%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU226+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:56:12 PM UTC 2026
% Result : Theorem 22.75s 4.25s
% Output : CNFRefutation 26.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 205
% Syntax : Number of formulae : 5727 (1378 unt; 1 def)
% Number of atoms : 15072 (3228 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 16694 (7349 ~;8214 |; 795 &)
% ( 135 <=>; 200 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-4 aty)
% Number of functors : 109 ( 109 usr; 10 con; 0-4 aty)
% Number of variables : 11277 ( 2 sgn11079 !; 198 ?;8091 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
=> ~ proper_subset(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f4,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& empty(X0)
& relation(X0) )
=> ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(f6,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f7,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f8,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f9,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f10,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f11,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation(X2)
=> ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f12,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/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f13,axiom,
! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_rng_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
fof(f14,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/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f15,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f16,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f17,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : X1 != ordered_pair(X2,X3)
& in(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f19,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f20,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f21,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f22,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
fof(f23,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f24,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f25,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f26,axiom,
! [X0,X1,X2] :
( X2 = cartesian_product2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f27,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
fof(f28,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f29,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f30,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f31,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f32,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f33,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f34,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f35,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f36,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,X1) = set_difference(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f37,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f38,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f39,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X1 = relation_inverse(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
fof(f40,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f41,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f42,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f43,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ! [X2] :
( element(X2,powerset(powerset(X0)))
=> ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( element(X3,powerset(X0))
=> ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(f44,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f45,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> function_inverse(X0) = relation_inverse(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
fof(f53,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f55,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f60,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f63,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f66,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f67,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(union_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(f68,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f69,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(meet_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(f70,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> element(subset_difference(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
fof(f71,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f72,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f73,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f76,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f77,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f78,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_relat_1) ).
fof(f81,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f82,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f83,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f84,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f86,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f87,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(f89,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f90,axiom,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funct_1) ).
fof(f91,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f92,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f93,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f94,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f95,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f96,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f97,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f98,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f99,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f100,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(f101,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f103,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f104,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f105,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(f106,axiom,
! [X0,X1] : ~ proper_subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f107,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f109,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f110,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f114,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f118,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f120,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f121,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f122,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f123,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f124,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f125,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f126,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f127,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f128,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f130,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> union_of_subsets(X0,X1) = union(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(f132,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f134,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f135,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f136,axiom,
! [X0,X1,X2,X3] :
~ ( X0 != X3
& X0 != X2
& unordered_pair(X0,X1) = unordered_pair(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f137,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
fof(f138,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_relat_1) ).
fof(f139,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng_restriction(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
fof(f140,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
fof(f141,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f142,axiom,
! [X0,X1] :
( relation(X1)
=> relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).
fof(f143,axiom,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f144,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f145,axiom,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
( in(X2,X1)
=> in(powerset(X2),X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(f146,axiom,
! [X0,X1,X2] :
( relation(X2)
=> relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_relat_1) ).
fof(f147,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).
fof(f148,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
fof(f149,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
fof(f150,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(negated_conjecture,[status(cth)],[f149]) ).
fof(f151,axiom,
! [X0,X1] :
( relation(X1)
=> relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_relat_1) ).
fof(f152,axiom,
! [X0] :
( relation(X0)
=> relation_image(X0,relation_dom(X0)) = relation_rng(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
fof(f153,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_relat_1) ).
fof(f154,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
fof(f155,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
fof(f156,axiom,
! [X0,X1] :
( relation(X1)
=> ~ ( relation_inverse_image(X1,X0) = empty_set
& subset(X0,relation_rng(X1))
& X0 != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
fof(f157,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( subset(X0,X1)
=> subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_relat_1) ).
fof(f159,axiom,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f160,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(f161,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f162,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f163,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f165,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f166,axiom,
! [X0] :
( relation(X0)
=> subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f167,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f168,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f169,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(X0,X1)
=> ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
fof(f170,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f171,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f172,axiom,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(f174,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f175,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f176,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f177,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(f178,axiom,
! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) = ordered_pair(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f179,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f180,axiom,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f181,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f182,axiom,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f183,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f184,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(f185,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f186,axiom,
! [X0,X1] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f187,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f188,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(f189,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f190,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f191,axiom,
! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f192,axiom,
! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f193,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,powerset(X0))
=> ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
fof(f194,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
fof(f195,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
fof(f197,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f198,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( complements_of_subsets(X0,X1) = empty_set
& X1 != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(f199,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f200,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_dom(X0),relation_rng(X1))
=> relation_rng(relation_composition(X1,X0)) = relation_rng(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
fof(f201,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_setfam_1) ).
fof(f202,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(f203,axiom,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f204,axiom,
! [X0] : set_difference(empty_set,X0) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
fof(f205,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f206,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f207,axiom,
! [X0] :
( X0 != empty_set
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f208,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = function_inverse(X0)
<=> ( ! [X2,X3] :
( ( ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) )
=> ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) )
=> ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f209,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,subset_complement(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f210,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f211,axiom,
! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
fof(f212,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( in(X0,relation_rng(X1))
& one_to_one(X1) )
=> ( X0 = apply(relation_composition(function_inverse(X1),X1),X0)
& X0 = apply(X1,apply(function_inverse(X1),X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f213,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f214,axiom,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f215,axiom,
! [X0,X1] :
~ ( proper_subset(X1,X0)
& subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f216,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
fof(f217,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f218,axiom,
! [X0] :
( relation(X0)
=> ( ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
=> X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
fof(f219,axiom,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = empty_set
<=> relation_rng(X0) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
fof(f220,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f221,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f222,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f223,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f224,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f225,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).
fof(f226,axiom,
! [X0] :
( relation_rng(identity_relation(X0)) = X0
& relation_dom(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f227,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
fof(f228,axiom,
! [X0,X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
fof(f229,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f230,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f231,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f232,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
fof(f233,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom_restriction(X1,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
fof(f234,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f235,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f236,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f237,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f238,axiom,
! [X0,X1] :
( relation(X1)
=> relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
fof(f239,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(f240,axiom,
! [X0,X1] :
( relation(X1)
=> relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).
fof(f241,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_1) ).
fof(f242,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f243,axiom,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
~ ( ! [X3] :
~ ( ! [X4] :
( subset(X4,X2)
=> in(X4,X3) )
& in(X3,X1) )
& in(X2,X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
fof(f244,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f245,plain,
! [X0] :
? [X1] :
( ! [X5] :
~ ( ~ in(X5,X1)
& ~ are_equipotent(X5,X1)
& subset(X5,X1) )
& ! [X4] :
( in(X4,X1)
=> in(powerset(X4),X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
inference(rectify,[],[f145]) ).
fof(f246,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X3] :
( in(X3,X1)
& in(X3,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f190]) ).
fof(f247,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X3] : in(X3,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f206]) ).
fof(f248,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f101]) ).
fof(f251,plain,
! [X0] :
? [X1] :
( ! [X7] :
~ ( ~ in(X7,X1)
& ~ are_equipotent(X7,X1)
& subset(X7,X1) )
& ! [X4] :
~ ( ! [X5] :
~ ( ! [X6] :
( subset(X6,X4)
=> in(X6,X5) )
& in(X5,X1) )
& in(X4,X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
inference(rectify,[],[f243]) ).
fof(f252,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(rectify,[],[f106]) ).
fof(f253,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f44]) ).
fof(f254,plain,
! [X0] :
? [X1] :
( ! [X4] :
( in(X4,X1)
=> in(powerset(X4),X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
inference(pure_predicate_removal,[],[f245]) ).
fof(f255,plain,
! [X0] :
? [X1] :
( ! [X4] :
~ ( ! [X5] :
~ ( ! [X6] :
( subset(X6,X4)
=> in(X6,X5) )
& in(X5,X1) )
& in(X4,X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
inference(pure_predicate_removal,[],[f251]) ).
fof(f257,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f109]) ).
fof(f258,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f110]) ).
fof(f260,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(ennf_transformation,[],[f114]) ).
fof(f261,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(flattening,[],[f260]) ).
fof(f263,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| element(X0,powerset(X1)) ),
inference(ennf_transformation,[],[f118]) ).
fof(f266,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f136]) ).
fof(f267,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) ) ),
inference(ennf_transformation,[],[f137]) ).
fof(f268,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
inference(ennf_transformation,[],[f138]) ).
fof(f269,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng_restriction(X0,X1),X1) ),
inference(ennf_transformation,[],[f139]) ).
fof(f270,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
inference(ennf_transformation,[],[f140]) ).
fof(f271,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
inference(ennf_transformation,[],[f141]) ).
fof(f272,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
inference(ennf_transformation,[],[f142]) ).
fof(f273,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(ennf_transformation,[],[f143]) ).
fof(f274,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(flattening,[],[f273]) ).
fof(f275,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(ennf_transformation,[],[f144]) ).
fof(f276,plain,
! [X0] :
? [X1] :
( ! [X4] :
( ~ in(X4,X1)
| in(powerset(X4),X1) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,X1)
| in(X3,X1) )
& in(X0,X1) ),
inference(ennf_transformation,[],[f254]) ).
fof(f277,plain,
! [X0] :
? [X1] :
( ! [X4] :
( ~ in(X4,X1)
| in(powerset(X4),X1) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,X1)
| in(X3,X1) )
& in(X0,X1) ),
inference(flattening,[],[f276]) ).
fof(f278,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) ),
inference(ennf_transformation,[],[f146]) ).
fof(f279,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) ) ),
inference(ennf_transformation,[],[f147]) ).
fof(f280,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_image(X1,X0),relation_rng(X1)) ),
inference(ennf_transformation,[],[f148]) ).
fof(f281,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ~ subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(ennf_transformation,[],[f150]) ).
fof(f282,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ~ subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(flattening,[],[f281]) ).
fof(f283,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
inference(ennf_transformation,[],[f151]) ).
fof(f284,plain,
! [X0] :
( ~ relation(X0)
| relation_image(X0,relation_dom(X0)) = relation_rng(X0) ),
inference(ennf_transformation,[],[f152]) ).
fof(f285,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f153]) ).
fof(f286,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) ) ),
inference(ennf_transformation,[],[f154]) ).
fof(f287,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
inference(ennf_transformation,[],[f155]) ).
fof(f288,plain,
! [X0,X1] :
( ~ relation(X1)
| empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0 ),
inference(ennf_transformation,[],[f156]) ).
fof(f289,plain,
! [X0,X1] :
( ~ relation(X1)
| empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0 ),
inference(flattening,[],[f288]) ).
fof(f290,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ subset(X0,X1)
| subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(ennf_transformation,[],[f157]) ).
fof(f291,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ subset(X0,X1)
| subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(flattening,[],[f290]) ).
fof(f292,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(ennf_transformation,[],[f159]) ).
fof(f293,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(flattening,[],[f292]) ).
fof(f294,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f162]) ).
fof(f295,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f294]) ).
fof(f298,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
inference(ennf_transformation,[],[f165]) ).
fof(f299,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
inference(flattening,[],[f298]) ).
fof(f300,plain,
! [X0] :
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(ennf_transformation,[],[f166]) ).
fof(f301,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ),
inference(ennf_transformation,[],[f167]) ).
fof(f302,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ),
inference(flattening,[],[f301]) ).
fof(f303,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ),
inference(ennf_transformation,[],[f168]) ).
fof(f304,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ),
inference(flattening,[],[f303]) ).
fof(f305,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(X0,X1)
| ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) ) ) ),
inference(ennf_transformation,[],[f169]) ).
fof(f306,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(X0,X1)
| ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) ) ) ),
inference(flattening,[],[f305]) ).
fof(f307,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
inference(ennf_transformation,[],[f170]) ).
fof(f308,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(ennf_transformation,[],[f171]) ).
fof(f309,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ),
inference(ennf_transformation,[],[f176]) ).
fof(f310,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ),
inference(flattening,[],[f309]) ).
fof(f311,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(ennf_transformation,[],[f177]) ).
fof(f312,plain,
! [X0,X1,X2,X3] :
( ordered_pair(X2,X3) != ordered_pair(X0,X1)
| ( X1 = X3
& X0 = X2 ) ),
inference(ennf_transformation,[],[f178]) ).
fof(f313,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(ennf_transformation,[],[f179]) ).
fof(f314,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(flattening,[],[f313]) ).
fof(f315,plain,
! [X0,X1] :
( ~ in(X1,X0)
| apply(identity_relation(X0),X1) = X1 ),
inference(ennf_transformation,[],[f180]) ).
fof(f316,plain,
! [X0] :
( ~ relation(X0)
| ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f182]) ).
fof(f317,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X0) ) )
& ( ? [X2] :
( in(X2,X1)
& in(X2,X0) )
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f246]) ).
fof(f318,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(ennf_transformation,[],[f191]) ).
fof(f319,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| ! [X2] :
( ~ element(X2,powerset(X0))
| ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
inference(ennf_transformation,[],[f193]) ).
fof(f320,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f194]) ).
fof(f321,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ) ),
inference(ennf_transformation,[],[f195]) ).
fof(f323,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ),
inference(ennf_transformation,[],[f197]) ).
fof(f324,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ),
inference(flattening,[],[f323]) ).
fof(f325,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set != complements_of_subsets(X0,X1)
| empty_set = X1 ),
inference(ennf_transformation,[],[f198]) ).
fof(f326,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set != complements_of_subsets(X0,X1)
| empty_set = X1 ),
inference(flattening,[],[f325]) ).
fof(f327,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(ennf_transformation,[],[f199]) ).
fof(f328,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(relation_dom(X0),relation_rng(X1))
| relation_rng(relation_composition(X1,X0)) = relation_rng(X0) ) ),
inference(ennf_transformation,[],[f200]) ).
fof(f329,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(relation_dom(X0),relation_rng(X1))
| relation_rng(relation_composition(X1,X0)) = relation_rng(X0) ) ),
inference(flattening,[],[f328]) ).
fof(f330,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ),
inference(ennf_transformation,[],[f201]) ).
fof(f331,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ),
inference(flattening,[],[f330]) ).
fof(f332,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ),
inference(ennf_transformation,[],[f202]) ).
fof(f333,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ),
inference(flattening,[],[f332]) ).
fof(f334,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
& ( ? [X2] : in(X2,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f247]) ).
fof(f335,plain,
! [X0] :
( empty_set = X0
| ! [X1] :
( ~ element(X1,powerset(X0))
| ! [X2] :
( ~ element(X2,X0)
| in(X2,X1)
| in(X2,subset_complement(X0,X1)) ) ) ),
inference(ennf_transformation,[],[f207]) ).
fof(f336,plain,
! [X0] :
( empty_set = X0
| ! [X1] :
( ~ element(X1,powerset(X0))
| ! [X2] :
( ~ element(X2,X0)
| in(X2,X1)
| in(X2,subset_complement(X0,X1)) ) ) ),
inference(flattening,[],[f335]) ).
fof(f337,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = function_inverse(X0)
<=> ( ! [X2,X3] :
( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ),
inference(ennf_transformation,[],[f208]) ).
fof(f338,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = function_inverse(X0)
<=> ( ! [X2,X3] :
( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ),
inference(flattening,[],[f337]) ).
fof(f339,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(ennf_transformation,[],[f209]) ).
fof(f340,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(flattening,[],[f339]) ).
fof(f341,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f210]) ).
fof(f342,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ),
inference(flattening,[],[f341]) ).
fof(f343,plain,
! [X0] :
( ~ relation(X0)
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f211]) ).
fof(f344,plain,
! [X0] :
( ~ relation(X0)
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| X0 = empty_set ),
inference(flattening,[],[f343]) ).
fof(f345,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ( X0 = apply(relation_composition(function_inverse(X1),X1),X0)
& X0 = apply(X1,apply(function_inverse(X1),X0)) ) ),
inference(ennf_transformation,[],[f212]) ).
fof(f346,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ( X0 = apply(relation_composition(function_inverse(X1),X1),X0)
& X0 = apply(X1,apply(function_inverse(X1),X0)) ) ),
inference(flattening,[],[f345]) ).
fof(f347,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f215]) ).
fof(f348,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| one_to_one(function_inverse(X0)) ),
inference(ennf_transformation,[],[f216]) ).
fof(f349,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| one_to_one(function_inverse(X0)) ),
inference(flattening,[],[f348]) ).
fof(f350,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(ennf_transformation,[],[f217]) ).
fof(f351,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(flattening,[],[f350]) ).
fof(f352,plain,
! [X0] :
( ~ relation(X0)
| ( empty_set != relation_rng(X0)
& relation_dom(X0) != empty_set )
| X0 = empty_set ),
inference(ennf_transformation,[],[f218]) ).
fof(f353,plain,
! [X0] :
( ~ relation(X0)
| ( empty_set != relation_rng(X0)
& relation_dom(X0) != empty_set )
| X0 = empty_set ),
inference(flattening,[],[f352]) ).
fof(f354,plain,
! [X0] :
( ~ relation(X0)
| ( relation_dom(X0) = empty_set
<=> relation_rng(X0) = empty_set ) ),
inference(ennf_transformation,[],[f219]) ).
fof(f355,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f221]) ).
fof(f356,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
inference(flattening,[],[f355]) ).
fof(f357,plain,
! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(ennf_transformation,[],[f224]) ).
fof(f358,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(ennf_transformation,[],[f225]) ).
fof(f359,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(flattening,[],[f358]) ).
fof(f360,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(ennf_transformation,[],[f227]) ).
fof(f361,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(flattening,[],[f360]) ).
fof(f362,plain,
! [X0,X1,X2,X3] :
( ~ relation(X3)
| ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f228]) ).
fof(f363,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
inference(ennf_transformation,[],[f232]) ).
fof(f364,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_dom_restriction(X1,X0),X1) ),
inference(ennf_transformation,[],[f233]) ).
fof(f365,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(ordered_pair(X0,X1),X2)
<=> ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) ) ),
inference(ennf_transformation,[],[f235]) ).
fof(f366,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(ordered_pair(X0,X1),X2)
<=> ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) ) ),
inference(flattening,[],[f365]) ).
fof(f367,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(set_union2(X0,X2),X1) ),
inference(ennf_transformation,[],[f236]) ).
fof(f368,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(set_union2(X0,X2),X1) ),
inference(flattening,[],[f367]) ).
fof(f369,plain,
! [X0,X1,X2] :
( singleton(X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(ennf_transformation,[],[f237]) ).
fof(f370,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
inference(ennf_transformation,[],[f238]) ).
fof(f371,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(ennf_transformation,[],[f239]) ).
fof(f372,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
inference(ennf_transformation,[],[f240]) ).
fof(f373,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
inference(ennf_transformation,[],[f241]) ).
fof(f374,plain,
! [X0,X1,X2] :
( singleton(X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(ennf_transformation,[],[f244]) ).
fof(f375,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f174]) ).
fof(f376,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f223]) ).
fof(f377,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f378,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f379,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X1,X0)) ),
inference(ennf_transformation,[],[f92]) ).
fof(f380,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(ennf_transformation,[],[f89]) ).
fof(f381,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_union2(X0,X1)) ),
inference(ennf_transformation,[],[f87]) ).
fof(f382,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_union2(X0,X1)) ),
inference(flattening,[],[f381]) ).
fof(f383,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(ennf_transformation,[],[f134]) ).
fof(f384,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f213]) ).
fof(f385,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f205]) ).
fof(f386,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f385]) ).
fof(f389,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f161]) ).
fof(f390,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f122]) ).
fof(f391,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( element(X1,X0)
<=> empty(X1) ) )
& ( empty(X0)
| ( element(X1,X0)
<=> in(X1,X0) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f392,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| union_of_subsets(X0,X1) = union(X1) ),
inference(ennf_transformation,[],[f130]) ).
fof(f393,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f394,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f395,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( subset(X0,X1)
<=> ! [X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) ) ) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f396,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f397,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f398,plain,
! [X0,X1] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(ennf_transformation,[],[f95]) ).
fof(f399,plain,
! [X0,X1] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(flattening,[],[f398]) ).
fof(f400,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f401,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f93]) ).
fof(f402,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(flattening,[],[f401]) ).
fof(f403,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f71]) ).
fof(f404,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f405,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f98]) ).
fof(f406,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f96]) ).
fof(f407,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f406]) ).
fof(f408,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f73]) ).
fof(f409,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( X2 = relation_rng_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f410,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f99]) ).
fof(f411,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(ennf_transformation,[],[f97]) ).
fof(f412,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(flattening,[],[f411]) ).
fof(f413,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(ennf_transformation,[],[f82]) ).
fof(f414,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(flattening,[],[f413]) ).
fof(f415,plain,
! [X0] :
? [X1] :
( ! [X4] :
( ? [X5] :
( ! [X6] :
( ~ subset(X6,X4)
| in(X6,X5) )
& in(X5,X1) )
| ~ in(X4,X1) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,X1)
| in(X3,X1) )
& in(X0,X1) ),
inference(ennf_transformation,[],[f255]) ).
fof(f416,plain,
! [X0] :
? [X1] :
( ! [X4] :
( ? [X5] :
( ! [X6] :
( ~ subset(X6,X4)
| in(X6,X5) )
& in(X5,X1) )
| ~ in(X4,X1) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,X1)
| in(X3,X1) )
& in(X0,X1) ),
inference(flattening,[],[f415]) ).
fof(f417,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f418,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,[],[f12]) ).
fof(f419,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,[],[f418]) ).
fof(f420,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f421,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,[],[f14]) ).
fof(f422,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,[],[f421]) ).
fof(f423,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f100]) ).
fof(f424,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f423]) ).
fof(f425,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f426,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f425]) ).
fof(f427,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
inference(ennf_transformation,[],[f77]) ).
fof(f428,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
inference(flattening,[],[f427]) ).
fof(f429,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f66]) ).
fof(f430,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f429]) ).
fof(f431,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f432,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f433,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(flattening,[],[f432]) ).
fof(f434,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(ennf_transformation,[],[f38]) ).
fof(f435,plain,
! [X0,X1] :
( ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f436,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(ennf_transformation,[],[f104]) ).
fof(f437,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f90]) ).
fof(f438,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) ) ),
inference(flattening,[],[f437]) ).
fof(f439,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f78]) ).
fof(f440,plain,
! [X0] :
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(ennf_transformation,[],[f63]) ).
fof(f441,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| function_inverse(X0) = relation_inverse(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f442,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| function_inverse(X0) = relation_inverse(X0) ),
inference(flattening,[],[f441]) ).
