_image(X0,X4),X5),X6,relation_image(X1,relation_image(X2,X3))))) = sK2(set_intersection2(relation_image(X0,X4),X5),X6,relation_image(X1,relation_image(X2,X3))) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(set_intersection2(relation_image(X0,X4),X5),X6,relation_image(X1,relation_image(X2,X3)))))) = sK13(X1,relation_image(X2,X3),sK2(set_intersection2(relation_image(X0,X4),X5),X6,relation_image(X1,relation_image(X2,X3)))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370293,c_369672]) ).
tcf(c_440234,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,sK15(sK5)),sK5)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = sK15(sK5) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),X3,sK15(sK5)))) = sK2(set_intersection2(relation_image(X0,X1),X2),X3,sK15(sK5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370293,c_412536]) ).
tcf(c_440235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,sK15(sK8)),sK8)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = sK15(sK8) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),X3,sK15(sK8)))) = sK2(set_intersection2(relation_image(X0,X1),X2),X3,sK15(sK8)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370293,c_413867]) ).
tcf(c_440236,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),set_intersection2(relation_image(X0,X1),X2)) = set_intersection2(relation_image(X0,X1),X2) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),set_intersection2(relation_image(X0,X1),X2),set_intersection2(relation_image(X0,X1),X2)))) = sK2(set_intersection2(relation_image(X0,X1),X2),set_intersection2(relation_image(X0,X1),X2),set_intersection2(relation_image(X0,X1),X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370293,c_423425]) ).
tcf(c_440237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_image(X0,X1),X2),X3,sK16(powerset(X4))),X4)
| ( set_intersection2(set_intersection2(relation_image(X0,X1),X2),X3) = sK16(powerset(X4)) )
| ( apply(X0,sK13(X0,X1,sK2(set_intersection2(relation_image(X0,X1),X2),X3,sK16(powerset(X4))))) = sK2(set_intersection2(relation_image(X0,X1),X2),X3,sK16(powerset(X4))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370293,c_430730]) ).
tcf(c_440254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(empty_set,X1),X2) = X3 )
| ( apply(empty_set,sK13(empty_set,X0,sK2(set_intersection2(empty_set,X1),X2,X3))) = sK2(set_intersection2(empty_set,X1),X2,X3) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_440211,c_375097]) ).
tcf(c_440255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(empty_set,X1),X2,X3),X3)
| ( set_intersection2(set_intersection2(empty_set,X1),X2) = X3 )
| ( apply(empty_set,sK13(empty_set,X0,sK2(set_intersection2(empty_set,X1),X2,X3))) = sK2(set_intersection2(empty_set,X1),X2,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_440254,c_368630,c_103]) ).
tcf(c_440570,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK16(powerset(X1)),X2),X2)
| in(sK2(X0,set_intersection2(sK16(powerset(X1)),X1),X2),sK16(powerset(X1)))
| ( set_intersection2(X0,set_intersection2(sK16(powerset(X1)),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_370493]) ).
tcf(c_440571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X1),X3),set_intersection2(X1,X2))
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X1)) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_370493]) ).
tcf(c_440572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X2),X3),set_intersection2(X1,X2))
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_370493]) ).
tcf(c_440573,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),X1)
| in(sK2(X0,set_intersection2(sK15(sK5),sK5),X1),sK15(sK5))
| ( set_intersection2(X0,set_intersection2(sK15(sK5),sK5)) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_370493]) ).
tcf(c_440574,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),X1)
| in(sK2(X0,set_intersection2(sK15(sK8),sK8),X1),sK15(sK8))
| ( set_intersection2(X0,set_intersection2(sK15(sK8),sK8)) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_370493]) ).
tcf(c_440576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,X1),X3),X3)
| in(sK2(X0,set_intersection2(X2,X1),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_63,c_370493]) ).
tcf(c_440578,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X1)
| in(sK2(X0,set_intersection2(empty_set,X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,empty_set)) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_370493]) ).
tcf(c_440579,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),empty_set)
| in(sK2(X0,set_intersection2(X1,empty_set),X2),X2)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_370493]) ).
tcf(c_440580,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK16(powerset(X1)),X2),X1)
| in(sK2(X0,set_intersection2(sK16(powerset(X1)),X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_370493]) ).
tcf(c_440581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X1)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X1),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_370493]) ).
tcf(c_440582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,X1),X3),X1)
| in(sK2(X0,set_intersection2(set_intersection2(X2,X1),X1),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_370493]) ).
tcf(c_440583,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),sK5)
| in(sK2(X0,set_intersection2(sK15(sK5),sK5),X1),X1)
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_370493]) ).
tcf(c_440584,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),sK8)
| in(sK2(X0,set_intersection2(sK15(sK8),sK8),X1),X1)
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_370493]) ).
tcf(c_440585,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X2,X1),X0),X2)
| ( set_intersection2(X0,set_intersection2(X2,X1)) = X0 )
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X0 )
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),X0)
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370493,c_54]) ).
tcf(c_440586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(X4,X3),X0),X1)
| in(sK2(X2,set_intersection2(X3,X4),X0),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370493,c_321]) ).
tcf(c_440588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X3,X2),X0),X3)
| ( set_intersection2(X1,set_intersection2(X3,X2)) = X0 )
| ~ in(X0,sK2(X1,set_intersection2(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_370493,c_97]) ).
tcf(c_440589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X4,X3),X0),X1)
| in(sK2(X2,set_intersection2(X3,X4),X0),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370493,c_96]) ).
tcf(c_440590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,set_intersection2(X2,X1),X3),X3)
| in(sK2(X0,set_intersection2(X1,X2),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_370493,c_93]) ).
tcf(c_440592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X2,X1),set_intersection2(X3,X4)),X4)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370493,c_59]) ).
tcf(c_440593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X2,X1),set_intersection2(X3,X4)),X3)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370493,c_58]) ).
tcf(c_440594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X2)
| in(apply(X0,sK2(X1,set_intersection2(X3,X2),relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370493,c_88]) ).
tcf(c_440595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X2)
| in(sK2(X1,set_intersection2(X3,X2),relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370493,c_87]) ).
tcf(c_440596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X2,X1),relation_dom(X3)),X2)
| ( set_intersection2(X0,set_intersection2(X2,X1)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(X0,set_intersection2(X1,X2),relation_dom(X3))))) = apply(X3,sK2(X0,set_intersection2(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370493,c_369671]) ).
tcf(c_440601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X4,X3),relation_image(X0,X1)),X4)
| ( set_intersection2(X2,set_intersection2(X4,X3)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)))) = sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370493,c_112]) ).
tcf(c_440602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X2,X1),relation_dom(X3)),X2)
| ( set_intersection2(X0,set_intersection2(X2,X1)) = relation_dom(X3) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370493,c_369501]) ).
tcf(c_440604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X3,X2),X4),X3)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X3,X2)) = X4 )
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X4 )
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(X2,X3),X4),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_370493,c_370220]) ).
tcf(c_440605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X3,X2),X0),X3)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X3,X2)) = X0 )
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_370493,c_368471]) ).
tcf(c_440606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X5,X4),relation_image(X0,relation_image(X1,X2))),X5)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(X3,set_intersection2(X5,X4)) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,X5),relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,X5),relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370493,c_369672]) ).
tcf(c_440607,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X2,X1),sK15(sK5)),sK5)
| in(sK2(X0,set_intersection2(X1,X2),sK15(sK5)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_370493,c_412536]) ).
tcf(c_440608,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X2,X1),sK15(sK8)),sK8)
| in(sK2(X0,set_intersection2(X1,X2),sK15(sK8)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_370493,c_413867]) ).
tcf(c_440609,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X1,X0),set_intersection2(X0,X1)),X1)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X1,X0)) = set_intersection2(X0,X1) )
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_370493,c_423425]) ).
tcf(c_440610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,X1),sK16(powerset(X3))),X3)
| in(sK2(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK16(powerset(X3)) ) ),
inference(superposition,[status(thm)],[c_370493,c_430730]) ).
tcf(c_440611,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X1,X0),set_intersection2(X0,X1)),X1)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1),set_intersection2(X0,X1)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X1,X0)) = set_intersection2(X0,X1) )
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1),set_intersection2(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_370493,c_426065]) ).
tcf(c_440612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X4,X3),X0),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X4,X3)) = X0 )
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4)) = X0 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),set_intersection2(X3,X4)) ),
inference(superposition,[status(thm)],[c_370493,c_370217]) ).
tcf(c_440613,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X0),X2),X2)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = X2 )
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_370493,c_54]) ).
tcf(c_440614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(X0,X3),X4),X1)
| in(sK2(X2,set_intersection2(X3,X0),X4),X4)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370493,c_321]) ).
tcf(c_440615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X0),X4),X4)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370493,c_320]) ).
tcf(c_440616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X0),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ~ in(X0,sK2(X1,set_intersection2(X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_370493,c_97]) ).
tcf(c_440617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X0),X4),X4)
| in(sK2(X2,set_intersection2(X0,X3),X4),X1)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370493,c_96]) ).
tcf(c_440618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,set_intersection2(X1,X2),X3),X1)
| in(sK2(X0,set_intersection2(X2,X1),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_370493,c_93]) ).
tcf(c_440619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X0),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370493,c_91]) ).
tcf(c_440620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X3,set_intersection2(X1,X2)),X4),X4)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X2)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X3)) = X4 ) ),
inference(superposition,[status(thm)],[c_370493,c_59]) ).
tcf(c_440621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X3,set_intersection2(X1,X2)),X4),X4)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X1)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X3)) = X4 ) ),
inference(superposition,[status(thm)],[c_370493,c_58]) ).
tcf(c_440622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X3,relation_inverse_image(X0,X2)),X4),X4)
| in(apply(X0,sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),X4)),X2)
| ( set_intersection2(X1,set_intersection2(relation_inverse_image(X0,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370493,c_88]) ).
tcf(c_440623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X3,relation_inverse_image(X0,X2)),X4),X4)
| in(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),X4),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(relation_inverse_image(X0,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370493,c_87]) ).
tcf(c_440624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X2,relation_dom(X1)),X3),X3)
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = X3 )
| ( apply(X1,sK13(X1,X4,apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),X3)))) = apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),X3)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X4) ),
inference(superposition,[status(thm)],[c_370493,c_369671]) ).
tcf(c_440625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,relation_image(X2,X0)),X5),X5)
| ( set_intersection2(X3,set_intersection2(relation_image(X2,X0),X4)) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370493,c_369799]) ).
tcf(c_440626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X4,relation_image(X0,X3)),X5),X5)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X3),X4)) = X5 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370493,c_369798]) ).
tcf(c_440627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,relation_image(X0,X1)),X4),X4)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X1),X3)) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370493,c_369596]) ).
tcf(c_440628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X3,relation_image(X0,X2)),X4),X4)
| ( set_intersection2(X1,set_intersection2(relation_image(X0,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370493,c_369558]) ).
tcf(c_440629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,relation_image(X0,X1)),X4),X4)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X1),X3)) = X4 )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(relation_image(X0,X1),X3),X4))) = sK2(X2,set_intersection2(relation_image(X0,X1),X3),X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370493,c_112]) ).
tcf(c_440630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X2,relation_dom(X1)),X3),X3)
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X4))
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X4) ),
inference(superposition,[status(thm)],[c_370493,c_369501]) ).
tcf(c_440631,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,empty_set),X2),X2)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_370493,c_372426]) ).
tcf(c_440632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X3,X2),X2),X2)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X2 )
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(X2,X3),X2),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X2),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X2),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_370493,c_370220]) ).
tcf(c_440633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X0),X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X2)) = X3 )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),set_intersection2(X0,X2)) ),
inference(superposition,[status(thm)],[c_370493,c_368471]) ).
tcf(c_440634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,relation_image(X0,relation_image(X1,X2))),X5),X5)
| ( set_intersection2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4)) = X5 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),X5)))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370493,c_369672]) ).
tcf(c_440635,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(sK15(sK5),X1),X2),sK5)
| in(sK2(X0,set_intersection2(X1,sK15(sK5)),X2),X2)
| ( set_intersection2(X0,set_intersection2(sK15(sK5),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_370493,c_412536]) ).
tcf(c_440636,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(sK15(sK8),X1),X2),sK8)
| in(sK2(X0,set_intersection2(X1,sK15(sK8)),X2),X2)
| ( set_intersection2(X0,set_intersection2(sK15(sK8),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_370493,c_413867]) ).
tcf(c_440637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,sK16(powerset(X1))),X3),X3)
| in(sK2(X0,set_intersection2(sK16(powerset(X1)),X2),X3),X1)
| ( set_intersection2(X0,set_intersection2(sK16(powerset(X1)),X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_370493,c_430730]) ).
tcf(c_440638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X0),X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3)) = X4 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),set_intersection2(X0,X3)) ),
inference(superposition,[status(thm)],[c_370493,c_370217]) ).
tcf(c_440639,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,set_intersection2(X1,X1),X1),X1)
| ( set_intersection2(X0,set_intersection2(X1,X1)) = X1 ) ),
inference(equality_factoring,[status(thm)],[c_370493]) ).
tcf(c_440648,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,empty_set,X1),empty_set)
| in(sK2(X2,set_intersection2(X0,empty_set),X1),X1)
| ( set_intersection2(empty_set,X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_440579,c_425546]) ).
tcf(c_440649,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,empty_set,X0),empty_set)
| in(sK2(X1,empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_440648,c_64,c_368545]) ).
tcf(c_440672,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),sK8)
| in(sK2(X0,set_intersection2(sK15(sK8),sK8),X1),X1)
| ( set_intersection2(X0,sK15(sK8)) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_440584,c_411956]) ).
tcf(c_440676,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),sK5)
| in(sK2(X0,set_intersection2(sK15(sK5),sK5),X1),X1)
| ( set_intersection2(X0,sK15(sK5)) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_440583,c_411955]) ).
tcf(c_440772,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X0),X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_440613,c_397136]) ).
tcf(c_440978,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,empty_set,X1),X1)
| in(sK2(X2,set_intersection2(X0,empty_set),X1),X0)
| ( set_intersection2(X0,empty_set) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_370495,c_425312]) ).
tcf(c_440979,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,empty_set,X0),X2)
| in(sK2(X1,empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_440978,c_64]) ).
tcf(c_440990,plain,
! [X0: $i] :
( element(sK16(sK16(powerset(X0))),X0)
| empty(set_intersection2(sK16(powerset(X0)),X0)) ),
inference(superposition,[status(thm)],[c_397130,c_401505]) ).
tcf(c_440991,plain,
! [X0: $i,X1: $i] :
( element(sK16(set_intersection2(X0,X1)),X0)
| empty(set_intersection2(set_intersection2(X0,X1),X0)) ),
inference(superposition,[status(thm)],[c_397136,c_401505]) ).
tcf(c_440992,plain,
! [X0: $i,X1: $i] :
( element(sK16(set_intersection2(X0,X1)),X1)
| empty(set_intersection2(set_intersection2(X0,X1),X1)) ),
inference(superposition,[status(thm)],[c_397137,c_401505]) ).
tcf(c_440996,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(X1,powerset(X0)))
| subset(sK16(set_intersection2(powerset(X0),X1)),X0) ),
inference(superposition,[status(thm)],[c_401505,c_99]) ).
tcf(c_441014,plain,
! [X0: $i] :
( empty(set_intersection2(sK16(powerset(X0)),X0))
| element(sK16(sK16(powerset(X0))),sK16(powerset(X0))) ),
inference(superposition,[status(thm)],[c_397130,c_411223]) ).
tcf(c_441015,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),X0))
| element(sK16(set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397136,c_411223]) ).
tcf(c_441016,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(set_intersection2(X0,X1),X1))
| element(sK16(set_intersection2(X0,X1)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_397137,c_411223]) ).
tcf(c_441017,plain,
( empty(set_intersection2(sK15(sK5),sK5))
| element(sK16(sK15(sK5)),sK15(sK5)) ),
inference(superposition,[status(thm)],[c_411955,c_411223]) ).
tcf(c_441018,plain,
( empty(set_intersection2(sK15(sK8),sK8))
| element(sK16(sK15(sK8)),sK15(sK8)) ),
inference(superposition,[status(thm)],[c_411956,c_411223]) ).
tcf(c_441020,plain,
! [X0: $i,X1: $i] :
( empty(set_intersection2(powerset(X1),X0))
| subset(sK16(set_intersection2(X0,powerset(X1))),X1) ),
inference(superposition,[status(thm)],[c_411223,c_99]) ).
tcf(c_441034,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK16(powerset(X1)),X2),sK16(powerset(X1)))
| in(sK2(X0,set_intersection2(sK16(powerset(X1)),X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(sK16(powerset(X1)),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_370498]) ).
tcf(c_441035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),set_intersection2(X1,X2))
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X1),X3),X3)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X1)) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_370498]) ).
tcf(c_441036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),set_intersection2(X1,X2))
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X2),X3),X3)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_370498]) ).
tcf(c_441037,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),sK15(sK5))
| in(sK2(X0,set_intersection2(sK15(sK5),sK5),X1),X1)
| ( set_intersection2(X0,set_intersection2(sK15(sK5),sK5)) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_370498]) ).
tcf(c_441038,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),sK15(sK8))
| in(sK2(X0,set_intersection2(sK15(sK8),sK8),X1),X1)
| ( set_intersection2(X0,set_intersection2(sK15(sK8),sK8)) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_370498]) ).
tcf(c_441042,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X2)
| in(sK2(X0,set_intersection2(empty_set,X1),X2),X1)
| ( set_intersection2(X0,set_intersection2(X1,empty_set)) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_370498]) ).
tcf(c_441043,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X2)
| in(sK2(X0,set_intersection2(X1,empty_set),X2),empty_set)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_370498]) ).
tcf(c_441044,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK16(powerset(X1)),X2),X2)
| in(sK2(X0,set_intersection2(sK16(powerset(X1)),X1),X2),X1)
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_370498]) ).
tcf(c_441045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X1),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_370498]) ).
tcf(c_441046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,X1),X3),X3)
| in(sK2(X0,set_intersection2(set_intersection2(X2,X1),X1),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_370498]) ).
tcf(c_441047,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),X1)
| in(sK2(X0,set_intersection2(sK15(sK5),sK5),X1),sK5)
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_370498]) ).
tcf(c_441048,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),X1)
| in(sK2(X0,set_intersection2(sK15(sK8),sK8),X1),sK8)
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_370498]) ).
tcf(c_441049,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X0,X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,X0)) = X2 )
| ( set_intersection2(X0,set_intersection2(X0,X1)) = X2 )
| ~ in(sK2(X0,set_intersection2(X1,X0),X2),X2)
| ~ in(sK2(X0,set_intersection2(X1,X0),X2),set_intersection2(X1,X0)) ),
inference(superposition,[status(thm)],[c_370498,c_54]) ).
tcf(c_441050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(X3,X0),X4),X1)
| in(sK2(X2,set_intersection2(X0,X3),X4),X4)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370498,c_321]) ).
tcf(c_441052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X0,X2),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ~ in(X0,sK2(X1,set_intersection2(X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_370498,c_97]) ).
tcf(c_441053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X0),X4),X1)
| in(sK2(X2,set_intersection2(X0,X3),X4),X4)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370498,c_96]) ).
tcf(c_441054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,set_intersection2(X2,X1),X3),X1)
| in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_370498,c_93]) ).
tcf(c_441056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X3,set_intersection2(X1,X2)),X4),X2)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X4)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X3)) = X4 ) ),
inference(superposition,[status(thm)],[c_370498,c_59]) ).
tcf(c_441057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X3,set_intersection2(X1,X2)),X4),X1)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X4)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X3)) = X4 ) ),
inference(superposition,[status(thm)],[c_370498,c_58]) ).
tcf(c_441058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),X4),X4)
| in(apply(X0,sK2(X1,set_intersection2(X3,relation_inverse_image(X0,X2)),X4)),X2)
| ( set_intersection2(X1,set_intersection2(relation_inverse_image(X0,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370498,c_88]) ).
tcf(c_441059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),X4),X4)
| in(sK2(X1,set_intersection2(X3,relation_inverse_image(X0,X2)),X4),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(relation_inverse_image(X0,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370498,c_87]) ).
tcf(c_441060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(relation_dom(X2),X1),X3),X3)
| ( set_intersection2(X0,set_intersection2(relation_dom(X2),X1)) = X3 )
| ( apply(X2,sK13(X2,X4,apply(X2,sK2(X0,set_intersection2(X1,relation_dom(X2)),X3)))) = apply(X2,sK2(X0,set_intersection2(X1,relation_dom(X2)),X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,set_intersection2(X1,relation_dom(X2)),X3),X4) ),
inference(superposition,[status(thm)],[c_370498,c_369671]) ).
tcf(c_441065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(relation_image(X0,X1),X3),X4),X4)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X1),X3)) = X4 )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,relation_image(X0,X1)),X4))) = sK2(X2,set_intersection2(X3,relation_image(X0,X1)),X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370498,c_112]) ).
tcf(c_441066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(relation_dom(X2),X1),X3),X3)
| ( set_intersection2(X0,set_intersection2(relation_dom(X2),X1)) = X3 )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_image(X2,X4))
| ~ in(sK2(X0,set_intersection2(X1,relation_dom(X2)),X3),X4) ),
inference(superposition,[status(thm)],[c_370498,c_369501]) ).
tcf(c_441068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X3,X2),X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X3,X2)) = X3 )
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X3 )
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(X2,X3),X3),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X3),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X3),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_370498,c_370220]) ).
tcf(c_441069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X0)) = X3 )
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X2)) = X3 )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X0),X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X0),X3),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X0),X3),set_intersection2(X2,X0)) ),
inference(superposition,[status(thm)],[c_370498,c_368471]) ).
tcf(c_441070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),X5),X5)
| ( set_intersection2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4)) = X5 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,relation_image(X0,relation_image(X1,X2))),X5)))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,relation_image(X0,relation_image(X1,X2))),X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370498,c_369672]) ).
tcf(c_441071,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,sK15(sK5)),X2),sK5)
| in(sK2(X0,set_intersection2(sK15(sK5),X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(sK15(sK5),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_370498,c_412536]) ).
tcf(c_441072,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,sK15(sK8)),X2),sK8)
| in(sK2(X0,set_intersection2(sK15(sK8),X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(sK15(sK8),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_370498,c_413867]) ).
tcf(c_441073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,sK16(powerset(X1))),X3),X1)
| in(sK2(X0,set_intersection2(sK16(powerset(X1)),X2),X3),X3)
| ( set_intersection2(X0,set_intersection2(sK16(powerset(X1)),X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_370498,c_430730]) ).
tcf(c_441074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X0)) = X4 )
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3)) = X4 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X0),X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X0),X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X0),X4),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X0),X4),set_intersection2(X3,X0)) ),
inference(superposition,[status(thm)],[c_370498,c_370217]) ).
tcf(c_441075,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X2,X1),X0),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X0 )
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),X0)
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370498,c_54]) ).
tcf(c_441076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(X3,X4),X0),X1)
| in(sK2(X2,set_intersection2(X4,X3),X0),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370498,c_321]) ).
tcf(c_441077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X4,X3),X0),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370498,c_320]) ).
tcf(c_441078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X3,X2),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ~ in(X0,sK2(X1,set_intersection2(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_370498,c_97]) ).
tcf(c_441079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X4,X3),X0),X3)
| in(sK2(X2,set_intersection2(X3,X4),X0),X1)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370498,c_96]) ).
tcf(c_441080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,set_intersection2(X1,X2),X3),X3)
| in(sK2(X0,set_intersection2(X2,X1),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_370498,c_93]) ).
tcf(c_441081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X3,X2),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370498,c_91]) ).
tcf(c_441082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X2,X1),set_intersection2(X3,X4)),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X4)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370498,c_59]) ).
tcf(c_441083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X2,X1),set_intersection2(X3,X4)),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370498,c_58]) ).
tcf(c_441084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X3,X2),relation_inverse_image(X0,X4)),X2)
| in(apply(X0,sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370498,c_88]) ).
tcf(c_441085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X3,X2),relation_inverse_image(X0,X4)),X2)
| in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370498,c_87]) ).
tcf(c_441086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X2,X1),relation_dom(X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(X0,set_intersection2(X1,X2),relation_dom(X3))))) = apply(X3,sK2(X0,set_intersection2(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370498,c_369671]) ).
tcf(c_441087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X5,X4),relation_image(X2,X0)),X4)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = relation_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370498,c_369799]) ).
tcf(c_441088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X4,X3),relation_image(X0,X5)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_image(X0,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370498,c_369798]) ).
tcf(c_441089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X4,X3),relation_image(X0,X1)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370498,c_369596]) ).
tcf(c_441090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X3,X2),relation_image(X0,X4)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370498,c_369558]) ).
tcf(c_441091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X4,X3),relation_image(X0,X1)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)))) = sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370498,c_112]) ).
tcf(c_441092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X2,X1),relation_dom(X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370498,c_369501]) ).
tcf(c_441093,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X2,X1),empty_set),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_370498,c_372426]) ).
tcf(c_441094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X3,X2),X4),X2)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X4 )
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(X2,X3),X4),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_370498,c_370220]) ).
tcf(c_441095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X3,X2),X0),X2)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X0 )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_370498,c_368471]) ).
tcf(c_441096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X5,X4),relation_image(X0,relation_image(X1,X2))),X4)
| ( relation_image(X0,relation_image(X1,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,X5),relation_image(X0,relation_image(X1,X2)))))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,X5),relation_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370498,c_369672]) ).
tcf(c_441097,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK5)),sK5)
| in(sK2(X0,set_intersection2(X2,X1),sK15(sK5)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK15(sK5) ) ),
inference(superposition,[status(thm)],[c_370498,c_412536]) ).
tcf(c_441098,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK8)),sK8)
| in(sK2(X0,set_intersection2(X2,X1),sK15(sK8)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK15(sK8) ) ),
inference(superposition,[status(thm)],[c_370498,c_413867]) ).
tcf(c_441099,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X1,X0),set_intersection2(X0,X1)),X0)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X1)) = set_intersection2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_370498,c_423425]) ).
tcf(c_441100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,X1),sK16(powerset(X3))),X1)
| in(sK2(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK16(powerset(X3)) ) ),
inference(superposition,[status(thm)],[c_370498,c_430730]) ).
tcf(c_441101,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X1,X0),set_intersection2(X0,X1)),X0)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1),set_intersection2(X0,X1)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) = set_intersection2(X0,X1) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1),set_intersection2(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_370498,c_426065]) ).
tcf(c_441102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X4,X3),X0),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4)) = X0 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),set_intersection2(X3,X4)) ),
inference(superposition,[status(thm)],[c_370498,c_370217]) ).
tcf(c_441131,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),X1)
| in(sK2(X0,set_intersection2(sK15(sK8),sK8),X1),sK8)
| ( set_intersection2(X0,sK15(sK8)) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_441048,c_411956]) ).
tcf(c_441135,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),X1)
| in(sK2(X0,set_intersection2(sK15(sK5),sK5),X1),sK5)
| ( set_intersection2(X0,sK15(sK5)) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_441047,c_411955]) ).
tcf(c_441267,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X0,X1),X2),X2)
| ( set_intersection2(X1,X0) = X2 )
| ( set_intersection2(X0,X1) = X2 )
| ~ in(sK2(X0,set_intersection2(X1,X0),X2),X2)
| ~ in(sK2(X0,set_intersection2(X1,X0),X2),set_intersection2(X1,X0)) ),
inference(light_normalisation,[status(thm)],[c_441049,c_397136,c_397137]) ).
tcf(c_441573,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(sK2(X0,set_intersection2(X1,X2),X0),set_intersection2(X1,X2))
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),X0)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_370502,c_370502,c_371685,c_423440]) ).
tcf(c_441574,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,set_intersection2(X1,X2)) = X0 )
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),X0)
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),set_intersection2(X1,X2)) ),
inference(renaming,[status(thm)],[c_441573]) ).
tcf(c_441583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X2) = relation_image(X1,X3) )
| ( set_intersection2(X0,sK15(X0)) = sK15(X0) )
| ( apply(X1,sK12(X1,X3,relation_image(X0,X2))) = sK11(X1,X3,relation_image(X0,X2)) )
| ( apply(X0,sK13(X0,X2,sK11(X1,X3,relation_image(X0,X2)))) = sK11(X1,X3,relation_image(X0,X2)) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411951,c_369667]) ).
tcf(c_441584,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,sK15(X0)) = sK15(X0) )
| ( set_intersection2(X2,relation_image(X0,X1)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,relation_image(X0,X1),relation_image(X0,X1)))) = sK2(X2,relation_image(X0,X1),relation_image(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411951,c_370152]) ).