fof(f443,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( X1 = relation_inverse(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f444,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f103]) ).
fof(f445,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f60]) ).
fof(f446,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( ~ element(X3,powerset(X0))
| ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f447,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,X1) = set_difference(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f448,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f105]) ).
fof(f449,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f72]) ).
fof(f450,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(union_of_subsets(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f67]) ).
fof(f451,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(meet_of_subsets(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f69]) ).
fof(f452,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(ennf_transformation,[],[f132]) ).
fof(f453,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(flattening,[],[f452]) ).
fof(f454,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_difference(X0,X1,X2),powerset(X0)) ),
inference(ennf_transformation,[],[f70]) ).
fof(f455,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_difference(X0,X1,X2),powerset(X0)) ),
inference(flattening,[],[f454]) ).
fof(f456,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f457,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(flattening,[],[f456]) ).
fof(f458,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f459,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
inference(flattening,[],[f458]) ).
fof(f460,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f461,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(flattening,[],[f460]) ).
fof(f462,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f253]) ).
fof(f463,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(flattening,[],[f462]) ).
fof(f464,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| ~ proper_subset(X1,X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f465,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f234]) ).
fof(f466,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f229]) ).
fof(f467,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f476,plain,
! [X0,X1] :
( ( in(sK1(X0,X1),X0)
& ~ in(sK1(X0,X1),X1) )
| element(X0,powerset(X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f263]) ).
fof(f479,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f135]) ).
fof(f480,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f479]) ).
fof(f481,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ( in(X0,relation_rng(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) ) ),
inference(nnf_transformation,[],[f267]) ).
fof(f482,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ( in(X0,relation_rng(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) ) ),
inference(flattening,[],[f481]) ).
fof(f483,plain,
! [X0] :
( ! [X4] :
( ~ in(X4,sK2(X0))
| in(powerset(X4),sK2(X0)) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,sK2(X0))
| in(X3,sK2(X0)) )
& in(X0,sK2(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f277]) ).
fof(f484,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_image(X2,X1))
| ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) )
| in(X0,relation_image(X2,X1)) ) ) ),
inference(nnf_transformation,[],[f279]) ).
fof(f485,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_image(X2,X1))
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) )
| in(X0,relation_image(X2,X1)) ) ) ),
inference(rectify,[],[f484]) ).
fof(f486,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_image(X2,X1))
| ( in(sK3(X0,X1,X2),X1)
& in(ordered_pair(sK3(X0,X1,X2),X0),X2)
& in(sK3(X0,X1,X2),relation_dom(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) )
| in(X0,relation_image(X2,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X1,X2))],[f485]) ).
fof(f487,plain,
( function(sK5)
& relation(sK5)
& ~ subset(relation_image(sK5,relation_inverse_image(sK5,sK4)),sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f282]) ).
fof(f488,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_inverse_image(X2,X1))
| ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) )
| in(X0,relation_inverse_image(X2,X1)) ) ) ),
inference(nnf_transformation,[],[f286]) ).
fof(f489,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_inverse_image(X2,X1))
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) )
| in(X0,relation_inverse_image(X2,X1)) ) ) ),
inference(rectify,[],[f488]) ).
fof(f490,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_inverse_image(X2,X1))
| ( in(sK6(X0,X1,X2),X1)
& in(ordered_pair(X0,sK6(X0,X1,X2)),X2)
& in(sK6(X0,X1,X2),relation_rng(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) )
| in(X0,relation_inverse_image(X2,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X4,sK6(X0,X1,X2))],[f489]) ).
fof(f491,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
& ( ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| in(X0,relation_dom(relation_composition(X2,X1))) ) ) ) ),
inference(nnf_transformation,[],[f299]) ).
fof(f492,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
& ( ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| in(X0,relation_dom(relation_composition(X2,X1))) ) ) ) ),
inference(flattening,[],[f491]) ).
fof(f493,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(nnf_transformation,[],[f314]) ).
fof(f494,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(flattening,[],[f493]) ).
fof(f495,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(rectify,[],[f494]) ).
fof(f496,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ( in(sK7(X0,X1),X0)
& sK7(X0,X1) != apply(X1,sK7(X0,X1)) )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f495]) ).
fof(f497,plain,
! [X0,X1] :
( ( empty_set != set_difference(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f183]) ).
fof(f498,plain,
! [X0,X1] :
( ( ~ subset(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f184]) ).
fof(f499,plain,
! [X0,X1,X2] :
( ( ~ subset(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f185]) ).
fof(f500,plain,
! [X0,X1,X2] :
( ( ~ subset(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f499]) ).
fof(f501,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f187]) ).
fof(f502,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f501]) ).
fof(f503,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X0) ) )
& ( ( in(sK8(X0,X1),X1)
& in(sK8(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f317]) ).
fof(f504,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| ! [X2] :
( ~ element(X2,powerset(X0))
| ( ( ~ disjoint(X1,X2)
| subset(X1,subset_complement(X0,X2)) )
& ( ~ subset(X1,subset_complement(X0,X2))
| disjoint(X1,X2) ) ) ) ),
inference(nnf_transformation,[],[f319]) ).
fof(f505,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
& ( in(sK9(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f334]) ).
fof(f509,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X2,X3] :
( sP0(X0,X2,X3,X1)
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ? [X2,X3] :
( ~ sP0(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_rng(X0) != relation_dom(X1)
| X1 = function_inverse(X0) ) ) ) ),
inference(nnf_transformation,[],[f469]) ).
fof(f510,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X2,X3] :
( sP0(X0,X2,X3,X1)
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ? [X2,X3] :
( ~ sP0(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_rng(X0) != relation_dom(X1)
| X1 = function_inverse(X0) ) ) ) ),
inference(flattening,[],[f509]) ).
fof(f511,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X4,X5] :
( sP0(X0,X4,X5,X1)
& ( apply(X1,X4) != X5
| ~ in(X4,relation_rng(X0))
| ( apply(X0,X5) = X4
& in(X5,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ? [X2,X3] :
( ~ sP0(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_rng(X0) != relation_dom(X1)
| X1 = function_inverse(X0) ) ) ) ),
inference(rectify,[],[f510]) ).
fof(f512,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X4,X5] :
( sP0(X0,X4,X5,X1)
& ( apply(X1,X4) != X5
| ~ in(X4,relation_rng(X0))
| ( apply(X0,X5) = X4
& in(X5,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ~ sP0(X0,sK10(X0,X1),sK11(X0,X1),X1)
| ( sK11(X0,X1) = apply(X1,sK10(X0,X1))
& in(sK10(X0,X1),relation_rng(X0))
& ( sK10(X0,X1) != apply(X0,sK11(X0,X1))
| ~ in(sK11(X0,X1),relation_dom(X0)) ) )
| relation_rng(X0) != relation_dom(X1)
| X1 = function_inverse(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X2,sK10(X0,X1)),skolemize(X3,sK11(X0,X1))],[f511]) ).
fof(f513,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK12(X0),sK13(X0)),X0)
| X0 = empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0))],[f344]) ).
fof(f514,plain,
! [X0] :
( ~ relation(X0)
| ( ( relation_dom(X0) != empty_set
| relation_rng(X0) = empty_set )
& ( empty_set != relation_rng(X0)
| relation_dom(X0) = empty_set ) ) ),
inference(nnf_transformation,[],[f354]) ).
fof(f515,plain,
! [X0,X1] :
( ( set_difference(X0,singleton(X1)) != X0
| ~ in(X1,X0) )
& ( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ) ),
inference(nnf_transformation,[],[f220]) ).
fof(f516,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(nnf_transformation,[],[f356]) ).
fof(f517,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(flattening,[],[f516]) ).
fof(f518,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(rectify,[],[f517]) ).
fof(f519,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ( in(sK14(X1,X2),relation_dom(X1))
& apply(X1,sK14(X1,X2)) != apply(X2,sK14(X1,X2)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X1,X2))],[f518]) ).
fof(f520,plain,
! [X0,X1,X2,X3] :
( ~ relation(X3)
| ( ( ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) )
& ( ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ) ) ),
inference(nnf_transformation,[],[f362]) ).
fof(f521,plain,
! [X0,X1,X2,X3] :
( ~ relation(X3)
| ( ( ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) )
& ( ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ) ) ),
inference(flattening,[],[f520]) ).
fof(f522,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 )
& ( set_difference(X0,X1) != X0
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f231]) ).
fof(f523,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) ) ),
inference(nnf_transformation,[],[f363]) ).
fof(f524,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) ) ),
inference(flattening,[],[f523]) ).
fof(f525,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(ordered_pair(X0,X1),X2)
| ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) )
& ( apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| in(ordered_pair(X0,X1),X2) ) ) ),
inference(nnf_transformation,[],[f366]) ).
fof(f526,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(ordered_pair(X0,X1),X2)
| ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) )
& ( apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| in(ordered_pair(X0,X1),X2) ) ) ),
inference(flattening,[],[f525]) ).
fof(f527,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f375]) ).
fof(f528,plain,
! [X0,X1] :
( ( ( in(sK15(X0,X1),X0)
| in(sK15(X0,X1),X1) )
& ( ~ in(sK15(X0,X1),X0)
| ~ in(sK15(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X2,sK15(X0,X1))],[f527]) ).
fof(f529,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f530,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f529]) ).
fof(f531,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK16(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X1,sK16(X0))],[f530]) ).
fof(f532,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f533,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f532]) ).
fof(f534,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK17(X0,X1),X1)
| sK17(X0,X1) = X0 )
& ( ~ in(sK17(X0,X1),X1)
| sK17(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X2,sK17(X0,X1))],[f533]) ).
fof(f535,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,[],[f377]) ).
fof(f536,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,[],[f535]) ).
fof(f537,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK18(X0,X1),X0)
& ~ in(sK18(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X2,sK18(X0,X1))],[f536]) ).
fof(f538,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f539,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(flattening,[],[f538]) ).
fof(f540,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(rectify,[],[f539]) ).
fof(f541,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK19(X0,X1,X2),X2)
| in(sK19(X0,X1,X2),X1)
| in(sK19(X0,X1,X2),X0) )
& ( ~ in(sK19(X0,X1,X2),X2)
| ( ~ in(sK19(X0,X1,X2),X1)
& ~ in(sK19(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X3,sK19(X0,X1,X2))],[f540]) ).
fof(f542,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set )
& ( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f543,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f544,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f543]) ).
fof(f545,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f546,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) ) ),
inference(flattening,[],[f545]) ).
fof(f547,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) ) ),
inference(rectify,[],[f546]) ).
fof(f548,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& in(X4,X0) ) )
& ( in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK20(X0,X1,X2),X2)
| ( ~ in(sK20(X0,X1,X2),X1)
& in(sK20(X0,X1,X2),X0) ) )
& ( ~ in(sK20(X0,X1,X2),X2)
| in(sK20(X0,X1,X2),X1)
| ~ in(sK20(X0,X1,X2),X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X3,sK20(X0,X1,X2))],[f547]) ).
fof(f549,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f189]) ).
fof(f550,plain,
! [X0] :
( empty(sK21(X0))
& element(sK21(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X1,sK21(X0))],[f126]) ).
fof(f551,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK22(X0))
& element(sK22(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X1,sK22(X0))],[f390]) ).
fof(f552,plain,
! [X0] : element(sK23(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X1,sK23(X0))],[f76]) ).
fof(f553,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( ( ~ element(X1,X0)
| empty(X1) )
& ( ~ empty(X1)
| element(X1,X0) ) ) )
& ( empty(X0)
| ( ( ~ element(X1,X0)
| in(X1,X0) )
& ( ~ in(X1,X0)
| element(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f391]) ).
fof(f554,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| subset(X2,X0) )
& ( ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f555,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(rectify,[],[f554]) ).
fof(f556,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK24(X0,X1),X1)
| subset(sK24(X0,X1),X0) )
& ( ~ in(sK24(X0,X1),X1)
| ~ subset(sK24(X0,X1),X0) ) )
| X1 = powerset(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(X2,sK24(X0,X1))],[f555]) ).
fof(f557,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f558,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( in(X7,X0)
& in(X5,X7) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( in(X4,X0)
& in(X2,X4) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(rectify,[],[f557]) ).
fof(f559,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK27(X0,X5),X0)
& in(X5,sK27(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK25(X0,X1),X1)
| ( in(sK26(X0,X1),X0)
& in(sK25(X0,X1),sK26(X0,X1)) ) )
& ( ~ in(sK25(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK25(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26,sK27]),skolemize(X2,sK25(X0,X1)),skolemize(X4,sK26(X0,X1)),skolemize(X7,sK27(X0,X5))],[f558]) ).
fof(f560,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f393]) ).
fof(f561,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X7,X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X4,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f560]) ).
fof(f562,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK30(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK28(X0,X1),X1)
| in(ordered_pair(sK29(X0,X1),sK28(X0,X1)),X0) )
& ( ~ in(sK28(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK28(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29,sK30]),skolemize(X2,sK28(X0,X1)),skolemize(X4,sK29(X0,X1)),skolemize(X7,sK30(X0,X5))],[f561]) ).
fof(f563,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(nnf_transformation,[],[f394]) ).
fof(f564,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X5,X7),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X2,X4),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(rectify,[],[f563]) ).
fof(f565,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK33(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK31(X0,X1),X1)
| in(ordered_pair(sK31(X0,X1),sK32(X0,X1)),X0) )
& ( ~ in(sK31(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK31(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31,sK32,sK33]),skolemize(X2,sK31(X0,X1)),skolemize(X4,sK32(X0,X1)),skolemize(X7,sK33(X0,X5))],[f564]) ).
fof(f566,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( ~ subset(X0,X1)
| ! [X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) ) )
& ( ? [X2,X3] :
( in(ordered_pair(X2,X3),X0)
& ~ in(ordered_pair(X2,X3),X1) )
| subset(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f395]) ).
fof(f567,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( ~ subset(X0,X1)
| ! [X4,X5] :
( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X1) ) )
& ( ? [X2,X3] :
( in(ordered_pair(X2,X3),X0)
& ~ in(ordered_pair(X2,X3),X1) )
| subset(X0,X1) ) ) ) ),
inference(rectify,[],[f566]) ).
fof(f568,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( ~ subset(X0,X1)
| ! [X4,X5] :
( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X1) ) )
& ( ( in(ordered_pair(sK34(X0,X1),sK35(X0,X1)),X0)
& ~ in(ordered_pair(sK34(X0,X1),sK35(X0,X1)),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34,sK35]),skolemize(X2,sK34(X0,X1)),skolemize(X3,sK35(X0,X1))],[f567]) ).
fof(f569,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( X0 != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| X0 = X1 ) ) ) ),
inference(nnf_transformation,[],[f396]) ).
fof(f570,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( X0 != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X1) )
& ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X4,X5),X0) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| X0 = X1 ) ) ) ),
inference(rectify,[],[f569]) ).
fof(f571,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( X0 != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X1) )
& ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X4,X5),X0) ) ) )
& ( ( ( in(ordered_pair(sK36(X0,X1),sK37(X0,X1)),X0)
| in(ordered_pair(sK36(X0,X1),sK37(X0,X1)),X1) )
& ( ~ in(ordered_pair(sK36(X0,X1),sK37(X0,X1)),X0)
| ~ in(ordered_pair(sK36(X0,X1),sK37(X0,X1)),X1) ) )
| X0 = X1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36,sK37]),skolemize(X2,sK36(X0,X1)),skolemize(X3,sK37(X0,X1))],[f570]) ).
fof(f572,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) )
& ( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
| relation(X0) ) ),
inference(nnf_transformation,[],[f397]) ).
fof(f573,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) ) )
& ( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
| relation(X0) ) ),
inference(rectify,[],[f572]) ).
fof(f574,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X4] :
( ordered_pair(sK39(X4),sK40(X4)) = X4
| ~ in(X4,X0) ) )
& ( ( ! [X2,X3] : ordered_pair(X2,X3) != sK38(X0)
& in(sK38(X0),X0) )
| relation(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38,sK39,sK40]),skolemize(X1,sK38(X0)),skolemize(X5,sK39(X4)),skolemize(X6,sK40(X4))],[f573]) ).
fof(f575,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) )
& ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f576,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X8] :
( ( ~ in(X8,X2)
| ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) ) )
& ( ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) )
| in(X8,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(rectify,[],[f575]) ).
fof(f577,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X8] :
( ( ~ in(X8,X2)
| ( ordered_pair(sK44(X0,X1,X8),sK45(X0,X1,X8)) = X8
& in(sK45(X0,X1,X8),X1)
& in(sK44(X0,X1,X8),X0) ) )
& ( ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) )
| in(X8,X2) ) ) )
& ( ( ( in(sK41(X0,X1,X2),X2)
| ( sK41(X0,X1,X2) = ordered_pair(sK42(X0,X1,X2),sK43(X0,X1,X2))
& in(sK43(X0,X1,X2),X1)
& in(sK42(X0,X1,X2),X0) ) )
& ( ~ in(sK41(X0,X1,X2),X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != sK41(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41,sK42,sK43,sK44,sK45]),skolemize(X3,sK41(X0,X1,X2)),skolemize(X6,sK42(X0,X1,X2)),skolemize(X7,sK43(X0,X1,X2)),skolemize(X11,sK44(X0,X1,X8)),skolemize(X12,sK45(X0,X1,X8))],[f576]) ).
fof(f578,plain,
( function(sK46)
& empty(sK46)
& relation(sK46) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(X0,sK46)],[f124]) ).
fof(f579,plain,
( function(sK47)
& relation(sK47) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(X0,sK47)],[f120]) ).
fof(f580,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f404]) ).
fof(f581,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(flattening,[],[f580]) ).
fof(f582,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) ) )
& ( ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(rectify,[],[f581]) ).
fof(f583,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) ) )
& ( ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ( ( in(ordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),X2)
| ( in(ordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),X0)
& in(sK48(X0,X1,X2),X1) ) )
& ( ~ in(ordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),X0)
| ~ in(sK48(X0,X1,X2),X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48,sK49]),skolemize(X3,sK48(X0,X1,X2)),skolemize(X4,sK49(X0,X1,X2))],[f582]) ).
fof(f584,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f585,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f584]) ).
fof(f586,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(rectify,[],[f585]) ).
fof(f587,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ( ( in(sK50(X0,X1,X2),X2)
| sK50(X0,X1,X2) = X1
| sK50(X0,X1,X2) = X0 )
& ( ~ in(sK50(X0,X1,X2),X2)
| ( sK50(X0,X1,X2) != X1
& sK50(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(X3,sK50(X0,X1,X2))],[f586]) ).
fof(f588,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f409]) ).
fof(f589,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(flattening,[],[f588]) ).
fof(f590,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X1)
& in(X6,X0) ) )
& ( ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(rectify,[],[f589]) ).
fof(f591,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X1)
& in(X6,X0) ) )
& ( ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ( ( in(ordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),X2)
| ( in(ordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),X1)
& in(sK52(X0,X1,X2),X0) ) )
& ( ~ in(ordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),X1)
| ~ in(sK52(X0,X1,X2),X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51,sK52]),skolemize(X3,sK51(X0,X1,X2)),skolemize(X4,sK52(X0,X1,X2))],[f590]) ).
fof(f592,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,[],[f29]) ).
fof(f593,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,[],[f592]) ).
fof(f594,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,[],[f593]) ).
fof(f595,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(sK53(X0,X1,X2),X2)
| ( in(sK53(X0,X1,X2),X1)
& in(sK53(X0,X1,X2),X0) ) )
& ( ~ in(sK53(X0,X1,X2),X2)
| ~ in(sK53(X0,X1,X2),X1)
| ~ in(sK53(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(X3,sK53(X0,X1,X2))],[f594]) ).
fof(f596,plain,
! [X0] :
( ! [X4] :
( ( ! [X6] :
( ~ subset(X6,X4)
| in(X6,sK55(X0,X4)) )
& in(sK55(X0,X4),sK54(X0)) )
| ~ in(X4,sK54(X0)) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,sK54(X0))
| in(X3,sK54(X0)) )
& in(X0,sK54(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54,sK55]),skolemize(X1,sK54(X0)),skolemize(X5,sK55(X0,X4))],[f416]) ).
fof(f597,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) )
& ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f417]) ).
fof(f598,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(rectify,[],[f597]) ).
fof(f599,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK58(X0,X1,X6),X1)
& in(ordered_pair(sK58(X0,X1,X6),X6),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK56(X0,X1,X2),X2)
| ( in(sK57(X0,X1,X2),X1)
& in(ordered_pair(sK57(X0,X1,X2),sK56(X0,X1,X2)),X0) ) )
& ( ~ in(sK56(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK56(X0,X1,X2)),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56,sK57,sK58]),skolemize(X3,sK56(X0,X1,X2)),skolemize(X5,sK57(X0,X1,X2)),skolemize(X8,sK58(X0,X1,X6))],[f598]) ).
fof(f600,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,[],[f419]) ).
fof(f601,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,[],[f600]) ).
fof(f602,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( apply(X0,sK61(X0,X1,X6)) = X6
& in(sK61(X0,X1,X6),X1)
& in(sK61(X0,X1,X6),relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ( ( in(sK59(X0,X1,X2),X2)
| ( sK59(X0,X1,X2) = apply(X0,sK60(X0,X1,X2))
& in(sK60(X0,X1,X2),X1)
& in(sK60(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK59(X0,X1,X2),X2)
| ! [X4] :
( apply(X0,X4) != sK59(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59,sK60,sK61]),skolemize(X3,sK59(X0,X1,X2)),skolemize(X5,sK60(X0,X1,X2)),skolemize(X8,sK61(X0,X1,X6))],[f601]) ).
fof(f603,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f420]) ).
fof(f604,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X6,X8),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( in(X5,X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f603]) ).
fof(f605,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK64(X0,X1,X6),X1)
& in(ordered_pair(X6,sK64(X0,X1,X6)),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK62(X0,X1,X2),X2)
| ( in(sK63(X0,X1,X2),X1)
& in(ordered_pair(sK62(X0,X1,X2),sK63(X0,X1,X2)),X0) ) )
& ( ~ in(sK62(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK62(X0,X1,X2),X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62,sK63,sK64]),skolemize(X3,sK62(X0,X1,X2)),skolemize(X5,sK63(X0,X1,X2)),skolemize(X8,sK64(X0,X1,X6))],[f604]) ).
fof(f606,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,[],[f422]) ).
fof(f607,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,[],[f606]) ).
fof(f608,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,[],[f607]) ).
fof(f609,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(sK65(X0,X1,X2),X2)
| ( in(apply(X0,sK65(X0,X1,X2)),X1)
& in(sK65(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK65(X0,X1,X2),X2)
| ~ in(apply(X0,sK65(X0,X1,X2)),X1)
| ~ in(sK65(X0,X1,X2),relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(X3,sK65(X0,X1,X2))],[f608]) ).
fof(f610,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f431]) ).
fof(f611,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X2)
| ? [X10] :
( in(ordered_pair(X10,X8),X1)
& in(ordered_pair(X7,X10),X0) ) )
& ( ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) )
| in(ordered_pair(X7,X8),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ? [X6] :
( in(ordered_pair(X6,X4),X1)
& in(ordered_pair(X3,X6),X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(rectify,[],[f610]) ).
fof(f612,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X2)
| ( in(ordered_pair(sK69(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK69(X0,X1,X7,X8)),X0) ) )
& ( ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) )
| in(ordered_pair(X7,X8),X2) ) ) )
& ( ( ( in(ordered_pair(sK66(X0,X1,X2),sK67(X0,X1,X2)),X2)
| ( in(ordered_pair(sK68(X0,X1,X2),sK67(X0,X1,X2)),X1)
& in(ordered_pair(sK66(X0,X1,X2),sK68(X0,X1,X2)),X0) ) )
& ( ~ in(ordered_pair(sK66(X0,X1,X2),sK67(X0,X1,X2)),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,sK67(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK66(X0,X1,X2),X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66,sK67,sK68,sK69]),skolemize(X3,sK66(X0,X1,X2)),skolemize(X4,sK67(X0,X1,X2)),skolemize(X6,sK68(X0,X1,X2)),skolemize(X10,sK69(X0,X1,X7,X8))],[f611]) ).
fof(f613,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| X2 = empty_set )
& ( empty_set != X2
| X2 = apply(X0,X1) ) ) )
& ( ~ in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| in(ordered_pair(X1,X2),X0) )
& ( ~ in(ordered_pair(X1,X2),X0)
| X2 = apply(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f433]) ).
fof(f614,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( X2 != X3
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(nnf_transformation,[],[f435]) ).
fof(f615,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( X2 != X3
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(flattening,[],[f614]) ).
fof(f616,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| ( X4 = X5
& in(X4,X0) ) )
& ( X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(rectify,[],[f615]) ).
fof(f617,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| ( X4 = X5
& in(X4,X0) ) )
& ( X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ( ( in(ordered_pair(sK70(X0,X1),sK71(X0,X1)),X1)
| ( sK70(X0,X1) = sK71(X0,X1)
& in(sK70(X0,X1),X0) ) )
& ( ~ in(ordered_pair(sK70(X0,X1),sK71(X0,X1)),X1)
| sK70(X0,X1) != sK71(X0,X1)
| ~ in(sK70(X0,X1),X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70,sK71]),skolemize(X2,sK70(X0,X1)),skolemize(X3,sK71(X0,X1))],[f616]) ).
fof(f618,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( relation_inverse(X0) != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X0) )
& ( ~ in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X0) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_inverse(X0) ) ) ) ),
inference(nnf_transformation,[],[f443]) ).
fof(f619,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( relation_inverse(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X5,X4),X0) )
& ( ~ in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X0) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_inverse(X0) ) ) ) ),
inference(rectify,[],[f618]) ).
fof(f620,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( relation_inverse(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X5,X4),X0) )
& ( ~ in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ( ( in(ordered_pair(sK72(X0,X1),sK73(X0,X1)),X1)
| in(ordered_pair(sK73(X0,X1),sK72(X0,X1)),X0) )
& ( ~ in(ordered_pair(sK72(X0,X1),sK73(X0,X1)),X1)
| ~ in(ordered_pair(sK73(X0,X1),sK72(X0,X1)),X0) ) )
| X1 = relation_inverse(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72,sK73]),skolemize(X2,sK72(X0,X1)),skolemize(X3,sK73(X0,X1))],[f619]) ).
fof(f621,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X3] :
( ~ element(X3,powerset(X0))
| ( ( ~ in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(subset_complement(X0,X3),X1)
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f446]) ).
fof(f622,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X3] :
( ~ element(X3,powerset(X0))
| ( ( ~ in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(subset_complement(X0,X3),X1)
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(flattening,[],[f621]) ).
fof(f623,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X4] :
( ~ element(X4,powerset(X0))
| ( ( ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) )
& ( ~ in(subset_complement(X0,X4),X1)
| in(X4,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(rectify,[],[f622]) ).
fof(f624,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X4] :
( ~ element(X4,powerset(X0))
| ( ( ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) )
& ( ~ in(subset_complement(X0,X4),X1)
| in(X4,X2) ) ) ) )
& ( ( element(sK74(X0,X1,X2),powerset(X0))
& ( in(sK74(X0,X1,X2),X2)
| in(subset_complement(X0,sK74(X0,X1,X2)),X1) )
& ( ~ in(sK74(X0,X1,X2),X2)
| ~ in(subset_complement(X0,sK74(X0,X1,X2)),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(X3,sK74(X0,X1,X2))],[f623]) ).
fof(f625,plain,
( one_to_one(sK75)
& function(sK75)
& relation(sK75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(X0,sK75)],[f128]) ).
fof(f626,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(nnf_transformation,[],[f457]) ).
fof(f627,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(rectify,[],[f626]) ).
fof(f628,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ( apply(X0,sK76(X0)) = apply(X0,sK77(X0))
& in(sK77(X0),relation_dom(X0))
& in(sK76(X0),relation_dom(X0))
& sK76(X0) != sK77(X0) )
| one_to_one(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76,sK77]),skolemize(X1,sK76(X0)),skolemize(X2,sK77(X0))],[f627]) ).
fof(f629,plain,
~ empty(sK78),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(X0,sK78)],[f127]) ).
fof(f630,plain,
( relation(sK79)
& ~ empty(sK79) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(X0,sK79)],[f125]) ).
fof(f631,plain,
empty(sK80),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(X0,sK80)],[f123]) ).
fof(f632,plain,
( relation(sK81)
& empty(sK81) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(X0,sK81)],[f121]) ).
fof(f633,plain,
! [X0] : empty_set != singleton(X0),
inference(cnf_transformation,[],[f107]) ).
fof(f635,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f257]) ).
fof(f636,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f258]) ).
fof(f642,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f650,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f476]) ).
fof(f651,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f476]) ).
fof(f655,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f480]) ).
fof(f656,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f480]) ).
fof(f658,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f266]) ).
fof(f659,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| in(X0,relation_rng(X2)) ),
inference(cnf_transformation,[],[f482]) ).
fof(f660,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f482]) ).
fof(f661,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f482]) ).
fof(f662,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f663,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng_restriction(X0,X1),X1) ),
inference(cnf_transformation,[],[f269]) ).
fof(f664,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
inference(cnf_transformation,[],[f270]) ).
fof(f665,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
inference(cnf_transformation,[],[f271]) ).
fof(f666,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f271]) ).
fof(f667,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
inference(cnf_transformation,[],[f272]) ).
fof(f668,plain,
! [X2,X3,X0,X1] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(cnf_transformation,[],[f274]) ).
fof(f669,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f275]) ).
fof(f670,plain,
! [X0,X4] :
( ~ in(X4,sK2(X0))
| in(powerset(X4),sK2(X0)) ),
inference(cnf_transformation,[],[f483]) ).
fof(f671,plain,
! [X2,X3,X0] :
( ~ subset(X3,X2)
| ~ in(X2,sK2(X0))
| in(X3,sK2(X0)) ),
inference(cnf_transformation,[],[f483]) ).
fof(f672,plain,
! [X0] : in(X0,sK2(X0)),
inference(cnf_transformation,[],[f483]) ).
fof(f673,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) ),
inference(cnf_transformation,[],[f278]) ).
fof(f674,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(sK3(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f486]) ).
fof(f675,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(ordered_pair(sK3(X0,X1,X2),X0),X2) ),
inference(cnf_transformation,[],[f486]) ).
fof(f676,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(sK3(X0,X1,X2),relation_dom(X2)) ),
inference(cnf_transformation,[],[f486]) ).
fof(f678,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_image(X1,X0),relation_rng(X1)) ),
inference(cnf_transformation,[],[f280]) ).
fof(f679,plain,
function(sK5),
inference(cnf_transformation,[],[f487]) ).
fof(f680,plain,
relation(sK5),
inference(cnf_transformation,[],[f487]) ).
fof(f681,plain,
~ subset(relation_image(sK5,relation_inverse_image(sK5,sK4)),sK4),
inference(cnf_transformation,[],[f487]) ).
fof(f682,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
inference(cnf_transformation,[],[f283]) ).
fof(f683,plain,
! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_image(X0,relation_dom(X0)) ),
inference(cnf_transformation,[],[f284]) ).
fof(f684,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ),
inference(cnf_transformation,[],[f285]) ).
fof(f685,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(sK6(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f490]) ).
fof(f686,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(ordered_pair(X0,sK6(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f490]) ).
fof(f687,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(sK6(X0,X1,X2),relation_rng(X2)) ),
inference(cnf_transformation,[],[f490]) ).
fof(f689,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f287]) ).
fof(f690,plain,
! [X0,X1] :
( ~ relation(X1)
| empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0 ),
inference(cnf_transformation,[],[f289]) ).
fof(f691,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ subset(X0,X1)
| subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(cnf_transformation,[],[f291]) ).
fof(f693,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f293]) ).
fof(f694,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f295]) ).
fof(f695,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[],[f163]) ).
fof(f698,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| in(apply(X2,X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f492]) ).
fof(f699,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f492]) ).
fof(f700,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| in(X0,relation_dom(relation_composition(X2,X1))) ),
inference(cnf_transformation,[],[f492]) ).
fof(f701,plain,
! [X0] :
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(cnf_transformation,[],[f300]) ).
fof(f702,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ),
inference(cnf_transformation,[],[f302]) ).
fof(f703,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf_transformation,[],[f304]) ).
fof(f704,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(X0,X1)
| subset(relation_rng(X0),relation_rng(X1)) ),
inference(cnf_transformation,[],[f306]) ).
fof(f705,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(X0,X1)
| subset(relation_dom(X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f306]) ).
fof(f706,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f307]) ).
fof(f707,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f308]) ).
fof(f708,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f175]) ).
fof(f709,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_field(X2)) ),
inference(cnf_transformation,[],[f310]) ).
fof(f710,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f310]) ).
fof(f711,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f311]) ).
fof(f712,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) != ordered_pair(X0,X1)
| X1 = X3 ),
inference(cnf_transformation,[],[f312]) ).
fof(f713,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) != ordered_pair(X0,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f312]) ).
fof(f716,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| in(sK7(X0,X1),X0)
| relation_dom(X1) != X0
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f496]) ).
fof(f717,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| sK7(X0,X1) != apply(X1,sK7(X0,X1))
| relation_dom(X1) != X0
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f496]) ).
fof(f718,plain,
! [X0,X1] :
( ~ in(X1,X0)
| apply(identity_relation(X0),X1) = X1 ),
inference(cnf_transformation,[],[f315]) ).
fof(f719,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f181]) ).
fof(f720,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) = relation_rng(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f316]) ).
fof(f721,plain,
! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_dom(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f316]) ).
fof(f722,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f497]) ).
fof(f723,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f497]) ).
fof(f725,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f498]) ).
fof(f726,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f500]) ).
fof(f727,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f500]) ).
fof(f728,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f500]) ).
fof(f729,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f186]) ).
fof(f730,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f502]) ).
fof(f733,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,X1)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f503]) ).
fof(f734,plain,
! [X0,X1] :
( in(sK8(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f503]) ).
fof(f735,plain,
! [X0,X1] :
( in(sK8(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f503]) ).
fof(f736,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f318]) ).
fof(f737,plain,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(cnf_transformation,[],[f192]) ).
fof(f738,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| ~ disjoint(X1,X2)
| subset(X1,subset_complement(X0,X2)) ),
inference(cnf_transformation,[],[f504]) ).
fof(f739,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| ~ subset(X1,subset_complement(X0,X2))
| disjoint(X1,X2) ),
inference(cnf_transformation,[],[f504]) ).
fof(f740,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ),
inference(cnf_transformation,[],[f320]) ).
fof(f741,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ),
inference(cnf_transformation,[],[f321]) ).
fof(f743,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(X0) = relation_dom(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f324]) ).
fof(f744,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set != complements_of_subsets(X0,X1)
| empty_set = X1 ),
inference(cnf_transformation,[],[f326]) ).
fof(f745,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(cnf_transformation,[],[f327]) ).
fof(f746,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(relation_dom(X0),relation_rng(X1))
| relation_rng(X0) = relation_rng(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f329]) ).
fof(f747,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f748,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ),
inference(cnf_transformation,[],[f333]) ).
fof(f749,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f203]) ).
fof(f750,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f505]) ).
fof(f751,plain,
! [X0,X1] :
( in(sK9(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f505]) ).
fof(f752,plain,
! [X2,X0,X1] :
( empty_set = X0
| ~ element(X1,powerset(X0))
| ~ element(X2,X0)
| in(X2,X1)
| in(X2,subset_complement(X0,X1)) ),
inference(cnf_transformation,[],[f336]) ).
fof(f758,plain,
! [X0,X1,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| function_inverse(X0) != X1
| sP0(X0,X4,X5,X1) ),
inference(cnf_transformation,[],[f512]) ).
fof(f760,plain,
! [X0,X1,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| function_inverse(X0) != X1
| apply(X1,X4) != X5
| ~ in(X4,relation_rng(X0))
| in(X5,relation_dom(X0)) ),
inference(cnf_transformation,[],[f512]) ).
fof(f762,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ sP0(X0,sK10(X0,X1),sK11(X0,X1),X1)
| sK11(X0,X1) = apply(X1,sK10(X0,X1))
| relation_rng(X0) != relation_dom(X1)
| function_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f512]) ).
fof(f763,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ sP0(X0,sK10(X0,X1),sK11(X0,X1),X1)
| in(sK10(X0,X1),relation_rng(X0))
| relation_rng(X0) != relation_dom(X1)
| function_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f512]) ).
fof(f764,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ sP0(X0,sK10(X0,X1),sK11(X0,X1),X1)
| sK10(X0,X1) != apply(X0,sK11(X0,X1))
| ~ in(sK11(X0,X1),relation_dom(X0))
| relation_rng(X0) != relation_dom(X1)
| function_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f512]) ).
fof(f765,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(cnf_transformation,[],[f340]) ).
fof(f766,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_dom(X0) = relation_rng(function_inverse(X0)) ),
inference(cnf_transformation,[],[f342]) ).
fof(f767,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(cnf_transformation,[],[f342]) ).
fof(f768,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK12(X0),sK13(X0)),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f513]) ).
fof(f769,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| apply(relation_composition(function_inverse(X1),X1),X0) = X0 ),
inference(cnf_transformation,[],[f346]) ).
fof(f770,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| apply(X1,apply(function_inverse(X1),X0)) = X0 ),
inference(cnf_transformation,[],[f346]) ).
fof(f771,plain,
empty_set = relation_rng(empty_set),
inference(cnf_transformation,[],[f214]) ).
fof(f772,plain,
empty_set = relation_dom(empty_set),
inference(cnf_transformation,[],[f214]) ).
fof(f773,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f347]) ).
fof(f774,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| one_to_one(function_inverse(X0)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f775,plain,
! [X2,X0,X1] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(cnf_transformation,[],[f351]) ).
fof(f776,plain,
! [X0] :
( ~ relation(X0)
| empty_set != relation_rng(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f353]) ).
fof(f777,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) != empty_set
| empty_set = X0 ),
inference(cnf_transformation,[],[f353]) ).
fof(f778,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) != empty_set
| empty_set = relation_rng(X0) ),
inference(cnf_transformation,[],[f514]) ).
fof(f779,plain,
! [X0] :
( ~ relation(X0)
| empty_set != relation_rng(X0)
| relation_dom(X0) = empty_set ),
inference(cnf_transformation,[],[f514]) ).
fof(f780,plain,
! [X0,X1] :
( set_difference(X0,singleton(X1)) != X0
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f515]) ).
fof(f781,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ),
inference(cnf_transformation,[],[f515]) ).
fof(f784,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| in(sK14(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) = X1 ),
inference(cnf_transformation,[],[f519]) ).
fof(f785,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| apply(X1,sK14(X1,X2)) != apply(X2,sK14(X1,X2))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) = X1 ),
inference(cnf_transformation,[],[f519]) ).
fof(f786,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f222]) ).
fof(f787,plain,
! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f357]) ).
fof(f788,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(cnf_transformation,[],[f359]) ).
fof(f789,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f226]) ).
fof(f790,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f226]) ).
fof(f791,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(cnf_transformation,[],[f361]) ).
fof(f792,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| in(ordered_pair(X0,X1),X3) ),
inference(cnf_transformation,[],[f521]) ).
fof(f793,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f521]) ).
fof(f794,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ),
inference(cnf_transformation,[],[f521]) ).
fof(f795,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f230]) ).
fof(f796,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 ),
inference(cnf_transformation,[],[f522]) ).
fof(f797,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f522]) ).
fof(f798,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f524]) ).
fof(f799,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f524]) ).
fof(f800,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ),
inference(cnf_transformation,[],[f524]) ).
fof(f801,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_dom_restriction(X1,X0),X1) ),
inference(cnf_transformation,[],[f364]) ).
fof(f802,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| apply(X2,X0) = X1 ),
inference(cnf_transformation,[],[f526]) ).
fof(f804,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f526]) ).
fof(f805,plain,
! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(set_union2(X0,X2),X1) ),
inference(cnf_transformation,[],[f368]) ).
fof(f806,plain,
! [X2,X0,X1] :
( singleton(X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f369]) ).
fof(f807,plain,
! [X0,X1] :
( ~ relation(X1)
| set_intersection2(relation_dom(X1),X0) = relation_dom(relation_dom_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f370]) ).
fof(f808,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(cnf_transformation,[],[f371]) ).
fof(f809,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
inference(cnf_transformation,[],[f372]) ).
fof(f810,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
inference(cnf_transformation,[],[f373]) ).
fof(f811,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f242]) ).
fof(f812,plain,
! [X2,X0,X1] :
( singleton(X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f374]) ).
fof(f813,plain,
! [X0,X1] :
( in(sK15(X0,X1),X0)
| in(sK15(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f528]) ).
fof(f814,plain,
! [X0,X1] :
( ~ in(sK15(X0,X1),X0)
| ~ in(sK15(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f528]) ).
fof(f815,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f376]) ).
fof(f816,plain,
relation(empty_set),
inference(cnf_transformation,[],[f94]) ).
fof(f818,plain,
empty(empty_set),
inference(cnf_transformation,[],[f84]) ).
fof(f819,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f531]) ).
fof(f820,plain,
! [X0] :
( in(sK16(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f531]) ).
fof(f822,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f534]) ).
fof(f824,plain,
! [X0,X1] :
( in(sK17(X0,X1),X1)
| sK17(X0,X1) = X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f534]) ).
fof(f825,plain,
! [X0,X1] :
( ~ in(sK17(X0,X1),X1)
| sK17(X0,X1) != X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f534]) ).
fof(f826,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f537]) ).
fof(f827,plain,
! [X0,X1] :
( in(sK18(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f537]) ).
fof(f828,plain,
! [X0,X1] :
( ~ in(sK18(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f537]) ).
fof(f829,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f378]) ).
fof(f830,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f160]) ).
fof(f831,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f248]) ).
fof(f832,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X1,X0)) ),
inference(cnf_transformation,[],[f379]) ).
fof(f833,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f380]) ).
fof(f834,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f382]) ).
fof(f835,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f541]) ).
fof(f836,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f837,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f838,plain,
! [X2,X0,X1] :
( in(sK19(X0,X1,X2),X2)
| in(sK19(X0,X1,X2),X1)
| in(sK19(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f541]) ).
fof(f839,plain,
! [X2,X0,X1] :
( ~ in(sK19(X0,X1,X2),X2)
| ~ in(sK19(X0,X1,X2),X1)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f541]) ).
fof(f840,plain,
! [X2,X0,X1] :
( ~ in(sK19(X0,X1,X2),X2)
| ~ in(sK19(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f541]) ).
fof(f841,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f842,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f383]) ).
fof(f843,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f542]) ).
fof(f844,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f542]) ).
fof(f846,plain,
! [X0,X1] :
( X0 != X1
| subset(X1,X0) ),
inference(cnf_transformation,[],[f544]) ).
fof(f848,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f544]) ).
fof(f849,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f204]) ).
fof(f850,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f188]) ).
fof(f851,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| ~ in(X4,X1) ),
inference(cnf_transformation,[],[f548]) ).
fof(f852,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f548]) ).
fof(f853,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f548]) ).
fof(f854,plain,
! [X2,X0,X1] :
( in(sK20(X0,X1,X2),X2)
| ~ in(sK20(X0,X1,X2),X1)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f548]) ).
fof(f855,plain,
! [X2,X0,X1] :
( in(sK20(X0,X1,X2),X2)
| in(sK20(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f548]) ).
fof(f856,plain,
! [X2,X0,X1] :
( ~ in(sK20(X0,X1,X2),X2)
| in(sK20(X0,X1,X2),X1)
| ~ in(sK20(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f548]) ).
fof(f857,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f384]) ).
fof(f858,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f386]) ).
fof(f859,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f549]) ).
fof(f860,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f549]) ).
fof(f862,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f389]) ).
fof(f863,plain,
! [X0] : empty(sK21(X0)),
inference(cnf_transformation,[],[f550]) ).
fof(f864,plain,
! [X0] : element(sK21(X0),powerset(X0)),
inference(cnf_transformation,[],[f550]) ).
fof(f865,plain,
! [X0] :
( empty(X0)
| ~ empty(sK22(X0)) ),
inference(cnf_transformation,[],[f551]) ).
fof(f866,plain,
! [X0] :
( empty(X0)
| element(sK22(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f551]) ).
fof(f867,plain,
! [X0] : element(sK23(X0),X0),
inference(cnf_transformation,[],[f552]) ).
fof(f868,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ element(X1,X0)
| empty(X1) ),
inference(cnf_transformation,[],[f553]) ).