tcf(c_441585,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,sK15(X0)) = sK15(X0) )
| ( set_intersection2(relation_image(X0,X1),X2) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(relation_image(X0,X1),X2,relation_image(X0,X1)))) = sK2(relation_image(X0,X1),X2,relation_image(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411951,c_370084]) ).
tcf(c_441607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(X0,X4)
| in(sK2(X1,set_intersection2(X2,X3),sK10(X0,X4)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK10(X0,X4) )
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK10(X0,X4))) ),
inference(superposition,[status(thm)],[c_369021,c_370505]) ).
tcf(c_441608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X0)
| in(sK2(X1,set_intersection2(X2,X3),sK16(X0)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK16(X0) )
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK16(X0))) ),
inference(superposition,[status(thm)],[c_370747,c_370505]) ).
tcf(c_441609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X0),X4)
| in(sK2(X1,set_intersection2(X2,X3),sK2(X4,X5,X0)),X2)
| ( set_intersection2(X4,X5) = X0 )
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK2(X4,X5,X0) )
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK2(X4,X5,X0))) ),
inference(superposition,[status(thm)],[c_369015,c_370505]) ).
tcf(c_441610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X5,X0),X5)
| in(sK2(X1,set_intersection2(X2,X3),sK2(X4,X5,X0)),X2)
| ( set_intersection2(X4,X5) = X0 )
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK2(X4,X5,X0) )
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK2(X4,X5,X0))) ),
inference(superposition,[status(thm)],[c_369014,c_370505]) ).
tcf(c_441611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,X4,X5),X5)
| in(sK2(X1,set_intersection2(X2,X3),sK2(X0,X4,X5)),X2)
| ( set_intersection2(X0,X4) = X5 )
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK2(X0,X4,X5) )
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK2(X0,X4,X5))) ),
inference(superposition,[status(thm)],[c_369012,c_370505]) ).
tcf(c_441612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,X0,X5),X5)
| in(sK2(X1,set_intersection2(X2,X3),sK2(X4,X0,X5)),X2)
| ( set_intersection2(X4,X0) = X5 )
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK2(X4,X0,X5) )
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK2(X4,X0,X5))) ),
inference(superposition,[status(thm)],[c_369013,c_370505]) ).
tcf(c_441613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(X2,X3),sK13(X4,X0,X5)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK13(X4,X0,X5) )
| ~ function(X4)
| ~ relation(X4)
| ~ in(X5,relation_image(X4,X0))
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK13(X4,X0,X5))) ),
inference(superposition,[status(thm)],[c_369594,c_370505]) ).
tcf(c_441614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(X2,X3),sK13(X0,X4,X5)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK13(X0,X4,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_image(X0,X4))
| ~ subset(relation_dom(X0),sK2(X1,set_intersection2(X2,X3),sK13(X0,X4,X5))) ),
inference(superposition,[status(thm)],[c_369556,c_370505]) ).
tcf(c_441615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X4,X0,X5),X5)
| in(sK2(X1,set_intersection2(X2,X3),sK12(X4,X0,X5)),X2)
| ( relation_image(X4,X0) = X5 )
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK12(X4,X0,X5) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK12(X4,X0,X5))) ),
inference(superposition,[status(thm)],[c_369299,c_370505]) ).
tcf(c_441616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(X2,X3),sK11(X4,X5,X0)),X2)
| ( relation_image(X4,X5) = X0 )
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK11(X4,X5,X0) )
| ( apply(X4,sK12(X4,X5,X0)) = sK11(X4,X5,X0) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK11(X4,X5,X0))) ),
inference(superposition,[status(thm)],[c_369436,c_370505]) ).
tcf(c_441617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X4,X5,X0),X5)
| in(sK2(X1,set_intersection2(X2,X3),sK11(X4,X5,X0)),X2)
| ( relation_image(X4,X5) = X0 )
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK11(X4,X5,X0) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK11(X4,X5,X0))) ),
inference(superposition,[status(thm)],[c_369307,c_370505]) ).
tcf(c_441618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X4,X5,X0),relation_dom(X4))
| in(sK2(X1,set_intersection2(X2,X3),sK11(X4,X5,X0)),X2)
| ( relation_image(X4,X5) = X0 )
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK11(X4,X5,X0) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK11(X4,X5,X0))) ),
inference(superposition,[status(thm)],[c_369206,c_370505]) ).
tcf(c_441619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X4,X5,X0),relation_dom(X4))
| in(sK2(X1,set_intersection2(X2,X3),sK7(X4,X5,X0)),X2)
| ( relation_inverse_image(X4,X5) = X0 )
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK7(X4,X5,X0) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK7(X4,X5,X0))) ),
inference(superposition,[status(thm)],[c_369020,c_370505]) ).
tcf(c_441620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X4,sK7(X4,X5,X0)),X5)
| in(sK2(X1,set_intersection2(X2,X3),sK7(X4,X5,X0)),X2)
| ( relation_inverse_image(X4,X5) = X0 )
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK7(X4,X5,X0) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK7(X4,X5,X0))) ),
inference(superposition,[status(thm)],[c_369019,c_370505]) ).
tcf(c_441621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,X4,X5),X5)
| in(sK2(X1,set_intersection2(X2,X3),sK7(X0,X4,X5)),X2)
| ( relation_inverse_image(X0,X4) = X5 )
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK7(X0,X4,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(X1,set_intersection2(X2,X3),sK7(X0,X4,X5))) ),
inference(superposition,[status(thm)],[c_369017,c_370505]) ).
tcf(c_441622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X0,X4,X5),X5)
| in(sK2(X1,set_intersection2(X2,X3),sK12(X0,X4,X5)),X2)
| ( relation_image(X0,X4) = X5 )
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK12(X0,X4,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(X1,set_intersection2(X2,X3),sK12(X0,X4,X5))) ),
inference(superposition,[status(thm)],[c_369214,c_370505]) ).
tcf(c_441623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X4,X0,X5),X5)
| in(sK2(X1,set_intersection2(X2,X3),apply(X4,sK7(X4,X0,X5))),X2)
| ( relation_inverse_image(X4,X0) = X5 )
| ( apply(X4,sK7(X4,X0,X5)) = set_intersection2(X1,set_intersection2(X2,X3)) )
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),apply(X4,sK7(X4,X0,X5)))) ),
inference(superposition,[status(thm)],[c_369018,c_370505]) ).
tcf(c_441624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),sK2(X0,X4,X0)),X2)
| ( set_intersection2(X0,X4) = X0 )
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK2(X0,X4,X0) )
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK2(X0,X4,X0))) ),
inference(superposition,[status(thm)],[c_370077,c_370505]) ).
tcf(c_441625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),sK2(X4,X0,X0)),X2)
| ( set_intersection2(X4,X0) = X0 )
| ( set_intersection2(X1,set_intersection2(X2,X3)) = sK2(X4,X0,X0) )
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK2(X4,X0,X0))) ),
inference(superposition,[status(thm)],[c_370145,c_370505]) ).
tcf(c_441626,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK16(sK15(sK5))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK16(sK15(sK5)) )
| ~ subset(sK5,sK2(X0,set_intersection2(X1,X2),sK16(sK15(sK5)))) ),
inference(superposition,[status(thm)],[c_420696,c_370505]) ).
tcf(c_441627,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK16(sK15(sK8))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK16(sK15(sK8)) )
| ~ subset(sK8,sK2(X0,set_intersection2(X1,X2),sK16(sK15(sK8)))) ),
inference(superposition,[status(thm)],[c_423415,c_370505]) ).
tcf(c_441628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X4,X5),X6,X0),X4)
| in(sK2(X1,set_intersection2(X2,X3),sK2(set_intersection2(X4,X5),X6,X0)),X2)
| ( set_intersection2(set_intersection2(X4,X5),X6) = X0 )
| ( sK2(set_intersection2(X4,X5),X6,X0) = set_intersection2(X1,set_intersection2(X2,X3)) )
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK2(set_intersection2(X4,X5),X6,X0))) ),
inference(superposition,[status(thm)],[c_370274,c_370505]) ).
tcf(c_441629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X0,X4),X5,X6),X6)
| in(sK2(X1,set_intersection2(X2,X3),sK2(set_intersection2(X0,X4),X5,X6)),X2)
| ( set_intersection2(set_intersection2(X0,X4),X5) = X6 )
| ( sK2(set_intersection2(X0,X4),X5,X6) = set_intersection2(X1,set_intersection2(X2,X3)) )
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK2(set_intersection2(X0,X4),X5,X6))) ),
inference(superposition,[status(thm)],[c_370286,c_370505]) ).
tcf(c_441630,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,set_intersection2(X2,X2),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,X2)) = X0 )
| ~ in(X0,sK2(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_53,c_370505]) ).
tcf(c_441633,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,set_intersection2(X2,empty_set),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,empty_set)) = X0 )
| ~ in(X0,sK2(X1,empty_set,X0)) ),
inference(superposition,[status(thm)],[c_64,c_370505]) ).
tcf(c_441634,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,set_intersection2(empty_set,X2),X0),empty_set)
| ( set_intersection2(X1,set_intersection2(empty_set,X2)) = X0 )
| ~ in(X0,sK2(X1,empty_set,X0)) ),
inference(superposition,[status(thm)],[c_368545,c_370505]) ).
tcf(c_441635,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,set_intersection2(X2,sK16(powerset(X2))),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,sK16(powerset(X2)))) = X0 )
| ~ in(X0,sK2(X1,sK16(powerset(X2)),X0)) ),
inference(superposition,[status(thm)],[c_397130,c_370505]) ).
tcf(c_441636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,set_intersection2(X2,X3)),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X2,X3))) = X0 )
| ~ in(X0,sK2(X1,set_intersection2(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_397136,c_370505]) ).
tcf(c_441637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X3,set_intersection2(X2,X3)),X0),X3)
| ( set_intersection2(X1,set_intersection2(X3,set_intersection2(X2,X3))) = X0 )
| ~ in(X0,sK2(X1,set_intersection2(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_397137,c_370505]) ).
tcf(c_441638,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,set_intersection2(sK5,sK15(sK5)),X0),sK5)
| ( set_intersection2(X1,set_intersection2(sK5,sK15(sK5))) = X0 )
| ~ in(X0,sK2(X1,sK15(sK5),X0)) ),
inference(superposition,[status(thm)],[c_411955,c_370505]) ).
tcf(c_441639,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,set_intersection2(sK8,sK15(sK8)),X0),sK8)
| ( set_intersection2(X1,set_intersection2(sK8,sK15(sK8))) = X0 )
| ~ in(X0,sK2(X1,sK15(sK8),X0)) ),
inference(superposition,[status(thm)],[c_411956,c_370505]) ).
tcf(c_441640,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(empty_set,X2)) = X0 )
| ~ in(X0,sK2(X1,empty_set,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_441634,c_372426]) ).
tcf(c_441649,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK15(sK8),X0),sK8)
| ( set_intersection2(X1,sK15(sK8)) = X0 )
| ~ in(X0,sK2(X1,sK15(sK8),X0)) ),
inference(light_normalisation,[status(thm)],[c_441639,c_411956]) ).
tcf(c_441653,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK15(sK5),X0),sK5)
| ( set_intersection2(X1,sK15(sK5)) = X0 )
| ~ in(X0,sK2(X1,sK15(sK5),X0)) ),
inference(light_normalisation,[status(thm)],[c_441638,c_411955]) ).
tcf(c_441824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X3)
| in(sK2(X2,set_intersection2(X3,X3),X0),X1)
| ( set_intersection2(X2,set_intersection2(X3,X3)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_370506]) ).
tcf(c_441827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,empty_set,X0),X3)
| in(sK2(X2,set_intersection2(X3,empty_set),X0),X1)
| ( set_intersection2(X2,set_intersection2(X3,empty_set)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_370506]) ).
tcf(c_441829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,sK16(powerset(X3)),X0),X3)
| in(sK2(X2,set_intersection2(X3,sK16(powerset(X3))),X0),X1)
| ( set_intersection2(X2,set_intersection2(X3,sK16(powerset(X3)))) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397130,c_370506]) ).
tcf(c_441830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),X0),X3)
| in(sK2(X2,set_intersection2(X3,set_intersection2(X3,X4)),X0),X1)
| ( set_intersection2(X2,set_intersection2(X3,set_intersection2(X3,X4))) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397136,c_370506]) ).
tcf(c_441831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X4,X3),X0),X3)
| in(sK2(X2,set_intersection2(X3,set_intersection2(X4,X3)),X0),X1)
| ( set_intersection2(X2,set_intersection2(X3,set_intersection2(X4,X3))) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397137,c_370506]) ).
tcf(c_441832,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,sK15(sK5),X0),sK5)
| in(sK2(X2,set_intersection2(sK5,sK15(sK5)),X0),X1)
| ( set_intersection2(X2,set_intersection2(sK5,sK15(sK5))) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_411955,c_370506]) ).
tcf(c_441833,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,sK15(sK8),X0),sK8)
| in(sK2(X2,set_intersection2(sK8,sK15(sK8)),X0),X1)
| ( set_intersection2(X2,set_intersection2(sK8,sK15(sK8))) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_411956,c_370506]) ).
tcf(c_441834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,X0),X1)
| in(sK2(X2,set_intersection2(X3,X3),X0),X3)
| ( set_intersection2(X2,set_intersection2(X3,X3)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_370506]) ).
tcf(c_441837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,empty_set,X0),X1)
| in(sK2(X2,set_intersection2(X3,empty_set),X0),X3)
| ( set_intersection2(X2,set_intersection2(X3,empty_set)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_370506]) ).
tcf(c_441838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,empty_set,X0),X1)
| in(sK2(X2,set_intersection2(empty_set,X3),X0),empty_set)
| ( set_intersection2(X2,set_intersection2(empty_set,X3)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_368545,c_370506]) ).
tcf(c_441839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,sK16(powerset(X3)),X0),X1)
| in(sK2(X2,set_intersection2(X3,sK16(powerset(X3))),X0),X3)
| ( set_intersection2(X2,set_intersection2(X3,sK16(powerset(X3)))) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397130,c_370506]) ).
tcf(c_441840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),X0),X1)
| in(sK2(X2,set_intersection2(X3,set_intersection2(X3,X4)),X0),X3)
| ( set_intersection2(X2,set_intersection2(X3,set_intersection2(X3,X4))) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397136,c_370506]) ).
tcf(c_441841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X4,X3),X0),X1)
| in(sK2(X2,set_intersection2(X3,set_intersection2(X4,X3)),X0),X3)
| ( set_intersection2(X2,set_intersection2(X3,set_intersection2(X4,X3))) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397137,c_370506]) ).
tcf(c_441842,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,sK15(sK5),X0),X1)
| in(sK2(X2,set_intersection2(sK5,sK15(sK5)),X0),sK5)
| ( set_intersection2(X2,set_intersection2(sK5,sK15(sK5))) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_411955,c_370506]) ).
tcf(c_441843,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,sK15(sK8),X0),X1)
| in(sK2(X2,set_intersection2(sK8,sK15(sK8)),X0),sK8)
| ( set_intersection2(X2,set_intersection2(sK8,sK15(sK8))) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_411956,c_370506]) ).
tcf(c_441844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X0,X1),X2),X3)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = X2 )
| ~ subset(X2,X3)
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_370506,c_54]) ).
tcf(c_441845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X4,set_intersection2(X2,X5),X0),X3)
| in(sK2(X4,set_intersection2(X2,X5),X0),X1)
| ( set_intersection2(X4,set_intersection2(X2,X5)) = X0 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_321]) ).
tcf(c_441846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,set_intersection2(X2,X5),X0),X1)
| ( set_intersection2(X4,set_intersection2(X2,X5)) = X0 )
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_320]) ).
tcf(c_441847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X0,X2),X3),X4)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ~ subset(X3,X4)
| ~ in(X0,sK2(X1,set_intersection2(X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_370506,c_97]) ).
tcf(c_441848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,set_intersection2(X2,X5),X0),X3)
| in(sK2(X4,set_intersection2(X2,X5),X0),X1)
| ( set_intersection2(X4,set_intersection2(X2,X5)) = X0 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_96]) ).
tcf(c_441849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(X3,X4),X0),X3)
| in(sK2(X2,set_intersection2(X3,X4),X0),X1)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_93]) ).
tcf(c_441850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,set_intersection2(X2,X4),X0),X1)
| ( set_intersection2(X3,set_intersection2(X2,X4)) = X0 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_91]) ).
tcf(c_441851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(set_intersection2(X3,X4),X5),X0),X4)
| in(sK2(X2,set_intersection2(set_intersection2(X3,X4),X5),X0),X1)
| ( set_intersection2(X2,set_intersection2(set_intersection2(X3,X4),X5)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_59]) ).
tcf(c_441852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(set_intersection2(X3,X4),X5),X0),X3)
| in(sK2(X2,set_intersection2(set_intersection2(X3,X4),X5),X0),X1)
| ( set_intersection2(X2,set_intersection2(set_intersection2(X3,X4),X5)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_58]) ).
tcf(c_441853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(relation_inverse_image(X2,X4),X5),X0),X1)
| in(apply(X2,sK2(X3,set_intersection2(relation_inverse_image(X2,X4),X5),X0)),X4)
| ( set_intersection2(X3,set_intersection2(relation_inverse_image(X2,X4),X5)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_88]) ).
tcf(c_441854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(relation_inverse_image(X2,X4),X5),X0),X1)
| in(sK2(X3,set_intersection2(relation_inverse_image(X2,X4),X5),X0),relation_dom(X2))
| ( set_intersection2(X3,set_intersection2(relation_inverse_image(X2,X4),X5)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_87]) ).
tcf(c_441855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X5)
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = X3 )
| ( apply(X1,sK13(X1,X4,apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),X3)))) = apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),X3)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X5)
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X4) ),
inference(superposition,[status(thm)],[c_370506,c_369671]) ).
tcf(c_441856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X5,set_intersection2(relation_image(X4,X2),X6),X0),X1)
| ( set_intersection2(X5,set_intersection2(relation_image(X4,X2),X6)) = X0 )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_369799]) ).
tcf(c_441857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(relation_image(X0,X5),X6),X2),X3)
| ( set_intersection2(X4,set_intersection2(relation_image(X0,X5),X6)) = X2 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370506,c_369798]) ).
tcf(c_441858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,set_intersection2(relation_image(X2,X3),X5),X0),X1)
| ( set_intersection2(X4,set_intersection2(relation_image(X2,X3),X5)) = X0 )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_369596]) ).
tcf(c_441859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(relation_image(X2,X4),X5),X0),X1)
| ( set_intersection2(X3,set_intersection2(relation_image(X2,X4),X5)) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_369558]) ).
tcf(c_441860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,set_intersection2(relation_image(X2,X3),X5),X0),X1)
| ( set_intersection2(X4,set_intersection2(relation_image(X2,X3),X5)) = X0 )
| ( apply(X2,sK13(X2,X3,sK2(X4,set_intersection2(relation_image(X2,X3),X5),X0))) = sK2(X4,set_intersection2(relation_image(X2,X3),X5),X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_112]) ).
tcf(c_441861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X5)
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X3,X5)
| ~ empty(relation_image(X1,X4))
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X4) ),
inference(superposition,[status(thm)],[c_370506,c_369501]) ).
tcf(c_441862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,set_intersection2(empty_set,X3),X0),X1)
| ( set_intersection2(X2,set_intersection2(empty_set,X3)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_372426]) ).
tcf(c_441863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X2),X4)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X2 )
| ~ subset(X2,X4)
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(X2,X3),X2),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X2),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X2),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_370506,c_370220]) ).
tcf(c_441864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),X4)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X2)) = X3 )
| ~ subset(X3,X4)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),set_intersection2(X0,X2)) ),
inference(superposition,[status(thm)],[c_370506,c_368471]) ).
tcf(c_441865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X5,set_intersection2(relation_image(X2,relation_image(X3,X4)),X6),X0),X1)
| ( set_intersection2(X5,set_intersection2(relation_image(X2,relation_image(X3,X4)),X6)) = X0 )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK2(X5,set_intersection2(relation_image(X2,relation_image(X3,X4)),X6),X0)))) = sK13(X2,relation_image(X3,X4),sK2(X5,set_intersection2(relation_image(X2,relation_image(X3,X4)),X6),X0)) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_369672]) ).
tcf(c_441866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,set_intersection2(sK15(sK5),X3),X0),sK5)
| in(sK2(X2,set_intersection2(sK15(sK5),X3),X0),X1)
| ( set_intersection2(X2,set_intersection2(sK15(sK5),X3)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_412536]) ).
tcf(c_441867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,set_intersection2(sK15(sK8),X3),X0),sK8)
| in(sK2(X2,set_intersection2(sK15(sK8),X3),X0),X1)
| ( set_intersection2(X2,set_intersection2(sK15(sK8),X3)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_413867]) ).
tcf(c_441868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(sK16(powerset(X3)),X4),X0),X3)
| in(sK2(X2,set_intersection2(sK16(powerset(X3)),X4),X0),X1)
| ( set_intersection2(X2,set_intersection2(sK16(powerset(X3)),X4)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_430730]) ).
tcf(c_441869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X5)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3)) = X4 )
| ~ subset(X4,X5)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),set_intersection2(X0,X3)) ),
inference(superposition,[status(thm)],[c_370506,c_370217]) ).
tcf(c_441870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 )
| ~ subset(X3,X0)
| ~ in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| ~ in(sK2(X0,set_intersection2(X1,X2),X3),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370506,c_54]) ).
tcf(c_441871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X3,set_intersection2(X4,X5),X0),X2)
| in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_321]) ).
tcf(c_441872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ~ empty(X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_320]) ).
tcf(c_441873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),X4),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X4 )
| ~ subset(X4,X0)
| ~ in(X0,sK2(X1,set_intersection2(X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_370506,c_97]) ).
tcf(c_441874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| in(sK2(X3,set_intersection2(X4,X5),X0),X2)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370506,c_96]) ).
tcf(c_441877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| in(sK2(X3,set_intersection2(X4,X5),X0),X2)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370506,c_59]) ).
tcf(c_441878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| in(sK2(X3,set_intersection2(X4,X5),X0),X1)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370506,c_58]) ).
tcf(c_441879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| in(apply(X1,sK2(X3,set_intersection2(X4,X5),X0)),X2)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370506,c_88]) ).
tcf(c_441880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| in(sK2(X3,set_intersection2(X4,X5),X0),relation_dom(X1))
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370506,c_87]) ).
tcf(c_441881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 )
| ( apply(X5,sK13(X5,X4,apply(X5,sK2(X0,set_intersection2(X1,X2),X3)))) = apply(X5,sK2(X0,set_intersection2(X1,X2),X3)) )
| ~ function(X5)
| ~ relation(X5)
| ~ subset(X3,relation_dom(X5))
| ~ in(sK2(X0,set_intersection2(X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_370506,c_369671]) ).
tcf(c_441882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X5,X6),X0),X5)
| ( set_intersection2(X4,set_intersection2(X5,X6)) = X0 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370506,c_369799]) ).
tcf(c_441883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X5,X6),X0),X5)
| ( set_intersection2(X4,set_intersection2(X5,X6)) = X0 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370506,c_369798]) ).
tcf(c_441884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370506,c_369596]) ).
tcf(c_441885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370506,c_369558]) ).
tcf(c_441886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ( apply(X1,sK13(X1,X2,sK2(X3,set_intersection2(X4,X5),X0))) = sK2(X3,set_intersection2(X4,X5),X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370506,c_112]) ).
tcf(c_441887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X5)
| ~ relation(X5)
| ~ subset(X3,relation_dom(X5))
| ~ empty(relation_image(X5,X4))
| ~ in(sK2(X0,set_intersection2(X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_370506,c_369501]) ).
tcf(c_441888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(X1,set_intersection2(X2,X3),X0),X4)
| in(sK2(X1,set_intersection2(X2,X3),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ~ subset(X0,sK10(sK2(X1,set_intersection2(X2,X3),X0),X4)) ),
inference(superposition,[status(thm)],[c_370506,c_369085]) ).
tcf(c_441889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X3),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_370506,c_372426]) ).
tcf(c_441890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(sK2(X1,set_intersection2(X2,X3),X0))
| in(sK2(X1,set_intersection2(X2,X3),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ~ subset(X0,sK16(sK2(X1,set_intersection2(X2,X3),X0))) ),
inference(superposition,[status(thm)],[c_370506,c_370746]) ).
tcf(c_441891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| in(sK2(X1,X2,sK2(X3,set_intersection2(X4,X5),X0)),X1)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ( sK2(X3,set_intersection2(X4,X5),X0) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X3,set_intersection2(X4,X5),X0))) ),
inference(superposition,[status(thm)],[c_370506,c_369079]) ).
tcf(c_441892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| in(sK2(X1,X2,sK2(X3,set_intersection2(X4,X5),X0)),X2)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ( sK2(X3,set_intersection2(X4,X5),X0) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X3,set_intersection2(X4,X5),X0))) ),
inference(superposition,[status(thm)],[c_370506,c_369078]) ).
tcf(c_441893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(X2,X3),X0),X2)
| in(sK2(sK2(X1,set_intersection2(X2,X3),X0),X4,X5),X5)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ( set_intersection2(sK2(X1,set_intersection2(X2,X3),X0),X4) = X5 )
| ~ subset(X0,sK2(sK2(X1,set_intersection2(X2,X3),X0),X4,X5)) ),
inference(superposition,[status(thm)],[c_370506,c_369076]) ).
tcf(c_441894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),X2)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X4 )
| ~ subset(X4,X4)
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(X2,X3),X4),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_370506,c_370220]) ).
tcf(c_441895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),X2)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X4 )
| ~ subset(X4,X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),X4)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_370506,c_368471]) ).
tcf(c_441896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,X4),X0),X3)
| in(sK2(X1,sK2(X2,set_intersection2(X3,X4),X0),X5),X5)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ( set_intersection2(X1,sK2(X2,set_intersection2(X3,X4),X0)) = X5 )
| ~ subset(X0,sK2(X1,sK2(X2,set_intersection2(X3,X4),X0),X5)) ),
inference(superposition,[status(thm)],[c_370506,c_369077]) ).
tcf(c_441897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,X4),X0),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X5,relation_image(X1,sK2(X2,set_intersection2(X3,X4),X0)))
| ~ subset(X0,sK13(X1,sK2(X2,set_intersection2(X3,X4),X0),X5)) ),
inference(superposition,[status(thm)],[c_370506,c_369593]) ).
tcf(c_441898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X5,X6),X0),X5)
| ( set_intersection2(X4,set_intersection2(X5,X6)) = X0 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,set_intersection2(X5,X6),X0)))) = sK13(X1,relation_image(X2,X3),sK2(X4,set_intersection2(X5,X6),X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_370506,c_369672]) ).
tcf(c_441899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,X4),X0),X3)
| in(sK11(X1,sK2(X2,set_intersection2(X3,X4),X0),X5),X5)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ( relation_image(X1,sK2(X2,set_intersection2(X3,X4),X0)) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK2(X2,set_intersection2(X3,X4),X0),X5)) ),
inference(superposition,[status(thm)],[c_370506,c_369298]) ).
tcf(c_441900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ( sK2(X3,set_intersection2(X4,X5),X0) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK2(X3,set_intersection2(X4,X5),X0))) = sK11(X1,X2,sK2(X3,set_intersection2(X4,X5),X0)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,set_intersection2(X4,X5),X0))) ),
inference(superposition,[status(thm)],[c_370506,c_369435]) ).
tcf(c_441901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| in(sK12(X1,X2,sK2(X3,set_intersection2(X4,X5),X0)),X2)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ( sK2(X3,set_intersection2(X4,X5),X0) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,set_intersection2(X4,X5),X0))) ),
inference(superposition,[status(thm)],[c_370506,c_369306]) ).
tcf(c_441902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| in(sK12(X1,X2,sK2(X3,set_intersection2(X4,X5),X0)),relation_dom(X1))
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ( sK2(X3,set_intersection2(X4,X5),X0) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,set_intersection2(X4,X5),X0))) ),
inference(superposition,[status(thm)],[c_370506,c_369205]) ).
tcf(c_441903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X3),X0),sK5)
| in(sK2(X1,set_intersection2(X2,X3),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_370506,c_412536]) ).
tcf(c_441904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X3),X0),sK8)
| in(sK2(X1,set_intersection2(X2,X3),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_370506,c_413867]) ).
tcf(c_441905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| in(sK7(X1,X2,sK2(X3,set_intersection2(X4,X5),X0)),relation_dom(X1))
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ( sK2(X3,set_intersection2(X4,X5),X0) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X3,set_intersection2(X4,X5),X0))) ),
inference(superposition,[status(thm)],[c_370506,c_369084]) ).
tcf(c_441906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),X0),X4)
| in(apply(X1,sK7(X1,X2,sK2(X3,set_intersection2(X4,X5),X0))),X2)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = X0 )
| ( sK2(X3,set_intersection2(X4,X5),X0) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X3,set_intersection2(X4,X5),X0))) ),
inference(superposition,[status(thm)],[c_370506,c_369083]) ).
tcf(c_441907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,X4),X0),X3)
| in(sK7(X1,sK2(X2,set_intersection2(X3,X4),X0),X5),X5)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ( relation_inverse_image(X1,sK2(X2,set_intersection2(X3,X4),X0)) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK2(X2,set_intersection2(X3,X4),X0),X5))) ),
inference(superposition,[status(thm)],[c_370506,c_369082]) ).
tcf(c_441908,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X0),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X0 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370506,c_423425]) ).
tcf(c_441909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ( set_intersection2(sK2(X1,set_intersection2(X2,X3),X0),X4) = sK2(X1,set_intersection2(X2,X3),X0) )
| ~ subset(X0,sK2(sK2(X1,set_intersection2(X2,X3),X0),X4,sK2(X1,set_intersection2(X2,X3),X0))) ),
inference(superposition,[status(thm)],[c_370506,c_370076]) ).
tcf(c_441910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),X0),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ( set_intersection2(X1,sK2(X2,set_intersection2(X3,X4),X0)) = sK2(X2,set_intersection2(X3,X4),X0) )
| ~ subset(X0,sK2(X1,sK2(X2,set_intersection2(X3,X4),X0),sK2(X2,set_intersection2(X3,X4),X0))) ),
inference(superposition,[status(thm)],[c_370506,c_370144]) ).
tcf(c_441911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),X0),X3)
| in(sK2(X2,set_intersection2(X3,X4),X0),X1)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_370506,c_430730]) ).
tcf(c_441912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X2)
| in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X0 )
| ~ subset(X0,set_intersection2(X2,X3))
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X1) ),
inference(superposition,[status(thm)],[c_370506,c_426065]) ).
tcf(c_441913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X5),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4)) = X5 )
| ~ subset(X5,X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X5),X5)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X5),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X5),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X5),set_intersection2(X3,X4)) ),
inference(superposition,[status(thm)],[c_370506,c_370217]) ).
tcf(c_441914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X5,X6),X0),X5)
| in(sK2(set_intersection2(X1,X2),X3,sK2(X4,set_intersection2(X5,X6),X0)),X1)
| ( set_intersection2(X4,set_intersection2(X5,X6)) = X0 )
| ( sK2(X4,set_intersection2(X5,X6),X0) = set_intersection2(set_intersection2(X1,X2),X3) )
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK2(X4,set_intersection2(X5,X6),X0))) ),
inference(superposition,[status(thm)],[c_370506,c_370273]) ).
tcf(c_441915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X1,set_intersection2(X2,X3),X0),X2)
| in(sK2(set_intersection2(sK2(X1,set_intersection2(X2,X3),X0),X4),X5,X6),X6)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ( set_intersection2(set_intersection2(sK2(X1,set_intersection2(X2,X3),X0),X4),X5) = X6 )
| ~ subset(X0,sK2(set_intersection2(sK2(X1,set_intersection2(X2,X3),X0),X4),X5,X6)) ),
inference(superposition,[status(thm)],[c_370506,c_370285]) ).
tcf(c_441916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X5,X6),X0),X5)
| in(sK2(X1,set_intersection2(X2,X3),sK2(X4,set_intersection2(X5,X6),X0)),X2)
| ( set_intersection2(X4,set_intersection2(X5,X6)) = X0 )
| ( sK2(X4,set_intersection2(X5,X6),X0) = set_intersection2(X1,set_intersection2(X2,X3)) )
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK2(X4,set_intersection2(X5,X6),X0))) ),
inference(superposition,[status(thm)],[c_370506,c_370505]) ).
tcf(c_441917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,set_intersection2(X1,X3),X0),X1)
| ( set_intersection2(X2,set_intersection2(X1,X3)) = X0 )
| ~ subset(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_370506]) ).
tcf(c_441935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,empty_set,X0),X1)
| ( set_intersection2(X2,set_intersection2(empty_set,X3)) = X0 )
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_441838,c_372426]) ).
tcf(c_442142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X0,X1),X2),X3)
| ( set_intersection2(X0,X1) = X2 )
| ~ subset(X2,X3)
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_441844,c_397136]) ).
tcf(c_442593,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,X1,X2),X2)
| in(sK2(X0,set_intersection2(X1,X1),X2),X1)
| ( set_intersection2(X0,set_intersection2(X1,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_53,c_370507]) ).
tcf(c_442596,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,empty_set,X2),X2)
| in(sK2(X0,set_intersection2(X1,empty_set),X2),X1)
| ( set_intersection2(X0,set_intersection2(X1,empty_set)) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_370507]) ).
tcf(c_442597,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,empty_set,X2),X2)
| in(sK2(X0,set_intersection2(empty_set,X1),X2),empty_set)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_370507]) ).
tcf(c_442598,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,sK16(powerset(X1)),X2),X2)
| in(sK2(X0,set_intersection2(X1,sK16(powerset(X1))),X2),X1)
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_370507]) ).
tcf(c_442599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,set_intersection2(X1,X2),X3),X3)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_370507]) ).
tcf(c_442600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,set_intersection2(X2,X1),X3),X3)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_370507]) ).
tcf(c_442601,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK15(sK5),X1),X1)
| in(sK2(X0,set_intersection2(sK5,sK15(sK5)),X1),sK5)
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_370507]) ).
tcf(c_442602,plain,
! [X0: $i,X1: $i] :
( element(sK2(X0,sK15(sK8),X1),X1)
| in(sK2(X0,set_intersection2(sK8,sK15(sK8)),X1),sK8)
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_370507]) ).
tcf(c_442603,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X1)
| element(sK2(X0,set_intersection2(X1,X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_53,c_370507]) ).
tcf(c_442606,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),X1)
| element(sK2(X0,set_intersection2(X1,empty_set),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,empty_set)) = X2 ) ),
inference(superposition,[status(thm)],[c_64,c_370507]) ).
tcf(c_442607,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,empty_set,X2),empty_set)
| element(sK2(X0,set_intersection2(empty_set,X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_368545,c_370507]) ).
tcf(c_442608,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK16(powerset(X1)),X2),X1)
| element(sK2(X0,set_intersection2(X1,sK16(powerset(X1))),X2),X2)
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X1)))) = X2 ) ),
inference(superposition,[status(thm)],[c_397130,c_370507]) ).
tcf(c_442609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X1)
| element(sK2(X0,set_intersection2(X1,set_intersection2(X1,X2)),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X1,X2))) = X3 ) ),
inference(superposition,[status(thm)],[c_397136,c_370507]) ).
tcf(c_442610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X2,X1),X3),X1)
| element(sK2(X0,set_intersection2(X1,set_intersection2(X2,X1)),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X1))) = X3 ) ),
inference(superposition,[status(thm)],[c_397137,c_370507]) ).
tcf(c_442611,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),sK5)
| element(sK2(X0,set_intersection2(sK5,sK15(sK5)),X1),X1)
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = X1 ) ),
inference(superposition,[status(thm)],[c_411955,c_370507]) ).
tcf(c_442612,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),sK8)
| element(sK2(X0,set_intersection2(sK8,sK15(sK8)),X1),X1)
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = X1 ) ),
inference(superposition,[status(thm)],[c_411956,c_370507]) ).
tcf(c_442614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(sK2(X0,set_intersection2(X1,X2),powerset(X3)),X3)
| in(sK2(X0,set_intersection2(X1,X2),powerset(X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = powerset(X3) ) ),
inference(superposition,[status(thm)],[c_370507,c_99]) ).
tcf(c_442615,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,set_intersection2(X0,X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = X2 )
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_370507,c_54]) ).
tcf(c_442616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(X0,X3),X4),X4)
| element(sK2(X2,set_intersection2(X0,X3),X4),X1)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370507,c_321]) ).
tcf(c_442617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(X0,X3),X4),X4)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370507,c_320]) ).
tcf(c_442618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X1,set_intersection2(X0,X2),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ~ in(X0,sK2(X1,set_intersection2(X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_370507,c_97]) ).
tcf(c_442619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(X0,X3),X4),X4)
| in(sK2(X2,set_intersection2(X0,X3),X4),X1)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370507,c_96]) ).
tcf(c_442620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,set_intersection2(X1,X2),X3),X3)
| element(sK2(X0,set_intersection2(X1,X2),X3),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_370507,c_93]) ).
tcf(c_442621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X1,set_intersection2(X0,X2),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370507,c_91]) ).
tcf(c_442622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X4)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X2)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X3)) = X4 ) ),
inference(superposition,[status(thm)],[c_370507,c_59]) ).
tcf(c_442623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X4)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),X4),X1)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X3)) = X4 ) ),
inference(superposition,[status(thm)],[c_370507,c_58]) ).
tcf(c_442624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),X4),X4)
| in(apply(X0,sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),X4)),X2)
| ( set_intersection2(X1,set_intersection2(relation_inverse_image(X0,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370507,c_88]) ).
tcf(c_442625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),X4),X4)
| in(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),X4),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(relation_inverse_image(X0,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370507,c_87]) ).
tcf(c_442626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X3)
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = X3 )
| ( apply(X1,sK13(X1,X4,apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),X3)))) = apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),X3)) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X4) ),
inference(superposition,[status(thm)],[c_370507,c_369671]) ).
tcf(c_442627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X3,set_intersection2(relation_image(X2,X0),X4),X5),X5)
| ( set_intersection2(X3,set_intersection2(relation_image(X2,X0),X4)) = X5 )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370507,c_369799]) ).
tcf(c_442628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X2,set_intersection2(relation_image(X0,X3),X4),X5),X5)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X3),X4)) = X5 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370507,c_369798]) ).
tcf(c_442629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(relation_image(X0,X1),X3),X4),X4)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X1),X3)) = X4 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370507,c_369596]) ).
tcf(c_442630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X1,set_intersection2(relation_image(X0,X2),X3),X4),X4)
| ( set_intersection2(X1,set_intersection2(relation_image(X0,X2),X3)) = X4 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370507,c_369558]) ).
tcf(c_442631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(relation_image(X0,X1),X3),X4),X4)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X1),X3)) = X4 )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(relation_image(X0,X1),X3),X4))) = sK2(X2,set_intersection2(relation_image(X0,X1),X3),X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370507,c_112]) ).
tcf(c_442632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X3)
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = X3 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X4))
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X4) ),
inference(superposition,[status(thm)],[c_370507,c_369501]) ).
tcf(c_442633,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,set_intersection2(empty_set,X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_370507,c_372426]) ).
tcf(c_442634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X2),X2)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X2 )
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(X2,X3),X2),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X2),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X2),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_370507,c_370220]) ).
tcf(c_442635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),X3)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X2)) = X3 )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),set_intersection2(X0,X2)) ),
inference(superposition,[status(thm)],[c_370507,c_368471]) ).
tcf(c_442636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),X5),X5)
| ( set_intersection2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4)) = X5 )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),X5)))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370507,c_369672]) ).
tcf(c_442637,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(sK15(sK5),X1),X2),sK5)
| element(sK2(X0,set_intersection2(sK15(sK5),X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(sK15(sK5),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_370507,c_412536]) ).
tcf(c_442638,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(sK15(sK8),X1),X2),sK8)
| element(sK2(X0,set_intersection2(sK15(sK8),X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(sK15(sK8),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_370507,c_413867]) ).
tcf(c_442639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X0,set_intersection2(sK16(powerset(X1)),X2),X3),X3)
| in(sK2(X0,set_intersection2(sK16(powerset(X1)),X2),X3),X1)
| ( set_intersection2(X0,set_intersection2(sK16(powerset(X1)),X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_370507,c_430730]) ).
tcf(c_442640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3)) = X4 )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),set_intersection2(X0,X3)) ),
inference(superposition,[status(thm)],[c_370507,c_370217]) ).
tcf(c_442646,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,empty_set,X1),empty_set)
| element(sK2(X2,set_intersection2(empty_set,X0),X1),X1)
| ( set_intersection2(empty_set,X0) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_442607,c_425546]) ).
tcf(c_442647,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,empty_set,X0),empty_set)
| element(sK2(X1,empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_442646,c_368545]) ).
tcf(c_442649,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,empty_set,X1),X0)
| element(sK2(X2,set_intersection2(X0,empty_set),X1),X1)
| ( set_intersection2(X0,empty_set) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_442606,c_425312]) ).
tcf(c_442650,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X1,empty_set,X0),X0)
| in(sK2(X1,empty_set,X0),X2)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_442649,c_64]) ).
tcf(c_442745,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK2(X0,set_intersection2(X0,X1),X2),X2)
| ( set_intersection2(X0,X1) = X2 )
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_442615,c_397136]) ).
tcf(c_442959,plain,
! [X0: $i,X1: $i] :
( subset(sK15(sK5),X1)
| element(sK10(sK15(sK5),X1),X0)
| ~ subset(sK5,X0) ),
inference(superposition,[status(thm)],[c_412593,c_321]) ).
tcf(c_442961,plain,
! [X0: $i] :
( subset(sK15(sK5),X0)
| ~ in(sK5,sK10(sK15(sK5),X0)) ),
inference(superposition,[status(thm)],[c_412593,c_97]) ).
tcf(c_442962,plain,
! [X0: $i,X1: $i] :
( subset(sK15(sK5),X1)
| in(sK10(sK15(sK5),X1),X0)
| ~ subset(sK5,X0) ),
inference(superposition,[status(thm)],[c_412593,c_96]) ).
tcf(c_442963,plain,
! [X0: $i] :
( subset(sK15(sK5),X0)
| element(sK10(sK15(sK5),X0),sK5) ),
inference(superposition,[status(thm)],[c_412593,c_93]) ).
tcf(c_442966,plain,
! [X0: $i] :
( subset(sK15(sK5),set_intersection2(sK5,X0))
| ~ in(sK10(sK15(sK5),set_intersection2(sK5,X0)),X0) ),
inference(superposition,[status(thm)],[c_412593,c_368972]) ).
tcf(c_443053,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,X2)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_53,c_370508]) ).
tcf(c_443056,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,empty_set,X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_64,c_370508]) ).
tcf(c_443058,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK16(powerset(X2)),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,sK16(powerset(X2)))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370508]) ).
tcf(c_443059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X3),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X2,X3))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370508]) ).
tcf(c_443060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X3,X2),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X3,X2))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370508]) ).
tcf(c_443061,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK15(sK5),X0),sK5)
| ( set_intersection2(X1,set_intersection2(sK5,sK15(sK5))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_411955,c_370508]) ).
tcf(c_443062,plain,
! [X0: $i,X1: $i] :
( in(sK2(X1,sK15(sK8),X0),sK8)
| ( set_intersection2(X1,set_intersection2(sK8,sK15(sK8))) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_411956,c_370508]) ).
tcf(c_443063,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,set_intersection2(X0,X1)) = X2 )
| ~ empty(X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_370508,c_54]) ).
tcf(c_443064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X3,set_intersection2(X0,X4),X2),X1)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X2 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370508,c_321]) ).
tcf(c_443065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,set_intersection2(X0,X4)) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370508,c_320]) ).
tcf(c_443066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ~ empty(X3)
| ~ in(X0,sK2(X1,set_intersection2(X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_370508,c_97]) ).
tcf(c_443067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X2),X1)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X2 )
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370508,c_96]) ).
tcf(c_443068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK2(X1,set_intersection2(X2,X3),X0),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370508,c_93]) ).
tcf(c_443069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,set_intersection2(X1,X3)) = X0 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370508,c_91]) ).
tcf(c_443070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(set_intersection2(X2,X3),X4),X0),X3)
| ( set_intersection2(X1,set_intersection2(set_intersection2(X2,X3),X4)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370508,c_59]) ).
tcf(c_443071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(set_intersection2(X2,X3),X4),X0),X2)
| ( set_intersection2(X1,set_intersection2(set_intersection2(X2,X3),X4)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370508,c_58]) ).
tcf(c_443072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(X2,set_intersection2(relation_inverse_image(X0,X3),X4),X1)),X3)
| ( set_intersection2(X2,set_intersection2(relation_inverse_image(X0,X3),X4)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370508,c_88]) ).
tcf(c_443073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(relation_inverse_image(X0,X3),X4),X1),relation_dom(X0))
| ( set_intersection2(X2,set_intersection2(relation_inverse_image(X0,X3),X4)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370508,c_87]) ).
tcf(c_443074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = X3 )
| ( apply(X1,sK13(X1,X4,apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),X3)))) = apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),X3)) )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X4) ),
inference(superposition,[status(thm)],[c_370508,c_369671]) ).
tcf(c_443075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X4,set_intersection2(relation_image(X2,X0),X5)) = X3 )
| ~ empty(X3)
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370508,c_369799]) ).
tcf(c_443076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X3,set_intersection2(relation_image(X0,X4),X5)) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370508,c_369798]) ).
tcf(c_443077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,set_intersection2(relation_image(X0,X2),X4)) = X1 )
| ~ empty(X2)
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370508,c_369596]) ).
tcf(c_443078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X2,set_intersection2(relation_image(X0,X3),X4)) = X1 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370508,c_369558]) ).
tcf(c_443079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,set_intersection2(relation_image(X0,X2),X4)) = X1 )
| ( apply(X0,sK13(X0,X2,sK2(X3,set_intersection2(relation_image(X0,X2),X4),X1))) = sK2(X3,set_intersection2(relation_image(X0,X2),X4),X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370508,c_112]) ).
tcf(c_443080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = X3 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X4))
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),X3),X4) ),
inference(superposition,[status(thm)],[c_370508,c_369501]) ).
tcf(c_443081,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X1,set_intersection2(empty_set,X2)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370508,c_372426]) ).
tcf(c_443082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X2 )
| ~ empty(X2)
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(X2,X3),X2),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X2),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X2),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_370508,c_370220]) ).
tcf(c_443083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X2)) = X3 )
| ~ empty(X3)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),X3)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),X3),set_intersection2(X0,X2)) ),
inference(superposition,[status(thm)],[c_370508,c_368471]) ).
tcf(c_443084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X4,set_intersection2(relation_image(X0,relation_image(X1,X3)),X5)) = X2 )
| ( apply(X1,sK13(X1,X3,sK13(X0,relation_image(X1,X3),sK2(X4,set_intersection2(relation_image(X0,relation_image(X1,X3)),X5),X2)))) = sK13(X0,relation_image(X1,X3),sK2(X4,set_intersection2(relation_image(X0,relation_image(X1,X3)),X5),X2)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370508,c_369672]) ).
tcf(c_443085,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,set_intersection2(sK15(sK5),X2),X0),sK5)
| ( set_intersection2(X1,set_intersection2(sK15(sK5),X2)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370508,c_412536]) ).
tcf(c_443086,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,set_intersection2(sK15(sK8),X2),X0),sK8)
| ( set_intersection2(X1,set_intersection2(sK15(sK8),X2)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370508,c_413867]) ).
tcf(c_443087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(sK16(powerset(X2)),X3),X0),X2)
| ( set_intersection2(X1,set_intersection2(sK16(powerset(X2)),X3)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370508,c_430730]) ).
tcf(c_443088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3)) = X4 )
| ~ empty(X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),X4),set_intersection2(X0,X3)) ),
inference(superposition,[status(thm)],[c_370508,c_370217]) ).
tcf(c_443176,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ empty(X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_443063,c_397136]) ).
tcf(c_443295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X3)
| in(sK2(X0,set_intersection2(X1,X1),set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_53,c_370509]) ).
tcf(c_443298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,empty_set,set_intersection2(X2,X3)),X3)
| in(sK2(X0,set_intersection2(X1,empty_set),set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,empty_set)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_64,c_370509]) ).
tcf(c_443299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,empty_set,set_intersection2(X2,X3)),X3)
| in(sK2(X0,set_intersection2(empty_set,X1),set_intersection2(X2,X3)),empty_set)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368545,c_370509]) ).
tcf(c_443300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,sK16(powerset(X1)),set_intersection2(X2,X3)),X3)
| in(sK2(X0,set_intersection2(X1,sK16(powerset(X1))),set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X1)))) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397130,c_370509]) ).
tcf(c_443301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X4)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X1,X2)),set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X1,X2))) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397136,c_370509]) ).
tcf(c_443302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X2,X1),set_intersection2(X3,X4)),X4)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X1)),set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X1))) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397137,c_370509]) ).
tcf(c_443303,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK15(sK5),set_intersection2(X1,X2)),X2)
| in(sK2(X0,set_intersection2(sK5,sK15(sK5)),set_intersection2(X1,X2)),sK5)
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411955,c_370509]) ).
tcf(c_443304,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK15(sK8),set_intersection2(X1,X2)),X2)
| in(sK2(X0,set_intersection2(sK8,sK15(sK8)),set_intersection2(X1,X2)),sK8)
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411956,c_370509]) ).
tcf(c_443305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X3) ) ),
inference(superposition,[status(thm)],[c_53,c_370509]) ).
tcf(c_443306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X4,X3)),X4)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_63,c_370509]) ).
tcf(c_443309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),X3)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(empty_set,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(empty_set,X3) ) ),
inference(superposition,[status(thm)],[c_368545,c_370509]) ).
tcf(c_443310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK16(powerset(X3))),sK16(powerset(X3)))
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,sK16(powerset(X3)))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,sK16(powerset(X3))) ) ),
inference(superposition,[status(thm)],[c_397130,c_370509]) ).
tcf(c_443311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,X1)),set_intersection2(X0,X1))
| in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,set_intersection2(X0,X1))),X3)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X2,set_intersection2(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_397136,c_370509]) ).
tcf(c_443312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X1,X0)),set_intersection2(X1,X0))
| in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,set_intersection2(X1,X0))),X3)
| ( set_intersection2(X0,set_intersection2(X1,X0)) = set_intersection2(X2,set_intersection2(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_397137,c_370509]) ).
tcf(c_443313,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK5)),sK15(sK5))
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(sK5,sK15(sK5))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(sK5,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_411955,c_370509]) ).
tcf(c_443314,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK8)),sK15(sK8))
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(sK8,sK15(sK8))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(sK8,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_411956,c_370509]) ).
tcf(c_443315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X1)
| in(sK2(X0,set_intersection2(X1,X1),set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,set_intersection2(X1,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_53,c_370509]) ).
tcf(c_443318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,empty_set,set_intersection2(X2,X3)),X1)
| in(sK2(X0,set_intersection2(X1,empty_set),set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,set_intersection2(X1,empty_set)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_64,c_370509]) ).
tcf(c_443319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,empty_set,set_intersection2(X2,X3)),empty_set)
| in(sK2(X0,set_intersection2(empty_set,X1),set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368545,c_370509]) ).
tcf(c_443320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,sK16(powerset(X1)),set_intersection2(X2,X3)),X1)
| in(sK2(X0,set_intersection2(X1,sK16(powerset(X1))),set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X1)))) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397130,c_370509]) ).
tcf(c_443321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X1,X2)),set_intersection2(X3,X4)),X4)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X1,X2))) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397136,c_370509]) ).
tcf(c_443322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X2,X1),set_intersection2(X3,X4)),X1)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X1)),set_intersection2(X3,X4)),X4)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X1))) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397137,c_370509]) ).
tcf(c_443323,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK15(sK5),set_intersection2(X1,X2)),sK5)
| in(sK2(X0,set_intersection2(sK5,sK15(sK5)),set_intersection2(X1,X2)),X2)
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411955,c_370509]) ).
tcf(c_443324,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK15(sK8),set_intersection2(X1,X2)),sK8)
| in(sK2(X0,set_intersection2(sK8,sK15(sK8)),set_intersection2(X1,X2)),X2)
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411956,c_370509]) ).
tcf(c_443325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X3)),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X3) ) ),
inference(superposition,[status(thm)],[c_53,c_370509]) ).
tcf(c_443326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X4,X3)),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X4)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_63,c_370509]) ).
tcf(c_443328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,empty_set)),empty_set)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,empty_set) ) ),
inference(superposition,[status(thm)],[c_64,c_370509]) ).
tcf(c_443329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(empty_set,X3)),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(empty_set,X3) ) ),
inference(superposition,[status(thm)],[c_368545,c_370509]) ).
tcf(c_443330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,sK16(powerset(X3)))),sK16(powerset(X3)))
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,sK16(powerset(X3))) ) ),
inference(superposition,[status(thm)],[c_397130,c_370509]) ).
tcf(c_443331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,X1)),X3)
| in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,set_intersection2(X0,X1))),set_intersection2(X0,X1))
| ( set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X2,set_intersection2(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_397136,c_370509]) ).
tcf(c_443332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X1,X0)),X3)
| in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,set_intersection2(X1,X0))),set_intersection2(X1,X0))
| ( set_intersection2(X0,set_intersection2(X1,X0)) = set_intersection2(X2,set_intersection2(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_397137,c_370509]) ).
tcf(c_443333,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK5)),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(sK5,sK15(sK5))),sK15(sK5))
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(sK5,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_411955,c_370509]) ).
tcf(c_443334,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK8)),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(sK8,sK15(sK8))),sK15(sK8))
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(sK8,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_411956,c_370509]) ).
tcf(c_443335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X0)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X0) )
| ~ in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X0)),set_intersection2(X3,X0))
| ~ in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X0)),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370509,c_54]) ).
tcf(c_443336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X2,set_intersection2(X3,X4),set_intersection2(X5,X0)),X1)
| in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X5,X0)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = set_intersection2(X5,X0) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370509,c_321]) ).
tcf(c_443337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X5,X0)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = set_intersection2(X5,X0) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370509,c_320]) ).
tcf(c_443338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),set_intersection2(X4,X0)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = set_intersection2(X4,X0) )
| ~ in(X0,sK2(X1,set_intersection2(X2,X3),set_intersection2(X4,X0))) ),
inference(superposition,[status(thm)],[c_370509,c_97]) ).
tcf(c_443339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X5,X0)),X3)
| in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X5,X0)),X1)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = set_intersection2(X5,X0) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370509,c_96]) ).
tcf(c_443340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X4)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370509,c_93]) ).
tcf(c_443341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),set_intersection2(X4,X0)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = set_intersection2(X4,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370509,c_91]) ).
tcf(c_443342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,set_intersection2(X4,X5))),X5)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,set_intersection2(X4,X5))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) ) ),
inference(superposition,[status(thm)],[c_370509,c_59]) ).
tcf(c_443343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,set_intersection2(X4,X5))),X4)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,set_intersection2(X4,X5))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) ) ),
inference(superposition,[status(thm)],[c_370509,c_58]) ).
tcf(c_443344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),set_intersection2(X1,relation_inverse_image(X0,X2))),X4)
| in(apply(X0,sK2(X3,set_intersection2(X4,X5),set_intersection2(X1,relation_inverse_image(X0,X2)))),X2)
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370509,c_88]) ).
tcf(c_443345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),set_intersection2(X1,relation_inverse_image(X0,X2))),X4)
| in(sK2(X3,set_intersection2(X4,X5),set_intersection2(X1,relation_inverse_image(X0,X2))),relation_dom(X0))
| ( set_intersection2(X1,relation_inverse_image(X0,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370509,c_87]) ).
tcf(c_443346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,relation_dom(X4))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,relation_dom(X4)) )
| ( apply(X4,sK13(X4,X5,apply(X4,sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,relation_dom(X4)))))) = apply(X4,sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,relation_dom(X4)))) )
| ~ function(X4)
| ~ relation(X4)
| ~ in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,relation_dom(X4))),X5) ),
inference(superposition,[status(thm)],[c_370509,c_369671]) ).
tcf(c_443347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X5,X6),set_intersection2(X3,relation_image(X2,X0))),X5)
| ( set_intersection2(X3,relation_image(X2,X0)) = set_intersection2(X4,set_intersection2(X5,X6)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370509,c_369799]) ).
tcf(c_443348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X5,X6),set_intersection2(X2,relation_image(X0,X3))),X5)
| ( set_intersection2(X2,relation_image(X0,X3)) = set_intersection2(X4,set_intersection2(X5,X6)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370509,c_369798]) ).