fof(f869,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| element(X1,X0) ),
inference(cnf_transformation,[],[f553]) ).
fof(f870,plain,
! [X0,X1] :
( empty(X0)
| ~ element(X1,X0)
| in(X1,X0) ),
inference(cnf_transformation,[],[f553]) ).
fof(f872,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f83]) ).
fof(f873,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f556]) ).
fof(f874,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f556]) ).
fof(f875,plain,
! [X0,X1] :
( in(sK24(X0,X1),X1)
| subset(sK24(X0,X1),X0)
| powerset(X0) = X1 ),
inference(cnf_transformation,[],[f556]) ).
fof(f876,plain,
! [X0,X1] :
( ~ in(sK24(X0,X1),X1)
| ~ subset(sK24(X0,X1),X0)
| powerset(X0) = X1 ),
inference(cnf_transformation,[],[f556]) ).
fof(f877,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| union_of_subsets(X0,X1) = union(X1) ),
inference(cnf_transformation,[],[f392]) ).
fof(f878,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(sK27(X0,X5),X0) ),
inference(cnf_transformation,[],[f559]) ).
fof(f879,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(X5,sK27(X0,X5)) ),
inference(cnf_transformation,[],[f559]) ).
fof(f880,plain,
! [X0,X1,X6,X5] :
( union(X0) != X1
| ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,X1) ),
inference(cnf_transformation,[],[f559]) ).
fof(f881,plain,
! [X0,X1] :
( in(sK25(X0,X1),X1)
| in(sK26(X0,X1),X0)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f559]) ).
fof(f882,plain,
! [X0,X1] :
( in(sK25(X0,X1),X1)
| in(sK25(X0,X1),sK26(X0,X1))
| union(X0) = X1 ),
inference(cnf_transformation,[],[f559]) ).
fof(f883,plain,
! [X3,X0,X1] :
( ~ in(sK25(X0,X1),X1)
| ~ in(X3,X0)
| ~ in(sK25(X0,X1),X3)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f559]) ).
fof(f885,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK30(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f562]) ).
fof(f886,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f562]) ).
fof(f887,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK28(X0,X1),X1)
| in(ordered_pair(sK29(X0,X1),sK28(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f562]) ).
fof(f888,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK28(X0,X1),X1)
| ~ in(ordered_pair(X3,sK28(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f562]) ).
fof(f889,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK33(X0,X5)),X0) ),
inference(cnf_transformation,[],[f565]) ).
fof(f890,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f565]) ).
fof(f891,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK31(X0,X1),X1)
| in(ordered_pair(sK31(X0,X1),sK32(X0,X1)),X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f565]) ).
fof(f892,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK31(X0,X1),X1)
| ~ in(ordered_pair(sK31(X0,X1),X3),X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f565]) ).
fof(f894,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK34(X0,X1),sK35(X0,X1)),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f568]) ).
fof(f895,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK34(X0,X1),sK35(X0,X1)),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f568]) ).
fof(f898,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK36(X0,X1),sK37(X0,X1)),X0)
| in(ordered_pair(sK36(X0,X1),sK37(X0,X1)),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f571]) ).
fof(f899,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK36(X0,X1),sK37(X0,X1)),X0)
| ~ in(ordered_pair(sK36(X0,X1),sK37(X0,X1)),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f571]) ).
fof(f900,plain,
! [X0,X4] :
( ~ relation(X0)
| ordered_pair(sK39(X4),sK40(X4)) = X4
| ~ in(X4,X0) ),
inference(cnf_transformation,[],[f574]) ).
fof(f901,plain,
! [X2,X3,X0] :
( ordered_pair(X2,X3) != sK38(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f574]) ).
fof(f902,plain,
! [X0] :
( in(sK38(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[],[f574]) ).
fof(f903,plain,
! [X0,X1] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f399]) ).
fof(f904,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| ordered_pair(sK44(X0,X1,X8),sK45(X0,X1,X8)) = X8 ),
inference(cnf_transformation,[],[f577]) ).
fof(f905,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK45(X0,X1,X8),X1) ),
inference(cnf_transformation,[],[f577]) ).
fof(f906,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK44(X0,X1,X8),X0) ),
inference(cnf_transformation,[],[f577]) ).
fof(f907,plain,
! [X2,X10,X0,X1,X8,X9] :
( cartesian_product2(X0,X1) != X2
| ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(X8,X2) ),
inference(cnf_transformation,[],[f577]) ).
fof(f908,plain,
! [X2,X0,X1] :
( in(sK41(X0,X1,X2),X2)
| sK41(X0,X1,X2) = ordered_pair(sK42(X0,X1,X2),sK43(X0,X1,X2))
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f577]) ).
fof(f909,plain,
! [X2,X0,X1] :
( in(sK41(X0,X1,X2),X2)
| in(sK43(X0,X1,X2),X1)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f577]) ).
fof(f910,plain,
! [X2,X0,X1] :
( in(sK41(X0,X1,X2),X2)
| in(sK42(X0,X1,X2),X0)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f577]) ).
fof(f911,plain,
! [X2,X0,X1,X4,X5] :
( ~ in(sK41(X0,X1,X2),X2)
| ordered_pair(X4,X5) != sK41(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f577]) ).
fof(f912,plain,
function(sK46),
inference(cnf_transformation,[],[f578]) ).
fof(f913,plain,
empty(sK46),
inference(cnf_transformation,[],[f578]) ).
fof(f914,plain,
relation(sK46),
inference(cnf_transformation,[],[f578]) ).
fof(f915,plain,
function(sK47),
inference(cnf_transformation,[],[f579]) ).
fof(f916,plain,
relation(sK47),
inference(cnf_transformation,[],[f579]) ).
fof(f917,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f400]) ).
fof(f918,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f402]) ).
fof(f920,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f403]) ).
fof(f921,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(ordered_pair(X5,X6),X0) ),
inference(cnf_transformation,[],[f583]) ).
fof(f922,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(X5,X1) ),
inference(cnf_transformation,[],[f583]) ).
fof(f923,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ),
inference(cnf_transformation,[],[f583]) ).
fof(f924,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(ordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),X2)
| in(ordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),X0)
| relation_dom_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f583]) ).
fof(f925,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(ordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),X2)
| in(sK48(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f583]) ).
fof(f926,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| ~ in(ordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),X0)
| ~ in(sK48(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f583]) ).
fof(f927,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_dom(X0)) ),
inference(cnf_transformation,[],[f405]) ).
fof(f928,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f405]) ).
fof(f929,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f407]) ).
fof(f930,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f91]) ).
fof(f931,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f37]) ).
fof(f932,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| ~ in(X4,X2)
| X1 = X4
| X0 = X4 ),
inference(cnf_transformation,[],[f587]) ).
fof(f933,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X1 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f587]) ).
fof(f934,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f587]) ).
fof(f935,plain,
! [X2,X0,X1] :
( in(sK50(X0,X1,X2),X2)
| sK50(X0,X1,X2) = X1
| sK50(X0,X1,X2) = X0
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f587]) ).
fof(f936,plain,
! [X2,X0,X1] :
( ~ in(sK50(X0,X1,X2),X2)
| sK50(X0,X1,X2) != X1
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f587]) ).
fof(f937,plain,
! [X2,X0,X1] :
( ~ in(sK50(X0,X1,X2),X2)
| sK50(X0,X1,X2) != X0
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f587]) ).
fof(f938,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f939,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f408]) ).
fof(f940,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(ordered_pair(X5,X6),X1) ),
inference(cnf_transformation,[],[f591]) ).
fof(f941,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(X6,X0) ),
inference(cnf_transformation,[],[f591]) ).
fof(f942,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ),
inference(cnf_transformation,[],[f591]) ).
fof(f943,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),X2)
| in(ordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),X1)
| relation_rng_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f591]) ).
fof(f944,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),X2)
| in(sK52(X0,X1,X2),X0)
| relation_rng_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f591]) ).
fof(f945,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),X1)
| ~ in(sK52(X0,X1,X2),X0)
| relation_rng_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f591]) ).
fof(f946,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_rng(X0)) ),
inference(cnf_transformation,[],[f410]) ).
fof(f947,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f410]) ).
fof(f948,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f412]) ).
fof(f949,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f172]) ).
fof(f951,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f414]) ).
fof(f952,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f595]) ).
fof(f954,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f595]) ).
fof(f955,plain,
! [X2,X0,X1] :
( in(sK53(X0,X1,X2),X2)
| in(sK53(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f595]) ).
fof(f956,plain,
! [X2,X0,X1] :
( in(sK53(X0,X1,X2),X2)
| in(sK53(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f595]) ).
fof(f957,plain,
! [X2,X0,X1] :
( ~ in(sK53(X0,X1,X2),X2)
| ~ in(sK53(X0,X1,X2),X1)
| ~ in(sK53(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f595]) ).
fof(f958,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f959,plain,
! [X0,X6,X4] :
( ~ subset(X6,X4)
| in(X6,sK55(X0,X4))
| ~ in(X4,sK54(X0)) ),
inference(cnf_transformation,[],[f596]) ).
fof(f960,plain,
! [X0,X4] :
( in(sK55(X0,X4),sK54(X0))
| ~ in(X4,sK54(X0)) ),
inference(cnf_transformation,[],[f596]) ).
fof(f961,plain,
! [X2,X3,X0] :
( ~ subset(X3,X2)
| ~ in(X2,sK54(X0))
| in(X3,sK54(X0)) ),
inference(cnf_transformation,[],[f596]) ).
fof(f962,plain,
! [X0] : in(X0,sK54(X0)),
inference(cnf_transformation,[],[f596]) ).
fof(f963,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK58(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f599]) ).
fof(f964,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(ordered_pair(sK58(X0,X1,X6),X6),X0) ),
inference(cnf_transformation,[],[f599]) ).
fof(f965,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f599]) ).
fof(f966,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK56(X0,X1,X2),X2)
| in(sK57(X0,X1,X2),X1)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f599]) ).
fof(f967,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK56(X0,X1,X2),X2)
| in(ordered_pair(sK57(X0,X1,X2),sK56(X0,X1,X2)),X0)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f599]) ).
fof(f968,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK56(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK56(X0,X1,X2)),X0)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f599]) ).
fof(f969,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| apply(X0,sK61(X0,X1,X6)) = X6 ),
inference(cnf_transformation,[],[f602]) ).
fof(f970,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK61(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f602]) ).
fof(f971,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK61(X0,X1,X6),relation_dom(X0)) ),
inference(cnf_transformation,[],[f602]) ).
fof(f972,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,[],[f602]) ).
fof(f973,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK59(X0,X1,X2),X2)
| sK59(X0,X1,X2) = apply(X0,sK60(X0,X1,X2))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f602]) ).
fof(f974,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK59(X0,X1,X2),X2)
| in(sK60(X0,X1,X2),X1)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f602]) ).
fof(f975,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK59(X0,X1,X2),X2)
| in(sK60(X0,X1,X2),relation_dom(X0))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f602]) ).
fof(f976,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK59(X0,X1,X2),X2)
| apply(X0,X4) != sK59(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f602]) ).
fof(f977,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK64(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f605]) ).
fof(f978,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(ordered_pair(X6,sK64(X0,X1,X6)),X0) ),
inference(cnf_transformation,[],[f605]) ).
fof(f979,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f605]) ).
fof(f980,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK62(X0,X1,X2),X2)
| in(sK63(X0,X1,X2),X1)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f605]) ).
fof(f981,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK62(X0,X1,X2),X2)
| in(ordered_pair(sK62(X0,X1,X2),sK63(X0,X1,X2)),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f605]) ).
fof(f982,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK62(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(ordered_pair(sK62(X0,X1,X2),X4),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f605]) ).
fof(f983,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,[],[f609]) ).
fof(f984,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,[],[f609]) ).
fof(f985,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,[],[f609]) ).
fof(f986,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK65(X0,X1,X2),X2)
| in(apply(X0,sK65(X0,X1,X2)),X1)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f609]) ).
fof(f987,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK65(X0,X1,X2),X2)
| in(sK65(X0,X1,X2),relation_dom(X0))
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f609]) ).
fof(f988,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK65(X0,X1,X2),X2)
| ~ in(apply(X0,sK65(X0,X1,X2)),X1)
| ~ in(sK65(X0,X1,X2),relation_dom(X0))
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f609]) ).
fof(f989,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f424]) ).
fof(f990,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| empty(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f424]) ).
fof(f991,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f426]) ).
fof(f992,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f426]) ).
fof(f993,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f428]) ).
fof(f994,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| empty(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f428]) ).
fof(f995,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f430]) ).
fof(f996,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X7,X8),X2)
| in(ordered_pair(sK69(X0,X1,X7,X8),X8),X1) ),
inference(cnf_transformation,[],[f612]) ).
fof(f997,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X7,X8),X2)
| in(ordered_pair(X7,sK69(X0,X1,X7,X8)),X0) ),
inference(cnf_transformation,[],[f612]) ).
fof(f998,plain,
! [X2,X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0)
| in(ordered_pair(X7,X8),X2) ),
inference(cnf_transformation,[],[f612]) ).
fof(f999,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK66(X0,X1,X2),sK67(X0,X1,X2)),X2)
| in(ordered_pair(sK68(X0,X1,X2),sK67(X0,X1,X2)),X1)
| relation_composition(X0,X1) = X2 ),
inference(cnf_transformation,[],[f612]) ).
fof(f1000,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK66(X0,X1,X2),sK67(X0,X1,X2)),X2)
| in(ordered_pair(sK66(X0,X1,X2),sK68(X0,X1,X2)),X0)
| relation_composition(X0,X1) = X2 ),
inference(cnf_transformation,[],[f612]) ).
fof(f1001,plain,
! [X2,X0,X1,X5] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sK66(X0,X1,X2),sK67(X0,X1,X2)),X2)
| ~ in(ordered_pair(X5,sK67(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK66(X0,X1,X2),X5),X0)
| relation_composition(X0,X1) = X2 ),
inference(cnf_transformation,[],[f612]) ).
fof(f1002,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| empty_set = X2 ),
inference(cnf_transformation,[],[f613]) ).
fof(f1006,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(cnf_transformation,[],[f434]) ).
fof(f1007,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f1008,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f1009,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f68]) ).
fof(f1010,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(ordered_pair(X4,X5),X1)
| X4 = X5 ),
inference(cnf_transformation,[],[f617]) ).
fof(f1011,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(ordered_pair(X4,X5),X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f617]) ).
fof(f1012,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ),
inference(cnf_transformation,[],[f617]) ).
fof(f1013,plain,
! [X0,X1] :
( ~ relation(X1)
| in(ordered_pair(sK70(X0,X1),sK71(X0,X1)),X1)
| sK70(X0,X1) = sK71(X0,X1)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f617]) ).
fof(f1014,plain,
! [X0,X1] :
( ~ relation(X1)
| in(ordered_pair(sK70(X0,X1),sK71(X0,X1)),X1)
| in(sK70(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f617]) ).
fof(f1015,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(ordered_pair(sK70(X0,X1),sK71(X0,X1)),X1)
| sK70(X0,X1) != sK71(X0,X1)
| ~ in(sK70(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f617]) ).
fof(f1016,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(cnf_transformation,[],[f436]) ).
fof(f1017,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| function(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f438]) ).
fof(f1019,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f439]) ).
fof(f1020,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f439]) ).
fof(f1021,plain,
! [X0] :
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f440]) ).
fof(f1022,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_inverse(X0) = function_inverse(X0) ),
inference(cnf_transformation,[],[f442]) ).
fof(f1023,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X5,X4),X0) ),
inference(cnf_transformation,[],[f620]) ).
fof(f1024,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X1) ),
inference(cnf_transformation,[],[f620]) ).
fof(f1025,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK72(X0,X1),sK73(X0,X1)),X1)
| in(ordered_pair(sK73(X0,X1),sK72(X0,X1)),X0)
| relation_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f620]) ).
fof(f1026,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK72(X0,X1),sK73(X0,X1)),X1)
| ~ in(ordered_pair(sK73(X0,X1),sK72(X0,X1)),X0)
| relation_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f620]) ).
fof(f1027,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f444]) ).
fof(f1028,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f445]) ).
fof(f1029,plain,
! [X2,X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| complements_of_subsets(X0,X1) != X2
| ~ element(X4,powerset(X0))
| ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) ),
inference(cnf_transformation,[],[f624]) ).
fof(f1030,plain,
! [X2,X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| complements_of_subsets(X0,X1) != X2
| ~ element(X4,powerset(X0))
| ~ in(subset_complement(X0,X4),X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f624]) ).
fof(f1031,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| element(sK74(X0,X1,X2),powerset(X0))
| complements_of_subsets(X0,X1) = X2 ),
inference(cnf_transformation,[],[f624]) ).
fof(f1032,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| in(sK74(X0,X1,X2),X2)
| in(subset_complement(X0,sK74(X0,X1,X2)),X1)
| complements_of_subsets(X0,X1) = X2 ),
inference(cnf_transformation,[],[f624]) ).
fof(f1033,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| ~ in(sK74(X0,X1,X2),X2)
| ~ in(subset_complement(X0,sK74(X0,X1,X2)),X1)
| complements_of_subsets(X0,X1) = X2 ),
inference(cnf_transformation,[],[f624]) ).
fof(f1034,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| set_difference(X0,X1) = subset_complement(X0,X1) ),
inference(cnf_transformation,[],[f447]) ).
fof(f1035,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f448]) ).
fof(f1036,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f449]) ).
fof(f1037,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f55]) ).
fof(f1038,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f32]) ).
fof(f1039,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(union_of_subsets(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f450]) ).
fof(f1040,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(meet_of_subsets(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f451]) ).
fof(f1041,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(cnf_transformation,[],[f453]) ).
fof(f1042,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_difference(X0,X1,X2),powerset(X0)) ),
inference(cnf_transformation,[],[f455]) ).
fof(f1043,plain,
one_to_one(sK75),
inference(cnf_transformation,[],[f625]) ).
fof(f1044,plain,
function(sK75),
inference(cnf_transformation,[],[f625]) ).
fof(f1045,plain,
relation(sK75),
inference(cnf_transformation,[],[f625]) ).
fof(f1046,plain,
! [X3,X0,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ),
inference(cnf_transformation,[],[f628]) ).
fof(f1047,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK76(X0)) = apply(X0,sK77(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f628]) ).
fof(f1048,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK77(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f628]) ).
fof(f1049,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK76(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f628]) ).
fof(f1050,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK76(X0) != sK77(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f628]) ).
fof(f1051,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f459]) ).
fof(f1054,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f461]) ).
fof(f1055,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f461]) ).
fof(f1056,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f252]) ).
fof(f1057,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f463]) ).
fof(f1058,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| ~ proper_subset(X1,X0) ),
inference(cnf_transformation,[],[f464]) ).
fof(f1059,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f465]) ).
fof(f1060,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f466]) ).
fof(f1061,plain,
~ empty(sK78),
inference(cnf_transformation,[],[f629]) ).
fof(f1062,plain,
relation(sK79),
inference(cnf_transformation,[],[f630]) ).
fof(f1063,plain,
~ empty(sK79),
inference(cnf_transformation,[],[f630]) ).
fof(f1064,plain,
empty(sK80),
inference(cnf_transformation,[],[f631]) ).
fof(f1065,plain,
relation(sK81),
inference(cnf_transformation,[],[f632]) ).
fof(f1066,plain,
empty(sK81),
inference(cnf_transformation,[],[f632]) ).
fof(f1067,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f467]) ).
fof(f1068,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f931,f786]) ).
fof(f1069,plain,
! [X0] : empty_set != unordered_pair(X0,X0),
inference(definition_unfolding,[],[f633,f786]) ).
fof(f1071,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f635,f786]) ).
fof(f1072,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f636,f786]) ).
fof(f1075,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0) ),
inference(definition_unfolding,[],[f642,f786]) ).
fof(f1083,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f656,f1068]) ).
fof(f1084,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f655,f1068]) ).
fof(f1085,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_rng_restriction(X0,X1)) = set_difference(relation_rng(X1),set_difference(relation_rng(X1),X0)) ),
inference(definition_unfolding,[],[f667,f749]) ).
fof(f1087,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(unordered_pair(unordered_pair(sK3(X0,X1,X2),X0),unordered_pair(sK3(X0,X1,X2),sK3(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f675,f1068]) ).
fof(f1088,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_image(X1,X0) = relation_image(X1,set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0))) ),
inference(definition_unfolding,[],[f682,f749]) ).
fof(f1090,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(unordered_pair(unordered_pair(X0,sK6(X0,X1,X2)),unordered_pair(X0,X0)),X2) ),
inference(definition_unfolding,[],[f686,f1068]) ).
fof(f1092,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(definition_unfolding,[],[f693,f749]) ).
fof(f1093,plain,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(definition_unfolding,[],[f695,f786]) ).
fof(f1096,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2))) ),
inference(definition_unfolding,[],[f706,f749,f749]) ).
fof(f1097,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,set_difference(X0,X1)) = X0 ),
inference(definition_unfolding,[],[f707,f749]) ).
fof(f1098,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X0,relation_field(X2)) ),
inference(definition_unfolding,[],[f710,f1068]) ).
fof(f1099,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X1,relation_field(X2)) ),
inference(definition_unfolding,[],[f709,f1068]) ).
fof(f1100,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| X0 = X2 ),
inference(definition_unfolding,[],[f713,f1068,f1068]) ).
fof(f1101,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| X1 = X3 ),
inference(definition_unfolding,[],[f712,f1068,f1068]) ).
fof(f1102,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f725,f786]) ).
fof(f1106,plain,
! [X0,X1] :
( ~ subset(X0,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = X0
| empty_set = X0 ),
inference(definition_unfolding,[],[f730,f786,f786]) ).
fof(f1107,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(unordered_pair(X0,X0),X1) = X1 ),
inference(definition_unfolding,[],[f745,f786]) ).
fof(f1108,plain,
! [X0,X1] :
( in(sK9(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f751,f749]) ).
fof(f1109,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f750,f749]) ).
fof(f1110,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK12(X0),sK13(X0)),unordered_pair(sK12(X0),sK12(X0))),X0)
| empty_set = X0 ),
inference(definition_unfolding,[],[f768,f1068]) ).
fof(f1111,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) = X0 ),
inference(definition_unfolding,[],[f781,f786]) ).