tcf(c_443349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),set_intersection2(X2,relation_image(X0,X1))),X4)
| ( set_intersection2(X2,relation_image(X0,X1)) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370509,c_369596]) ).
tcf(c_443350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),set_intersection2(X1,relation_image(X0,X2))),X4)
| ( set_intersection2(X1,relation_image(X0,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370509,c_369558]) ).
tcf(c_443351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X5,relation_image(X0,X1))),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = set_intersection2(X5,relation_image(X0,X1)) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,X4),set_intersection2(X5,relation_image(X0,X1))))) = sK2(X2,set_intersection2(X3,X4),set_intersection2(X5,relation_image(X0,X1))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370509,c_112]) ).
tcf(c_443352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,relation_dom(X4))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,relation_dom(X4)) )
| ~ function(X4)
| ~ relation(X4)
| ~ empty(relation_image(X4,X5))
| ~ in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,relation_dom(X4))),X5) ),
inference(superposition,[status(thm)],[c_370509,c_369501]) ).
tcf(c_443353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,empty_set)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,empty_set) ) ),
inference(superposition,[status(thm)],[c_370509,c_372426]) ).
tcf(c_443354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),set_intersection2(X4,X0)),X2)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(X4,X0) )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),set_intersection2(X4,X0)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),set_intersection2(X4,X0)),set_intersection2(X4,X0))
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),set_intersection2(X4,X0)),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_370509,c_368471]) ).
tcf(c_443355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X3,set_intersection2(X4,X5),set_intersection2(X6,relation_image(X0,relation_image(X1,X2)))),X4)
| ( set_intersection2(X6,relation_image(X0,relation_image(X1,X2))) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,X5),set_intersection2(X6,relation_image(X0,relation_image(X1,X2))))))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,X5),set_intersection2(X6,relation_image(X0,relation_image(X1,X2))))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370509,c_369672]) ).
tcf(c_443356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,sK15(sK5))),sK5)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,sK15(sK5))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_370509,c_412536]) ).
tcf(c_443357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,sK15(sK8))),sK8)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,sK15(sK8))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_370509,c_413867]) ).
tcf(c_443358,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(X0,set_intersection2(X1,X2)),set_intersection2(X1,X2),set_intersection2(X0,set_intersection2(X1,X2))),X1)
| ( set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),set_intersection2(X1,X2)) = set_intersection2(X0,set_intersection2(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_370509,c_423425]) ).
tcf(c_443359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,sK16(powerset(X4)))),X4)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,sK16(powerset(X4)))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,sK16(powerset(X4))) ) ),
inference(superposition,[status(thm)],[c_370509,c_430730]) ).
tcf(c_443360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3),set_intersection2(X1,X2),set_intersection2(X0,set_intersection2(X1,X2))),X1)
| in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3),set_intersection2(X1,X2),set_intersection2(X0,set_intersection2(X1,X2))),set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3))
| ( set_intersection2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3),set_intersection2(X1,X2)) = set_intersection2(X0,set_intersection2(X1,X2)) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,set_intersection2(X1,X2)),X3),set_intersection2(X1,X2),set_intersection2(X0,set_intersection2(X1,X2))),X3) ),
inference(superposition,[status(thm)],[c_370509,c_426065]) ).
tcf(c_443361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),set_intersection2(X5,X0)),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4)) = set_intersection2(X5,X0) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),set_intersection2(X5,X0)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),set_intersection2(X5,X0)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),set_intersection2(X5,X0)),set_intersection2(X5,X0))
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),set_intersection2(X5,X0)),set_intersection2(X3,X4)) ),
inference(superposition,[status(thm)],[c_370509,c_370217]) ).
tcf(c_443362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X0,X1),set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X2,X3) )
| ~ in(sK2(X0,set_intersection2(X0,X1),set_intersection2(X2,X3)),set_intersection2(X2,X3))
| ~ in(sK2(X0,set_intersection2(X0,X1),set_intersection2(X2,X3)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_370509,c_54]) ).
tcf(c_443363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X2,set_intersection2(X0,X3),set_intersection2(X4,X5)),X1)
| in(sK2(X2,set_intersection2(X0,X3),set_intersection2(X4,X5)),X5)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = set_intersection2(X4,X5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370509,c_321]) ).
tcf(c_443364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X0,X3),set_intersection2(X4,X5)),X5)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370509,c_320]) ).
tcf(c_443365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X0,X2),set_intersection2(X3,X4)),X4)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = set_intersection2(X3,X4) )
| ~ in(X0,sK2(X1,set_intersection2(X0,X2),set_intersection2(X3,X4))) ),
inference(superposition,[status(thm)],[c_370509,c_97]) ).
tcf(c_443366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X0,X3),set_intersection2(X4,X5)),X5)
| in(sK2(X2,set_intersection2(X0,X3),set_intersection2(X4,X5)),X1)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = set_intersection2(X4,X5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370509,c_96]) ).
tcf(c_443367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X4)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370509,c_93]) ).
tcf(c_443368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X0,X2),set_intersection2(X3,X4)),X4)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = set_intersection2(X3,X4) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370509,c_91]) ).
tcf(c_443369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),set_intersection2(X4,X5)),X5)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),set_intersection2(X4,X5)),X2)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X3)) = set_intersection2(X4,X5) ) ),
inference(superposition,[status(thm)],[c_370509,c_59]) ).
tcf(c_443370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),set_intersection2(X4,X5)),X5)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),set_intersection2(X4,X5)),X1)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X3)) = set_intersection2(X4,X5) ) ),
inference(superposition,[status(thm)],[c_370509,c_58]) ).
tcf(c_443371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),set_intersection2(X4,X5)),X5)
| in(apply(X0,sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),set_intersection2(X4,X5))),X2)
| ( set_intersection2(X1,set_intersection2(relation_inverse_image(X0,X2),X3)) = set_intersection2(X4,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370509,c_88]) ).
tcf(c_443372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),set_intersection2(X4,X5)),X5)
| in(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),set_intersection2(X4,X5)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(relation_inverse_image(X0,X2),X3)) = set_intersection2(X4,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370509,c_87]) ).
tcf(c_443373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(X3,X4)),X4)
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X5,apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(X3,X4))))) = apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(X3,X4))) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370509,c_369671]) ).
tcf(c_443374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X3,set_intersection2(relation_image(X2,X0),X4),set_intersection2(X5,X6)),X6)
| ( set_intersection2(X3,set_intersection2(relation_image(X2,X0),X4)) = set_intersection2(X5,X6) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370509,c_369799]) ).
tcf(c_443375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X2,set_intersection2(relation_image(X0,X3),X4),set_intersection2(X5,X6)),X6)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X3),X4)) = set_intersection2(X5,X6) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370509,c_369798]) ).
tcf(c_443376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(relation_image(X0,X1),X3),set_intersection2(X4,X5)),X5)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X1),X3)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370509,c_369596]) ).
tcf(c_443377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(relation_image(X0,X2),X3),set_intersection2(X4,X5)),X5)
| ( set_intersection2(X1,set_intersection2(relation_image(X0,X2),X3)) = set_intersection2(X4,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370509,c_369558]) ).
tcf(c_443378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(relation_image(X0,X1),X3),set_intersection2(X4,X5)),X5)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X1),X3)) = set_intersection2(X4,X5) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(relation_image(X0,X1),X3),set_intersection2(X4,X5)))) = sK2(X2,set_intersection2(relation_image(X0,X1),X3),set_intersection2(X4,X5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370509,c_112]) ).
tcf(c_443379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(X3,X4)),X4)
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X5))
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370509,c_369501]) ).
tcf(c_443380,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(empty_set,X1),set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_370509,c_372426]) ).
tcf(c_443381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X2,X3),X4),set_intersection2(X2,X3)),X3)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X2,X3),X4)) = set_intersection2(X2,X3) )
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(set_intersection2(X2,X3),X4),set_intersection2(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X2,X3),X4),set_intersection2(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X2,X3),X4),set_intersection2(X2,X3)),set_intersection2(set_intersection2(X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_370509,c_370220]) ).
tcf(c_443382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),set_intersection2(X3,X4)),X4)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X2)) = set_intersection2(X3,X4) )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),set_intersection2(X3,X4)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),set_intersection2(X3,X4)),set_intersection2(X3,X4))
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),set_intersection2(X3,X4)),set_intersection2(X0,X2)) ),
inference(superposition,[status(thm)],[c_370509,c_368471]) ).
tcf(c_443383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),set_intersection2(X5,X6)),X6)
| ( set_intersection2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4)) = set_intersection2(X5,X6) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),set_intersection2(X5,X6))))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),set_intersection2(X5,X6))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370509,c_369672]) ).
tcf(c_443384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(sK15(sK5),X1),set_intersection2(X2,X3)),sK5)
| in(sK2(X0,set_intersection2(sK15(sK5),X1),set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,set_intersection2(sK15(sK5),X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_370509,c_412536]) ).
tcf(c_443385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(sK15(sK8),X1),set_intersection2(X2,X3)),sK8)
| in(sK2(X0,set_intersection2(sK15(sK8),X1),set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,set_intersection2(sK15(sK8),X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_370509,c_413867]) ).
tcf(c_443386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(sK16(powerset(X1)),X2),set_intersection2(X3,X4)),X4)
| in(sK2(X0,set_intersection2(sK16(powerset(X1)),X2),set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(sK16(powerset(X1)),X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370509,c_430730]) ).
tcf(c_443387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),set_intersection2(X4,X5)),X5)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3)) = set_intersection2(X4,X5) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),set_intersection2(X4,X5)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),set_intersection2(X4,X5)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),set_intersection2(X4,X5)),set_intersection2(X4,X5))
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),set_intersection2(X4,X5)),set_intersection2(X0,X3)) ),
inference(superposition,[status(thm)],[c_370509,c_370217]) ).
tcf(c_443388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X1)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X1) ) ),
inference(equality_factoring,[status(thm)],[c_370509]) ).
tcf(c_443392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,set_intersection2(empty_set,X2),set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(light_normalisation,[status(thm)],[c_443380,c_425546]) ).
tcf(c_443414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_443328,c_372426]) ).
tcf(c_443420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,empty_set,set_intersection2(X0,X1)),empty_set)
| in(sK2(X3,set_intersection2(empty_set,X2),set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(light_normalisation,[status(thm)],[c_443319,c_425546]) ).
tcf(c_443422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,empty_set,set_intersection2(X0,X1)),X2)
| in(sK2(X3,set_intersection2(X2,empty_set),set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_443318,c_425312]) ).
tcf(c_443435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,empty_set,set_intersection2(X0,X1)),X1)
| in(sK2(X3,set_intersection2(empty_set,X2),set_intersection2(X0,X1)),empty_set)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(light_normalisation,[status(thm)],[c_443299,c_425546]) ).
tcf(c_443436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,empty_set,set_intersection2(X0,X1)),X1)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_443435,c_372426]) ).
tcf(c_443439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,empty_set,set_intersection2(X0,X1)),X1)
| in(sK2(X3,set_intersection2(X2,empty_set),set_intersection2(X0,X1)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_443298,c_425312]) ).
tcf(c_443470,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK8)),X1)
| in(sK2(X0,set_intersection2(X1,X2),sK15(sK8)),sK15(sK8))
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK15(sK8) ) ),
inference(light_normalisation,[status(thm)],[c_443334,c_411956]) ).
tcf(c_443474,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK5)),X1)
| in(sK2(X0,set_intersection2(X1,X2),sK15(sK5)),sK15(sK5))
| ( set_intersection2(X0,set_intersection2(X1,X2)) = sK15(sK5) ) ),
inference(light_normalisation,[status(thm)],[c_443333,c_411955]) ).
tcf(c_443564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),set_intersection2(X3,X4))
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(light_normalisation,[status(thm)],[c_443332,c_397137]) ).
tcf(c_443633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X0,X1),set_intersection2(X2,X3)),X3)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ~ in(sK2(X0,set_intersection2(X0,X1),set_intersection2(X2,X3)),set_intersection2(X2,X3))
| ~ in(sK2(X0,set_intersection2(X0,X1),set_intersection2(X2,X3)),set_intersection2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_443362,c_397136]) ).
tcf(c_444044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X2)
| in(sK2(X0,set_intersection2(X1,X1),set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_53,c_370510]) ).
tcf(c_444047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,empty_set,set_intersection2(X2,X3)),X2)
| in(sK2(X0,set_intersection2(X1,empty_set),set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,empty_set)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_64,c_370510]) ).
tcf(c_444048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,empty_set,set_intersection2(X2,X3)),X2)
| in(sK2(X0,set_intersection2(empty_set,X1),set_intersection2(X2,X3)),empty_set)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368545,c_370510]) ).
tcf(c_444049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,sK16(powerset(X1)),set_intersection2(X2,X3)),X2)
| in(sK2(X0,set_intersection2(X1,sK16(powerset(X1))),set_intersection2(X2,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X1)))) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397130,c_370510]) ).
tcf(c_444050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X3)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X1,X2)),set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X1,X2))) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397136,c_370510]) ).
tcf(c_444051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X2,X1),set_intersection2(X3,X4)),X3)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X1)),set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X1))) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397137,c_370510]) ).
tcf(c_444052,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK15(sK5),set_intersection2(X1,X2)),X1)
| in(sK2(X0,set_intersection2(sK5,sK15(sK5)),set_intersection2(X1,X2)),sK5)
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411955,c_370510]) ).
tcf(c_444053,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK15(sK8),set_intersection2(X1,X2)),X1)
| in(sK2(X0,set_intersection2(sK8,sK15(sK8)),set_intersection2(X1,X2)),sK8)
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411956,c_370510]) ).
tcf(c_444055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X4,X3)),X3)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_63,c_370510]) ).
tcf(c_444059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X3)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,sK16(powerset(X3)))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,sK16(powerset(X3))) ) ),
inference(superposition,[status(thm)],[c_397130,c_370510]) ).
tcf(c_444060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,X1)),X0)
| in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,set_intersection2(X0,X1))),X3)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X2,set_intersection2(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_397136,c_370510]) ).
tcf(c_444061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X1,X0)),X0)
| in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,set_intersection2(X1,X0))),X3)
| ( set_intersection2(X0,set_intersection2(X1,X0)) = set_intersection2(X2,set_intersection2(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_397137,c_370510]) ).
tcf(c_444062,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK5)),sK5)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(sK5,sK15(sK5))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(sK5,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_411955,c_370510]) ).
tcf(c_444063,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK8)),sK8)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(sK8,sK15(sK8))),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(sK8,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_411956,c_370510]) ).
tcf(c_444064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,X1,set_intersection2(X2,X3)),X1)
| in(sK2(X0,set_intersection2(X1,X1),set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,set_intersection2(X1,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_53,c_370510]) ).
tcf(c_444067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,empty_set,set_intersection2(X2,X3)),X1)
| in(sK2(X0,set_intersection2(X1,empty_set),set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,set_intersection2(X1,empty_set)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_64,c_370510]) ).
tcf(c_444068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,empty_set,set_intersection2(X2,X3)),empty_set)
| in(sK2(X0,set_intersection2(empty_set,X1),set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_368545,c_370510]) ).
tcf(c_444069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,sK16(powerset(X1)),set_intersection2(X2,X3)),X1)
| in(sK2(X0,set_intersection2(X1,sK16(powerset(X1))),set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,set_intersection2(X1,sK16(powerset(X1)))) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_397130,c_370510]) ).
tcf(c_444070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X1,X2)),set_intersection2(X3,X4)),X3)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X1,X2))) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397136,c_370510]) ).
tcf(c_444071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X2,X1),set_intersection2(X3,X4)),X1)
| in(sK2(X0,set_intersection2(X1,set_intersection2(X2,X1)),set_intersection2(X3,X4)),X3)
| ( set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,X1))) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_397137,c_370510]) ).
tcf(c_444072,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK15(sK5),set_intersection2(X1,X2)),sK5)
| in(sK2(X0,set_intersection2(sK5,sK15(sK5)),set_intersection2(X1,X2)),X1)
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411955,c_370510]) ).
tcf(c_444073,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,sK15(sK8),set_intersection2(X1,X2)),sK8)
| in(sK2(X0,set_intersection2(sK8,sK15(sK8)),set_intersection2(X1,X2)),X1)
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = set_intersection2(X1,X2) ) ),
inference(superposition,[status(thm)],[c_411956,c_370510]) ).
tcf(c_444075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X4,X3)),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_63,c_370510]) ).
tcf(c_444077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,empty_set)),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,empty_set) ) ),
inference(superposition,[status(thm)],[c_64,c_370510]) ).
tcf(c_444078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(empty_set,X3)),empty_set)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(empty_set,X3) ) ),
inference(superposition,[status(thm)],[c_368545,c_370510]) ).
tcf(c_444079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK16(powerset(X3))),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,sK16(powerset(X3)))),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,sK16(powerset(X3))) ) ),
inference(superposition,[status(thm)],[c_397130,c_370510]) ).
tcf(c_444080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,X1)),X3)
| in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,set_intersection2(X0,X1))),X0)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X2,set_intersection2(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_397136,c_370510]) ).
tcf(c_444081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X1,X0)),X3)
| in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,set_intersection2(X1,X0))),X0)
| ( set_intersection2(X0,set_intersection2(X1,X0)) = set_intersection2(X2,set_intersection2(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_397137,c_370510]) ).
tcf(c_444082,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK5)),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(sK5,sK15(sK5))),sK5)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(sK5,sK15(sK5)) ) ),
inference(superposition,[status(thm)],[c_411955,c_370510]) ).
tcf(c_444083,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(X1,X2),sK15(sK8)),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(sK8,sK15(sK8))),sK8)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(sK8,sK15(sK8)) ) ),
inference(superposition,[status(thm)],[c_411956,c_370510]) ).
tcf(c_444084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X0,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X0,X3) )
| ~ in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X0,X3)),set_intersection2(X1,X2))
| ~ in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X0,X3)),set_intersection2(X0,X3)) ),
inference(superposition,[status(thm)],[c_370510,c_54]) ).
tcf(c_444085,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,X5)),X1)
| in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,X5)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = set_intersection2(X0,X5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370510,c_321]) ).
tcf(c_444086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,X5)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = set_intersection2(X0,X5) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370510,c_320]) ).
tcf(c_444087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),set_intersection2(X0,X4)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = set_intersection2(X0,X4) )
| ~ in(X0,sK2(X1,set_intersection2(X2,X3),set_intersection2(X0,X4))) ),
inference(superposition,[status(thm)],[c_370510,c_97]) ).
tcf(c_444088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,X5)),X3)
| in(sK2(X2,set_intersection2(X3,X4),set_intersection2(X0,X5)),X1)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = set_intersection2(X0,X5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370510,c_96]) ).
tcf(c_444089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X3)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370510,c_93]) ).
tcf(c_444090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),set_intersection2(X0,X4)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = set_intersection2(X0,X4) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370510,c_91]) ).
tcf(c_444091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),set_intersection2(set_intersection2(X0,X1),X2)),X4)
| in(sK2(X3,set_intersection2(X4,X5),set_intersection2(set_intersection2(X0,X1),X2)),X1)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,set_intersection2(X4,X5)) ) ),
inference(superposition,[status(thm)],[c_370510,c_59]) ).
tcf(c_444092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),set_intersection2(set_intersection2(X0,X1),X2)),X4)
| in(sK2(X3,set_intersection2(X4,X5),set_intersection2(set_intersection2(X0,X1),X2)),X0)
| ( set_intersection2(set_intersection2(X0,X1),X2) = set_intersection2(X3,set_intersection2(X4,X5)) ) ),
inference(superposition,[status(thm)],[c_370510,c_58]) ).
tcf(c_444093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),set_intersection2(relation_inverse_image(X0,X1),X2)),X4)
| in(apply(X0,sK2(X3,set_intersection2(X4,X5),set_intersection2(relation_inverse_image(X0,X1),X2))),X1)
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370510,c_88]) ).
tcf(c_444094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),set_intersection2(relation_inverse_image(X0,X1),X2)),X4)
| in(sK2(X3,set_intersection2(X4,X5),set_intersection2(relation_inverse_image(X0,X1),X2)),relation_dom(X0))
| ( set_intersection2(relation_inverse_image(X0,X1),X2) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370510,c_87]) ).
tcf(c_444095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(relation_dom(X3),X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(relation_dom(X3),X4) )
| ( apply(X3,sK13(X3,X5,apply(X3,sK2(X0,set_intersection2(X1,X2),set_intersection2(relation_dom(X3),X4))))) = apply(X3,sK2(X0,set_intersection2(X1,X2),set_intersection2(relation_dom(X3),X4))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(X0,set_intersection2(X1,X2),set_intersection2(relation_dom(X3),X4)),X5) ),
inference(superposition,[status(thm)],[c_370510,c_369671]) ).
tcf(c_444096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X5,X6),set_intersection2(relation_image(X2,X0),X3)),X5)
| ( set_intersection2(relation_image(X2,X0),X3) = set_intersection2(X4,set_intersection2(X5,X6)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370510,c_369799]) ).
tcf(c_444097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X5,X6),set_intersection2(relation_image(X0,X2),X3)),X5)
| ( set_intersection2(relation_image(X0,X2),X3) = set_intersection2(X4,set_intersection2(X5,X6)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370510,c_369798]) ).
tcf(c_444098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),set_intersection2(relation_image(X0,X1),X2)),X4)
| ( set_intersection2(relation_image(X0,X1),X2) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370510,c_369596]) ).
tcf(c_444099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),set_intersection2(relation_image(X0,X1),X2)),X4)
| ( set_intersection2(relation_image(X0,X1),X2) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370510,c_369558]) ).
tcf(c_444100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,X4),set_intersection2(relation_image(X0,X1),X5)),X3)
| ( set_intersection2(relation_image(X0,X1),X5) = set_intersection2(X2,set_intersection2(X3,X4)) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,X4),set_intersection2(relation_image(X0,X1),X5)))) = sK2(X2,set_intersection2(X3,X4),set_intersection2(relation_image(X0,X1),X5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370510,c_112]) ).
tcf(c_444101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(relation_dom(X3),X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(relation_dom(X3),X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X5))
| ~ in(sK2(X0,set_intersection2(X1,X2),set_intersection2(relation_dom(X3),X4)),X5) ),
inference(superposition,[status(thm)],[c_370510,c_369501]) ).
tcf(c_444102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(empty_set,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(empty_set,X3) ) ),
inference(superposition,[status(thm)],[c_370510,c_372426]) ).
tcf(c_444103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),set_intersection2(X0,X4)),X2)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(X0,X4) )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),set_intersection2(X0,X4)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),set_intersection2(X0,X4)),set_intersection2(X2,X3))
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),set_intersection2(X0,X4)),set_intersection2(X0,X4)) ),
inference(superposition,[status(thm)],[c_370510,c_368471]) ).
tcf(c_444104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X3,set_intersection2(X4,X5),set_intersection2(relation_image(X0,relation_image(X1,X2)),X6)),X4)
| ( set_intersection2(relation_image(X0,relation_image(X1,X2)),X6) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,X5),set_intersection2(relation_image(X0,relation_image(X1,X2)),X6))))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(X4,X5),set_intersection2(relation_image(X0,relation_image(X1,X2)),X6))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370510,c_369672]) ).
tcf(c_444105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(sK15(sK5),X3)),sK5)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(sK15(sK5),X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(sK15(sK5),X3) ) ),
inference(superposition,[status(thm)],[c_370510,c_412536]) ).
tcf(c_444106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(sK15(sK8),X3)),sK8)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(sK15(sK8),X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(sK15(sK8),X3) ) ),
inference(superposition,[status(thm)],[c_370510,c_413867]) ).
tcf(c_444107,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X0)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) = set_intersection2(set_intersection2(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_370510,c_423425]) ).
tcf(c_444108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(sK16(powerset(X3)),X4)),X3)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(sK16(powerset(X3)),X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(sK16(powerset(X3)),X4) ) ),
inference(superposition,[status(thm)],[c_370510,c_430730]) ).
tcf(c_444109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X0)
| in(sK2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3))
| ( set_intersection2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),set_intersection2(X0,X1)) = set_intersection2(set_intersection2(X0,X1),X2) )
| ~ in(sK2(set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),X3),set_intersection2(X0,X1),set_intersection2(set_intersection2(X0,X1),X2)),X3) ),
inference(superposition,[status(thm)],[c_370510,c_426065]) ).
tcf(c_444110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),set_intersection2(X0,X5)),X3)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4)) = set_intersection2(X0,X5) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),set_intersection2(X0,X5)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),set_intersection2(X0,X5)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),set_intersection2(X0,X5)),set_intersection2(X3,X4))
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),set_intersection2(X0,X5)),set_intersection2(X0,X5)) ),
inference(superposition,[status(thm)],[c_370510,c_370217]) ).
tcf(c_444111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X0,X1),set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X2,X3) )
| ~ in(sK2(X0,set_intersection2(X0,X1),set_intersection2(X2,X3)),set_intersection2(X2,X3))
| ~ in(sK2(X0,set_intersection2(X0,X1),set_intersection2(X2,X3)),set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_370510,c_54]) ).
tcf(c_444112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X2,set_intersection2(X0,X3),set_intersection2(X4,X5)),X1)
| in(sK2(X2,set_intersection2(X0,X3),set_intersection2(X4,X5)),X4)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = set_intersection2(X4,X5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370510,c_321]) ).
tcf(c_444113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X0,X3),set_intersection2(X4,X5)),X4)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370510,c_320]) ).
tcf(c_444114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X0,X2),set_intersection2(X3,X4)),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = set_intersection2(X3,X4) )
| ~ in(X0,sK2(X1,set_intersection2(X0,X2),set_intersection2(X3,X4))) ),
inference(superposition,[status(thm)],[c_370510,c_97]) ).
tcf(c_444115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X0,X3),set_intersection2(X4,X5)),X4)
| in(sK2(X2,set_intersection2(X0,X3),set_intersection2(X4,X5)),X1)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = set_intersection2(X4,X5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370510,c_96]) ).
tcf(c_444116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X1)
| in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X3,X4)),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370510,c_93]) ).
tcf(c_444117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X0,X2),set_intersection2(X3,X4)),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = set_intersection2(X3,X4) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_370510,c_91]) ).
tcf(c_444118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),set_intersection2(X4,X5)),X4)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),set_intersection2(X4,X5)),X2)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X3)) = set_intersection2(X4,X5) ) ),
inference(superposition,[status(thm)],[c_370510,c_59]) ).
tcf(c_444119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),set_intersection2(X4,X5)),X4)
| in(sK2(X0,set_intersection2(set_intersection2(X1,X2),X3),set_intersection2(X4,X5)),X1)
| ( set_intersection2(X0,set_intersection2(set_intersection2(X1,X2),X3)) = set_intersection2(X4,X5) ) ),
inference(superposition,[status(thm)],[c_370510,c_58]) ).
tcf(c_444120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),set_intersection2(X4,X5)),X4)
| in(apply(X0,sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),set_intersection2(X4,X5))),X2)
| ( set_intersection2(X1,set_intersection2(relation_inverse_image(X0,X2),X3)) = set_intersection2(X4,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370510,c_88]) ).
tcf(c_444121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),set_intersection2(X4,X5)),X4)
| in(sK2(X1,set_intersection2(relation_inverse_image(X0,X2),X3),set_intersection2(X4,X5)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(relation_inverse_image(X0,X2),X3)) = set_intersection2(X4,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370510,c_87]) ).
tcf(c_444122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(X3,X4)),X3)
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = set_intersection2(X3,X4) )
| ( apply(X1,sK13(X1,X5,apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(X3,X4))))) = apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(X3,X4))) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370510,c_369671]) ).
tcf(c_444123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X3,set_intersection2(relation_image(X2,X0),X4),set_intersection2(X5,X6)),X5)
| ( set_intersection2(X3,set_intersection2(relation_image(X2,X0),X4)) = set_intersection2(X5,X6) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370510,c_369799]) ).
tcf(c_444124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X2,set_intersection2(relation_image(X0,X3),X4),set_intersection2(X5,X6)),X5)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X3),X4)) = set_intersection2(X5,X6) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370510,c_369798]) ).
tcf(c_444125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(relation_image(X0,X1),X3),set_intersection2(X4,X5)),X4)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X1),X3)) = set_intersection2(X4,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370510,c_369596]) ).
tcf(c_444126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(relation_image(X0,X2),X3),set_intersection2(X4,X5)),X4)
| ( set_intersection2(X1,set_intersection2(relation_image(X0,X2),X3)) = set_intersection2(X4,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370510,c_369558]) ).
tcf(c_444127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(relation_image(X0,X1),X3),set_intersection2(X4,X5)),X4)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X1),X3)) = set_intersection2(X4,X5) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(relation_image(X0,X1),X3),set_intersection2(X4,X5)))) = sK2(X2,set_intersection2(relation_image(X0,X1),X3),set_intersection2(X4,X5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370510,c_112]) ).
tcf(c_444128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(X3,X4)),X3)
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = set_intersection2(X3,X4) )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_image(X1,X5))
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),set_intersection2(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370510,c_369501]) ).
tcf(c_444129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(empty_set,X1),set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_370510,c_372426]) ).
tcf(c_444130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X2,X3),X4),set_intersection2(X2,X3)),X2)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X2,X3),X4)) = set_intersection2(X2,X3) )
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(set_intersection2(X2,X3),X4),set_intersection2(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X2,X3),X4),set_intersection2(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(set_intersection2(X2,X3),X4),set_intersection2(X2,X3)),set_intersection2(set_intersection2(X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_370510,c_370220]) ).
tcf(c_444131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),set_intersection2(X3,X4)),X3)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X2)) = set_intersection2(X3,X4) )
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),set_intersection2(X3,X4)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),set_intersection2(X3,X4)),set_intersection2(X3,X4))
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),set_intersection2(X3,X4)),set_intersection2(X0,X2)) ),
inference(superposition,[status(thm)],[c_370510,c_368471]) ).
tcf(c_444132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),set_intersection2(X5,X6)),X5)
| ( set_intersection2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4)) = set_intersection2(X5,X6) )
| ( apply(X1,sK13(X1,X2,sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),set_intersection2(X5,X6))))) = sK13(X0,relation_image(X1,X2),sK2(X3,set_intersection2(relation_image(X0,relation_image(X1,X2)),X4),set_intersection2(X5,X6))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370510,c_369672]) ).
tcf(c_444133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(sK15(sK5),X1),set_intersection2(X2,X3)),sK5)
| in(sK2(X0,set_intersection2(sK15(sK5),X1),set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,set_intersection2(sK15(sK5),X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_370510,c_412536]) ).
tcf(c_444134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(sK15(sK8),X1),set_intersection2(X2,X3)),sK8)
| in(sK2(X0,set_intersection2(sK15(sK8),X1),set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,set_intersection2(sK15(sK8),X1)) = set_intersection2(X2,X3) ) ),
inference(superposition,[status(thm)],[c_370510,c_413867]) ).
tcf(c_444135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(sK16(powerset(X1)),X2),set_intersection2(X3,X4)),X3)
| in(sK2(X0,set_intersection2(sK16(powerset(X1)),X2),set_intersection2(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(sK16(powerset(X1)),X2)) = set_intersection2(X3,X4) ) ),
inference(superposition,[status(thm)],[c_370510,c_430730]) ).
tcf(c_444136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),set_intersection2(X4,X5)),X4)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3)) = set_intersection2(X4,X5) )
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),set_intersection2(X4,X5)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),set_intersection2(X4,X5)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),set_intersection2(X4,X5)),set_intersection2(X4,X5))
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),set_intersection2(X4,X5)),set_intersection2(X0,X3)) ),
inference(superposition,[status(thm)],[c_370510,c_370217]) ).
tcf(c_444137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),set_intersection2(X1,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(X1,X3) ) ),
inference(equality_factoring,[status(thm)],[c_370510]) ).
tcf(c_444141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,set_intersection2(empty_set,X2),set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(light_normalisation,[status(thm)],[c_444129,c_425546]) ).
tcf(c_444160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = set_intersection2(empty_set,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_444078,c_372426]) ).
tcf(c_444166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,empty_set,set_intersection2(X0,X1)),empty_set)
| in(sK2(X3,set_intersection2(empty_set,X2),set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(light_normalisation,[status(thm)],[c_444068,c_425546]) ).
tcf(c_444168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,empty_set,set_intersection2(X0,X1)),X2)
| in(sK2(X3,set_intersection2(X2,empty_set),set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_444067,c_425312]) ).
tcf(c_444175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,empty_set,set_intersection2(X0,X1)),X0)
| in(sK2(X3,set_intersection2(empty_set,X2),set_intersection2(X0,X1)),empty_set)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(light_normalisation,[status(thm)],[c_444048,c_425546]) ).
tcf(c_444176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,empty_set,set_intersection2(X0,X1)),X0)
| ( set_intersection2(X0,X1) = set_intersection2(empty_set,X2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_444175,c_372426]) ).
tcf(c_444179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X3,empty_set,set_intersection2(X0,X1)),X0)
| in(sK2(X3,set_intersection2(X2,empty_set),set_intersection2(X0,X1)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(X2,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_444047,c_425312]) ).
tcf(c_444364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X0,X1),set_intersection2(X2,X3)),X2)
| ( set_intersection2(X0,X1) = set_intersection2(X2,X3) )
| ~ in(sK2(X0,set_intersection2(X0,X1),set_intersection2(X2,X3)),set_intersection2(X2,X3))
| ~ in(sK2(X0,set_intersection2(X0,X1),set_intersection2(X2,X3)),set_intersection2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_444111,c_397136]) ).
tcf(c_444753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,X3)),X2)
| in(apply(X0,sK2(X1,set_intersection2(X2,X2),relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(X1,set_intersection2(X2,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370511]) ).
tcf(c_444756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,empty_set,relation_inverse_image(X0,X3)),X2)
| in(apply(X0,sK2(X1,set_intersection2(X2,empty_set),relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(X1,set_intersection2(X2,empty_set)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370511]) ).
tcf(c_444758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,sK16(powerset(X2)),relation_inverse_image(X0,X3)),X2)
| in(apply(X0,sK2(X1,set_intersection2(X2,sK16(powerset(X2))),relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(X1,set_intersection2(X2,sK16(powerset(X2)))) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370511]) ).
tcf(c_444759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X2)
| in(apply(X0,sK2(X1,set_intersection2(X2,set_intersection2(X2,X3)),relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X2,X3))) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370511]) ).
tcf(c_444760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X3,X2),relation_inverse_image(X0,X4)),X2)
| in(apply(X0,sK2(X1,set_intersection2(X2,set_intersection2(X3,X2)),relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X3,X2))) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370511]) ).
tcf(c_444761,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK5),relation_inverse_image(X0,X2)),sK5)
| in(apply(X0,sK2(X1,set_intersection2(sK5,sK15(sK5)),relation_inverse_image(X0,X2))),X2)
| ( set_intersection2(X1,set_intersection2(sK5,sK15(sK5))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_370511]) ).
tcf(c_444762,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK8),relation_inverse_image(X0,X2)),sK8)
| in(apply(X0,sK2(X1,set_intersection2(sK8,sK15(sK8)),relation_inverse_image(X0,X2))),X2)
| ( set_intersection2(X1,set_intersection2(sK8,sK15(sK8))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_370511]) ).
tcf(c_444763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),X1)
| in(apply(empty_set,sK2(X0,set_intersection2(X1,X2),relation_inverse_image(empty_set,X3))),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_inverse_image(empty_set,X3) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370511]) ).
tcf(c_444764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(X1,X2,relation_inverse_image(X0,X3))),X3)
| in(sK2(X1,set_intersection2(X2,X2),relation_inverse_image(X0,X3)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370511]) ).
tcf(c_444767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(X1,empty_set,relation_inverse_image(X0,X3))),X3)
| in(sK2(X1,set_intersection2(X2,empty_set),relation_inverse_image(X0,X3)),X2)
| ( set_intersection2(X1,set_intersection2(X2,empty_set)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370511]) ).
tcf(c_444768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(empty_set,X2),relation_inverse_image(X0,X3)),empty_set)
| in(apply(X0,sK2(X1,empty_set,relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(X1,set_intersection2(empty_set,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_370511]) ).
tcf(c_444769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(X1,sK16(powerset(X2)),relation_inverse_image(X0,X3))),X3)
| in(sK2(X1,set_intersection2(X2,sK16(powerset(X2))),relation_inverse_image(X0,X3)),X2)
| ( set_intersection2(X1,set_intersection2(X2,sK16(powerset(X2)))) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370511]) ).
tcf(c_444770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4))),X4)
| in(sK2(X1,set_intersection2(X2,set_intersection2(X2,X3)),relation_inverse_image(X0,X4)),X2)
| ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X2,X3))) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370511]) ).
tcf(c_444771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(X1,set_intersection2(X3,X2),relation_inverse_image(X0,X4))),X4)
| in(sK2(X1,set_intersection2(X2,set_intersection2(X3,X2)),relation_inverse_image(X0,X4)),X2)
| ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X3,X2))) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370511]) ).
tcf(c_444772,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,set_intersection2(sK5,sK15(sK5)),relation_inverse_image(X0,X2)),sK5)
| in(apply(X0,sK2(X1,sK15(sK5),relation_inverse_image(X0,X2))),X2)
| ( set_intersection2(X1,set_intersection2(sK5,sK15(sK5))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_370511]) ).
tcf(c_444773,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,set_intersection2(sK8,sK15(sK8)),relation_inverse_image(X0,X2)),sK8)
| in(apply(X0,sK2(X1,sK15(sK8),relation_inverse_image(X0,X2))),X2)
| ( set_intersection2(X1,set_intersection2(sK8,sK15(sK8))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_370511]) ).
tcf(c_444774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(empty_set,sK2(X0,set_intersection2(X1,X2),empty_set)),X3)
| in(sK2(X0,set_intersection2(X1,X2),relation_inverse_image(empty_set,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_inverse_image(empty_set,X3) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370511]) ).
tcf(c_444775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK2(X0,set_intersection2(X0,X1),relation_inverse_image(X2,X3))),X3)
| ( set_intersection2(X0,set_intersection2(X0,X1)) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),relation_inverse_image(X2,X3)),set_intersection2(X0,X1))
| ~ in(sK2(X0,set_intersection2(X0,X1),relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_370511,c_54]) ).
tcf(c_444776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X3,set_intersection2(X0,X4),relation_inverse_image(X2,X5)),X1)
| in(apply(X2,sK2(X3,set_intersection2(X0,X4),relation_inverse_image(X2,X5))),X5)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = relation_inverse_image(X2,X5) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370511,c_321]) ).
tcf(c_444777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK2(X3,set_intersection2(X0,X4),relation_inverse_image(X2,X5))),X5)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370511,c_320]) ).
tcf(c_444778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK2(X1,set_intersection2(X0,X2),relation_inverse_image(X3,X4))),X4)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(X0,sK2(X1,set_intersection2(X0,X2),relation_inverse_image(X3,X4))) ),
inference(superposition,[status(thm)],[c_370511,c_97]) ).
tcf(c_444779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),relation_inverse_image(X2,X5)),X1)
| in(apply(X2,sK2(X3,set_intersection2(X0,X4),relation_inverse_image(X2,X5))),X5)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = relation_inverse_image(X2,X5) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370511,c_96]) ).
tcf(c_444780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X2)
| in(apply(X0,sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_93]) ).
tcf(c_444781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK2(X2,set_intersection2(X1,X3),relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(X2,set_intersection2(X1,X3)) = relation_inverse_image(X0,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_91]) ).
tcf(c_444782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(set_intersection2(X2,X3),X4),relation_inverse_image(X0,X5)),X3)
| in(apply(X0,sK2(X1,set_intersection2(set_intersection2(X2,X3),X4),relation_inverse_image(X0,X5))),X5)
| ( set_intersection2(X1,set_intersection2(set_intersection2(X2,X3),X4)) = relation_inverse_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_59]) ).
tcf(c_444783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(set_intersection2(X2,X3),X4),relation_inverse_image(X0,X5)),X2)
| in(apply(X0,sK2(X1,set_intersection2(set_intersection2(X2,X3),X4),relation_inverse_image(X0,X5))),X5)
| ( set_intersection2(X1,set_intersection2(set_intersection2(X2,X3),X4)) = relation_inverse_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_58]) ).
tcf(c_444784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X1,sK2(X2,set_intersection2(relation_inverse_image(X1,X3),X4),relation_inverse_image(X0,X5))),X3)
| in(apply(X0,sK2(X2,set_intersection2(relation_inverse_image(X1,X3),X4),relation_inverse_image(X0,X5))),X5)
| ( set_intersection2(X2,set_intersection2(relation_inverse_image(X1,X3),X4)) = relation_inverse_image(X0,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_88]) ).
tcf(c_444785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(relation_inverse_image(X1,X3),X4),relation_inverse_image(X0,X5)),relation_dom(X1))
| in(apply(X0,sK2(X2,set_intersection2(relation_inverse_image(X1,X3),X4),relation_inverse_image(X0,X5))),X5)
| ( set_intersection2(X2,set_intersection2(relation_inverse_image(X1,X3),X4)) = relation_inverse_image(X0,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_87]) ).
tcf(c_444786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X3,sK2(X0,set_intersection2(relation_dom(X1),X2),relation_inverse_image(X3,X4))),X4)
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = relation_inverse_image(X3,X4) )
| ( apply(X1,sK13(X1,X5,apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),relation_inverse_image(X3,X4))))) = apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),relation_inverse_image(X3,X4))) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),relation_inverse_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370511,c_369671]) ).
tcf(c_444787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(apply(X2,sK2(X4,set_intersection2(relation_image(X3,X0),X5),relation_inverse_image(X2,X6))),X6)
| ( set_intersection2(X4,set_intersection2(relation_image(X3,X0),X5)) = relation_inverse_image(X2,X6) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370511,c_369799]) ).
tcf(c_444788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(apply(X2,sK2(X3,set_intersection2(relation_image(X0,X4),X5),relation_inverse_image(X2,X6))),X6)
| ( set_intersection2(X3,set_intersection2(relation_image(X0,X4),X5)) = relation_inverse_image(X2,X6) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370511,c_369798]) ).
tcf(c_444789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK2(X3,set_intersection2(relation_image(X1,X2),X4),relation_inverse_image(X0,X5))),X5)
| ( set_intersection2(X3,set_intersection2(relation_image(X1,X2),X4)) = relation_inverse_image(X0,X5) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_369596]) ).
tcf(c_444790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X1,sK2(X2,set_intersection2(relation_image(X0,X3),X4),relation_inverse_image(X1,X5))),X5)
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X3),X4)) = relation_inverse_image(X1,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370511,c_369558]) ).
tcf(c_444791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,sK2(X3,set_intersection2(relation_image(X1,X2),X4),relation_inverse_image(X0,X5))),X5)
| ( set_intersection2(X3,set_intersection2(relation_image(X1,X2),X4)) = relation_inverse_image(X0,X5) )
| ( apply(X1,sK13(X1,X2,sK2(X3,set_intersection2(relation_image(X1,X2),X4),relation_inverse_image(X0,X5)))) = sK2(X3,set_intersection2(relation_image(X1,X2),X4),relation_inverse_image(X0,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_112]) ).
tcf(c_444792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X3,sK2(X0,set_intersection2(relation_dom(X1),X2),relation_inverse_image(X3,X4))),X4)
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_image(X1,X5))
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),relation_inverse_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370511,c_369501]) ).
tcf(c_444793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(X1,set_intersection2(empty_set,X2),relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(X1,set_intersection2(empty_set,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_372426]) ).
tcf(c_444794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X2,sK2(set_intersection2(X0,X1),set_intersection2(relation_inverse_image(X2,X3),X4),relation_inverse_image(X2,X3))),X3)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(relation_inverse_image(X2,X3),X4)) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(relation_inverse_image(X2,X3),X4),relation_inverse_image(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(relation_inverse_image(X2,X3),X4),relation_inverse_image(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(relation_inverse_image(X2,X3),X4),relation_inverse_image(X2,X3)),set_intersection2(relation_inverse_image(X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_370511,c_370220]) ).
tcf(c_444795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X3,sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),relation_inverse_image(X3,X4))),X4)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X2)) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),relation_inverse_image(X3,X4)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),relation_inverse_image(X3,X4)),set_intersection2(X0,X2))
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),relation_inverse_image(X3,X4)),relation_inverse_image(X3,X4)) ),
inference(superposition,[status(thm)],[c_370511,c_368471]) ).
tcf(c_444796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(apply(X0,sK2(X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5),relation_inverse_image(X0,X6))),X6)
| ( set_intersection2(X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5)) = relation_inverse_image(X0,X6) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5),relation_inverse_image(X0,X6))))) = sK13(X1,relation_image(X2,X3),sK2(X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5),relation_inverse_image(X0,X6))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_369672]) ).
tcf(c_444797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(sK15(sK5),X2),relation_inverse_image(X0,X3)),sK5)
| in(apply(X0,sK2(X1,set_intersection2(sK15(sK5),X2),relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(X1,set_intersection2(sK15(sK5),X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_412536]) ).
tcf(c_444798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(sK15(sK8),X2),relation_inverse_image(X0,X3)),sK8)
| in(apply(X0,sK2(X1,set_intersection2(sK15(sK8),X2),relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(X1,set_intersection2(sK15(sK8),X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_413867]) ).
tcf(c_444799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(sK16(powerset(X2)),X3),relation_inverse_image(X0,X4)),X2)
| in(apply(X0,sK2(X1,set_intersection2(sK16(powerset(X2)),X3),relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(X1,set_intersection2(sK16(powerset(X2)),X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_430730]) ).
tcf(c_444800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X4,sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_inverse_image(X4,X5))),X5)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3)) = relation_inverse_image(X4,X5) )
| ~ function(X4)
| ~ relation(X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_inverse_image(X4,X5)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_inverse_image(X4,X5)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_inverse_image(X4,X5)),set_intersection2(X0,X3))
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_inverse_image(X4,X5)),relation_inverse_image(X4,X5)) ),
inference(superposition,[status(thm)],[c_370511,c_370217]) ).
tcf(c_444801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X2,X0)),X4)
| element(apply(X2,sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X2,X0))),X1)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = relation_inverse_image(X2,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370511,c_321]) ).
tcf(c_444802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X2,X0)),X4)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = relation_inverse_image(X2,X0) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370511,c_320]) ).
tcf(c_444803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),relation_inverse_image(X1,X0)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_inverse_image(X1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,apply(X1,sK2(X2,set_intersection2(X3,X4),relation_inverse_image(X1,X0)))) ),
inference(superposition,[status(thm)],[c_370511,c_97]) ).
tcf(c_444804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X2,X0)),X4)
| in(apply(X2,sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X2,X0))),X1)
| ( set_intersection2(X3,set_intersection2(X4,X5)) = relation_inverse_image(X2,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370511,c_96]) ).
tcf(c_444805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X2)
| element(apply(X0,sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4))),X4)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_93]) ).
tcf(c_444806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),relation_inverse_image(X0,X1)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_inverse_image(X0,X1) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_91]) ).
tcf(c_444807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X0,set_intersection2(X1,X2))),X4)
| in(apply(X0,sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X0,set_intersection2(X1,X2)))),X2)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_59]) ).
tcf(c_444808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X0,set_intersection2(X1,X2))),X4)
| in(apply(X0,sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X0,set_intersection2(X1,X2)))),X1)
| ( relation_inverse_image(X0,set_intersection2(X1,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_58]) ).
tcf(c_444809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X0,set_intersection2(X1,X2),relation_inverse_image(X3,X4)),X1)
| in(sK2(X0,set_intersection2(X1,X2),relation_inverse_image(X3,X4)),relation_inverse_image(X3,X4))
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(X0,set_intersection2(X1,X2),relation_inverse_image(X3,X4)),relation_dom(X3)) ),
inference(superposition,[status(thm)],[c_370511,c_86]) ).
tcf(c_444810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X0,relation_inverse_image(X1,X2))),X4)
| in(apply(X1,apply(X0,sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X0,relation_inverse_image(X1,X2))))),X2)
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_88]) ).
tcf(c_444811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X0,relation_inverse_image(X1,X2))),X4)
| in(apply(X0,sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X0,relation_inverse_image(X1,X2)))),relation_dom(X1))
| ( relation_inverse_image(X0,relation_inverse_image(X1,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_87]) ).
tcf(c_444812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,relation_dom(X4))),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,relation_dom(X4)) )
| ( apply(X4,sK13(X4,X5,apply(X4,apply(X0,sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,relation_dom(X4))))))) = apply(X4,apply(X0,sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,relation_dom(X4))))) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ in(apply(X0,sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,relation_dom(X4)))),X5) ),
inference(superposition,[status(thm)],[c_370511,c_369671]) ).
tcf(c_444813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X5,X6),relation_inverse_image(X2,relation_image(X3,X0))),X5)
| ( relation_inverse_image(X2,relation_image(X3,X0)) = set_intersection2(X4,set_intersection2(X5,X6)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370511,c_369799]) ).
tcf(c_444814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X5,X6),relation_inverse_image(X2,relation_image(X0,X3))),X5)
| ( relation_inverse_image(X2,relation_image(X0,X3)) = set_intersection2(X4,set_intersection2(X5,X6)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370511,c_369798]) ).
tcf(c_444815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X0,relation_image(X1,X2))),X4)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_369596]) ).
tcf(c_444816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X1,relation_image(X0,X2))),X4)
| ( relation_inverse_image(X1,relation_image(X0,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370511,c_369558]) ).
tcf(c_444817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X0,relation_image(X1,X2))),X4)
| ( relation_inverse_image(X0,relation_image(X1,X2)) = set_intersection2(X3,set_intersection2(X4,X5)) )
| ( apply(X1,sK13(X1,X2,apply(X0,sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X0,relation_image(X1,X2)))))) = apply(X0,sK2(X3,set_intersection2(X4,X5),relation_inverse_image(X0,relation_image(X1,X2)))) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_112]) ).
tcf(c_444818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,relation_dom(X4))),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,relation_dom(X4)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ relation(X0)
| ~ empty(relation_image(X4,X5))
| ~ in(apply(X0,sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,relation_dom(X4)))),X5) ),
inference(superposition,[status(thm)],[c_370511,c_369501]) ).
tcf(c_444819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,empty_set)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,empty_set) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_372426]) ).
tcf(c_444820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X5,X6),relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))),X5)
| ( relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3))) = set_intersection2(X4,set_intersection2(X5,X6)) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),apply(X0,sK2(X4,set_intersection2(X5,X6),relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))))))) = sK13(X1,relation_image(X2,X3),apply(X0,sK2(X4,set_intersection2(X5,X6),relation_inverse_image(X0,relation_image(X1,relation_image(X2,X3)))))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_369672]) ).
tcf(c_444821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,sK15(sK5))),X2)
| in(apply(X0,sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,sK15(sK5)))),sK5)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,sK15(sK5)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_412536]) ).
tcf(c_444822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,sK15(sK8))),X2)
| in(apply(X0,sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,sK15(sK8)))),sK8)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,sK15(sK8)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_413867]) ).
tcf(c_444823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,sK16(powerset(X4)))),X2)
| in(apply(X0,sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,sK16(powerset(X4))))),X4)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,sK16(powerset(X4))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370511,c_430730]) ).
tcf(c_444854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(empty_set,sK2(X0,set_intersection2(X1,X2),empty_set)),X3)
| in(sK2(X0,set_intersection2(X1,X2),relation_inverse_image(empty_set,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_inverse_image(empty_set,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_444774,c_368630,c_103]) ).
tcf(c_444858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK2(X1,empty_set,relation_inverse_image(X0,X3))),X3)
| ( set_intersection2(X1,set_intersection2(empty_set,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_444768,c_372426]) ).
tcf(c_444873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),X1)
| in(apply(empty_set,sK2(X0,set_intersection2(X1,X2),relation_inverse_image(empty_set,X3))),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_inverse_image(empty_set,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_444763,c_368630,c_103]) ).
tcf(c_445125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X2,sK2(X0,set_intersection2(X0,X1),relation_inverse_image(X2,X3))),X3)
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X1) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),relation_inverse_image(X2,X3)),set_intersection2(X0,X1))
| ~ in(sK2(X0,set_intersection2(X0,X1),relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3)) ),
inference(light_normalisation,[status(thm)],[c_444775,c_397136]) ).
tcf(c_445540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,X3)),X2)
| in(sK2(X1,set_intersection2(X2,X2),relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370512]) ).
tcf(c_445543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,empty_set,relation_inverse_image(X0,X3)),X2)
| in(sK2(X1,set_intersection2(X2,empty_set),relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,empty_set)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370512]) ).
tcf(c_445545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,sK16(powerset(X2)),relation_inverse_image(X0,X3)),X2)
| in(sK2(X1,set_intersection2(X2,sK16(powerset(X2))),relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,sK16(powerset(X2)))) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370512]) ).
tcf(c_445546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X2)
| in(sK2(X1,set_intersection2(X2,set_intersection2(X2,X3)),relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X2,X3))) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370512]) ).
tcf(c_445547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X3,X2),relation_inverse_image(X0,X4)),X2)
| in(sK2(X1,set_intersection2(X2,set_intersection2(X3,X2)),relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X3,X2))) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370512]) ).
tcf(c_445548,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK5),relation_inverse_image(X0,X2)),sK5)
| in(sK2(X1,set_intersection2(sK5,sK15(sK5)),relation_inverse_image(X0,X2)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(sK5,sK15(sK5))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_370512]) ).
tcf(c_445549,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK8),relation_inverse_image(X0,X2)),sK8)
| in(sK2(X1,set_intersection2(sK8,sK15(sK8)),relation_inverse_image(X0,X2)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(sK8,sK15(sK8))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_370512]) ).
tcf(c_445550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),X1)
| in(sK2(X0,set_intersection2(X1,X2),relation_inverse_image(empty_set,X3)),relation_dom(empty_set))
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_inverse_image(empty_set,X3) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370512]) ).
tcf(c_445551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,X2,relation_inverse_image(X0,X3)),relation_dom(X0))
| in(sK2(X1,set_intersection2(X2,X2),relation_inverse_image(X0,X3)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370512]) ).
tcf(c_445554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,empty_set,relation_inverse_image(X0,X3)),relation_dom(X0))
| in(sK2(X1,set_intersection2(X2,empty_set),relation_inverse_image(X0,X3)),X2)
| ( set_intersection2(X1,set_intersection2(X2,empty_set)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370512]) ).
tcf(c_445555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,empty_set,relation_inverse_image(X0,X3)),relation_dom(X0))
| in(sK2(X1,set_intersection2(empty_set,X2),relation_inverse_image(X0,X3)),empty_set)
| ( set_intersection2(X1,set_intersection2(empty_set,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_368545,c_370512]) ).
tcf(c_445556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,sK16(powerset(X2)),relation_inverse_image(X0,X3)),relation_dom(X0))
| in(sK2(X1,set_intersection2(X2,sK16(powerset(X2))),relation_inverse_image(X0,X3)),X2)
| ( set_intersection2(X1,set_intersection2(X2,sK16(powerset(X2)))) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370512]) ).
tcf(c_445557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),relation_dom(X0))
| in(sK2(X1,set_intersection2(X2,set_intersection2(X2,X3)),relation_inverse_image(X0,X4)),X2)
| ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X2,X3))) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370512]) ).
tcf(c_445558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X3,X2),relation_inverse_image(X0,X4)),relation_dom(X0))
| in(sK2(X1,set_intersection2(X2,set_intersection2(X3,X2)),relation_inverse_image(X0,X4)),X2)
| ( set_intersection2(X1,set_intersection2(X2,set_intersection2(X3,X2))) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370512]) ).
tcf(c_445559,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK5),relation_inverse_image(X0,X2)),relation_dom(X0))
| in(sK2(X1,set_intersection2(sK5,sK15(sK5)),relation_inverse_image(X0,X2)),sK5)
| ( set_intersection2(X1,set_intersection2(sK5,sK15(sK5))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_370512]) ).
tcf(c_445560,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK8),relation_inverse_image(X0,X2)),relation_dom(X0))
| in(sK2(X1,set_intersection2(sK8,sK15(sK8)),relation_inverse_image(X0,X2)),sK8)
| ( set_intersection2(X1,set_intersection2(sK8,sK15(sK8))) = relation_inverse_image(X0,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_370512]) ).
tcf(c_445561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),relation_dom(empty_set))
| in(sK2(X0,set_intersection2(X1,X2),relation_inverse_image(empty_set,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_inverse_image(empty_set,X3) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_373747,c_370512]) ).
tcf(c_445563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X0,X1),relation_inverse_image(X2,X3)),relation_dom(X2))
| ( set_intersection2(X0,set_intersection2(X0,X1)) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),relation_inverse_image(X2,X3)),set_intersection2(X0,X1))
| ~ in(sK2(X0,set_intersection2(X0,X1),relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_370512,c_54]) ).