fof(f1112,plain,
! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) != X0
| ~ in(X1,X0) ),
inference(definition_unfolding,[],[f780,f786]) ).
fof(f1113,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| apply(X1,sK14(X1,X2)) != apply(X2,sK14(X1,X2))
| relation_dom(X1) != set_difference(relation_dom(X2),set_difference(relation_dom(X2),X0))
| relation_dom_restriction(X2,X0) = X1 ),
inference(definition_unfolding,[],[f785,f749]) ).
fof(f1114,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| in(sK14(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_difference(relation_dom(X2),set_difference(relation_dom(X2),X0))
| relation_dom_restriction(X2,X0) = X1 ),
inference(definition_unfolding,[],[f784,f749]) ).
fof(f1116,plain,
! [X0,X1] :
( ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1))
| X0 = X1 ),
inference(definition_unfolding,[],[f787,f786,f786]) ).
fof(f1117,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3)) ),
inference(definition_unfolding,[],[f794,f1068,f1068]) ).
fof(f1118,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f793,f1068]) ).
fof(f1119,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3) ),
inference(definition_unfolding,[],[f792,f1068,f1068]) ).
fof(f1120,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(definition_unfolding,[],[f804,f1068]) ).
fof(f1122,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| apply(X2,X0) = X1 ),
inference(definition_unfolding,[],[f802,f1068]) ).
fof(f1123,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(definition_unfolding,[],[f806,f786]) ).
fof(f1124,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom(relation_dom_restriction(X1,X0)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0)) ),
inference(definition_unfolding,[],[f807,f749]) ).
fof(f1125,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(definition_unfolding,[],[f812,f786]) ).
fof(f1127,plain,
! [X0,X1] :
( ~ in(sK17(X0,X1),X1)
| sK17(X0,X1) != X0
| unordered_pair(X0,X0) = X1 ),
inference(definition_unfolding,[],[f825,f786]) ).
fof(f1128,plain,
! [X0,X1] :
( in(sK17(X0,X1),X1)
| sK17(X0,X1) = X0
| unordered_pair(X0,X0) = X1 ),
inference(definition_unfolding,[],[f824,f786]) ).
fof(f1130,plain,
! [X3,X0,X1] :
( unordered_pair(X0,X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(definition_unfolding,[],[f822,f786]) ).
fof(f1131,plain,
! [X0,X1] :
( empty_set != set_difference(X0,set_difference(X0,X1))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f844,f749]) ).
fof(f1132,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| empty_set = set_difference(X0,set_difference(X0,X1)) ),
inference(definition_unfolding,[],[f843,f749]) ).
fof(f1134,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK28(X0,X1),X1)
| ~ in(unordered_pair(unordered_pair(X3,sK28(X0,X1)),unordered_pair(X3,X3)),X0)
| relation_rng(X0) = X1 ),
inference(definition_unfolding,[],[f888,f1068]) ).
fof(f1135,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK28(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK29(X0,X1),sK28(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X0)
| relation_rng(X0) = X1 ),
inference(definition_unfolding,[],[f887,f1068]) ).
fof(f1136,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(unordered_pair(unordered_pair(X6,X5),unordered_pair(X6,X6)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f886,f1068]) ).
fof(f1137,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(sK30(X0,X5),X5),unordered_pair(sK30(X0,X5),sK30(X0,X5))),X0) ),
inference(definition_unfolding,[],[f885,f1068]) ).
fof(f1138,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK31(X0,X1),X1)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1),X3),unordered_pair(sK31(X0,X1),sK31(X0,X1))),X0)
| relation_dom(X0) = X1 ),
inference(definition_unfolding,[],[f892,f1068]) ).
fof(f1139,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK31(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK31(X0,X1),sK31(X0,X1))),X0)
| relation_dom(X0) = X1 ),
inference(definition_unfolding,[],[f891,f1068]) ).
fof(f1140,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f890,f1068]) ).
fof(f1141,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,sK33(X0,X5)),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f889,f1068]) ).
fof(f1142,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK34(X0,X1),sK35(X0,X1)),unordered_pair(sK34(X0,X1),sK34(X0,X1))),X1)
| subset(X0,X1) ),
inference(definition_unfolding,[],[f895,f1068]) ).
fof(f1143,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK34(X0,X1),sK35(X0,X1)),unordered_pair(sK34(X0,X1),sK34(X0,X1))),X0)
| subset(X0,X1) ),
inference(definition_unfolding,[],[f894,f1068]) ).
fof(f1145,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK36(X0,X1),sK37(X0,X1)),unordered_pair(sK36(X0,X1),sK36(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK36(X0,X1),sK37(X0,X1)),unordered_pair(sK36(X0,X1),sK36(X0,X1))),X1)
| X0 = X1 ),
inference(definition_unfolding,[],[f899,f1068,f1068]) ).
fof(f1146,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK36(X0,X1),sK37(X0,X1)),unordered_pair(sK36(X0,X1),sK36(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK36(X0,X1),sK37(X0,X1)),unordered_pair(sK36(X0,X1),sK36(X0,X1))),X1)
| X0 = X1 ),
inference(definition_unfolding,[],[f898,f1068,f1068]) ).
fof(f1149,plain,
! [X2,X3,X0] :
( sK38(X0) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| relation(X0) ),
inference(definition_unfolding,[],[f901,f1068]) ).
fof(f1150,plain,
! [X0,X4] :
( ~ relation(X0)
| unordered_pair(unordered_pair(sK39(X4),sK40(X4)),unordered_pair(sK39(X4),sK39(X4))) = X4
| ~ in(X4,X0) ),
inference(definition_unfolding,[],[f900,f1068]) ).
fof(f1151,plain,
! [X2,X0,X1,X4,X5] :
( ~ in(sK41(X0,X1,X2),X2)
| sK41(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X1)
| ~ in(X4,X0)
| cartesian_product2(X0,X1) = X2 ),
inference(definition_unfolding,[],[f911,f1068]) ).
fof(f1152,plain,
! [X2,X0,X1] :
( in(sK41(X0,X1,X2),X2)
| sK41(X0,X1,X2) = unordered_pair(unordered_pair(sK42(X0,X1,X2),sK43(X0,X1,X2)),unordered_pair(sK42(X0,X1,X2),sK42(X0,X1,X2)))
| cartesian_product2(X0,X1) = X2 ),
inference(definition_unfolding,[],[f908,f1068]) ).
fof(f1153,plain,
! [X2,X10,X0,X1,X8,X9] :
( cartesian_product2(X0,X1) != X2
| unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(X8,X2) ),
inference(definition_unfolding,[],[f907,f1068]) ).
fof(f1154,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| unordered_pair(unordered_pair(sK44(X0,X1,X8),sK45(X0,X1,X8)),unordered_pair(sK44(X0,X1,X8),sK44(X0,X1,X8))) = X8 ),
inference(definition_unfolding,[],[f904,f1068]) ).
fof(f1155,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),unordered_pair(sK48(X0,X1,X2),sK48(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),unordered_pair(sK48(X0,X1,X2),sK48(X0,X1,X2))),X0)
| ~ in(sK48(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f926,f1068,f1068]) ).
fof(f1156,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),unordered_pair(sK48(X0,X1,X2),sK48(X0,X1,X2))),X2)
| in(sK48(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f925,f1068]) ).
fof(f1157,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),unordered_pair(sK48(X0,X1,X2),sK48(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),unordered_pair(sK48(X0,X1,X2),sK48(X0,X1,X2))),X0)
| relation_dom_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f924,f1068,f1068]) ).
fof(f1158,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2) ),
inference(definition_unfolding,[],[f923,f1068,f1068]) ).
fof(f1159,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| in(X5,X1) ),
inference(definition_unfolding,[],[f922,f1068]) ).
fof(f1160,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f921,f1068,f1068]) ).
fof(f1161,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),unordered_pair(sK51(X0,X1,X2),sK51(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),unordered_pair(sK51(X0,X1,X2),sK51(X0,X1,X2))),X1)
| ~ in(sK52(X0,X1,X2),X0)
| relation_rng_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f945,f1068,f1068]) ).
fof(f1162,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),unordered_pair(sK51(X0,X1,X2),sK51(X0,X1,X2))),X2)
| in(sK52(X0,X1,X2),X0)
| relation_rng_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f944,f1068]) ).
fof(f1163,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),unordered_pair(sK51(X0,X1,X2),sK51(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),unordered_pair(sK51(X0,X1,X2),sK51(X0,X1,X2))),X1)
| relation_rng_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f943,f1068,f1068]) ).
fof(f1164,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1)
| ~ in(X6,X0)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2) ),
inference(definition_unfolding,[],[f942,f1068,f1068]) ).
fof(f1165,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| in(X6,X0) ),
inference(definition_unfolding,[],[f941,f1068]) ).
fof(f1166,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1) ),
inference(definition_unfolding,[],[f940,f1068,f1068]) ).
fof(f1167,plain,
! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)),
inference(definition_unfolding,[],[f949,f749]) ).
fof(f1169,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f951,f749]) ).
fof(f1170,plain,
! [X2,X0,X1] :
( ~ in(sK53(X0,X1,X2),X2)
| ~ in(sK53(X0,X1,X2),X1)
| ~ in(sK53(X0,X1,X2),X0)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f957,f749]) ).
fof(f1171,plain,
! [X2,X0,X1] :
( in(sK53(X0,X1,X2),X2)
| in(sK53(X0,X1,X2),X0)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f956,f749]) ).
fof(f1172,plain,
! [X2,X0,X1] :
( in(sK53(X0,X1,X2),X2)
| in(sK53(X0,X1,X2),X1)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f955,f749]) ).
fof(f1173,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,set_difference(X0,X1)) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(definition_unfolding,[],[f954,f749]) ).
fof(f1175,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,set_difference(X0,X1)) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(definition_unfolding,[],[f952,f749]) ).
fof(f1176,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f958,f749,f749]) ).
fof(f1177,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK56(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(X4,sK56(X0,X1,X2)),unordered_pair(X4,X4)),X0)
| relation_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f968,f1068]) ).
fof(f1178,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK56(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK57(X0,X1,X2),sK56(X0,X1,X2)),unordered_pair(sK57(X0,X1,X2),sK57(X0,X1,X2))),X0)
| relation_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f967,f1068]) ).
fof(f1179,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X0)
| in(X6,X2) ),
inference(definition_unfolding,[],[f965,f1068]) ).
fof(f1180,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(unordered_pair(unordered_pair(sK58(X0,X1,X6),X6),unordered_pair(sK58(X0,X1,X6),sK58(X0,X1,X6))),X0) ),
inference(definition_unfolding,[],[f964,f1068]) ).
fof(f1181,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK62(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(sK62(X0,X1,X2),X4),unordered_pair(sK62(X0,X1,X2),sK62(X0,X1,X2))),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f982,f1068]) ).
fof(f1182,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK62(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK62(X0,X1,X2),sK63(X0,X1,X2)),unordered_pair(sK62(X0,X1,X2),sK62(X0,X1,X2))),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f981,f1068]) ).
fof(f1183,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X0)
| in(X6,X2) ),
inference(definition_unfolding,[],[f979,f1068]) ).
fof(f1184,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(unordered_pair(unordered_pair(X6,sK64(X0,X1,X6)),unordered_pair(X6,X6)),X0) ),
inference(definition_unfolding,[],[f978,f1068]) ).
fof(f1185,plain,
! [X2,X0,X1,X5] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(sK66(X0,X1,X2),sK67(X0,X1,X2)),unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(X5,sK67(X0,X1,X2)),unordered_pair(X5,X5)),X1)
| ~ in(unordered_pair(unordered_pair(sK66(X0,X1,X2),X5),unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2))),X0)
| relation_composition(X0,X1) = X2 ),
inference(definition_unfolding,[],[f1001,f1068,f1068,f1068]) ).
fof(f1186,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK66(X0,X1,X2),sK67(X0,X1,X2)),unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK66(X0,X1,X2),sK68(X0,X1,X2)),unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2))),X0)
| relation_composition(X0,X1) = X2 ),
inference(definition_unfolding,[],[f1000,f1068,f1068]) ).
fof(f1187,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK66(X0,X1,X2),sK67(X0,X1,X2)),unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK68(X0,X1,X2),sK67(X0,X1,X2)),unordered_pair(sK68(X0,X1,X2),sK68(X0,X1,X2))),X1)
| relation_composition(X0,X1) = X2 ),
inference(definition_unfolding,[],[f999,f1068,f1068]) ).
fof(f1188,plain,
! [X2,X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X9,X8),unordered_pair(X9,X9)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X9),unordered_pair(X7,X7)),X0)
| in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2) ),
inference(definition_unfolding,[],[f998,f1068,f1068,f1068]) ).
fof(f1189,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| in(unordered_pair(unordered_pair(X7,sK69(X0,X1,X7,X8)),unordered_pair(X7,X7)),X0) ),
inference(definition_unfolding,[],[f997,f1068,f1068]) ).
fof(f1190,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| in(unordered_pair(unordered_pair(sK69(X0,X1,X7,X8),X8),unordered_pair(sK69(X0,X1,X7,X8),sK69(X0,X1,X7,X8))),X1) ),
inference(definition_unfolding,[],[f996,f1068,f1068]) ).
fof(f1193,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK70(X0,X1),sK71(X0,X1)),unordered_pair(sK70(X0,X1),sK70(X0,X1))),X1)
| sK70(X0,X1) != sK71(X0,X1)
| ~ in(sK70(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f1015,f1068]) ).
fof(f1194,plain,
! [X0,X1] :
( ~ relation(X1)
| in(unordered_pair(unordered_pair(sK70(X0,X1),sK71(X0,X1)),unordered_pair(sK70(X0,X1),sK70(X0,X1))),X1)
| in(sK70(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f1014,f1068]) ).
fof(f1195,plain,
! [X0,X1] :
( ~ relation(X1)
| in(unordered_pair(unordered_pair(sK70(X0,X1),sK71(X0,X1)),unordered_pair(sK70(X0,X1),sK70(X0,X1))),X1)
| sK70(X0,X1) = sK71(X0,X1)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f1013,f1068]) ).
fof(f1196,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| X4 != X5
| ~ in(X4,X0)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1) ),
inference(definition_unfolding,[],[f1012,f1068]) ).
fof(f1197,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| in(X4,X0) ),
inference(definition_unfolding,[],[f1011,f1068]) ).
fof(f1198,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| X4 = X5 ),
inference(definition_unfolding,[],[f1010,f1068]) ).
fof(f1199,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK72(X0,X1),sK73(X0,X1)),unordered_pair(sK72(X0,X1),sK72(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK73(X0,X1),sK72(X0,X1)),unordered_pair(sK73(X0,X1),sK73(X0,X1))),X0)
| relation_inverse(X0) = X1 ),
inference(definition_unfolding,[],[f1026,f1068,f1068]) ).
fof(f1200,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK72(X0,X1),sK73(X0,X1)),unordered_pair(sK72(X0,X1),sK72(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK73(X0,X1),sK72(X0,X1)),unordered_pair(sK73(X0,X1),sK73(X0,X1))),X0)
| relation_inverse(X0) = X1 ),
inference(definition_unfolding,[],[f1025,f1068,f1068]) ).
fof(f1201,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1) ),
inference(definition_unfolding,[],[f1024,f1068,f1068]) ).
fof(f1202,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f1023,f1068,f1068]) ).
fof(f1205,plain,
! [X1] :
( ~ function(X1)
| ~ relation(X1)
| sK7(relation_dom(X1),X1) != apply(X1,sK7(relation_dom(X1),X1))
| identity_relation(relation_dom(X1)) = X1 ),
inference(equality_resolution,[],[f717]) ).
fof(f1206,plain,
! [X1] :
( ~ function(X1)
| ~ relation(X1)
| in(sK7(relation_dom(X1),X1),relation_dom(X1))
| identity_relation(relation_dom(X1)) = X1 ),
inference(equality_resolution,[],[f716]) ).
fof(f1215,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| function_inverse(X0) != X1
| ~ in(X4,relation_rng(X0))
| in(apply(X1,X4),relation_dom(X0)) ),
inference(equality_resolution,[],[f760]) ).
fof(f1216,plain,
! [X0,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ in(X4,relation_rng(X0))
| in(apply(function_inverse(X0),X4),relation_dom(X0)) ),
inference(equality_resolution,[],[f1215]) ).
fof(f1219,plain,
! [X0,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| sP0(X0,X4,X5,function_inverse(X0)) ),
inference(equality_resolution,[],[f758]) ).
fof(f1222,plain,
! [X2,X0] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X2))
| in(unordered_pair(unordered_pair(X0,apply(X2,X0)),unordered_pair(X0,X0)),X2) ),
inference(equality_resolution,[],[f1120]) ).
fof(f1223,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f819]) ).
fof(f1226,plain,
! [X3,X0] :
( ~ in(X3,unordered_pair(X0,X0))
| X0 = X3 ),
inference(equality_resolution,[],[f1130]) ).
fof(f1227,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f837]) ).
fof(f1228,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f836]) ).
fof(f1229,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f835]) ).
fof(f1231,plain,
! [X1] : subset(X1,X1),
inference(equality_resolution,[],[f846]) ).
fof(f1232,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f853]) ).
fof(f1233,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f852]) ).
fof(f1234,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f851]) ).
fof(f1235,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f874]) ).
fof(f1236,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f873]) ).
fof(f1237,plain,
! [X0,X6,X5] :
( ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,union(X0)) ),
inference(equality_resolution,[],[f880]) ).
fof(f1238,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(X5,sK27(X0,X5)) ),
inference(equality_resolution,[],[f879]) ).
fof(f1239,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(sK27(X0,X5),X0) ),
inference(equality_resolution,[],[f878]) ).
fof(f1240,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),unordered_pair(X6,X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f1136]) ).
fof(f1241,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK30(X0,X5),X5),unordered_pair(sK30(X0,X5),sK30(X0,X5))),X0) ),
inference(equality_resolution,[],[f1137]) ).
fof(f1242,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f1140]) ).
fof(f1243,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(unordered_pair(unordered_pair(X5,sK33(X0,X5)),unordered_pair(X5,X5)),X0) ),
inference(equality_resolution,[],[f1141]) ).
fof(f1246,plain,
! [X2,X10,X0,X1,X9] :
( cartesian_product2(X0,X1) != X2
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),X2) ),
inference(equality_resolution,[],[f1153]) ).
fof(f1247,plain,
! [X10,X0,X1,X9] :
( ~ in(X10,X1)
| ~ in(X9,X0)
| in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f1246]) ).
fof(f1248,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK44(X0,X1,X8),X0) ),
inference(equality_resolution,[],[f906]) ).
fof(f1249,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK45(X0,X1,X8),X1) ),
inference(equality_resolution,[],[f905]) ).
fof(f1250,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(unordered_pair(sK44(X0,X1,X8),sK45(X0,X1,X8)),unordered_pair(sK44(X0,X1,X8),sK44(X0,X1,X8))) = X8 ),
inference(equality_resolution,[],[f1154]) ).
fof(f1251,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_dom_restriction(X0,X1)) ),
inference(equality_resolution,[],[f1158]) ).
fof(f1252,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_dom_restriction(X0,X1))
| in(X5,X1) ),
inference(equality_resolution,[],[f1159]) ).
fof(f1253,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_dom_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0) ),
inference(equality_resolution,[],[f1160]) ).
fof(f1254,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f934]) ).
fof(f1255,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f1254]) ).
fof(f1256,plain,
! [X2,X0,X4] :
( unordered_pair(X0,X4) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f933]) ).
fof(f1257,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f1256]) ).
fof(f1258,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f932]) ).
fof(f1259,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1)
| ~ in(X6,X0)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_rng_restriction(X0,X1)) ),
inference(equality_resolution,[],[f1164]) ).
fof(f1260,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_rng_restriction(X0,X1))
| in(X6,X0) ),
inference(equality_resolution,[],[f1165]) ).
fof(f1261,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_rng_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1) ),
inference(equality_resolution,[],[f1166]) ).
fof(f1262,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,set_difference(X0,X1))) ),
inference(equality_resolution,[],[f1173]) ).
fof(f1264,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,set_difference(X0,X1)))
| in(X4,X1) ),
inference(equality_resolution,[],[f1175]) ).
fof(f1265,plain,
! [X0,X1,X6,X7] :
( ~ relation(X0)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X0)
| in(X6,relation_image(X0,X1)) ),
inference(equality_resolution,[],[f1179]) ).
fof(f1266,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(unordered_pair(unordered_pair(sK58(X0,X1,X6),X6),unordered_pair(sK58(X0,X1,X6),sK58(X0,X1,X6))),X0) ),
inference(equality_resolution,[],[f1180]) ).
fof(f1267,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK58(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f963]) ).
fof(f1268,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,[],[f972]) ).
fof(f1269,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,[],[f1268]) ).
fof(f1270,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK61(X0,X1,X6),relation_dom(X0)) ),
inference(equality_resolution,[],[f971]) ).
fof(f1271,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK61(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f970]) ).
fof(f1272,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| apply(X0,sK61(X0,X1,X6)) = X6 ),
inference(equality_resolution,[],[f969]) ).
fof(f1273,plain,
! [X0,X1,X6,X7] :
( ~ relation(X0)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X0)
| in(X6,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f1183]) ).
fof(f1274,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(unordered_pair(unordered_pair(X6,sK64(X0,X1,X6)),unordered_pair(X6,X6)),X0) ),
inference(equality_resolution,[],[f1184]) ).
fof(f1275,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(sK64(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f977]) ).
fof(f1276,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,[],[f985]) ).
fof(f1277,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0)) ),
inference(equality_resolution,[],[f984]) ).
fof(f1278,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1) ),
inference(equality_resolution,[],[f983]) ).
fof(f1279,plain,
! [X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X9,X8),unordered_pair(X9,X9)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X9),unordered_pair(X7,X7)),X0)
| in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1)) ),
inference(equality_resolution,[],[f1188]) ).
fof(f1280,plain,
! [X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| in(unordered_pair(unordered_pair(X7,sK69(X0,X1,X7,X8)),unordered_pair(X7,X7)),X0) ),
inference(equality_resolution,[],[f1189]) ).
fof(f1281,plain,
! [X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| in(unordered_pair(unordered_pair(sK69(X0,X1,X7,X8),X8),unordered_pair(sK69(X0,X1,X7,X8),sK69(X0,X1,X7,X8))),X1) ),
inference(equality_resolution,[],[f1190]) ).
fof(f1284,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| empty_set = apply(X0,X1) ),
inference(equality_resolution,[],[f1002]) ).
fof(f1285,plain,
! [X0,X1,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(X5,X0)
| in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),X1) ),
inference(equality_resolution,[],[f1196]) ).
fof(f1286,plain,
! [X0,X5] :
( ~ relation(identity_relation(X0))
| ~ in(X5,X0)
| in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),identity_relation(X0)) ),
inference(equality_resolution,[],[f1285]) ).
fof(f1287,plain,
! [X0,X4,X5] :
( ~ relation(identity_relation(X0))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),identity_relation(X0))
| in(X4,X0) ),
inference(equality_resolution,[],[f1197]) ).
fof(f1288,plain,
! [X0,X4,X5] :
( ~ relation(identity_relation(X0))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),identity_relation(X0))
| X4 = X5 ),
inference(equality_resolution,[],[f1198]) ).
fof(f1289,plain,
! [X0,X4,X5] :
( ~ relation(X0)
| ~ relation(relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0)) ),
inference(equality_resolution,[],[f1201]) ).
fof(f1290,plain,
! [X0,X4,X5] :
( ~ relation(X0)
| ~ relation(relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0) ),
inference(equality_resolution,[],[f1202]) ).
fof(f1291,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X4,powerset(X0))
| ~ in(subset_complement(X0,X4),X1)
| in(X4,complements_of_subsets(X0,X1)) ),
inference(equality_resolution,[],[f1030]) ).
fof(f1292,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X4,powerset(X0))
| ~ in(X4,complements_of_subsets(X0,X1))
| in(subset_complement(X0,X4),X1) ),
inference(equality_resolution,[],[f1029]) ).
tcf(c_49,plain,
! [X0: $i] : unordered_pair(X0,X0) != empty_set,
inference(cnf_transformation,[],[f1069]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ),
inference(cnf_transformation,[],[f1071]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| disjoint(unordered_pair(X0,X0),X1) ),
inference(cnf_transformation,[],[f1072]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1075]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f651]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f650]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f1083]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f1084]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( X0 = X2 )
| ( unordered_pair(X0,X1) != unordered_pair(X2,X3) ) ),
inference(cnf_transformation,[],[f658]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_rng(relation_rng_restriction(X2,X1)))
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f661]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f660]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f659]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f662]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng_restriction(X1,X0),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f663]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f664]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f666]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f665]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(X0),set_difference(relation_rng(X0),X1)) = relation_rng(relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1085]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f668]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f669]) ).
tcf(c_86,plain,
! [X0: $i] : in(X0,sK2(X0)),
inference(cnf_transformation,[],[f672]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(X1))
| ~ subset(X2,X0)
| ~ in(X0,sK2(X1)) ),
inference(cnf_transformation,[],[f671]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( in(powerset(X0),sK2(X1))
| ~ in(X0,sK2(X1)) ),
inference(cnf_transformation,[],[f670]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X1,X0),X2) = relation_rng_restriction(X1,relation_dom_restriction(X0,X2)) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f673]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f676]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK3(X0,X2,X1),X0),unordered_pair(sK3(X0,X2,X1),sK3(X0,X2,X1))),X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f1087]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f674]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(X0,X1),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f678]) ).
tcf(c_95,negated_conjecture,
~ subset(relation_image(sK5,relation_inverse_image(sK5,sK4)),sK4),
inference(cnf_transformation,[],[f681]) ).
tcf(c_96,negated_conjecture,
relation(sK5),
inference(cnf_transformation,[],[f680]) ).
tcf(c_97,negated_conjecture,
function(sK5),
inference(cnf_transformation,[],[f679]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,set_difference(relation_dom(X0),set_difference(relation_dom(X0),X1))) = relation_image(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1088]) ).
tcf(c_99,plain,
! [X0: $i] :
( ( relation_image(X0,relation_dom(X0)) = relation_rng(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f683]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f684]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,X2,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f687]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK6(X0,X2,X1)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f1090]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,X2,X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f685]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(X0,X1),relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f689]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ~ relation(X0)
| ~ subset(X1,relation_rng(X0))
| ( relation_inverse_image(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f690]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f691]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1092]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f694]) ).
tcf(c_111,plain,
unordered_pair(empty_set,empty_set) = powerset(empty_set),
inference(cnf_transformation,[],[f1093]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_dom(relation_composition(X0,X2)))
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),relation_dom(X2)) ),
inference(cnf_transformation,[],[f700]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_composition(X1,X2))) ),
inference(cnf_transformation,[],[f699]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),relation_dom(X2))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_composition(X1,X2))) ),
inference(cnf_transformation,[],[f698]) ).
tcf(c_117,plain,
! [X0: $i] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f701]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_composition(X1,X2))) ),
inference(cnf_transformation,[],[f702]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f703]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f705]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f704]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1096]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = X0 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1097]) ).
tcf(c_124,plain,
! [X0: $i] : subset(empty_set,X0),
inference(cnf_transformation,[],[f708]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1098]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1099]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f711]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(cnf_transformation,[],[f1100]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(cnf_transformation,[],[f1101]) ).
tcf(c_130,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = X0 )
| ~ function(X0)
| ~ relation(X0)
| ( apply(X0,sK7(relation_dom(X0),X0)) != sK7(relation_dom(X0),X0) ) ),
inference(cnf_transformation,[],[f1205]) ).
tcf(c_131,plain,
! [X0: $i] :
( in(sK7(relation_dom(X0),X0),relation_dom(X0))
| ( identity_relation(relation_dom(X0)) = X0 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1206]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f718]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f719]) ).
tcf(c_136,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(X0)) = relation_rng(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f721]) ).
tcf(c_137,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(X0)) = relation_dom(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f720]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = empty_set )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f723]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f722]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1102]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(unordered_pair(X0,X2),X1)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f728]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f727]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f726]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
inference(cnf_transformation,[],[f729]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( unordered_pair(X1,X1) = X0 )
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f1106]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f735]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f734]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f733]) ).
tcf(c_152,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f736]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[],[f737]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1))
| ~ subset(X0,subset_complement(X1,X2)) ),
inference(cnf_transformation,[],[f739]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,subset_complement(X1,X2))
| ~ disjoint(X0,X2)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f738]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f740]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f741]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(X0,X1)) = relation_dom(X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_rng(X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f743]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ~ element(X1,powerset(powerset(X0)))
| ( complements_of_subsets(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f744]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(X0,X0),X1) = X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1107]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X1,X0)) = relation_rng(X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_rng(X1)) ),
inference(cnf_transformation,[],[f746]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X0)) = meet_of_subsets(X1,complements_of_subsets(X1,X0)) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f747]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X0)) = union_of_subsets(X1,complements_of_subsets(X1,X0)) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f748]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK9(X0,X1),set_difference(X0,set_difference(X0,X1))) ),
inference(cnf_transformation,[],[f1108]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(cnf_transformation,[],[f1109]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X2,subset_complement(X1,X0))
| ( X1 = empty_set )
| ~ element(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f752]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i] :
( ( function_inverse(X0) = X1 )
| ~ one_to_one(X0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK11(X0,X1),relation_dom(X0))
| ~ sP0(X0,sK10(X0,X1),sK11(X0,X1),X1)
| ( relation_dom(X1) != relation_rng(X0) )
| ( apply(X0,sK11(X0,X1)) != sK10(X0,X1) ) ),
inference(cnf_transformation,[],[f764]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] :
( in(sK10(X1,X0),relation_rng(X1))
| ( function_inverse(X1) = X0 )
| ~ one_to_one(X1)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ sP0(X1,sK10(X1,X0),sK11(X1,X0),X0)
| ( relation_dom(X0) != relation_rng(X1) ) ),
inference(cnf_transformation,[],[f763]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( ( function_inverse(X1) = X0 )
| ( apply(X0,sK10(X1,X0)) = sK11(X1,X0) )
| ~ one_to_one(X1)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ sP0(X1,sK10(X1,X0),sK11(X1,X0),X0)
| ( relation_dom(X0) != relation_rng(X1) ) ),
inference(cnf_transformation,[],[f762]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i] :
( in(apply(function_inverse(X1),X0),relation_dom(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(function_inverse(X1))
| ~ relation(function_inverse(X1))
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f1216]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2,function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f1219]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ element(X2,powerset(X1))
| ~ in(X0,subset_complement(X1,X2)) ),
inference(cnf_transformation,[],[f765]) ).
tcf(c_181,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(X0)) = relation_rng(X0) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f767]) ).
tcf(c_182,plain,
! [X0: $i] :
( ( relation_rng(function_inverse(X0)) = relation_dom(X0) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f766]) ).
tcf(c_183,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK12(X0),sK13(X0)),unordered_pair(sK12(X0),sK12(X0))),X0)
| ( X0 = empty_set )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1110]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,apply(function_inverse(X1),X0)) = X0 )
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f770]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0 )
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f769]) ).
tcf(c_186,plain,
relation_dom(empty_set) = empty_set,
inference(cnf_transformation,[],[f772]) ).
tcf(c_187,plain,
relation_rng(empty_set) = empty_set,
inference(cnf_transformation,[],[f771]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f773]) ).
tcf(c_189,plain,
! [X0: $i] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f774]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,X1)
| ~ subset(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f775]) ).
tcf(c_191,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ relation(X0)
| ( relation_dom(X0) != empty_set ) ),
inference(cnf_transformation,[],[f777]) ).
tcf(c_192,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ relation(X0)
| ( relation_rng(X0) != empty_set ) ),
inference(cnf_transformation,[],[f776]) ).
tcf(c_193,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ relation(X0)
| ( relation_rng(X0) != empty_set ) ),
inference(cnf_transformation,[],[f779]) ).
tcf(c_194,plain,
! [X0: $i] :
( ( relation_rng(X0) = empty_set )
| ~ relation(X0)
| ( relation_dom(X0) != empty_set ) ),
inference(cnf_transformation,[],[f778]) ).
tcf(c_195,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( set_difference(X0,unordered_pair(X1,X1)) = X0 ) ),
inference(cnf_transformation,[],[f1111]) ).
tcf(c_196,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ( set_difference(X0,unordered_pair(X1,X1)) != X0 ) ),
inference(cnf_transformation,[],[f1112]) ).
tcf(c_197,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(X1,X2) = X0 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ( apply(X0,sK14(X0,X1)) != apply(X1,sK14(X0,X1)) )
| ( set_difference(relation_dom(X1),set_difference(relation_dom(X1),X2)) != relation_dom(X0) ) ),
inference(cnf_transformation,[],[f1113]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK14(X2,X0),relation_dom(X2))
| ( relation_dom_restriction(X0,X1) = X2 )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ( set_difference(relation_dom(X0),set_difference(relation_dom(X0),X1)) != relation_dom(X2) ) ),
inference(cnf_transformation,[],[f1114]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f1116]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f788]) ).
tcf(c_203,plain,
! [X0: $i] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f790]) ).
tcf(c_204,plain,
! [X0: $i] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f789]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X2,X1),X0) = apply(X2,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f791]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X3),X2))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1117]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3)) ),
inference(cnf_transformation,[],[f1118]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3)) ),
inference(cnf_transformation,[],[f1119]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f795]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f797]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = X0 )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f796]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f800]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f799]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f798]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom_restriction(X0,X1),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f801]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,apply(X1,X0)),unordered_pair(X0,X0)),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f1222]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1122]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f805]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ( unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
inference(cnf_transformation,[],[f1123]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom(X0),set_difference(relation_dom(X0),X1)) = relation_dom(relation_dom_restriction(X0,X1)) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1124]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f808]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X1),X0) = relation_dom_restriction(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f809]) ).
tcf(c_224,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_dom_restriction(X0,X1)),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f810]) ).
tcf(c_225,plain,
! [X0: $i] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f811]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
inference(cnf_transformation,[],[f1125]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK15(X0,X1),X1)
| ~ in(sK15(X0,X1),X0) ),
inference(cnf_transformation,[],[f814]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i] :
( in(sK15(X0,X1),X1)
| in(sK15(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f813]) ).
tcf(c_229,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f815]) ).
tcf(c_231,plain,
relation(empty_set),
inference(cnf_transformation,[],[f816]) ).
tcf(c_232,plain,
empty(empty_set),
inference(cnf_transformation,[],[f818]) ).
tcf(c_233,plain,
! [X0: $i] :
( in(sK16(X0),X0)
| ( X0 = empty_set ) ),
inference(cnf_transformation,[],[f820]) ).
tcf(c_234,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f1223]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X0) = X1 )
| ~ in(sK17(X0,X1),X1)
| ( sK17(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f1127]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i] :
( in(sK17(X0,X1),X1)
| ( sK17(X0,X1) = X0 )
| ( unordered_pair(X0,X0) = X1 ) ),
inference(cnf_transformation,[],[f1128]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f1226]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK18(X0,X1),X1) ),
inference(cnf_transformation,[],[f828]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK18(X0,X1),X0) ),
inference(cnf_transformation,[],[f827]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f826]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f829]) ).
tcf(c_244,plain,
! [X0: $i] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f830]) ).
tcf(c_245,plain,
! [X0: $i] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f831]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f832]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f833]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f834]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK19(X0,X1,X2),X2)
| ~ in(sK19(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f840]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK19(X0,X1,X2),X2)
| ~ in(sK19(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f839]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK19(X0,X1,X2),X2)
| in(sK19(X0,X1,X2),X1)
| in(sK19(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f838]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1227]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1228]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f1229]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f841]) ).
tcf(c_256,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f842]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(X0,set_difference(X0,X1)) != empty_set ) ),
inference(cnf_transformation,[],[f1131]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = empty_set )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1132]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f848]) ).
tcf(c_262,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f1231]) ).
tcf(c_263,plain,
! [X0: $i] : set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[],[f849]) ).
tcf(c_264,plain,
! [X0: $i] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f850]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK20(X0,X1,X2),X1)
| ( set_difference(X0,X1) = X2 )
| ~ in(sK20(X0,X1,X2),X2)
| ~ in(sK20(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f856]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK20(X0,X1,X2),X2)
| in(sK20(X0,X1,X2),X0)
| ( set_difference(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f855]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK20(X0,X1,X2),X2)
| ( set_difference(X0,X1) = X2 )
| ~ in(sK20(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f854]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1232]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f1233]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f1234]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f857]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f858]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f860]) ).
tcf(c_274,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f859]) ).
tcf(c_276,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f862]) ).
tcf(c_277,plain,
! [X0: $i] : element(sK21(X0),powerset(X0)),
inference(cnf_transformation,[],[f864]) ).
tcf(c_278,plain,
! [X0: $i] : empty(sK21(X0)),
inference(cnf_transformation,[],[f863]) ).
tcf(c_279,plain,
! [X0: $i] :
( empty(X0)
| element(sK22(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f866]) ).
tcf(c_280,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK22(X0)) ),
inference(cnf_transformation,[],[f865]) ).
tcf(c_281,plain,
! [X0: $i] : element(sK23(X0),X0),
inference(cnf_transformation,[],[f867]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f870]) ).
tcf(c_284,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f869]) ).
tcf(c_285,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f868]) ).
tcf(c_286,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f872]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i] :
( ( powerset(X0) = X1 )
| ~ subset(sK24(X0,X1),X0)
| ~ in(sK24(X0,X1),X1) ),
inference(cnf_transformation,[],[f876]) ).
tcf(c_288,plain,
! [X0: $i,X1: $i] :
( subset(sK24(X0,X1),X0)
| in(sK24(X0,X1),X1)
| ( powerset(X0) = X1 ) ),
inference(cnf_transformation,[],[f875]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1235]) ).
tcf(c_290,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1236]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i] :
( ( union_of_subsets(X1,X0) = union(X0) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f877]) ).
tcf(c_292,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( union(X0) = X1 )
| ~ in(X2,X0)
| ~ in(sK25(X0,X1),X2)
| ~ in(sK25(X0,X1),X1) ),
inference(cnf_transformation,[],[f883]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i] :
( in(sK25(X0,X1),X1)
| in(sK25(X0,X1),sK26(X0,X1))
| ( union(X0) = X1 ) ),
inference(cnf_transformation,[],[f882]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i] :
( in(sK26(X0,X1),X0)
| in(sK25(X0,X1),X1)
| ( union(X0) = X1 ) ),
inference(cnf_transformation,[],[f881]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,union(X2))
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1237]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] :
( in(X0,sK27(X1,X0))
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f1238]) ).
tcf(c_297,plain,
! [X0: $i,X1: $i] :
( in(sK27(X1,X0),X1)
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f1239]) ).
tcf(c_299,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(X1) = X2 )
| ~ relation(X1)
| ~ in(sK28(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(X0,sK28(X1,X2)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f1134]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i] :
( in(sK28(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK29(X0,X1),sK28(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X0)
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1135]) ).
tcf(c_301,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1240]) ).
tcf(c_302,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK30(X1,X0),X0),unordered_pair(sK30(X1,X0),sK30(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f1241]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(X0) = X1 )
| ~ relation(X0)
| ~ in(sK31(X0,X1),X1)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1),X2),unordered_pair(sK31(X0,X1),sK31(X0,X1))),X0) ),
inference(cnf_transformation,[],[f1138]) ).
tcf(c_304,plain,
! [X0: $i,X1: $i] :
( in(sK31(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK31(X0,X1),sK32(X0,X1)),unordered_pair(sK31(X0,X1),sK31(X0,X1))),X0)
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1139]) ).
tcf(c_305,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1242]) ).
tcf(c_306,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK33(X1,X0)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f1243]) ).
tcf(c_307,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK34(X0,X1),sK35(X0,X1)),unordered_pair(sK34(X0,X1),sK34(X0,X1))),X1) ),
inference(cnf_transformation,[],[f1142]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK34(X0,X1),sK35(X0,X1)),unordered_pair(sK34(X0,X1),sK34(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1143]) ).
tcf(c_310,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK36(X0,X1),sK37(X0,X1)),unordered_pair(sK36(X0,X1),sK36(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK36(X0,X1),sK37(X0,X1)),unordered_pair(sK36(X0,X1),sK36(X0,X1))),X0) ),
inference(cnf_transformation,[],[f1145]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK36(X0,X1),sK37(X0,X1)),unordered_pair(sK36(X0,X1),sK36(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK36(X0,X1),sK37(X0,X1)),unordered_pair(sK36(X0,X1),sK36(X0,X1))),X0)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1146]) ).
tcf(c_314,plain,
! [X0: $i] :
( relation(X0)
| in(sK38(X0),X0) ),
inference(cnf_transformation,[],[f902]) ).
tcf(c_315,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X2)
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != sK38(X2) ) ),
inference(cnf_transformation,[],[f1149]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK39(X0),sK40(X0)),unordered_pair(sK39(X0),sK39(X0))) = X0 )
| ~ relation(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1150]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f903]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ~ in(X1,X3)
| ~ in(X0,X2)
| ~ in(sK41(X2,X3,X4),X4)
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != sK41(X2,X3,X4) ) ),
inference(cnf_transformation,[],[f1151]) ).
tcf(c_319,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK42(X0,X1,X2),X0)
| in(sK41(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f910]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK43(X0,X1,X2),X1)
| in(sK41(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f909]) ).
tcf(c_321,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK41(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 )
| ( unordered_pair(unordered_pair(sK42(X0,X1,X2),sK43(X0,X1,X2)),unordered_pair(sK42(X0,X1,X2),sK42(X0,X1,X2))) = sK41(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f1152]) ).
tcf(c_322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),cartesian_product2(X1,X3))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1247]) ).
tcf(c_323,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK44(X1,X2,X0),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f1248]) ).
tcf(c_324,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK45(X1,X2,X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f1249]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK44(X1,X2,X0),sK45(X1,X2,X0)),unordered_pair(sK44(X1,X2,X0),sK44(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f1250]) ).
tcf(c_326,plain,
relation(sK46),
inference(cnf_transformation,[],[f914]) ).
tcf(c_327,plain,
empty(sK46),
inference(cnf_transformation,[],[f913]) ).
tcf(c_328,plain,
function(sK46),
inference(cnf_transformation,[],[f912]) ).
tcf(c_329,plain,
relation(sK47),
inference(cnf_transformation,[],[f916]) ).
tcf(c_330,plain,
function(sK47),
inference(cnf_transformation,[],[f915]) ).
tcf(c_331,plain,
! [X0: $i] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f917]) ).
tcf(c_333,plain,
! [X0: $i,X1: $i] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f918]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f920]) ).
tcf(c_335,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK48(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),unordered_pair(sK48(X0,X1,X2),sK48(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2)),unordered_pair(sK48(X0,X1,X2),sK48(X0,X1,X2))),X0) ),
inference(cnf_transformation,[],[f1155]) ).
tcf(c_336,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK48(X0,X2,X1),X2)
| in(unordered_pair(unordered_pair(sK48(X0,X2,X1),sK49(X0,X2,X1)),unordered_pair(sK48(X0,X2,X1),sK48(X0,X2,X1))),X1)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1156]) ).
tcf(c_337,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK48(X0,X2,X1),sK49(X0,X2,X1)),unordered_pair(sK48(X0,X2,X1),sK48(X0,X2,X1))),X1)
| in(unordered_pair(unordered_pair(sK48(X0,X2,X1),sK49(X0,X2,X1)),unordered_pair(sK48(X0,X2,X1),sK48(X0,X2,X1))),X0)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1157]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1251]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ relation(X2)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f1252]) ).
tcf(c_340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f1253]) ).
tcf(c_341,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f928]) ).
tcf(c_342,plain,
! [X0: $i] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f927]) ).
tcf(c_343,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f929]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f930]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X0,X1) = X2 )
| ~ in(sK50(X0,X1,X2),X2)
| ( sK50(X0,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f937]) ).
tcf(c_346,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X0,X1) = X2 )
| ~ in(sK50(X0,X1,X2),X2)
| ( sK50(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f936]) ).
tcf(c_347,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK50(X0,X1,X2),X2)
| ( unordered_pair(X0,X1) = X2 )
| ( sK50(X0,X1,X2) = X1 )
| ( sK50(X0,X1,X2) = X0 ) ),
inference(cnf_transformation,[],[f935]) ).
tcf(c_348,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f1255]) ).
tcf(c_349,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f1257]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f1258]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f938]) ).
tcf(c_352,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f939]) ).