tcf(c_445564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X3,set_intersection2(X0,X4),relation_inverse_image(X2,X5)),X1)
| in(sK2(X3,set_intersection2(X0,X4),relation_inverse_image(X2,X5)),relation_dom(X2))
| ( set_intersection2(X3,set_intersection2(X0,X4)) = relation_inverse_image(X2,X5) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370512,c_321]) ).
tcf(c_445565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),relation_inverse_image(X2,X5)),relation_dom(X2))
| ( set_intersection2(X3,set_intersection2(X0,X4)) = relation_inverse_image(X2,X5) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370512,c_320]) ).
tcf(c_445566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X0,X2),relation_inverse_image(X3,X4)),relation_dom(X3))
| ( set_intersection2(X1,set_intersection2(X0,X2)) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(X0,sK2(X1,set_intersection2(X0,X2),relation_inverse_image(X3,X4))) ),
inference(superposition,[status(thm)],[c_370512,c_97]) ).
tcf(c_445567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),relation_inverse_image(X2,X5)),X1)
| in(sK2(X3,set_intersection2(X0,X4),relation_inverse_image(X2,X5)),relation_dom(X2))
| ( set_intersection2(X3,set_intersection2(X0,X4)) = relation_inverse_image(X2,X5) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370512,c_96]) ).
tcf(c_445568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X2)
| in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370512,c_93]) ).
tcf(c_445569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X1,X3),relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(X2,set_intersection2(X1,X3)) = relation_inverse_image(X0,X4) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370512,c_91]) ).
tcf(c_445570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(set_intersection2(X2,X3),X4),relation_inverse_image(X0,X5)),X3)
| in(sK2(X1,set_intersection2(set_intersection2(X2,X3),X4),relation_inverse_image(X0,X5)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(set_intersection2(X2,X3),X4)) = relation_inverse_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370512,c_59]) ).
tcf(c_445571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(set_intersection2(X2,X3),X4),relation_inverse_image(X0,X5)),X2)
| in(sK2(X1,set_intersection2(set_intersection2(X2,X3),X4),relation_inverse_image(X0,X5)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(set_intersection2(X2,X3),X4)) = relation_inverse_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370512,c_58]) ).
tcf(c_445572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(relation_inverse_image(X1,X3),X4),relation_inverse_image(X0,X5)),relation_dom(X0))
| in(apply(X1,sK2(X2,set_intersection2(relation_inverse_image(X1,X3),X4),relation_inverse_image(X0,X5))),X3)
| ( set_intersection2(X2,set_intersection2(relation_inverse_image(X1,X3),X4)) = relation_inverse_image(X0,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370512,c_88]) ).
tcf(c_445573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(relation_inverse_image(X1,X3),X4),relation_inverse_image(X0,X5)),relation_dom(X1))
| in(sK2(X2,set_intersection2(relation_inverse_image(X1,X3),X4),relation_inverse_image(X0,X5)),relation_dom(X0))
| ( set_intersection2(X2,set_intersection2(relation_inverse_image(X1,X3),X4)) = relation_inverse_image(X0,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370512,c_87]) ).
tcf(c_445574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(relation_dom(X1),X2),relation_inverse_image(X3,X4)),relation_dom(X3))
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = relation_inverse_image(X3,X4) )
| ( apply(X1,sK13(X1,X5,apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),relation_inverse_image(X3,X4))))) = apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),relation_inverse_image(X3,X4))) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),relation_inverse_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370512,c_369671]) ).
tcf(c_445575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(relation_image(X3,X0),X5),relation_inverse_image(X2,X6)),relation_dom(X2))
| ( set_intersection2(X4,set_intersection2(relation_image(X3,X0),X5)) = relation_inverse_image(X2,X6) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370512,c_369799]) ).
tcf(c_445576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X3,set_intersection2(relation_image(X0,X4),X5),relation_inverse_image(X2,X6)),relation_dom(X2))
| ( set_intersection2(X3,set_intersection2(relation_image(X0,X4),X5)) = relation_inverse_image(X2,X6) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370512,c_369798]) ).
tcf(c_445577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(relation_image(X1,X2),X4),relation_inverse_image(X0,X5)),relation_dom(X0))
| ( set_intersection2(X3,set_intersection2(relation_image(X1,X2),X4)) = relation_inverse_image(X0,X5) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370512,c_369596]) ).
tcf(c_445578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(relation_image(X0,X3),X4),relation_inverse_image(X1,X5)),relation_dom(X1))
| ( set_intersection2(X2,set_intersection2(relation_image(X0,X3),X4)) = relation_inverse_image(X1,X5) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370512,c_369558]) ).
tcf(c_445579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(relation_image(X1,X2),X4),relation_inverse_image(X0,X5)),relation_dom(X0))
| ( set_intersection2(X3,set_intersection2(relation_image(X1,X2),X4)) = relation_inverse_image(X0,X5) )
| ( apply(X1,sK13(X1,X2,sK2(X3,set_intersection2(relation_image(X1,X2),X4),relation_inverse_image(X0,X5)))) = sK2(X3,set_intersection2(relation_image(X1,X2),X4),relation_inverse_image(X0,X5)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370512,c_112]) ).
tcf(c_445580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(relation_dom(X1),X2),relation_inverse_image(X3,X4)),relation_dom(X3))
| ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_image(X1,X5))
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),relation_inverse_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370512,c_369501]) ).
tcf(c_445581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(empty_set,X2),relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(empty_set,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370512,c_372426]) ).
tcf(c_445582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(relation_inverse_image(X2,X3),X4),relation_inverse_image(X2,X3)),relation_dom(X2))
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(relation_inverse_image(X2,X3),X4)) = relation_inverse_image(X2,X3) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(relation_inverse_image(X2,X3),X4),relation_inverse_image(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(relation_inverse_image(X2,X3),X4),relation_inverse_image(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(relation_inverse_image(X2,X3),X4),relation_inverse_image(X2,X3)),set_intersection2(relation_inverse_image(X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_370512,c_370220]) ).
tcf(c_445583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),relation_inverse_image(X3,X4)),relation_dom(X3))
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X2)) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),relation_inverse_image(X3,X4)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),relation_inverse_image(X3,X4)),set_intersection2(X0,X2))
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),relation_inverse_image(X3,X4)),relation_inverse_image(X3,X4)) ),
inference(superposition,[status(thm)],[c_370512,c_368471]) ).
tcf(c_445584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5),relation_inverse_image(X0,X6)),relation_dom(X0))
| ( set_intersection2(X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5)) = relation_inverse_image(X0,X6) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5),relation_inverse_image(X0,X6))))) = sK13(X1,relation_image(X2,X3),sK2(X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5),relation_inverse_image(X0,X6))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370512,c_369672]) ).
tcf(c_445585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(sK15(sK5),X2),relation_inverse_image(X0,X3)),sK5)
| in(sK2(X1,set_intersection2(sK15(sK5),X2),relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(sK15(sK5),X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370512,c_412536]) ).
tcf(c_445586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(sK15(sK8),X2),relation_inverse_image(X0,X3)),sK8)
| in(sK2(X1,set_intersection2(sK15(sK8),X2),relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(sK15(sK8),X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370512,c_413867]) ).
tcf(c_445587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(sK16(powerset(X2)),X3),relation_inverse_image(X0,X4)),X2)
| in(sK2(X1,set_intersection2(sK16(powerset(X2)),X3),relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(sK16(powerset(X2)),X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370512,c_430730]) ).
tcf(c_445588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_inverse_image(X4,X5)),relation_dom(X4))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3)) = relation_inverse_image(X4,X5) )
| ~ function(X4)
| ~ relation(X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_inverse_image(X4,X5)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_inverse_image(X4,X5)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_inverse_image(X4,X5)),set_intersection2(X0,X3))
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_inverse_image(X4,X5)),relation_inverse_image(X4,X5)) ),
inference(superposition,[status(thm)],[c_370512,c_370217]) ).
tcf(c_445589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(relation_dom(X0),set_intersection2(X1,X2),relation_inverse_image(X0,X3)),X1)
| ( set_intersection2(relation_dom(X0),set_intersection2(X1,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(relation_dom(X0),set_intersection2(X1,X2),relation_inverse_image(X0,X3)),set_intersection2(X1,X2))
| ~ in(sK2(relation_dom(X0),set_intersection2(X1,X2),relation_inverse_image(X0,X3)),relation_inverse_image(X0,X3)) ),
inference(superposition,[status(thm)],[c_370512,c_54]) ).
tcf(c_445590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X2,set_intersection2(X3,X4),relation_inverse_image(X0,X5)),X1)
| in(sK2(X2,set_intersection2(X3,X4),relation_inverse_image(X0,X5)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_inverse_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370512,c_321]) ).
tcf(c_445591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,X4),relation_inverse_image(X0,X5)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_inverse_image(X0,X5) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370512,c_320]) ).
tcf(c_445592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4))) ),
inference(superposition,[status(thm)],[c_370512,c_97]) ).
tcf(c_445593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X3,X4),relation_inverse_image(X0,X5)),X3)
| in(sK2(X2,set_intersection2(X3,X4),relation_inverse_image(X0,X5)),X1)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_inverse_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370512,c_96]) ).
tcf(c_445594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X2)
| element(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370512,c_93]) ).
tcf(c_445595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370512,c_91]) ).
tcf(c_445596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(X1,X2),relation_inverse_image(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_inverse_image(X3,X4) )
| ( apply(X3,sK13(X3,X5,apply(X3,sK2(X0,set_intersection2(X1,X2),relation_inverse_image(X3,X4))))) = apply(X3,sK2(X0,set_intersection2(X1,X2),relation_inverse_image(X3,X4))) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(X0,set_intersection2(X1,X2),relation_inverse_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370512,c_369671]) ).
tcf(c_445597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(X1,X2),relation_inverse_image(X3,X4)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_inverse_image(X3,X4) )
| ~ function(X3)
| ~ relation(X3)
| ~ empty(relation_image(X3,X5))
| ~ in(sK2(X0,set_intersection2(X1,X2),relation_inverse_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370512,c_369501]) ).
tcf(c_445598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(relation_dom(X0),X1),set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X2)
| ( set_intersection2(set_intersection2(relation_dom(X0),X1),set_intersection2(X2,X3)) = relation_inverse_image(X0,X4) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),set_intersection2(X2,X3),relation_inverse_image(X0,X4)),X1)
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),set_intersection2(X2,X3),relation_inverse_image(X0,X4)),set_intersection2(X2,X3))
| ~ in(sK2(set_intersection2(relation_dom(X0),X1),set_intersection2(X2,X3),relation_inverse_image(X0,X4)),relation_inverse_image(X0,X4)) ),
inference(superposition,[status(thm)],[c_370512,c_368471]) ).
tcf(c_445599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),set_intersection2(X3,X4),relation_inverse_image(X0,X5)),X3)
| ( set_intersection2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),set_intersection2(X3,X4)) = relation_inverse_image(X0,X5) )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),set_intersection2(X3,X4),relation_inverse_image(X0,X5)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),set_intersection2(X3,X4),relation_inverse_image(X0,X5)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),set_intersection2(X3,X4),relation_inverse_image(X0,X5)),set_intersection2(X3,X4))
| ~ in(sK2(set_intersection2(set_intersection2(relation_dom(X0),X1),X2),set_intersection2(X3,X4),relation_inverse_image(X0,X5)),relation_inverse_image(X0,X5)) ),
inference(superposition,[status(thm)],[c_370512,c_370217]) ).
tcf(c_445600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(relation_dom(X0),X2),relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(relation_dom(X0),X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_factoring,[status(thm)],[c_370512]) ).
tcf(c_445632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),empty_set)
| in(sK2(X0,set_intersection2(X1,X2),relation_inverse_image(empty_set,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_inverse_image(empty_set,X3) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_445561,c_373108]) ).
tcf(c_445633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),relation_inverse_image(empty_set,X3)),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_inverse_image(empty_set,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_445632,c_372426,c_368630,c_103]) ).
tcf(c_445636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,empty_set,relation_inverse_image(X0,X3)),relation_dom(X0))
| ( set_intersection2(X1,set_intersection2(empty_set,X2)) = relation_inverse_image(X0,X3) )
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_445555,c_372426]) ).
tcf(c_445651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),X1)
| in(sK2(X0,set_intersection2(X1,X2),relation_inverse_image(empty_set,X3)),empty_set)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_inverse_image(empty_set,X3) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_445550,c_373108]) ).
tcf(c_445652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),empty_set),X1)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_inverse_image(empty_set,X3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_445651,c_372426,c_368630,c_103]) ).
tcf(c_445826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X0,X1),relation_inverse_image(X2,X3)),relation_dom(X2))
| ( relation_inverse_image(X2,X3) = set_intersection2(X0,X1) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),relation_inverse_image(X2,X3)),set_intersection2(X0,X1))
| ~ in(sK2(X0,set_intersection2(X0,X1),relation_inverse_image(X2,X3)),relation_inverse_image(X2,X3)) ),
inference(light_normalisation,[status(thm)],[c_445563,c_397136]) ).
tcf(c_446001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X3,relation_image(X0,X1)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X3)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,X3),relation_image(X0,X1)))) = sK2(X2,set_intersection2(X3,X3),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_53,c_370513]) ).
tcf(c_446004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,empty_set,relation_image(X0,X1)),X3)
| ( set_intersection2(X2,set_intersection2(X3,empty_set)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,empty_set),relation_image(X0,X1)))) = sK2(X2,set_intersection2(X3,empty_set),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_64,c_370513]) ).
tcf(c_446006,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,sK16(powerset(X3)),relation_image(X0,X1)),X3)
| ( set_intersection2(X2,set_intersection2(X3,sK16(powerset(X3)))) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,sK16(powerset(X3))),relation_image(X0,X1)))) = sK2(X2,set_intersection2(X3,sK16(powerset(X3))),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397130,c_370513]) ).
tcf(c_446007,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)),X3)
| ( set_intersection2(X2,set_intersection2(X3,set_intersection2(X3,X4))) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,set_intersection2(X3,X4)),relation_image(X0,X1)))) = sK2(X2,set_intersection2(X3,set_intersection2(X3,X4)),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397136,c_370513]) ).
tcf(c_446008,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X4,X3),relation_image(X0,X1)),X3)
| ( set_intersection2(X2,set_intersection2(X3,set_intersection2(X4,X3))) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,set_intersection2(X4,X3)),relation_image(X0,X1)))) = sK2(X2,set_intersection2(X3,set_intersection2(X4,X3)),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_397137,c_370513]) ).
tcf(c_446009,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,sK15(sK5),relation_image(X0,X1)),sK5)
| ( set_intersection2(X2,set_intersection2(sK5,sK15(sK5))) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(sK5,sK15(sK5)),relation_image(X0,X1)))) = sK2(X2,set_intersection2(sK5,sK15(sK5)),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411955,c_370513]) ).
tcf(c_446010,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,sK15(sK8),relation_image(X0,X1)),sK8)
| ( set_intersection2(X2,set_intersection2(sK8,sK15(sK8))) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(sK8,sK15(sK8)),relation_image(X0,X1)))) = sK2(X2,set_intersection2(sK8,sK15(sK8)),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_411956,c_370513]) ).
tcf(c_446011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X3),empty_set),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = relation_image(empty_set,X0) )
| ( apply(empty_set,sK13(empty_set,X0,sK2(X1,set_intersection2(X2,X3),relation_image(empty_set,X0)))) = sK2(X1,set_intersection2(X2,X3),relation_image(empty_set,X0)) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_375097,c_370513]) ).
tcf(c_446012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X0,set_intersection2(X0,X1)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(X0,set_intersection2(X0,X1),relation_image(X2,X3)))) = sK2(X0,set_intersection2(X0,X1),relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),relation_image(X2,X3)),set_intersection2(X0,X1))
| ~ in(sK2(X0,set_intersection2(X0,X1),relation_image(X2,X3)),relation_image(X2,X3)) ),
inference(superposition,[status(thm)],[c_370513,c_54]) ).
tcf(c_446013,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X4,set_intersection2(X0,X5),relation_image(X2,X3)),X1)
| ( set_intersection2(X4,set_intersection2(X0,X5)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(X4,set_intersection2(X0,X5),relation_image(X2,X3)))) = sK2(X4,set_intersection2(X0,X5),relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370513,c_321]) ).
tcf(c_446014,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X4,set_intersection2(X0,X5)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(X4,set_intersection2(X0,X5),relation_image(X2,X3)))) = sK2(X4,set_intersection2(X0,X5),relation_image(X2,X3)) )
| ~ empty(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370513,c_320]) ).
tcf(c_446015,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X1,set_intersection2(X0,X2)) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK2(X1,set_intersection2(X0,X2),relation_image(X3,X4)))) = sK2(X1,set_intersection2(X0,X2),relation_image(X3,X4)) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(X0,sK2(X1,set_intersection2(X0,X2),relation_image(X3,X4))) ),
inference(superposition,[status(thm)],[c_370513,c_97]) ).
tcf(c_446016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,set_intersection2(X0,X5),relation_image(X2,X3)),X1)
| ( set_intersection2(X4,set_intersection2(X0,X5)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(X4,set_intersection2(X0,X5),relation_image(X2,X3)))) = sK2(X4,set_intersection2(X0,X5),relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370513,c_96]) ).
tcf(c_446017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)),X3)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)))) = sK2(X2,set_intersection2(X3,X4),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370513,c_93]) ).
tcf(c_446018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(X3,set_intersection2(X1,X4)) = relation_image(X0,X2) )
| ( apply(X0,sK13(X0,X2,sK2(X3,set_intersection2(X1,X4),relation_image(X0,X2)))) = sK2(X3,set_intersection2(X1,X4),relation_image(X0,X2)) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370513,c_91]) ).
tcf(c_446019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(set_intersection2(X3,X4),X5),relation_image(X0,X1)),X4)
| ( set_intersection2(X2,set_intersection2(set_intersection2(X3,X4),X5)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(set_intersection2(X3,X4),X5),relation_image(X0,X1)))) = sK2(X2,set_intersection2(set_intersection2(X3,X4),X5),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370513,c_59]) ).
tcf(c_446020,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(set_intersection2(X3,X4),X5),relation_image(X0,X1)),X3)
| ( set_intersection2(X2,set_intersection2(set_intersection2(X3,X4),X5)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(set_intersection2(X3,X4),X5),relation_image(X0,X1)))) = sK2(X2,set_intersection2(set_intersection2(X3,X4),X5),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370513,c_58]) ).
tcf(c_446021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X1,sK2(X3,set_intersection2(relation_inverse_image(X1,X4),X5),relation_image(X0,X2))),X4)
| ( set_intersection2(X3,set_intersection2(relation_inverse_image(X1,X4),X5)) = relation_image(X0,X2) )
| ( apply(X0,sK13(X0,X2,sK2(X3,set_intersection2(relation_inverse_image(X1,X4),X5),relation_image(X0,X2)))) = sK2(X3,set_intersection2(relation_inverse_image(X1,X4),X5),relation_image(X0,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370513,c_88]) ).
tcf(c_446022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(relation_inverse_image(X1,X4),X5),relation_image(X0,X2)),relation_dom(X1))
| ( set_intersection2(X3,set_intersection2(relation_inverse_image(X1,X4),X5)) = relation_image(X0,X2) )
| ( apply(X0,sK13(X0,X2,sK2(X3,set_intersection2(relation_inverse_image(X1,X4),X5),relation_image(X0,X2)))) = sK2(X3,set_intersection2(relation_inverse_image(X1,X4),X5),relation_image(X0,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370513,c_87]) ).
tcf(c_446023,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK2(X0,set_intersection2(relation_dom(X1),X2),relation_image(X3,X4)))) = sK2(X0,set_intersection2(relation_dom(X1),X2),relation_image(X3,X4)) )
| ( apply(X1,sK13(X1,X5,apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),relation_image(X3,X4))))) = apply(X1,sK2(X0,set_intersection2(relation_dom(X1),X2),relation_image(X3,X4))) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),relation_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370513,c_369671]) ).
tcf(c_446024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( set_intersection2(X5,set_intersection2(relation_image(X3,X0),X6)) = relation_image(X2,X4) )
| ( apply(X2,sK13(X2,X4,sK2(X5,set_intersection2(relation_image(X3,X0),X6),relation_image(X2,X4)))) = sK2(X5,set_intersection2(relation_image(X3,X0),X6),relation_image(X2,X4)) )
| ~ empty(X1)
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370513,c_369799]) ).
tcf(c_446025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( set_intersection2(X4,set_intersection2(relation_image(X0,X5),X6)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(X4,set_intersection2(relation_image(X0,X5),X6),relation_image(X2,X3)))) = sK2(X4,set_intersection2(relation_image(X0,X5),X6),relation_image(X2,X3)) )
| ~ empty(X1)
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370513,c_369798]) ).
tcf(c_446026,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X4,set_intersection2(relation_image(X1,X2),X5)) = relation_image(X0,X3) )
| ( apply(X0,sK13(X0,X3,sK2(X4,set_intersection2(relation_image(X1,X2),X5),relation_image(X0,X3)))) = sK2(X4,set_intersection2(relation_image(X1,X2),X5),relation_image(X0,X3)) )
| ~ empty(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370513,c_369596]) ).
tcf(c_446027,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X3,set_intersection2(relation_image(X0,X4),X5)) = relation_image(X1,X2) )
| ( apply(X1,sK13(X1,X2,sK2(X3,set_intersection2(relation_image(X0,X4),X5),relation_image(X1,X2)))) = sK2(X3,set_intersection2(relation_image(X0,X4),X5),relation_image(X1,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_370513,c_369558]) ).
tcf(c_446028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X3,set_intersection2(relation_image(X1,X4),X5)) = relation_image(X0,X2) )
| ( apply(X1,sK13(X1,X4,sK2(X3,set_intersection2(relation_image(X1,X4),X5),relation_image(X0,X2)))) = sK2(X3,set_intersection2(relation_image(X1,X4),X5),relation_image(X0,X2)) )
| ( apply(X0,sK13(X0,X2,sK2(X3,set_intersection2(relation_image(X1,X4),X5),relation_image(X0,X2)))) = sK2(X3,set_intersection2(relation_image(X1,X4),X5),relation_image(X0,X2)) )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370513,c_112]) ).
tcf(c_446029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(X0,set_intersection2(relation_dom(X1),X2)) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK2(X0,set_intersection2(relation_dom(X1),X2),relation_image(X3,X4)))) = sK2(X0,set_intersection2(relation_dom(X1),X2),relation_image(X3,X4)) )
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| ~ empty(relation_image(X1,X5))
| ~ in(sK2(X0,set_intersection2(relation_dom(X1),X2),relation_image(X3,X4)),X5) ),
inference(superposition,[status(thm)],[c_370513,c_369501]) ).
tcf(c_446030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_intersection2(X2,set_intersection2(empty_set,X3)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(empty_set,X3),relation_image(X0,X1)))) = sK2(X2,set_intersection2(empty_set,X3),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370513,c_372426]) ).
tcf(c_446031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X0,X1),set_intersection2(relation_image(X2,X3),X4)) = relation_image(X2,X3) )
| ( apply(X2,sK13(X2,X3,sK2(set_intersection2(X0,X1),set_intersection2(relation_image(X2,X3),X4),relation_image(X2,X3)))) = sK2(set_intersection2(X0,X1),set_intersection2(relation_image(X2,X3),X4),relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(relation_image(X2,X3),X4),relation_image(X2,X3)),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(relation_image(X2,X3),X4),relation_image(X2,X3)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(relation_image(X2,X3),X4),relation_image(X2,X3)),set_intersection2(relation_image(X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_370513,c_370220]) ).
tcf(c_446032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X0,X2)) = relation_image(X3,X4) )
| ( apply(X3,sK13(X3,X4,sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),relation_image(X3,X4)))) = sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),relation_image(X3,X4)) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),relation_image(X3,X4)),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),relation_image(X3,X4)),set_intersection2(X0,X2))
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X0,X2),relation_image(X3,X4)),relation_image(X3,X4)) ),
inference(superposition,[status(thm)],[c_370513,c_368471]) ).
tcf(c_446033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( set_intersection2(X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5)) = relation_image(X0,X6) )
| ( apply(X0,sK13(X0,X6,sK2(X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5),relation_image(X0,X6)))) = sK2(X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5),relation_image(X0,X6)) )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5),relation_image(X0,X6))))) = sK13(X1,relation_image(X2,X3),sK2(X4,set_intersection2(relation_image(X1,relation_image(X2,X3)),X5),relation_image(X0,X6))) )
| ~ function(X2)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370513,c_369672]) ).
tcf(c_446034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,set_intersection2(sK15(sK5),X3),relation_image(X0,X1)),sK5)
| ( set_intersection2(X2,set_intersection2(sK15(sK5),X3)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(sK15(sK5),X3),relation_image(X0,X1)))) = sK2(X2,set_intersection2(sK15(sK5),X3),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370513,c_412536]) ).
tcf(c_446035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,set_intersection2(sK15(sK8),X3),relation_image(X0,X1)),sK8)
| ( set_intersection2(X2,set_intersection2(sK15(sK8),X3)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(sK15(sK8),X3),relation_image(X0,X1)))) = sK2(X2,set_intersection2(sK15(sK8),X3),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370513,c_413867]) ).
tcf(c_446036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(sK16(powerset(X3)),X4),relation_image(X0,X1)),X3)
| ( set_intersection2(X2,set_intersection2(sK16(powerset(X3)),X4)) = relation_image(X0,X1) )
| ( apply(X0,sK13(X0,X1,sK2(X2,set_intersection2(sK16(powerset(X3)),X4),relation_image(X0,X1)))) = sK2(X2,set_intersection2(sK16(powerset(X3)),X4),relation_image(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_370513,c_430730]) ).
tcf(c_446037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3)) = relation_image(X4,X5) )
| ( apply(X4,sK13(X4,X5,sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_image(X4,X5)))) = sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_image(X4,X5)) )
| ~ function(X4)
| ~ relation(X4)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_image(X4,X5)),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_image(X4,X5)),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_image(X4,X5)),set_intersection2(X0,X3))
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X3),relation_image(X4,X5)),relation_image(X4,X5)) ),
inference(superposition,[status(thm)],[c_370513,c_370217]) ).
tcf(c_446053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X3),empty_set),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = empty_set )
| ( apply(empty_set,sK13(empty_set,X0,sK2(X1,set_intersection2(X2,X3),empty_set))) = sK2(X1,set_intersection2(X2,X3),empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_446011,c_375097]) ).
tcf(c_446054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X2,X3),empty_set),X2)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = empty_set )
| ( apply(empty_set,sK13(empty_set,X0,sK2(X1,set_intersection2(X2,X3),empty_set))) = sK2(X1,set_intersection2(X2,X3),empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_446053,c_368630,c_103]) ).
tcf(c_446184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X2,X3) = set_intersection2(X0,X1) )
| ( apply(X2,sK13(X2,X3,sK2(X0,set_intersection2(X0,X1),relation_image(X2,X3)))) = sK2(X0,set_intersection2(X0,X1),relation_image(X2,X3)) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(sK2(X0,set_intersection2(X0,X1),relation_image(X2,X3)),set_intersection2(X0,X1))
| ~ in(sK2(X0,set_intersection2(X0,X1),relation_image(X2,X3)),relation_image(X2,X3)) ),
inference(light_normalisation,[status(thm)],[c_446012,c_397136]) ).
tcf(c_446363,plain,
! [X0: $i,X1: $i] :
( subset(sK15(sK8),X1)
| element(sK10(sK15(sK8),X1),X0)
| ~ subset(sK8,X0) ),
inference(superposition,[status(thm)],[c_413924,c_321]) ).
tcf(c_446365,plain,
! [X0: $i] :
( subset(sK15(sK8),X0)
| ~ in(sK8,sK10(sK15(sK8),X0)) ),
inference(superposition,[status(thm)],[c_413924,c_97]) ).
tcf(c_446366,plain,
! [X0: $i,X1: $i] :
( subset(sK15(sK8),X1)
| in(sK10(sK15(sK8),X1),X0)
| ~ subset(sK8,X0) ),
inference(superposition,[status(thm)],[c_413924,c_96]) ).
tcf(c_446367,plain,
! [X0: $i] :
( subset(sK15(sK8),X0)
| element(sK10(sK15(sK8),X0),sK8) ),
inference(superposition,[status(thm)],[c_413924,c_93]) ).
tcf(c_446370,plain,
! [X0: $i] :
( subset(sK15(sK8),set_intersection2(sK8,X0))
| ~ in(sK10(sK15(sK8),set_intersection2(sK8,X0)),X0) ),
inference(superposition,[status(thm)],[c_413924,c_368972]) ).
tcf(c_446404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(X0,X2)
| in(sK2(X1,set_intersection2(sK10(X0,X2),X3),X4),X4)
| ( set_intersection2(X1,set_intersection2(sK10(X0,X2),X3)) = X4 )
| ~ subset(X0,sK2(X1,set_intersection2(sK10(X0,X2),X3),X4)) ),
inference(superposition,[status(thm)],[c_369021,c_370518]) ).
tcf(c_446405,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X0)
| in(sK2(X1,set_intersection2(sK16(X0),X2),X3),X3)
| ( set_intersection2(X1,set_intersection2(sK16(X0),X2)) = X3 )
| ~ subset(X0,sK2(X1,set_intersection2(sK16(X0),X2),X3)) ),
inference(superposition,[status(thm)],[c_370747,c_370518]) ).
tcf(c_446406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,X3,X0),X2)
| in(sK2(X1,set_intersection2(sK2(X2,X3,X0),X4),X5),X5)
| ( set_intersection2(X2,X3) = X0 )
| ( set_intersection2(X1,set_intersection2(sK2(X2,X3,X0),X4)) = X5 )
| ~ subset(X0,sK2(X1,set_intersection2(sK2(X2,X3,X0),X4),X5)) ),
inference(superposition,[status(thm)],[c_369015,c_370518]) ).
tcf(c_446407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,X3,X0),X3)
| in(sK2(X1,set_intersection2(sK2(X2,X3,X0),X4),X5),X5)
| ( set_intersection2(X2,X3) = X0 )
| ( set_intersection2(X1,set_intersection2(sK2(X2,X3,X0),X4)) = X5 )
| ~ subset(X0,sK2(X1,set_intersection2(sK2(X2,X3,X0),X4),X5)) ),
inference(superposition,[status(thm)],[c_369014,c_370518]) ).
tcf(c_446408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,X2,X3),X3)
| in(sK2(X1,set_intersection2(sK2(X0,X2,X3),X4),X5),X5)
| ( set_intersection2(X0,X2) = X3 )
| ( set_intersection2(X1,set_intersection2(sK2(X0,X2,X3),X4)) = X5 )
| ~ subset(X0,sK2(X1,set_intersection2(sK2(X0,X2,X3),X4),X5)) ),
inference(superposition,[status(thm)],[c_369012,c_370518]) ).
tcf(c_446409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,X0,X3),X3)
| in(sK2(X1,set_intersection2(sK2(X2,X0,X3),X4),X5),X5)
| ( set_intersection2(X2,X0) = X3 )
| ( set_intersection2(X1,set_intersection2(sK2(X2,X0,X3),X4)) = X5 )
| ~ subset(X0,sK2(X1,set_intersection2(sK2(X2,X0,X3),X4),X5)) ),
inference(superposition,[status(thm)],[c_369013,c_370518]) ).
tcf(c_446410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(sK13(X2,X0,X3),X4),X5),X5)
| ( set_intersection2(X1,set_intersection2(sK13(X2,X0,X3),X4)) = X5 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_image(X2,X0))
| ~ subset(X0,sK2(X1,set_intersection2(sK13(X2,X0,X3),X4),X5)) ),
inference(superposition,[status(thm)],[c_369594,c_370518]) ).
tcf(c_446411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(sK13(X0,X2,X3),X4),X5),X5)
| ( set_intersection2(X1,set_intersection2(sK13(X0,X2,X3),X4)) = X5 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,relation_image(X0,X2))
| ~ subset(relation_dom(X0),sK2(X1,set_intersection2(sK13(X0,X2,X3),X4),X5)) ),
inference(superposition,[status(thm)],[c_369556,c_370518]) ).
tcf(c_446412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X2,X0,X3),X3)
| in(sK2(X1,set_intersection2(sK12(X2,X0,X3),X4),X5),X5)
| ( relation_image(X2,X0) = X3 )
| ( set_intersection2(X1,set_intersection2(sK12(X2,X0,X3),X4)) = X5 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,set_intersection2(sK12(X2,X0,X3),X4),X5)) ),
inference(superposition,[status(thm)],[c_369299,c_370518]) ).
tcf(c_446413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(sK11(X2,X3,X0),X4),X5),X5)
| ( relation_image(X2,X3) = X0 )
| ( apply(X2,sK12(X2,X3,X0)) = sK11(X2,X3,X0) )
| ( set_intersection2(X1,set_intersection2(sK11(X2,X3,X0),X4)) = X5 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,set_intersection2(sK11(X2,X3,X0),X4),X5)) ),
inference(superposition,[status(thm)],[c_369436,c_370518]) ).
tcf(c_446414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X3,X0),X3)
| in(sK2(X1,set_intersection2(sK11(X2,X3,X0),X4),X5),X5)
| ( relation_image(X2,X3) = X0 )
| ( set_intersection2(X1,set_intersection2(sK11(X2,X3,X0),X4)) = X5 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,set_intersection2(sK11(X2,X3,X0),X4),X5)) ),
inference(superposition,[status(thm)],[c_369307,c_370518]) ).
tcf(c_446415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK12(X2,X3,X0),relation_dom(X2))
| in(sK2(X1,set_intersection2(sK11(X2,X3,X0),X4),X5),X5)
| ( relation_image(X2,X3) = X0 )
| ( set_intersection2(X1,set_intersection2(sK11(X2,X3,X0),X4)) = X5 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,set_intersection2(sK11(X2,X3,X0),X4),X5)) ),
inference(superposition,[status(thm)],[c_369206,c_370518]) ).
tcf(c_446416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,X3,X0),relation_dom(X2))
| in(sK2(X1,set_intersection2(sK7(X2,X3,X0),X4),X5),X5)
| ( relation_inverse_image(X2,X3) = X0 )
| ( set_intersection2(X1,set_intersection2(sK7(X2,X3,X0),X4)) = X5 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,set_intersection2(sK7(X2,X3,X0),X4),X5)) ),
inference(superposition,[status(thm)],[c_369020,c_370518]) ).
tcf(c_446417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X2,sK7(X2,X3,X0)),X3)
| in(sK2(X1,set_intersection2(sK7(X2,X3,X0),X4),X5),X5)
| ( relation_inverse_image(X2,X3) = X0 )
| ( set_intersection2(X1,set_intersection2(sK7(X2,X3,X0),X4)) = X5 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,set_intersection2(sK7(X2,X3,X0),X4),X5)) ),
inference(superposition,[status(thm)],[c_369019,c_370518]) ).
tcf(c_446418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X0,X2,X3),X3)
| in(sK2(X1,set_intersection2(sK7(X0,X2,X3),X4),X5),X5)
| ( relation_inverse_image(X0,X2) = X3 )
| ( set_intersection2(X1,set_intersection2(sK7(X0,X2,X3),X4)) = X5 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(X1,set_intersection2(sK7(X0,X2,X3),X4),X5)) ),
inference(superposition,[status(thm)],[c_369017,c_370518]) ).
tcf(c_446419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK11(X0,X2,X3),X3)
| in(sK2(X1,set_intersection2(sK12(X0,X2,X3),X4),X5),X5)
| ( relation_image(X0,X2) = X3 )
| ( set_intersection2(X1,set_intersection2(sK12(X0,X2,X3),X4)) = X5 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),sK2(X1,set_intersection2(sK12(X0,X2,X3),X4),X5)) ),
inference(superposition,[status(thm)],[c_369214,c_370518]) ).
tcf(c_446420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK7(X2,X0,X3),X3)
| in(sK2(X1,set_intersection2(apply(X2,sK7(X2,X0,X3)),X4),X5),X5)
| ( relation_inverse_image(X2,X0) = X3 )
| ( set_intersection2(X1,set_intersection2(apply(X2,sK7(X2,X0,X3)),X4)) = X5 )
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,sK2(X1,set_intersection2(apply(X2,sK7(X2,X0,X3)),X4),X5)) ),
inference(superposition,[status(thm)],[c_369018,c_370518]) ).
tcf(c_446421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(sK2(X0,X2,X0),X3),X4),X4)
| ( set_intersection2(X0,X2) = X0 )
| ( set_intersection2(X1,set_intersection2(sK2(X0,X2,X0),X3)) = X4 )
| ~ subset(X0,sK2(X1,set_intersection2(sK2(X0,X2,X0),X3),X4)) ),
inference(superposition,[status(thm)],[c_370077,c_370518]) ).
tcf(c_446422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(sK2(X2,X0,X0),X3),X4),X4)
| ( set_intersection2(X2,X0) = X0 )
| ( set_intersection2(X1,set_intersection2(sK2(X2,X0,X0),X3)) = X4 )
| ~ subset(X0,sK2(X1,set_intersection2(sK2(X2,X0,X0),X3),X4)) ),
inference(superposition,[status(thm)],[c_370145,c_370518]) ).
tcf(c_446423,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(sK16(sK15(sK5)),X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(sK16(sK15(sK5)),X1)) = X2 )
| ~ subset(sK5,sK2(X0,set_intersection2(sK16(sK15(sK5)),X1),X2)) ),
inference(superposition,[status(thm)],[c_420696,c_370518]) ).
tcf(c_446424,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(sK16(sK15(sK8)),X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(sK16(sK15(sK8)),X1)) = X2 )
| ~ subset(sK8,sK2(X0,set_intersection2(sK16(sK15(sK8)),X1),X2)) ),
inference(superposition,[status(thm)],[c_423415,c_370518]) ).
tcf(c_446425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X2,X3),X4,X0),X2)
| in(sK2(X1,set_intersection2(sK2(set_intersection2(X2,X3),X4,X0),X5),X6),X6)
| ( set_intersection2(set_intersection2(X2,X3),X4) = X0 )
| ( set_intersection2(X1,set_intersection2(sK2(set_intersection2(X2,X3),X4,X0),X5)) = X6 )
| ~ subset(X0,sK2(X1,set_intersection2(sK2(set_intersection2(X2,X3),X4,X0),X5),X6)) ),
inference(superposition,[status(thm)],[c_370274,c_370518]) ).
tcf(c_446426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(set_intersection2(X0,X2),X3,X4),X4)
| in(sK2(X1,set_intersection2(sK2(set_intersection2(X0,X2),X3,X4),X5),X6),X6)
| ( set_intersection2(set_intersection2(X0,X2),X3) = X4 )
| ( set_intersection2(X1,set_intersection2(sK2(set_intersection2(X0,X2),X3,X4),X5)) = X6 )
| ~ subset(X0,sK2(X1,set_intersection2(sK2(set_intersection2(X0,X2),X3,X4),X5),X6)) ),
inference(superposition,[status(thm)],[c_370286,c_370518]) ).
tcf(c_446427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X2,set_intersection2(X3,X4),X0),X3)
| in(sK2(X1,set_intersection2(sK2(X2,set_intersection2(X3,X4),X0),X5),X6),X6)
| ( set_intersection2(X2,set_intersection2(X3,X4)) = X0 )
| ( set_intersection2(X1,set_intersection2(sK2(X2,set_intersection2(X3,X4),X0),X5)) = X6 )
| ~ subset(X0,sK2(X1,set_intersection2(sK2(X2,set_intersection2(X3,X4),X0),X5),X6)) ),
inference(superposition,[status(thm)],[c_370506,c_370518]) ).
tcf(c_446428,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,set_intersection2(X0,X0),X2),X2)
| ( set_intersection2(X1,set_intersection2(X0,X0)) = X2 )
| ~ in(X0,sK2(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_53,c_370518]) ).
tcf(c_446431,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,set_intersection2(X0,empty_set),X2),X2)
| ( set_intersection2(X1,set_intersection2(X0,empty_set)) = X2 )
| ~ in(X0,sK2(X1,empty_set,X2)) ),
inference(superposition,[status(thm)],[c_64,c_370518]) ).
tcf(c_446432,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,set_intersection2(empty_set,X2),X1),X1)
| ( set_intersection2(X0,set_intersection2(empty_set,X2)) = X1 )
| ~ in(empty_set,sK2(X0,empty_set,X1)) ),
inference(superposition,[status(thm)],[c_368545,c_370518]) ).
tcf(c_446433,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,set_intersection2(X0,sK16(powerset(X0))),X2),X2)
| ( set_intersection2(X1,set_intersection2(X0,sK16(powerset(X0)))) = X2 )
| ~ in(X0,sK2(X1,sK16(powerset(X0)),X2)) ),
inference(superposition,[status(thm)],[c_397130,c_370518]) ).
tcf(c_446434,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X0,set_intersection2(X0,X2)),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,set_intersection2(X0,X2))) = X3 )
| ~ in(X0,sK2(X1,set_intersection2(X0,X2),X3)) ),
inference(superposition,[status(thm)],[c_397136,c_370518]) ).
tcf(c_446435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X0,set_intersection2(X2,X0)),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,set_intersection2(X2,X0))) = X3 )
| ~ in(X0,sK2(X1,set_intersection2(X2,X0),X3)) ),
inference(superposition,[status(thm)],[c_397137,c_370518]) ).
tcf(c_446436,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,set_intersection2(sK5,sK15(sK5)),X1),X1)
| ( set_intersection2(X0,set_intersection2(sK5,sK15(sK5))) = X1 )
| ~ in(sK5,sK2(X0,sK15(sK5),X1)) ),
inference(superposition,[status(thm)],[c_411955,c_370518]) ).
tcf(c_446437,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,set_intersection2(sK8,sK15(sK8)),X1),X1)
| ( set_intersection2(X0,set_intersection2(sK8,sK15(sK8))) = X1 )
| ~ in(sK8,sK2(X0,sK15(sK8),X1)) ),
inference(superposition,[status(thm)],[c_411956,c_370518]) ).
tcf(c_446441,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,empty_set,X2),X2)
| ( set_intersection2(X1,empty_set) = X2 )
| ~ in(X0,sK2(X1,empty_set,X2)) ),
inference(light_normalisation,[status(thm)],[c_446431,c_64]) ).
tcf(c_446446,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK8),X1),X1)
| ( set_intersection2(X0,sK15(sK8)) = X1 )
| ~ in(sK8,sK2(X0,sK15(sK8),X1)) ),
inference(light_normalisation,[status(thm)],[c_446437,c_411956]) ).
tcf(c_446450,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,sK15(sK5),X1),X1)
| ( set_intersection2(X0,sK15(sK5)) = X1 )
| ~ in(sK5,sK2(X0,sK15(sK5),X1)) ),
inference(light_normalisation,[status(thm)],[c_446436,c_411955]) ).
tcf(c_446460,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK16(powerset(X0)),X2),X2)
| ( set_intersection2(X1,sK16(powerset(X0))) = X2 )
| ~ in(X0,sK2(X1,sK16(powerset(X0)),X2)) ),
inference(light_normalisation,[status(thm)],[c_446433,c_397130]) ).
tcf(c_446723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X0,X3),X3)
| in(sK2(X2,set_intersection2(X0,X0),X3),X1)
| ( set_intersection2(X2,set_intersection2(X0,X0)) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_370519]) ).
tcf(c_446726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,empty_set,X3),X3)
| in(sK2(X2,set_intersection2(X0,empty_set),X3),X1)
| ( set_intersection2(X2,set_intersection2(X0,empty_set)) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_370519]) ).
tcf(c_446727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,empty_set,X3),X3)
| in(sK2(X1,set_intersection2(empty_set,X2),X3),X0)
| ( set_intersection2(X1,set_intersection2(empty_set,X2)) = X3 )
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_368545,c_370519]) ).
tcf(c_446728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,sK16(powerset(X0)),X3),X3)
| in(sK2(X2,set_intersection2(X0,sK16(powerset(X0))),X3),X1)
| ( set_intersection2(X2,set_intersection2(X0,sK16(powerset(X0)))) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397130,c_370519]) ).
tcf(c_446729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X0,X3),X4),X4)
| in(sK2(X2,set_intersection2(X0,set_intersection2(X0,X3)),X4),X1)
| ( set_intersection2(X2,set_intersection2(X0,set_intersection2(X0,X3))) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397136,c_370519]) ).
tcf(c_446730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X0),X4),X4)
| in(sK2(X2,set_intersection2(X0,set_intersection2(X3,X0)),X4),X1)
| ( set_intersection2(X2,set_intersection2(X0,set_intersection2(X3,X0))) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397137,c_370519]) ).
tcf(c_446731,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK5),X2),X2)
| in(sK2(X1,set_intersection2(sK5,sK15(sK5)),X2),X0)
| ( set_intersection2(X1,set_intersection2(sK5,sK15(sK5))) = X2 )
| ~ subset(sK5,X0) ),
inference(superposition,[status(thm)],[c_411955,c_370519]) ).
tcf(c_446732,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK8),X2),X2)
| in(sK2(X1,set_intersection2(sK8,sK15(sK8)),X2),X0)
| ( set_intersection2(X1,set_intersection2(sK8,sK15(sK8))) = X2 )
| ~ subset(sK8,X0) ),
inference(superposition,[status(thm)],[c_411956,c_370519]) ).
tcf(c_446733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,X0,X3),X1)
| in(sK2(X2,set_intersection2(X0,X0),X3),X3)
| ( set_intersection2(X2,set_intersection2(X0,X0)) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_370519]) ).
tcf(c_446736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,empty_set,X3),X1)
| in(sK2(X2,set_intersection2(X0,empty_set),X3),X3)
| ( set_intersection2(X2,set_intersection2(X0,empty_set)) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_370519]) ).
tcf(c_446737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,empty_set,X3),X0)
| in(sK2(X1,set_intersection2(empty_set,X2),X3),X3)
| ( set_intersection2(X1,set_intersection2(empty_set,X2)) = X3 )
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_368545,c_370519]) ).
tcf(c_446738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,sK16(powerset(X0)),X3),X1)
| in(sK2(X2,set_intersection2(X0,sK16(powerset(X0))),X3),X3)
| ( set_intersection2(X2,set_intersection2(X0,sK16(powerset(X0)))) = X3 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397130,c_370519]) ).
tcf(c_446739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X0,X3),X4),X1)
| in(sK2(X2,set_intersection2(X0,set_intersection2(X0,X3)),X4),X4)
| ( set_intersection2(X2,set_intersection2(X0,set_intersection2(X0,X3))) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397136,c_370519]) ).
tcf(c_446740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X3,X0),X4),X1)
| in(sK2(X2,set_intersection2(X0,set_intersection2(X3,X0)),X4),X4)
| ( set_intersection2(X2,set_intersection2(X0,set_intersection2(X3,X0))) = X4 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_397137,c_370519]) ).
tcf(c_446741,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK5),X2),X0)
| in(sK2(X1,set_intersection2(sK5,sK15(sK5)),X2),X2)
| ( set_intersection2(X1,set_intersection2(sK5,sK15(sK5))) = X2 )
| ~ subset(sK5,X0) ),
inference(superposition,[status(thm)],[c_411955,c_370519]) ).
tcf(c_446742,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK8),X2),X0)
| in(sK2(X1,set_intersection2(sK8,sK15(sK8)),X2),X2)
| ( set_intersection2(X1,set_intersection2(sK8,sK15(sK8))) = X2 )
| ~ subset(sK8,X0) ),
inference(superposition,[status(thm)],[c_411956,c_370519]) ).
tcf(c_446743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X0),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X0 )
| ~ subset(X1,X3)
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),X0)
| ~ in(sK2(X0,set_intersection2(X1,X2),X0),set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370519,c_54]) ).
tcf(c_446744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X4,set_intersection2(X0,X5),X2),X3)
| in(sK2(X4,set_intersection2(X0,X5),X2),X1)
| ( set_intersection2(X4,set_intersection2(X0,X5)) = X2 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370519,c_321]) ).
tcf(c_446745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,set_intersection2(X0,X5),X2),X1)
| ( set_intersection2(X4,set_intersection2(X0,X5)) = X2 )
| ~ empty(X3)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370519,c_320]) ).
tcf(c_446746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),X0),X4)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X0 )
| ~ subset(X2,X4)
| ~ in(X0,sK2(X1,set_intersection2(X2,X3),X0)) ),
inference(superposition,[status(thm)],[c_370519,c_97]) ).
tcf(c_446747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,set_intersection2(X0,X5),X2),X3)
| in(sK2(X4,set_intersection2(X0,X5),X2),X1)
| ( set_intersection2(X4,set_intersection2(X0,X5)) = X2 )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370519,c_96]) ).
tcf(c_446754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X5)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ( apply(X3,sK13(X3,X4,apply(X3,sK2(X0,set_intersection2(X1,X2),relation_dom(X3))))) = apply(X3,sK2(X0,set_intersection2(X1,X2),relation_dom(X3))) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X5)
| ~ in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370519,c_369671]) ).
tcf(c_446755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X5,set_intersection2(X0,X6),relation_image(X4,X2)),X1)
| ( set_intersection2(X5,set_intersection2(X0,X6)) = relation_image(X4,X2) )
| ~ empty(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370519,c_369799]) ).
tcf(c_446756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X2,X5),relation_image(X0,X6)),X3)
| ( set_intersection2(X4,set_intersection2(X2,X5)) = relation_image(X0,X6) )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X3)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_370519,c_369798]) ).
tcf(c_446757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X4,set_intersection2(X0,X5),relation_image(X2,X3)),X1)
| ( set_intersection2(X4,set_intersection2(X0,X5)) = relation_image(X2,X3) )
| ~ empty(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370519,c_369596]) ).
tcf(c_446758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),relation_image(X2,X5)),X1)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = relation_image(X2,X5) )
| ~ function(X2)
| ~ relation(X2)
| ~ empty(relation_dom(X2))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370519,c_369558]) ).
tcf(c_446760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X5)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = relation_dom(X3) )
| ~ function(X3)
| ~ relation(X3)
| ~ subset(X1,X5)
| ~ empty(relation_image(X3,X4))
| ~ in(sK2(X0,set_intersection2(X1,X2),relation_dom(X3)),X4) ),
inference(superposition,[status(thm)],[c_370519,c_369501]) ).
tcf(c_446761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,set_intersection2(X0,X3),empty_set),X1)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370519,c_372426]) ).
tcf(c_446762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),X5)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X4 )
| ~ subset(X2,X5)
| ~ in(sK2(set_intersection2(X1,X0),set_intersection2(X2,X3),X4),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X4),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_370519,c_370220]) ).
tcf(c_446763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X4)
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X0 )
| ~ subset(X2,X4)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X1)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X0)
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),set_intersection2(X2,X3)) ),
inference(superposition,[status(thm)],[c_370519,c_368471]) ).
tcf(c_446764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X5,set_intersection2(X0,X6),relation_image(X2,relation_image(X3,X4))),X1)
| ( relation_image(X2,relation_image(X3,X4)) = set_intersection2(X5,set_intersection2(X0,X6)) )
| ( apply(X3,sK13(X3,X4,sK13(X2,relation_image(X3,X4),sK2(X5,set_intersection2(X0,X6),relation_image(X2,relation_image(X3,X4)))))) = sK13(X2,relation_image(X3,X4),sK2(X5,set_intersection2(X0,X6),relation_image(X2,relation_image(X3,X4)))) )
| ~ function(X3)
| ~ function(X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370519,c_369672]) ).
tcf(c_446765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,set_intersection2(X0,X3),sK15(sK5)),sK5)
| in(sK2(X2,set_intersection2(X0,X3),sK15(sK5)),X1)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = sK15(sK5) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370519,c_412536]) ).
tcf(c_446766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,set_intersection2(X0,X3),sK15(sK8)),sK8)
| in(sK2(X2,set_intersection2(X0,X3),sK15(sK8)),X1)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = sK15(sK8) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370519,c_413867]) ).
tcf(c_446768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X0,X3),sK16(powerset(X4))),X4)
| in(sK2(X2,set_intersection2(X0,X3),sK16(powerset(X4))),X1)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = sK16(powerset(X4)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370519,c_430730]) ).
tcf(c_446769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1),set_intersection2(X0,X1)),X3)
| in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1),set_intersection2(X0,X1)),set_intersection2(set_intersection2(X0,X1),X2))
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1)) = set_intersection2(X0,X1) )
| ~ subset(X0,X3)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X0,X1),set_intersection2(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_370519,c_426065]) ).
tcf(c_446770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X5)
| ( set_intersection2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4)) = X0 )
| ~ subset(X3,X5)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X2)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X1)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),X0)
| ~ in(sK2(set_intersection2(set_intersection2(X0,X1),X2),set_intersection2(X3,X4),X0),set_intersection2(X3,X4)) ),
inference(superposition,[status(thm)],[c_370519,c_370217]) ).
tcf(c_446772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( element(sK2(X3,set_intersection2(X0,X4),X5),X2)
| in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370519,c_321]) ).
tcf(c_446773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ~ empty(X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370519,c_320]) ).
tcf(c_446774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X2,X3),X4),X4)
| ( set_intersection2(X1,set_intersection2(X2,X3)) = X4 )
| ~ subset(X2,X0)
| ~ in(X0,sK2(X1,set_intersection2(X2,X3),X4)) ),
inference(superposition,[status(thm)],[c_370519,c_97]) ).
tcf(c_446775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| in(sK2(X3,set_intersection2(X0,X4),X5),X2)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_370519,c_96]) ).
tcf(c_446778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| in(sK2(X3,set_intersection2(X0,X4),X5),X2)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370519,c_59]) ).
tcf(c_446779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| in(sK2(X3,set_intersection2(X0,X4),X5),X1)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ~ subset(X0,set_intersection2(X1,X2)) ),
inference(superposition,[status(thm)],[c_370519,c_58]) ).
tcf(c_446780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| in(apply(X1,sK2(X3,set_intersection2(X0,X4),X5)),X2)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370519,c_88]) ).
tcf(c_446781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| in(sK2(X3,set_intersection2(X0,X4),X5),relation_dom(X1))
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370519,c_87]) ).
tcf(c_446782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 )
| ( apply(X5,sK13(X5,X4,apply(X5,sK2(X0,set_intersection2(X1,X2),X3)))) = apply(X5,sK2(X0,set_intersection2(X1,X2),X3)) )
| ~ function(X5)
| ~ relation(X5)
| ~ subset(X1,relation_dom(X5))
| ~ in(sK2(X0,set_intersection2(X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_370519,c_369671]) ).
tcf(c_446783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X0,X5),X6),X6)
| ( set_intersection2(X4,set_intersection2(X0,X5)) = X6 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370519,c_369799]) ).
tcf(c_446784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X0,X5),X6),X6)
| ( set_intersection2(X4,set_intersection2(X0,X5)) = X6 )
| ~ empty(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370519,c_369798]) ).
tcf(c_446785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ~ empty(X2)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370519,c_369596]) ).
tcf(c_446786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370519,c_369558]) ).
tcf(c_446787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ( apply(X1,sK13(X1,X2,sK2(X3,set_intersection2(X0,X4),X5))) = sK2(X3,set_intersection2(X0,X4),X5) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_370519,c_112]) ).
tcf(c_446788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X0,set_intersection2(X1,X2),X3),X3)
| ( set_intersection2(X0,set_intersection2(X1,X2)) = X3 )
| ~ function(X5)
| ~ relation(X5)
| ~ subset(X1,relation_dom(X5))
| ~ empty(relation_image(X5,X4))
| ~ in(sK2(X0,set_intersection2(X1,X2),X3),X4) ),
inference(superposition,[status(thm)],[c_370519,c_369501]) ).
tcf(c_446789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(sK2(X1,set_intersection2(X0,X2),X3),X4)
| in(sK2(X1,set_intersection2(X0,X2),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ~ subset(X0,sK10(sK2(X1,set_intersection2(X0,X2),X3),X4)) ),
inference(superposition,[status(thm)],[c_370519,c_369085]) ).
tcf(c_446790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X0,X2),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_370519,c_372426]) ).
tcf(c_446791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(sK2(X1,set_intersection2(X0,X2),X3))
| in(sK2(X1,set_intersection2(X0,X2),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ~ subset(X0,sK16(sK2(X1,set_intersection2(X0,X2),X3))) ),
inference(superposition,[status(thm)],[c_370519,c_370746]) ).
tcf(c_446792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| in(sK2(X1,X2,sK2(X3,set_intersection2(X0,X4),X5)),X1)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ( sK2(X3,set_intersection2(X0,X4),X5) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X3,set_intersection2(X0,X4),X5))) ),
inference(superposition,[status(thm)],[c_370519,c_369079]) ).