tcf(c_353,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng_restriction(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ in(sK52(X0,X1,X2),X0)
| ~ in(unordered_pair(unordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),unordered_pair(sK51(X0,X1,X2),sK51(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2)),unordered_pair(sK51(X0,X1,X2),sK51(X0,X1,X2))),X1) ),
inference(cnf_transformation,[],[f1161]) ).
tcf(c_354,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK52(X2,X0,X1),X2)
| in(unordered_pair(unordered_pair(sK51(X2,X0,X1),sK52(X2,X0,X1)),unordered_pair(sK51(X2,X0,X1),sK51(X2,X0,X1))),X1)
| ( relation_rng_restriction(X2,X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1162]) ).
tcf(c_355,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK51(X2,X0,X1),sK52(X2,X0,X1)),unordered_pair(sK51(X2,X0,X1),sK51(X2,X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK51(X2,X0,X1),sK52(X2,X0,X1)),unordered_pair(sK51(X2,X0,X1),sK51(X2,X0,X1))),X0)
| ( relation_rng_restriction(X2,X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1163]) ).
tcf(c_356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X3,X2))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ relation(relation_rng_restriction(X3,X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1259]) ).
tcf(c_357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ relation(X3)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f1260]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ relation(X3)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f1261]) ).
tcf(c_359,plain,
! [X0: $i] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f947]) ).
tcf(c_360,plain,
! [X0: $i] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f946]) ).
tcf(c_361,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f948]) ).
tcf(c_362,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,empty_set)) = empty_set,
inference(cnf_transformation,[],[f1167]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1169]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = X2 )
| ~ in(sK53(X0,X1,X2),X2)
| ~ in(sK53(X0,X1,X2),X1)
| ~ in(sK53(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f1170]) ).
tcf(c_366,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK53(X0,X1,X2),X2)
| in(sK53(X0,X1,X2),X0)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(cnf_transformation,[],[f1171]) ).
tcf(c_367,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK53(X0,X1,X2),X2)
| in(sK53(X0,X1,X2),X1)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(cnf_transformation,[],[f1172]) ).
tcf(c_368,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(X1,set_difference(X1,X2)))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1262]) ).
tcf(c_370,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(cnf_transformation,[],[f1264]) ).
tcf(c_371,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(cnf_transformation,[],[f1176]) ).
tcf(c_372,plain,
! [X0: $i] : in(X0,sK54(X0)),
inference(cnf_transformation,[],[f962]) ).
tcf(c_373,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK54(X1))
| ~ subset(X2,X0)
| ~ in(X0,sK54(X1)) ),
inference(cnf_transformation,[],[f961]) ).
tcf(c_374,plain,
! [X0: $i,X1: $i] :
( in(sK55(X1,X0),sK54(X1))
| ~ in(X0,sK54(X1)) ),
inference(cnf_transformation,[],[f960]) ).
tcf(c_375,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK55(X1,X0))
| ~ subset(X2,X0)
| ~ in(X0,sK54(X1)) ),
inference(cnf_transformation,[],[f959]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X1,X2) = X3 )
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(sK56(X1,X2,X3),X3)
| ~ in(unordered_pair(unordered_pair(X0,sK56(X1,X2,X3)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f1177]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK56(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK57(X0,X1,X2),sK56(X0,X1,X2)),unordered_pair(sK57(X0,X1,X2),sK57(X0,X1,X2))),X0)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1178]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK57(X0,X1,X2),X1)
| in(sK56(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f966]) ).
tcf(c_379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1265]) ).
tcf(c_380,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK58(X1,X2,X0),X0),unordered_pair(sK58(X1,X2,X0),sK58(X1,X2,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f1266]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK58(X1,X2,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f1267]) ).
tcf(c_382,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(sK59(X0,X1,X2),X2)
| ( sK59(X0,X1,X2) != apply(X0,X3) ) ),
inference(cnf_transformation,[],[f976]) ).
tcf(c_383,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK59(X0,X1,X2),X2)
| in(sK60(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f975]) ).
tcf(c_384,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK60(X0,X1,X2),X1)
| in(sK59(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f974]) ).
tcf(c_385,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK59(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK60(X0,X1,X2)) = sK59(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f973]) ).
tcf(c_386,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,[],[f1269]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK61(X1,X2,X0),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f1270]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK61(X1,X2,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f1271]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK61(X1,X2,X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f1272]) ).
tcf(c_390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ in(X3,X1)
| ~ in(sK62(X0,X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(sK62(X0,X1,X2),X3),unordered_pair(sK62(X0,X1,X2),sK62(X0,X1,X2))),X0) ),
inference(cnf_transformation,[],[f1181]) ).
tcf(c_391,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK62(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK62(X0,X1,X2),sK63(X0,X1,X2)),unordered_pair(sK62(X0,X1,X2),sK62(X0,X1,X2))),X0)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1182]) ).
tcf(c_392,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK63(X0,X1,X2),X1)
| in(sK62(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f980]) ).
tcf(c_393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1273]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK64(X1,X2,X0)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f1274]) ).
tcf(c_395,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK64(X1,X2,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f1275]) ).
tcf(c_396,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK65(X0,X1,X2),X2)
| ~ in(sK65(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK65(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f988]) ).
tcf(c_397,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK65(X0,X1,X2),X2)
| in(sK65(X0,X1,X2),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f987]) ).
tcf(c_398,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK65(X0,X1,X2),X2)
| in(apply(X0,sK65(X0,X1,X2)),X1)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f986]) ).
tcf(c_399,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,[],[f1276]) ).
tcf(c_400,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,[],[f1277]) ).
tcf(c_401,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,[],[f1278]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i] :
( empty(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f990]) ).
tcf(c_403,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f989]) ).
tcf(c_404,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f992]) ).
tcf(c_405,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f991]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i] :
( empty(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f994]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f993]) ).
tcf(c_408,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f995]) ).
tcf(c_409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X3,sK67(X0,X1,X2)),unordered_pair(X3,X3)),X1)
| ~ in(unordered_pair(unordered_pair(sK66(X0,X1,X2),X3),unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2))),X0)
| ~ in(unordered_pair(unordered_pair(sK66(X0,X1,X2),sK67(X0,X1,X2)),unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2))),X2) ),
inference(cnf_transformation,[],[f1185]) ).
tcf(c_410,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK66(X0,X1,X2),sK68(X0,X1,X2)),unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK66(X0,X1,X2),sK67(X0,X1,X2)),unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2))),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1186]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK68(X0,X1,X2),sK67(X0,X1,X2)),unordered_pair(sK68(X0,X1,X2),sK68(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK66(X0,X1,X2),sK67(X0,X1,X2)),unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2))),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1187]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),relation_composition(X4,X2))
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(relation_composition(X4,X2))
| ~ in(unordered_pair(unordered_pair(X3,X0),unordered_pair(X3,X3)),X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1279]) ).
tcf(c_413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,sK69(X2,X3,X0,X1)),unordered_pair(X0,X0)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3)) ),
inference(cnf_transformation,[],[f1280]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK69(X2,X3,X0,X1),X1),unordered_pair(sK69(X2,X3,X0,X1),sK69(X2,X3,X0,X1))),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3)) ),
inference(cnf_transformation,[],[f1281]) ).
tcf(c_418,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(X0))
| ( apply(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1284]) ).
tcf(c_419,plain,
! [X0: $i] :
( ( set_union2(relation_dom(X0),relation_rng(X0)) = relation_field(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1006]) ).
tcf(c_420,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f1008]) ).
tcf(c_421,plain,
! [X0: $i] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f1007]) ).
tcf(c_422,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f1009]) ).
tcf(c_423,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X0) = X1 )
| ~ relation(X1)
| ~ in(sK70(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK70(X0,X1),sK71(X0,X1)),unordered_pair(sK70(X0,X1),sK70(X0,X1))),X1)
| ( sK70(X0,X1) != sK71(X0,X1) ) ),
inference(cnf_transformation,[],[f1193]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i] :
( in(sK70(X1,X0),X1)
| in(unordered_pair(unordered_pair(sK70(X1,X0),sK71(X1,X0)),unordered_pair(sK70(X1,X0),sK70(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1194]) ).
tcf(c_425,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK70(X1,X0),sK71(X1,X0)),unordered_pair(sK70(X1,X0),sK70(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ( sK70(X1,X0) = sK71(X1,X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1195]) ).
tcf(c_426,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1286]) ).
tcf(c_427,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(identity_relation(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2)) ),
inference(cnf_transformation,[],[f1287]) ).
tcf(c_428,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ relation(identity_relation(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2)) ),
inference(cnf_transformation,[],[f1288]) ).
tcf(c_429,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(X0)) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1016]) ).
tcf(c_431,plain,
! [X0: $i] :
( function(relation_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1017]) ).
tcf(c_432,plain,
! [X0: $i] :
( empty(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f1020]) ).
tcf(c_433,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f1019]) ).
tcf(c_434,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1021]) ).
tcf(c_435,plain,
! [X0: $i] :
( ( relation_inverse(X0) = function_inverse(X0) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1022]) ).
tcf(c_436,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK72(X0,X1),sK73(X0,X1)),unordered_pair(sK72(X0,X1),sK72(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK73(X0,X1),sK72(X0,X1)),unordered_pair(sK73(X0,X1),sK73(X0,X1))),X0) ),
inference(cnf_transformation,[],[f1199]) ).
tcf(c_437,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK72(X0,X1),sK73(X0,X1)),unordered_pair(sK72(X0,X1),sK72(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK73(X0,X1),sK72(X0,X1)),unordered_pair(sK73(X0,X1),sK73(X0,X1))),X0)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1200]) ).
tcf(c_438,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),relation_inverse(X2))
| ~ relation(X2)
| ~ relation(relation_inverse(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1289]) ).
tcf(c_439,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2)
| ~ relation(X2)
| ~ relation(relation_inverse(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_inverse(X2)) ),
inference(cnf_transformation,[],[f1290]) ).
tcf(c_440,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1027]) ).
tcf(c_441,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1028]) ).
tcf(c_442,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( complements_of_subsets(X0,X1) = X2 )
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0)))
| ~ in(sK74(X0,X1,X2),X2)
| ~ in(subset_complement(X0,sK74(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f1033]) ).
tcf(c_443,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK74(X1,X0,X2),X2)
| in(subset_complement(X1,sK74(X1,X0,X2)),X0)
| ( complements_of_subsets(X1,X0) = X2 )
| ~ element(X2,powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1032]) ).
tcf(c_444,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK74(X1,X0,X2),powerset(X1))
| ( complements_of_subsets(X1,X0) = X2 )
| ~ element(X2,powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1031]) ).
tcf(c_445,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,complements_of_subsets(X0,X1))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(powerset(X0)))
| ~ in(subset_complement(X0,X2),X1)
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f1291]) ).
tcf(c_446,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X0,X2),X1)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(powerset(X0)))
| ~ in(X2,complements_of_subsets(X0,X1))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f1292]) ).
tcf(c_447,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,X0) = subset_complement(X1,X0) )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1034]) ).
tcf(c_448,plain,
! [X0: $i,X1: $i] :
( ( complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0 )
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1035]) ).
tcf(c_449,plain,
! [X0: $i,X1: $i] :
( element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1036]) ).
tcf(c_450,plain,
! [X0: $i] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f1037]) ).
tcf(c_451,plain,
! [X0: $i] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f1038]) ).
tcf(c_452,plain,
! [X0: $i,X1: $i] :
( element(union_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1039]) ).
tcf(c_453,plain,
! [X0: $i,X1: $i] :
( element(meet_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1040]) ).
tcf(c_454,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_difference(X1,X0,X2) = set_difference(X0,X2) )
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1041]) ).
tcf(c_455,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(subset_difference(X1,X0,X2),powerset(X1))
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1042]) ).
tcf(c_456,plain,
relation(sK75),
inference(cnf_transformation,[],[f1045]) ).
tcf(c_457,plain,
function(sK75),
inference(cnf_transformation,[],[f1044]) ).
tcf(c_458,plain,
one_to_one(sK75),
inference(cnf_transformation,[],[f1043]) ).
tcf(c_459,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ( sK76(X0) != sK77(X0) ) ),
inference(cnf_transformation,[],[f1050]) ).
tcf(c_460,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK76(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1049]) ).
tcf(c_461,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK77(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1048]) ).
tcf(c_462,plain,
! [X0: $i] :
( one_to_one(X0)
| ( apply(X0,sK76(X0)) = apply(X0,sK77(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1047]) ).
tcf(c_463,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| ( apply(X0,X1) != apply(X0,X2) ) ),
inference(cnf_transformation,[],[f1046]) ).
tcf(c_464,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1051]) ).
tcf(c_465,plain,
! [X0: $i] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1055]) ).
tcf(c_466,plain,
! [X0: $i] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1054]) ).
tcf(c_467,plain,
! [X0: $i] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f1056]) ).
tcf(c_468,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,X1)
| ( X0 = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1057]) ).
tcf(c_469,plain,
! [X0: $i,X1: $i] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f1058]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f1059]) ).
tcf(c_471,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1060]) ).
tcf(c_472,plain,
~ empty(sK78),
inference(cnf_transformation,[],[f1061]) ).
tcf(c_473,plain,
~ empty(sK79),
inference(cnf_transformation,[],[f1063]) ).
tcf(c_474,plain,
relation(sK79),
inference(cnf_transformation,[],[f1062]) ).
tcf(c_475,plain,
empty(sK80),
inference(cnf_transformation,[],[f1064]) ).
tcf(c_476,plain,
empty(sK81),
inference(cnf_transformation,[],[f1066]) ).
tcf(c_477,plain,
relation(sK81),
inference(cnf_transformation,[],[f1065]) ).
tcf(c_478,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f1067]) ).
tcf(c_750,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_464,c_478,c_331,c_464]) ).
tcf(c_757,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_404,c_408]) ).
tcf(c_769,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2,function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_179,c_466,c_465,c_179]) ).
tcf(c_800,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_273]) ).
tcf(c_854,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_273,c_440]) ).
tcf(c_856,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_273,c_441]) ).
tcf(c_858,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,X0) = subset_complement(X1,X0) )
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_273,c_447]) ).
tcf(c_860,plain,
! [X0: $i,X1: $i] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_274,c_66]) ).
tcf(c_861,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_860]) ).
tcf(c_862,plain,
! [X0: $i,X1: $i] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_274,c_67]) ).
tcf(c_863,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_862]) ).
tcf(c_914,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_334]) ).
tcf(c_924,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_352]) ).
tcf(c_930,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_434]) ).
tcf(c_966,plain,
! [X0: $i,X1: $i] :
( element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(prop_impl_just,[status(thm)],[c_449]) ).
tcf(c_1052,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK44(X1,X2,X0),sK45(X1,X2,X0)),unordered_pair(sK44(X1,X2,X0),sK44(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_325]) ).
tcf(c_1774,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| ~ subset(X0,X1)
| ~ element(X2,powerset(X1))
| ~ subset(X0,subset_complement(X1,X2)) ),
inference(bin_hyper_res,[status(thm)],[c_154,c_800]) ).
tcf(c_1775,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,subset_complement(X1,X0))
| ~ subset(X2,X1)
| ~ disjoint(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(bin_hyper_res,[status(thm)],[c_155,c_800]) ).
tcf(c_1776,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X2,subset_complement(X1,X0))
| ( X1 = empty_set )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_167,c_800]) ).
tcf(c_1777,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_271,c_800]) ).
tcf(c_1778,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_272,c_800]) ).
tcf(c_1779,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_difference(X1,X2,X0) = set_difference(X2,X0) )
| ~ subset(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(bin_hyper_res,[status(thm)],[c_454,c_800]) ).
tcf(c_1780,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(subset_difference(X1,X2,X0),powerset(X1))
| ~ subset(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(bin_hyper_res,[status(thm)],[c_455,c_800]) ).
tcf(c_1825,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_428,c_420]) ).
tcf(c_1826,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_427,c_420]) ).
tcf(c_1827,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),identity_relation(X1))
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_426,c_420]) ).
tcf(c_1918,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_inverse(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_439,c_930]) ).
tcf(c_1919,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),relation_inverse(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_438,c_930]) ).
tcf(c_1966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_339,c_914]) ).
tcf(c_1967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_340,c_914]) ).
tcf(c_1968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_338,c_914]) ).
tcf(c_1975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_357,c_924]) ).
tcf(c_1976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_358,c_924]) ).
tcf(c_1977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X3,X2))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_356,c_924]) ).
tcf(c_2304,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X1,X0),X2)
| ~ element(X0,powerset(X1))
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X0,complements_of_subsets(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_446,c_966]) ).
tcf(c_2305,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,complements_of_subsets(X0,X2))
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(powerset(X0)))
| ~ in(subset_complement(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_445,c_966]) ).
tcf(c_2418,plain,
! [X0: $i,X1: $i] :
( in(apply(function_inverse(X1),X0),relation_dom(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(function_inverse(X1))
| ~ in(X0,relation_rng(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_177,c_465]) ).
tcf(c_2426,plain,
! [X0: $i,X1: $i] :
( in(apply(function_inverse(X1),X0),relation_dom(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2418,c_466]) ).
tcf(c_2476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,sK69(X2,X3,X0,X1)),unordered_pair(X0,X0)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_413,c_757]) ).
tcf(c_2477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK69(X2,X3,X0,X1),X1),unordered_pair(sK69(X2,X3,X0,X1),sK69(X2,X3,X0,X1))),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_414,c_757]) ).
tcf(c_2478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),relation_composition(X4,X2))
| ~ relation(X4)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X0),unordered_pair(X3,X3)),X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_412,c_757]) ).
tcf(c_4010,plain,
! [X0: $i] : element(X0,powerset(X0)),
inference(light_normalisation,[status(thm)],[c_450,c_451]) ).
tcf(c_4095,plain,
! [X0: $i] : set_difference(X0,X0) = empty_set,
inference(light_normalisation,[status(thm)],[c_362,c_264]) ).
tcf(c_5092,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK33(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(demodulation,[status(thm)],[c_306,c_351]) ).
tcf(c_5190,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK12(X0),sK12(X0)),unordered_pair(sK12(X0),sK13(X0))),X0)
| ( X0 = empty_set )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_183,c_351]) ).
tcf(c_5226,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK64(X1,X2,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_394,c_351]) ).
tcf(c_5272,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK39(X0),sK39(X0)),unordered_pair(sK39(X0),sK40(X0))) = X0 )
| ~ relation(X1)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_316,c_351]) ).
tcf(c_5304,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK6(X0,X2,X1))),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_103,c_351]) ).
tcf(c_5374,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,apply(X1,X0))),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(demodulation,[status(thm)],[c_216,c_351]) ).
tcf(c_5399,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK30(X1,X0)),unordered_pair(sK30(X1,X0),sK30(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(demodulation,[status(thm)],[c_302,c_351]) ).
tcf(c_5479,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( subset_difference(X1,X1,meet_of_subsets(X1,X0)) = union_of_subsets(X1,complements_of_subsets(X1,X0)) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(demodulation,[status(thm)],[c_164,c_451]) ).
tcf(c_5489,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( subset_difference(X1,X1,union_of_subsets(X1,X0)) = meet_of_subsets(X1,complements_of_subsets(X1,X0)) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(demodulation,[status(thm)],[c_163,c_451]) ).
tcf(c_5571,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK34(X0,X1),sK34(X0,X1)),unordered_pair(sK34(X0,X1),sK35(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_308,c_351]) ).
tcf(c_5600,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK58(X1,X2,X0)),unordered_pair(sK58(X1,X2,X0),sK58(X1,X2,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_380,c_351]) ).
tcf(c_5610,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK34(X0,X1),sK34(X0,X1)),unordered_pair(sK34(X0,X1),sK35(X0,X1))),X1) ),
inference(demodulation,[status(thm)],[c_307,c_351]) ).
tcf(c_5623,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK3(X0,X2,X1)),unordered_pair(sK3(X0,X2,X1),sK3(X0,X2,X1))),X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_92,c_351]) ).
tcf(c_5649,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK44(X1,X2,X0),sK44(X1,X2,X0)),unordered_pair(sK44(X1,X2,X0),sK45(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(demodulation,[status(thm)],[c_1052,c_351]) ).
tcf(c_5684,plain,
! [X0: $i,X1: $i] :
( in(sK70(X1,X0),X1)
| in(unordered_pair(unordered_pair(sK70(X1,X0),sK70(X1,X0)),unordered_pair(sK70(X1,X0),sK71(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_424,c_351]) ).
tcf(c_5707,plain,
! [X0: $i,X1: $i] :
( in(sK31(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK31(X0,X1),sK31(X0,X1)),unordered_pair(sK31(X0,X1),sK32(X0,X1))),X0)
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_304,c_351]) ).
tcf(c_5728,plain,
! [X0: $i,X1: $i] :
( in(sK28(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK28(X0,X1),sK29(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X0)
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_300,c_351]) ).
tcf(c_5755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK69(X2,X3,X0,X1))),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3)) ),
inference(demodulation,[status(thm)],[c_2476,c_351]) ).
tcf(c_5804,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK70(X1,X0),sK70(X1,X0)),unordered_pair(sK70(X1,X0),sK71(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ( sK70(X1,X0) = sK71(X1,X0) )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_425,c_351]) ).
tcf(c_5859,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK62(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK62(X0,X1,X2),sK62(X0,X1,X2)),unordered_pair(sK62(X0,X1,X2),sK63(X0,X1,X2))),X0)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_391,c_351]) ).
tcf(c_5872,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK56(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK56(X0,X1,X2),sK57(X0,X1,X2)),unordered_pair(sK57(X0,X1,X2),sK57(X0,X1,X2))),X0)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_377,c_351]) ).
tcf(c_5909,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK41(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 )
| ( unordered_pair(unordered_pair(sK42(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK42(X0,X1,X2),sK43(X0,X1,X2))) = sK41(X0,X1,X2) ) ),
inference(demodulation,[status(thm)],[c_321,c_351]) ).
tcf(c_5933,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X1,sK69(X2,X3,X0,X1)),unordered_pair(sK69(X2,X3,X0,X1),sK69(X2,X3,X0,X1))),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3)) ),
inference(demodulation,[status(thm)],[c_2477,c_351]) ).