tcf(c_446793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| in(sK2(X1,X2,sK2(X3,set_intersection2(X0,X4),X5)),X2)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ( sK2(X3,set_intersection2(X0,X4),X5) = set_intersection2(X1,X2) )
| ~ subset(X0,sK2(X1,X2,sK2(X3,set_intersection2(X0,X4),X5))) ),
inference(superposition,[status(thm)],[c_370519,c_369078]) ).
tcf(c_446794,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X1,set_intersection2(X0,X2),X3),X3)
| in(sK2(sK2(X1,set_intersection2(X0,X2),X3),X4,X5),X5)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ( set_intersection2(sK2(X1,set_intersection2(X0,X2),X3),X4) = X5 )
| ~ subset(X0,sK2(sK2(X1,set_intersection2(X0,X2),X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_370519,c_369076]) ).
tcf(c_446797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X0,X3),X4),X4)
| in(sK2(X1,sK2(X2,set_intersection2(X0,X3),X4),X5),X5)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ( set_intersection2(X1,sK2(X2,set_intersection2(X0,X3),X4)) = X5 )
| ~ subset(X0,sK2(X1,sK2(X2,set_intersection2(X0,X3),X4),X5)) ),
inference(superposition,[status(thm)],[c_370519,c_369077]) ).
tcf(c_446798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X0,X3),X4),X4)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X5,relation_image(X1,sK2(X2,set_intersection2(X0,X3),X4)))
| ~ subset(X0,sK13(X1,sK2(X2,set_intersection2(X0,X3),X4),X5)) ),
inference(superposition,[status(thm)],[c_370519,c_369593]) ).
tcf(c_446799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X0,X5),X6),X6)
| ( set_intersection2(X4,set_intersection2(X0,X5)) = X6 )
| ( apply(X2,sK13(X2,X3,sK13(X1,relation_image(X2,X3),sK2(X4,set_intersection2(X0,X5),X6)))) = sK13(X1,relation_image(X2,X3),sK2(X4,set_intersection2(X0,X5),X6)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X0,relation_image(X1,relation_image(X2,X3))) ),
inference(superposition,[status(thm)],[c_370519,c_369672]) ).
tcf(c_446800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X0,X3),X4),X4)
| in(sK11(X1,sK2(X2,set_intersection2(X0,X3),X4),X5),X5)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ( relation_image(X1,sK2(X2,set_intersection2(X0,X3),X4)) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK12(X1,sK2(X2,set_intersection2(X0,X3),X4),X5)) ),
inference(superposition,[status(thm)],[c_370519,c_369298]) ).
tcf(c_446801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ( sK2(X3,set_intersection2(X0,X4),X5) = relation_image(X1,X2) )
| ( apply(X1,sK12(X1,X2,sK2(X3,set_intersection2(X0,X4),X5))) = sK11(X1,X2,sK2(X3,set_intersection2(X0,X4),X5)) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,set_intersection2(X0,X4),X5))) ),
inference(superposition,[status(thm)],[c_370519,c_369435]) ).
tcf(c_446802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| in(sK12(X1,X2,sK2(X3,set_intersection2(X0,X4),X5)),X2)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ( sK2(X3,set_intersection2(X0,X4),X5) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,set_intersection2(X0,X4),X5))) ),
inference(superposition,[status(thm)],[c_370519,c_369306]) ).
tcf(c_446803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| in(sK12(X1,X2,sK2(X3,set_intersection2(X0,X4),X5)),relation_dom(X1))
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ( sK2(X3,set_intersection2(X0,X4),X5) = relation_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK11(X1,X2,sK2(X3,set_intersection2(X0,X4),X5))) ),
inference(superposition,[status(thm)],[c_370519,c_369205]) ).
tcf(c_446804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X0,X2),X3),sK5)
| in(sK2(X1,set_intersection2(X0,X2),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ~ subset(X0,sK15(sK5)) ),
inference(superposition,[status(thm)],[c_370519,c_412536]) ).
tcf(c_446805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X1,set_intersection2(X0,X2),X3),sK8)
| in(sK2(X1,set_intersection2(X0,X2),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ~ subset(X0,sK15(sK8)) ),
inference(superposition,[status(thm)],[c_370519,c_413867]) ).
tcf(c_446806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| in(sK7(X1,X2,sK2(X3,set_intersection2(X0,X4),X5)),relation_dom(X1))
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ( sK2(X3,set_intersection2(X0,X4),X5) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X3,set_intersection2(X0,X4),X5))) ),
inference(superposition,[status(thm)],[c_370519,c_369084]) ).
tcf(c_446807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X3,set_intersection2(X0,X4),X5),X5)
| in(apply(X1,sK7(X1,X2,sK2(X3,set_intersection2(X0,X4),X5))),X2)
| ( set_intersection2(X3,set_intersection2(X0,X4)) = X5 )
| ( sK2(X3,set_intersection2(X0,X4),X5) = relation_inverse_image(X1,X2) )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,sK7(X1,X2,sK2(X3,set_intersection2(X0,X4),X5))) ),
inference(superposition,[status(thm)],[c_370519,c_369083]) ).
tcf(c_446808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(sK2(X2,set_intersection2(X0,X3),X4),X4)
| in(sK7(X1,sK2(X2,set_intersection2(X0,X3),X4),X5),X5)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ( relation_inverse_image(X1,sK2(X2,set_intersection2(X0,X3),X4)) = X5 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,apply(X1,sK7(X1,sK2(X2,set_intersection2(X0,X3),X4),X5))) ),
inference(superposition,[status(thm)],[c_370519,c_369082]) ).
tcf(c_446809,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X2,set_intersection2(X0,X1),X2),X2)
| ( set_intersection2(X2,set_intersection2(X0,X1)) = X2 )
| ~ subset(X0,set_intersection2(X0,X1)) ),
inference(superposition,[status(thm)],[c_370519,c_423425]) ).
tcf(c_446810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X1,set_intersection2(X0,X2),X3),X3)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ( set_intersection2(sK2(X1,set_intersection2(X0,X2),X3),X4) = sK2(X1,set_intersection2(X0,X2),X3) )
| ~ subset(X0,sK2(sK2(X1,set_intersection2(X0,X2),X3),X4,sK2(X1,set_intersection2(X0,X2),X3))) ),
inference(superposition,[status(thm)],[c_370519,c_370076]) ).
tcf(c_446811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X0,X3),X4),X4)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ( set_intersection2(X1,sK2(X2,set_intersection2(X0,X3),X4)) = sK2(X2,set_intersection2(X0,X3),X4) )
| ~ subset(X0,sK2(X1,sK2(X2,set_intersection2(X0,X3),X4),sK2(X2,set_intersection2(X0,X3),X4))) ),
inference(superposition,[status(thm)],[c_370519,c_370144]) ).
tcf(c_446812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK2(X2,set_intersection2(X0,X3),X4),X4)
| in(sK2(X2,set_intersection2(X0,X3),X4),X1)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ~ subset(X0,sK16(powerset(X1))) ),
inference(superposition,[status(thm)],[c_370519,c_430730]) ).
tcf(c_446813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X0)
| in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),set_intersection2(X0,X1))
| ( set_intersection2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = X0 )
| ~ subset(X2,set_intersection2(X2,X3))
| ~ in(sK2(set_intersection2(X0,X1),set_intersection2(X2,X3),X0),X1) ),
inference(superposition,[status(thm)],[c_370519,c_426065]) ).
tcf(c_446815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X0,X5),X6),X6)
| in(sK2(set_intersection2(X1,X2),X3,sK2(X4,set_intersection2(X0,X5),X6)),X1)
| ( set_intersection2(X4,set_intersection2(X0,X5)) = X6 )
| ( sK2(X4,set_intersection2(X0,X5),X6) = set_intersection2(set_intersection2(X1,X2),X3) )
| ~ subset(X0,sK2(set_intersection2(X1,X2),X3,sK2(X4,set_intersection2(X0,X5),X6))) ),
inference(superposition,[status(thm)],[c_370519,c_370273]) ).
tcf(c_446816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X1,set_intersection2(X0,X2),X3),X3)
| in(sK2(set_intersection2(sK2(X1,set_intersection2(X0,X2),X3),X4),X5,X6),X6)
| ( set_intersection2(X1,set_intersection2(X0,X2)) = X3 )
| ( set_intersection2(set_intersection2(sK2(X1,set_intersection2(X0,X2),X3),X4),X5) = X6 )
| ~ subset(X0,sK2(set_intersection2(sK2(X1,set_intersection2(X0,X2),X3),X4),X5,X6)) ),
inference(superposition,[status(thm)],[c_370519,c_370285]) ).
tcf(c_446817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X4,set_intersection2(X0,X5),X6),X6)
| in(sK2(X1,set_intersection2(X2,X3),sK2(X4,set_intersection2(X0,X5),X6)),X2)
| ( set_intersection2(X4,set_intersection2(X0,X5)) = X6 )
| ( sK2(X4,set_intersection2(X0,X5),X6) = set_intersection2(X1,set_intersection2(X2,X3)) )
| ~ subset(X0,sK2(X1,set_intersection2(X2,X3),sK2(X4,set_intersection2(X0,X5),X6))) ),
inference(superposition,[status(thm)],[c_370519,c_370505]) ).
tcf(c_446818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( in(sK2(X2,set_intersection2(X0,X3),X4),X4)
| in(sK2(X1,set_intersection2(sK2(X2,set_intersection2(X0,X3),X4),X5),X6),X6)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X4 )
| ( set_intersection2(X1,set_intersection2(sK2(X2,set_intersection2(X0,X3),X4),X5)) = X6 )
| ~ subset(X0,sK2(X1,set_intersection2(sK2(X2,set_intersection2(X0,X3),X4),X5),X6)) ),
inference(superposition,[status(thm)],[c_370519,c_370518]) ).
tcf(c_446819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,set_intersection2(X0,X3),X1),X1)
| ( set_intersection2(X2,set_intersection2(X0,X3)) = X1 )
| ~ subset(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_370519]) ).
tcf(c_446833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,empty_set,X2),X3)
| in(sK2(X0,set_intersection2(empty_set,X1),X2),X2)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = X2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_446737,c_369177]) ).
tcf(c_446836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,empty_set,X3),X3)
| in(sK2(X2,empty_set,X3),X1)
| ( set_intersection2(X2,empty_set) = X3 )
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_446736,c_64]) ).
tcf(c_446842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X0,empty_set,X2),X2)
| in(sK2(X0,set_intersection2(empty_set,X1),X2),X3)
| ( set_intersection2(X0,set_intersection2(empty_set,X1)) = X2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_446727,c_369177]) ).
tcf(c_446873,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK8),X2),X2)
| in(sK2(X1,sK15(sK8),X2),X0)
| ( set_intersection2(X1,sK15(sK8)) = X2 )
| ~ subset(sK8,X0) ),
inference(light_normalisation,[status(thm)],[c_446742,c_411956]) ).
tcf(c_446878,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,sK15(sK5),X2),X2)
| in(sK2(X1,sK15(sK5),X2),X0)
| ( set_intersection2(X1,sK15(sK5)) = X2 )
| ~ subset(sK5,X0) ),
inference(light_normalisation,[status(thm)],[c_446741,c_411955]) ).
tcf(c_446945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK2(X2,sK16(powerset(X0)),X3),X3)
| in(sK2(X2,sK16(powerset(X0)),X3),X1)
| ( set_intersection2(X2,sK16(powerset(X0))) = X3 )
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_446738,c_397130]) ).
tcf(c_447456,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_446945,c_446878,c_446873,c_446842,c_446836,c_446833,c_446819,c_446818,c_446817,c_446816,c_446815,c_446813,c_446812,c_446811,c_446810,c_446809,c_446808,c_446807,c_446806,c_446805,c_446804,c_446803,c_446802,c_446801,c_446800,c_446799,c_446798,c_446797,c_446794,c_446793,c_446792,c_446791,c_446790,c_446789,c_446788,c_446787,c_446786,c_446785,c_446784,c_446783,c_446782,c_446781,c_446780,c_446779,c_446778,c_446775,c_446774,c_446773,c_446772,c_446770,c_446769,c_446768,c_446766,c_446765,c_446764,c_446763,c_446762,c_446761,c_446760,c_446758,c_446757,c_446756,c_446755,c_446754,c_446747,c_446746,c_446745,c_446744,c_446743,c_446742,c_446741,c_446740,c_446739,c_446738,c_446737,c_446736,c_446733,c_446732,c_446731,c_446730,c_446729,c_446728,c_446727,c_446726,c_446723,c_446460,c_446450,c_446446,c_446441,c_446437,c_446436,c_446435,c_446434,c_446433,c_446432,c_446431,c_446428,c_446427,c_446426,c_446425,c_446424,c_446423,c_446422,c_446421,c_446420,c_446419,c_446418,c_446417,c_446416,c_446415,c_446414,c_446413,c_446412,c_446411,c_446410,c_446409,c_446408,c_446407,c_446406,c_446405,c_446404,c_446370,c_446184,c_446054,c_446053,c_446037,c_446036,c_446035,c_446034,c_446033,c_446032,c_446031,c_446030,c_446029,c_446028,c_446027,c_446026,c_446025,c_446024,c_446023,c_446022,c_446021,c_446020,c_446019,c_446018,c_446017,c_446016,c_446015,c_446014,c_446013,c_446012,c_446011,c_446010,c_446009,c_446008,c_446007,c_446006,c_446004,c_446001,c_445826,c_445652,c_445651,c_445636,c_445633,c_445632,c_445600,c_445599,c_445598,c_445597,c_445596,c_445595,c_445594,c_445593,c_445592,c_445591,c_445590,c_445589,c_445588,c_445587,c_445586,c_445585,c_445584,c_445583,c_445582,c_445581,c_445580,c_445579,c_445578,c_445577,c_445576,c_445575,c_445574,c_445573,c_445572,c_445571,c_445570,c_445569,c_445568,c_445567,c_445566,c_445565,c_445564,c_445563,c_445561,c_445560,c_445559,c_445558,c_445557,c_445556,c_445555,c_445554,c_445551,c_445550,c_445549,c_445548,c_445547,c_445546,c_445545,c_445543,c_445540,c_445125,c_444873,c_444858,c_444854,c_444823,c_444822,c_444821,c_444820,c_444819,c_444818,c_444817,c_444816,c_444815,c_444814,c_444813,c_444812,c_444811,c_444810,c_444809,c_444808,c_444807,c_444806,c_444805,c_444804,c_444803,c_444802,c_444801,c_444800,c_444799,c_444798,c_444797,c_444796,c_444795,c_444794,c_444793,c_444792,c_444791,c_444790,c_444789,c_444788,c_444787,c_444786,c_444785,c_444784,c_444783,c_444782,c_444781,c_444780,c_444779,c_444778,c_444777,c_444776,c_444775,c_444774,c_444773,c_444772,c_444771,c_444770,c_444769,c_444768,c_444767,c_444764,c_444763,c_444762,c_444761,c_444760,c_444759,c_444758,c_444756,c_444753,c_444364,c_444179,c_444176,c_444175,c_444168,c_444166,c_444160,c_444141,c_444137,c_444136,c_444135,c_444134,c_444133,c_444132,c_444131,c_444130,c_444129,c_444128,c_444127,c_444126,c_444125,c_444124,c_444123,c_444122,c_444121,c_444120,c_444119,c_444118,c_444117,c_444116,c_444115,c_444114,c_444113,c_444112,c_444111,c_444110,c_444109,c_444108,c_444107,c_444106,c_444105,c_444104,c_444103,c_444102,c_444101,c_444100,c_444099,c_444098,c_444097,c_444096,c_444095,c_444094,c_444093,c_444092,c_444091,c_444090,c_444089,c_444088,c_444087,c_444086,c_444085,c_444084,c_444083,c_444082,c_444081,c_444080,c_444079,c_444078,c_444077,c_444075,c_444073,c_444072,c_444071,c_444070,c_444069,c_444068,c_444067,c_444064,c_444063,c_444062,c_444061,c_444060,c_444059,c_444055,c_444053,c_444052,c_444051,c_444050,c_444049,c_444048,c_444047,c_444044,c_443633,c_443564,c_443474,c_443470,c_443439,c_443436,c_443435,c_443422,c_443420,c_443414,c_443392,c_443388,c_443387,c_443386,c_443385,c_443384,c_443383,c_443382,c_443381,c_443380,c_443379,c_443378,c_443377,c_443376,c_443375,c_443374,c_443373,c_443372,c_443371,c_443370,c_443369,c_443368,c_443367,c_443366,c_443365,c_443364,c_443363,c_443362,c_443361,c_443360,c_443359,c_443358,c_443357,c_443356,c_443355,c_443354,c_443353,c_443352,c_443351,c_443350,c_443349,c_443348,c_443347,c_443346,c_443345,c_443344,c_443343,c_443342,c_443341,c_443340,c_443339,c_443338,c_443337,c_443336,c_443335,c_443334,c_443333,c_443332,c_443331,c_443330,c_443329,c_443328,c_443326,c_443325,c_443324,c_443323,c_443322,c_443321,c_443320,c_443319,c_443318,c_443315,c_443314,c_443313,c_443312,c_443311,c_443310,c_443309,c_443306,c_443305,c_443304,c_443303,c_443302,c_443301,c_443300,c_443299,c_443298,c_443295,c_443176,c_443088,c_443087,c_443086,c_443085,c_443084,c_443083,c_443082,c_443080,c_443079,c_443078,c_443077,c_443076,c_443075,c_443074,c_443073,c_443072,c_443071,c_443070,c_443069,c_443068,c_443067,c_443066,c_443065,c_443064,c_443063,c_443062,c_443061,c_443060,c_443059,c_443058,c_443056,c_443053,c_442966,c_442745,c_442650,c_442647,c_442640,c_442639,c_442638,c_442637,c_442636,c_442635,c_442634,c_442633,c_442632,c_442631,c_442630,c_442629,c_442628,c_442627,c_442626,c_442625,c_442624,c_442623,c_442622,c_442621,c_442620,c_442619,c_442618,c_442617,c_442616,c_442615,c_442614,c_442612,c_442611,c_442610,c_442609,c_442608,c_442607,c_442606,c_442603,c_442602,c_442601,c_442600,c_442599,c_442598,c_442597,c_442596,c_442593,c_442142,c_441935,c_441917,c_441916,c_441915,c_441914,c_441913,c_441912,c_441911,c_441910,c_441909,c_441908,c_441907,c_441906,c_441905,c_441904,c_441903,c_441902,c_441901,c_441900,c_441899,c_441898,c_441897,c_441896,c_441895,c_441894,c_441893,c_441892,c_441891,c_441890,c_441889,c_441888,c_441887,c_441886,c_441885,c_441884,c_441883,c_441882,c_441881,c_441880,c_441879,c_441878,c_441877,c_441874,c_441873,c_441872,c_441871,c_441870,c_441869,c_441868,c_441867,c_441866,c_441865,c_441864,c_441863,c_441862,c_441861,c_441860,c_441859,c_441858,c_441857,c_441856,c_441855,c_441854,c_441853,c_441852,c_441851,c_441850,c_441849,c_441848,c_441847,c_441846,c_441845,c_441844,c_441843,c_441842,c_441841,c_441840,c_441839,c_441838,c_441837,c_441834,c_441833,c_441832,c_441831,c_441830,c_441829,c_441827,c_441824,c_441653,c_441649,c_441640,c_441639,c_441638,c_441637,c_441636,c_441635,c_441634,c_441633,c_441630,c_441629,c_441628,c_441627,c_441626,c_441625,c_441624,c_441623,c_441622,c_441621,c_441620,c_441619,c_441618,c_441617,c_441616,c_441615,c_441614,c_441613,c_441612,c_441611,c_441610,c_441609,c_441608,c_441607,c_441585,c_441584,c_441574,c_441267,c_441135,c_441131,c_441102,c_441101,c_441100,c_441099,c_441098,c_441097,c_441096,c_441095,c_441094,c_441093,c_441092,c_441091,c_441090,c_441089,c_441088,c_441087,c_441086,c_441085,c_441084,c_441083,c_441082,c_441081,c_441080,c_441079,c_441078,c_441077,c_441076,c_441075,c_441074,c_441073,c_441072,c_441071,c_441070,c_441069,c_441068,c_441066,c_441065,c_441060,c_441059,c_441058,c_441057,c_441056,c_441054,c_441053,c_441052,c_441050,c_441049,c_441048,c_441047,c_441046,c_441045,c_441044,c_441043,c_441042,c_441038,c_441037,c_441036,c_441035,c_441034,c_441018,c_441017,c_441016,c_441015,c_441014,c_440772,c_440676,c_440672,c_440649,c_440639,c_440638,c_440637,c_440636,c_440635,c_440634,c_440633,c_440632,c_440631,c_440630,c_440629,c_440628,c_440627,c_440626,c_440625,c_440624,c_440623,c_440622,c_440621,c_440620,c_440619,c_440618,c_440617,c_440616,c_440615,c_440614,c_440613,c_440612,c_440611,c_440610,c_440609,c_440608,c_440607,c_440606,c_440605,c_440604,c_440602,c_440601,c_440596,c_440595,c_440594,c_440593,c_440592,c_440590,c_440589,c_440588,c_440586,c_440585,c_440584,c_440583,c_440582,c_440581,c_440580,c_440579,c_440578,c_440576,c_440574,c_440573,c_440572,c_440571,c_440570,c_440255,c_440254,c_440237,c_440236,c_440235,c_440234,c_440233,c_440232,c_440231,c_440230,c_440229,c_440228,c_440227,c_440226,c_440225,c_440224,c_440223,c_440222,c_440221,c_440215,c_440214,c_440213,c_440211,c_440210,c_440209,c_440208,c_440207,c_440204,c_439873,c_439871,c_439870,c_439869,c_439868,c_439867,c_439866,c_439865,c_439864,c_439863,c_439862,c_439860,c_439859,c_439858,c_439857,c_439856,c_439855,c_439854,c_439853,c_439852,c_439851,c_439850,c_439849,c_439848,c_439847,c_439846,c_439845,c_439844,c_439838,c_439837,c_439836,c_439834,c_439833,c_439832,c_439831,c_439830,c_439829,c_439826,c_439825,c_439824,c_439823,c_439822,c_439821,c_439818,c_439183,c_439182,c_439181,c_439180,c_439179,c_439178,c_439177,c_439176,c_439175,c_439174,c_439173,c_439172,c_439171,c_439170,c_439169,c_439168,c_439167,c_439166,c_439165,c_439164,c_439163,c_439162,c_439161,c_439159,c_439158,c_439157,c_439156,c_439155,c_439154,c_439153,c_439152,c_439151,c_439150,c_439149,c_439148,c_439147,c_439146,c_439145,c_439144,c_439143,c_439137,c_439136,c_439135,c_439133,c_439132,c_439131,c_439130,c_439129,c_439126,c_439125,c_439124,c_439123,c_439122,c_439121,c_439118,c_438648,c_438645,c_438644,c_438643,c_438642,c_438641,c_438639,c_438638,c_438637,c_438636,c_438635,c_438634,c_438633,c_438632,c_438631,c_438630,c_438629,c_438628,c_438627,c_438626,c_438625,c_438624,c_438623,c_438622,c_438619,c_438618,c_438617,c_438616,c_438615,c_438614,c_438613,c_438612,c_438611,c_438609,c_438608,c_438607,c_438606,c_438605,c_438597,c_438596,c_438595,c_438593,c_438592,c_438591,c_438590,c_438589,c_438588,c_438587,c_438585,c_438583,c_438582,c_438581,c_438580,c_438577,c_438576,c_438575,c_438574,c_438573,c_438572,c_438571,c_438570,c_438568,c_438566,c_438565,c_438564,c_438563,c_438560,c_438445,c_438425,c_438189,c_438184,c_438127,c_438126,c_438125,c_438124,c_438123,c_438122,c_438121,c_438120,c_438119,c_438118,c_438117,c_438116,c_438115,c_438114,c_438113,c_438112,c_438111,c_438110,c_438109,c_438108,c_438107,c_438106,c_438105,c_438104,c_438103,c_438102,c_438101,c_438100,c_438099,c_438098,c_438097,c_438096,c_438095,c_438094,c_438093,c_438092,c_438091,c_438090,c_438089,c_438088,c_438087,c_438081,c_438080,c_438074,c_438073,c_438072,c_438071,c_438070,c_438069,c_438068,c_438067,c_438066,c_438064,c_438063,c_438062,c_438061,c_438060,c_438059,c_438058,c_438057,c_438056,c_438055,c_438054,c_438053,c_438052,c_438050,c_438049,c_438048,c_438047,c_438046,c_438045,c_438038,c_438032,c_438030,c_438028,c_438027,c_438026,c_438025,c_438024,c_438023,c_438022,c_438021,c_438020,c_438019,c_438018,c_438017,c_438016,c_438015,c_438014,c_438013,c_43801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8628,c_369151,c_368976,c_369765,c_369761,c_369132,c_369131,c_369138,c_369137,c_321,c_320,c_430671,c_377193,c_120,c_119,c_118,c_117,c_116,c_115,c_112,c_111,c_110,c_109,c_108,c_107,c_106,c_105,c_103,c_104,c_101,c_99,c_98,c_97,c_96,c_95,c_94,c_93,c_92,c_91,c_90,c_89,c_88,c_87,c_86,c_85,c_84,c_83,c_82,c_81,c_80,c_79,c_78,c_77,c_76,c_75,c_74,c_73,c_72,c_71,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_100,c_60,c_59,c_58,c_57,c_56,c_55,c_54,c_53,c_52,c_51,c_50,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU067+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:40:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/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
% 0.10/0.44 % Proving...
% 244.84/33.54 % SZS status Started for theBenchmark.p
% 244.84/33.54 % SZS status Theorem for theBenchmark.p
% 244.84/33.54
% 244.84/33.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 244.84/33.54
% 244.84/33.54 % ------ iProver source info
% 244.84/33.54
% 244.84/33.54 % git: date: 2026-07-19 20:42:38 +0200
% 244.84/33.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 244.84/33.54 % git: non_committed_changes: false
% 244.84/33.54
% 244.84/33.54 % ------ Parsing...
% 244.84/33.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 244.84/33.54
% 244.84/33.54 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 244.84/33.54
% 244.84/33.54 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 244.84/33.54
% 244.84/33.54 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 244.84/33.54 % ------ Proving...
% 244.84/33.54 % ------ Problem Properties
% 244.84/33.54
% 244.84/33.54 %
% 244.84/33.54 % clauses 69
% 244.84/33.54 % conjectures 3
% 244.84/33.54 % EPR 28
% 244.84/33.54 % Horn 59
% 244.84/33.54 % unary 24
% 244.84/33.54 % binary 17
% 244.84/33.54 % lits 169
% 244.84/33.54 % lits eq 20
% 244.84/33.54 % fd_pure 0
% 244.84/33.54 % fd_pseudo 0
% 244.84/33.54 % fd_cond 1
% 244.84/33.54 % fd_pseudo_cond 12
% 244.84/33.54 % AC symbols 0
% 244.84/33.54
% 244.84/33.54 % ------ Schedule dynamic 5 is on
% 244.84/33.54
% 244.84/33.54 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 244.84/33.54
% 244.84/33.54
% 244.84/33.54 % ------
% 244.84/33.54 % Current options:
% 244.84/33.54 % ------
% 244.84/33.54
% 244.84/33.54
% 244.84/33.54 %
% 244.84/33.54
% 244.84/33.54 % ------ Proving...
% 244.84/33.54 % Proof_search_loop: time out after: 5668 full_loop iterations
% 244.84/33.54
% 244.84/33.54 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 244.84/33.54
% 244.84/33.54
% 244.84/33.54 % ------
% 244.84/33.54 % Current options:
% 244.84/33.54 % ------
% 244.84/33.54
% 244.84/33.54
% 244.84/33.54 %
% 244.84/33.54
% 244.84/33.54 % ------ Proving...
% 244.84/33.54 % Proof_search_loop: time out after: 3852 full_loop iterations
% 244.84/33.54
% 244.84/33.54 % ------ Option_1: Negative Selections Time Limit: 35.
% 244.84/33.54
% 244.84/33.54
% 244.84/33.54 % ------
% 244.84/33.54 % Current options:
% 244.84/33.54 % ------
% 244.84/33.54
% 244.84/33.54
% 244.84/33.54 %
% 244.84/33.54
% 244.84/33.54 % ------ Proving...
% 244.84/33.54 %
% 244.84/33.54
% 244.84/33.54 % SZS status Theorem for theBenchmark.p
% 244.84/33.54
% 244.84/33.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 245.62/33.80
% 245.62/33.80
%------------------------------------------------------------------------------