tcf(c_5956,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK52(X2,X0,X1),X2)
| in(unordered_pair(unordered_pair(sK51(X2,X0,X1),sK51(X2,X0,X1)),unordered_pair(sK51(X2,X0,X1),sK52(X2,X0,X1))),X1)
| ( relation_rng_restriction(X2,X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_354,c_351]) ).
tcf(c_5972,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK48(X0,X2,X1),X2)
| in(unordered_pair(unordered_pair(sK48(X0,X2,X1),sK48(X0,X2,X1)),unordered_pair(sK48(X0,X2,X1),sK49(X0,X2,X1))),X1)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_336,c_351]) ).
tcf(c_5988,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X0) = X1 )
| ~ relation(X1)
| ~ in(sK70(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK70(X0,X1),sK70(X0,X1)),unordered_pair(sK70(X0,X1),sK71(X0,X1))),X1)
| ( sK70(X0,X1) != sK71(X0,X1) ) ),
inference(demodulation,[status(thm)],[c_423,c_351]) ).
tcf(c_6036,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK36(X0,X1),sK36(X0,X1)),unordered_pair(sK36(X0,X1),sK37(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK36(X0,X1),sK36(X0,X1)),unordered_pair(sK36(X0,X1),sK37(X0,X1))),X0)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_311,c_351]) ).
tcf(c_6052,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK73(X0,X1),sK72(X0,X1)),unordered_pair(sK72(X0,X1),sK72(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK73(X0,X1),sK73(X0,X1)),unordered_pair(sK73(X0,X1),sK72(X0,X1))),X0)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_437,c_351]) ).
tcf(c_6068,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK36(X0,X1),sK36(X0,X1)),unordered_pair(sK36(X0,X1),sK37(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK36(X0,X1),sK36(X0,X1)),unordered_pair(sK36(X0,X1),sK37(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_310,c_351]) ).
tcf(c_6084,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK73(X0,X1),sK72(X0,X1)),unordered_pair(sK72(X0,X1),sK72(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK73(X0,X1),sK73(X0,X1)),unordered_pair(sK73(X0,X1),sK72(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_436,c_351]) ).
tcf(c_6118,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK51(X2,X0,X1),sK51(X2,X0,X1)),unordered_pair(sK51(X2,X0,X1),sK52(X2,X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK51(X2,X0,X1),sK51(X2,X0,X1)),unordered_pair(sK51(X2,X0,X1),sK52(X2,X0,X1))),X0)
| ( relation_rng_restriction(X2,X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_355,c_351]) ).
tcf(c_6134,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK48(X0,X2,X1),sK48(X0,X2,X1)),unordered_pair(sK48(X0,X2,X1),sK49(X0,X2,X1))),X1)
| in(unordered_pair(unordered_pair(sK48(X0,X2,X1),sK48(X0,X2,X1)),unordered_pair(sK48(X0,X2,X1),sK49(X0,X2,X1))),X0)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_337,c_351]) ).
tcf(c_6170,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK67(X0,X1,X2),sK68(X0,X1,X2)),unordered_pair(sK68(X0,X1,X2),sK68(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2)),unordered_pair(sK66(X0,X1,X2),sK67(X0,X1,X2))),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_411,c_351]) ).
tcf(c_6189,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2)),unordered_pair(sK66(X0,X1,X2),sK68(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2)),unordered_pair(sK66(X0,X1,X2),sK67(X0,X1,X2))),X2)
| ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_410,c_351]) ).
tcf(c_6208,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng_restriction(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ in(sK52(X0,X1,X2),X0)
| ~ in(unordered_pair(unordered_pair(sK51(X0,X1,X2),sK51(X0,X1,X2)),unordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK51(X0,X1,X2),sK51(X0,X1,X2)),unordered_pair(sK51(X0,X1,X2),sK52(X0,X1,X2))),X1) ),
inference(demodulation,[status(thm)],[c_353,c_351]) ).
tcf(c_6227,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK48(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK48(X0,X1,X2),sK48(X0,X1,X2)),unordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK48(X0,X1,X2),sK48(X0,X1,X2)),unordered_pair(sK48(X0,X1,X2),sK49(X0,X1,X2))),X0) ),
inference(demodulation,[status(thm)],[c_335,c_351]) ).
tcf(c_6246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X3,sK67(X0,X1,X2)),unordered_pair(X3,X3)),X1)
| ~ in(unordered_pair(unordered_pair(sK66(X0,X1,X2),X3),unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2))),X0)
| ~ in(unordered_pair(unordered_pair(sK66(X0,X1,X2),sK66(X0,X1,X2)),unordered_pair(sK66(X0,X1,X2),sK67(X0,X1,X2))),X2) ),
inference(demodulation,[status(thm)],[c_409,c_351]) ).
tcf(c_6643,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_273]) ).
tcf(c_6679,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),identity_relation(X1))
| ~ in(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_1827]) ).
tcf(c_6699,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_854]) ).
tcf(c_6701,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_856]) ).
tcf(c_6703,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,X0) = subset_complement(X1,X0) )
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_858]) ).
tcf(c_6705,plain,
! [X0: $i,X1: $i] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_861]) ).
tcf(c_6706,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_6705]) ).
tcf(c_6707,plain,
! [X0: $i,X1: $i] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_863]) ).
tcf(c_6708,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_6707]) ).
tcf(c_6725,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2))
| in(X0,X2) ),
inference(prop_impl_just,[status(thm)],[c_1826]) ).
tcf(c_6726,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2)) ),
inference(renaming,[status(thm)],[c_6725]) ).
tcf(c_6825,plain,
! [X0: $i] :
( ~ empty(X0)
| one_to_one(X0) ),
inference(prop_impl_just,[status(thm)],[c_750]) ).
tcf(c_6826,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(X0) ),
inference(renaming,[status(thm)],[c_6825]) ).
tcf(c_6897,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK44(X1,X2,X0),sK44(X1,X2,X0)),unordered_pair(sK44(X1,X2,X0),sK45(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_5649]) ).
tcf(c_6907,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2)) ),
inference(prop_impl_just,[status(thm)],[c_1825]) ).
tcf(c_7602,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,subset_complement(X2,X1))
| ~ subset(X1,X2)
| ~ subset(X0,X2)
| ~ disjoint(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_1775,c_6643]) ).
tcf(c_7603,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_difference(X1,X2,X0) = set_difference(X2,X0) )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_1779,c_6643]) ).
tcf(c_7604,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(subset_difference(X1,X2,X0),powerset(X1))
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_1780,c_6643]) ).
tcf(c_7605,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X1,X0),X2)
| ~ subset(X0,X1)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X0,complements_of_subsets(X1,X2)) ),
inference(bin_hyper_res,[status(thm)],[c_2304,c_6643]) ).
tcf(c_19076,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_232,c_331]) ).
tcf(c_19077,plain,
! [X0: $i] : function(sK21(X0)),
inference(superposition,[status(thm)],[c_278,c_331]) ).
tcf(c_19079,plain,
function(sK80),
inference(superposition,[status(thm)],[c_475,c_331]) ).
tcf(c_19080,plain,
function(sK81),
inference(superposition,[status(thm)],[c_476,c_331]) ).
tcf(c_19087,plain,
! [X0: $i] : relation(sK21(X0)),
inference(superposition,[status(thm)],[c_278,c_478]) ).
tcf(c_19089,plain,
relation(sK80),
inference(superposition,[status(thm)],[c_475,c_478]) ).
tcf(c_19096,plain,
one_to_one(empty_set),
inference(superposition,[status(thm)],[c_232,c_6826]) ).
tcf(c_19097,plain,
! [X0: $i] : one_to_one(sK21(X0)),
inference(superposition,[status(thm)],[c_278,c_6826]) ).
tcf(c_19098,plain,
one_to_one(sK46),
inference(superposition,[status(thm)],[c_327,c_6826]) ).
tcf(c_19099,plain,
one_to_one(sK80),
inference(superposition,[status(thm)],[c_475,c_6826]) ).
tcf(c_19100,plain,
one_to_one(sK81),
inference(superposition,[status(thm)],[c_476,c_6826]) ).
tcf(c_19102,plain,
powerset(empty_set) != empty_set,
inference(superposition,[status(thm)],[c_111,c_49]) ).
tcf(c_19104,plain,
~ empty(powerset(empty_set)),
inference(superposition,[status(thm)],[c_111,c_344]) ).
tcf(c_19106,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( unordered_pair(X0,X1) != powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_111,c_74]) ).
tcf(c_19107,plain,
in(empty_set,powerset(empty_set)),
inference(superposition,[status(thm)],[c_111,c_349]) ).
tcf(c_19112,plain,
subset(empty_set,empty_set),
inference(superposition,[status(thm)],[c_263,c_135]) ).
tcf(c_19127,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_203,c_341]) ).
tcf(c_19129,plain,
! [X0: $i] :
( one_to_one(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_341,c_6826]) ).
tcf(c_19131,plain,
! [X0: $i] :
( function(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_341,c_331]) ).
tcf(c_19144,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_203,c_342]) ).
tcf(c_19154,plain,
! [X0: $i] :
( one_to_one(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_359,c_6826]) ).
tcf(c_19156,plain,
! [X0: $i] :
( function(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_359,c_331]) ).
tcf(c_19173,plain,
! [X0: $i] :
( one_to_one(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_432,c_6826]) ).
tcf(c_19175,plain,
! [X0: $i] :
( function(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_432,c_331]) ).
tcf(c_19197,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_111,c_128]) ).
tcf(c_19198,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(empty_set,X2),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_111,c_128]) ).
tcf(c_19209,plain,
! [X0: $i] : sK21(X0) = empty_set,
inference(superposition,[status(thm)],[c_278,c_229]) ).
tcf(c_19210,plain,
empty_set = sK46,
inference(superposition,[status(thm)],[c_327,c_229]) ).
tcf(c_19211,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_341,c_229]) ).
tcf(c_19212,plain,
! [X0: $i] :
( ( relation_rng(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_359,c_229]) ).
tcf(c_19213,plain,
! [X0: $i] :
( ( relation_inverse(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_432,c_229]) ).
tcf(c_19214,plain,
empty_set = sK80,
inference(superposition,[status(thm)],[c_475,c_229]) ).
tcf(c_19215,plain,
empty_set = sK81,
inference(superposition,[status(thm)],[c_476,c_229]) ).
tcf(c_19225,plain,
! [X0: $i] : element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[c_277,c_19209]) ).
tcf(c_19265,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_203,c_19129]) ).
tcf(c_19273,plain,
! [X0: $i] :
( function(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_203,c_19131]) ).
tcf(c_19303,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_111,c_129]) ).
tcf(c_19304,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(empty_set,X2),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_111,c_129]) ).
tcf(c_19314,plain,
! [X0: $i] : element(X0,sK2(X0)),
inference(superposition,[status(thm)],[c_86,c_276]) ).
tcf(c_19315,plain,
! [X0: $i] :
( relation(X0)
| element(sK38(X0),X0) ),
inference(superposition,[status(thm)],[c_314,c_276]) ).
tcf(c_19316,plain,
! [X0: $i,X1: $i] : element(X0,unordered_pair(X0,X1)),
inference(superposition,[status(thm)],[c_348,c_276]) ).
tcf(c_19317,plain,
! [X0: $i,X1: $i] : element(X0,unordered_pair(X1,X0)),
inference(superposition,[status(thm)],[c_349,c_276]) ).
tcf(c_19318,plain,
! [X0: $i] : element(X0,sK54(X0)),
inference(superposition,[status(thm)],[c_372,c_276]) ).
tcf(c_19319,plain,
element(empty_set,powerset(empty_set)),
inference(superposition,[status(thm)],[c_19107,c_276]) ).
tcf(c_19359,plain,
! [X0: $i] : ~ empty(sK2(X0)),
inference(superposition,[status(thm)],[c_86,c_471]) ).
tcf(c_19363,plain,
! [X0: $i] : ~ empty(sK54(X0)),
inference(superposition,[status(thm)],[c_372,c_471]) ).
tcf(c_19371,plain,
! [X0: $i] :
( in(empty_set,X0)
| disjoint(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_111,c_52]) ).
tcf(c_19372,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| disjoint(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_52,c_256]) ).
tcf(c_19379,plain,
! [X0: $i] : set_union2(X0,X0) = set_union2(X0,empty_set),
inference(superposition,[status(thm)],[c_4095,c_145]) ).
tcf(c_19381,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X1,X0))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_145,c_246]) ).
tcf(c_19395,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_149,c_471]) ).
tcf(c_19396,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| element(sK8(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_149,c_276]) ).
tcf(c_19397,plain,
! [X0: $i] : disjoint(empty_set,X0),
inference(superposition,[status(thm)],[c_149,c_234]) ).
tcf(c_19407,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_150,c_471]) ).
tcf(c_19408,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| element(sK8(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_150,c_276]) ).
tcf(c_19409,plain,
! [X0: $i] : disjoint(X0,empty_set),
inference(superposition,[status(thm)],[c_150,c_234]) ).
tcf(c_19418,plain,
! [X0: $i] :
( ( relation_rng_restriction(X0,empty_set) = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_79,c_152]) ).
tcf(c_19422,plain,
! [X0: $i] : relation_rng_restriction(X0,empty_set) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_19418,c_231]) ).
tcf(c_19436,plain,
( subset(empty_set,empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_19422,c_79]) ).
tcf(c_19442,plain,
! [X0: $i] :
( in(empty_set,X0)
| disjoint(X0,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_19371,c_256]) ).
tcf(c_19455,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ proper_subset(X0,relation_rng_restriction(X1,X0)) ),
inference(superposition,[status(thm)],[c_79,c_188]) ).
tcf(c_19456,plain,
! [X0: $i] : ~ proper_subset(X0,empty_set),
inference(superposition,[status(thm)],[c_124,c_188]) ).
tcf(c_19457,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_135,c_188]) ).
tcf(c_19458,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),X0),
inference(superposition,[status(thm)],[c_209,c_188]) ).
tcf(c_19465,plain,
~ proper_subset(empty_set,empty_set),
inference(superposition,[status(thm)],[c_263,c_19457]) ).
tcf(c_19475,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ proper_subset(X0,relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_215,c_188]) ).
tcf(c_19476,plain,
! [X0: $i] :
( ( relation_dom_restriction(empty_set,X0) = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_215,c_152]) ).
tcf(c_19477,plain,
! [X0: $i] : relation_dom_restriction(empty_set,X0) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_19476,c_231]) ).
tcf(c_19483,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X1,X0)) = set_difference(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_145,c_153]) ).
tcf(c_19484,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_153,c_19457]) ).
tcf(c_19485,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_153,c_135]) ).
tcf(c_19486,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_union2(X1,X0)) = set_union2(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_153,c_145]) ).
tcf(c_19487,plain,
! [X0: $i] : set_union2(X0,empty_set) = set_difference(X0,empty_set),
inference(superposition,[status(thm)],[c_153,c_264]) ).
tcf(c_19489,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_union2(X1,X0)) = set_union2(X0,X1),
inference(light_normalisation,[status(thm)],[c_19486,c_145]) ).
tcf(c_19499,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ proper_subset(union(X0),X1) ),
inference(superposition,[status(thm)],[c_222,c_188]) ).
tcf(c_19507,plain,
! [X0: $i] :
( element(sK16(X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_233,c_276]) ).
tcf(c_19515,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_241,c_471]) ).
tcf(c_19516,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| element(sK18(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_241,c_276]) ).
tcf(c_19526,plain,
! [X0: $i] : ~ in(sK2(X0),X0),
inference(superposition,[status(thm)],[c_86,c_243]) ).
tcf(c_19527,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ in(X0,sK8(X0,X1)) ),
inference(superposition,[status(thm)],[c_149,c_243]) ).
tcf(c_19528,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ in(X0,sK8(X1,X0)) ),
inference(superposition,[status(thm)],[c_150,c_243]) ).
tcf(c_19529,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK16(X0)) ),
inference(superposition,[status(thm)],[c_233,c_243]) ).
tcf(c_19530,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,sK18(X0,X1)) ),
inference(superposition,[status(thm)],[c_241,c_243]) ).
tcf(c_19531,plain,
! [X0: $i] :
( relation(X0)
| ~ in(X0,sK38(X0)) ),
inference(superposition,[status(thm)],[c_314,c_243]) ).
tcf(c_19532,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(X0,X1),X0),
inference(superposition,[status(thm)],[c_348,c_243]) ).
tcf(c_19533,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(X0,X1),X1),
inference(superposition,[status(thm)],[c_349,c_243]) ).
tcf(c_19534,plain,
! [X0: $i] : ~ in(sK54(X0),X0),
inference(superposition,[status(thm)],[c_372,c_243]) ).
tcf(c_19535,plain,
~ in(powerset(empty_set),empty_set),
inference(superposition,[status(thm)],[c_19107,c_243]) ).
tcf(c_19555,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ proper_subset(X0,X1) ),
inference(superposition,[status(thm)],[c_19515,c_188]) ).
tcf(c_19556,plain,
~ empty(relation_image(sK5,relation_inverse_image(sK5,sK4))),
inference(superposition,[status(thm)],[c_19515,c_95]) ).
tcf(c_19562,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),set_union2(set_union2(X0,X1),X1)),
inference(superposition,[status(thm)],[c_153,c_19485]) ).
tcf(c_19563,plain,
! [X0: $i] : subset(empty_set,set_union2(empty_set,X0)),
inference(superposition,[status(thm)],[c_263,c_19485]) ).
tcf(c_19564,plain,
! [X0: $i] : subset(X0,set_union2(X0,empty_set)),
inference(superposition,[status(thm)],[c_264,c_19485]) ).
tcf(c_19565,plain,
! [X0: $i] : subset(empty_set,set_union2(X0,X0)),
inference(superposition,[status(thm)],[c_4095,c_19485]) ).
tcf(c_19566,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X1,X0)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_145,c_19485]) ).
tcf(c_19567,plain,
! [X0: $i] : subset(set_difference(X0,empty_set),X0),
inference(superposition,[status(thm)],[c_244,c_19485]) ).
tcf(c_19568,plain,
! [X0: $i] : subset(set_difference(X0,X0),X0),
inference(superposition,[status(thm)],[c_245,c_19485]) ).
tcf(c_19593,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_255,c_19485]) ).
tcf(c_19594,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),X0) = set_difference(X1,X0),
inference(superposition,[status(thm)],[c_255,c_153]) ).
tcf(c_19595,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),X1),
inference(superposition,[status(thm)],[c_255,c_19458]) ).
tcf(c_19598,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_255,c_209]) ).
tcf(c_19599,plain,
! [X0: $i] : set_union2(empty_set,X0) = X0,
inference(superposition,[status(thm)],[c_255,c_244]) ).
tcf(c_19616,plain,
! [X0: $i] :
( empty(X0)
| subset(sK22(X0),X0) ),
inference(superposition,[status(thm)],[c_279,c_274]) ).
tcf(c_19617,plain,
! [X0: $i] : subset(sK23(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_281,c_274]) ).
tcf(c_19620,plain,
! [X0: $i] :
( relation(powerset(X0))
| subset(sK38(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_19315,c_274]) ).
tcf(c_19631,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_289,c_243]) ).
tcf(c_19632,plain,
! [X0: $i,X1: $i] :
( ~ empty(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_289,c_471]) ).
tcf(c_19634,plain,
! [X0: $i] : ~ subset(sK2(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_289,c_19526]) ).
tcf(c_19635,plain,
! [X0: $i,X1: $i] : ~ subset(unordered_pair(powerset(X0),X1),X0),
inference(superposition,[status(thm)],[c_289,c_19532]) ).
tcf(c_19636,plain,
! [X0: $i,X1: $i] : ~ subset(unordered_pair(X0,powerset(X1)),X1),
inference(superposition,[status(thm)],[c_289,c_19533]) ).
tcf(c_19637,plain,
! [X0: $i] : ~ subset(sK54(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_289,c_19534]) ).
tcf(c_19649,plain,
! [X0: $i,X1: $i] :
( disjoint(powerset(X0),X1)
| subset(sK8(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_149,c_290]) ).
tcf(c_19650,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,powerset(X1))
| subset(sK8(X0,powerset(X1)),X1) ),
inference(superposition,[status(thm)],[c_150,c_290]) ).
tcf(c_19651,plain,
! [X0: $i] :
( subset(sK16(powerset(X0)),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_233,c_290]) ).
tcf(c_19652,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| subset(sK18(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_241,c_290]) ).
tcf(c_19668,plain,
! [X0: $i] : ~ proper_subset(X0,sK23(powerset(X0))),
inference(superposition,[status(thm)],[c_19617,c_188]) ).
tcf(c_19669,plain,
sK23(powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_19617,c_152]) ).
tcf(c_19672,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_145,c_19595]) ).
tcf(c_19681,plain,
! [X0: $i] : subset(set_difference(empty_set,X0),X0),
inference(superposition,[status(thm)],[c_19599,c_19485]) ).
tcf(c_19682,plain,
! [X0: $i] : set_difference(X0,X0) = set_difference(empty_set,X0),
inference(superposition,[status(thm)],[c_19599,c_153]) ).
tcf(c_19687,plain,
! [X0: $i] : set_union2(empty_set,X0) = set_difference(X0,empty_set),
inference(superposition,[status(thm)],[c_19599,c_145]) ).
tcf(c_19697,plain,
! [X0: $i] :
( empty(X0)
| ~ proper_subset(X0,sK22(X0)) ),
inference(superposition,[status(thm)],[c_19616,c_188]) ).
tcf(c_19701,plain,
! [X0: $i] : ~ empty(sK2(powerset(X0))),
inference(superposition,[status(thm)],[c_19515,c_19634]) ).
tcf(c_19702,plain,
! [X0: $i] : ~ in(sK2(powerset(union(X0))),X0),
inference(superposition,[status(thm)],[c_222,c_19634]) ).
tcf(c_19704,plain,
! [X0: $i] : ~ empty(sK54(powerset(X0))),
inference(superposition,[status(thm)],[c_19515,c_19637]) ).
tcf(c_19705,plain,
! [X0: $i] : ~ in(sK54(powerset(union(X0))),X0),
inference(superposition,[status(thm)],[c_222,c_19637]) ).
tcf(c_19710,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),set_union2(X1,set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_153,c_19593]) ).
tcf(c_19711,plain,
! [X0: $i] : subset(empty_set,set_union2(X0,empty_set)),
inference(superposition,[status(thm)],[c_263,c_19593]) ).
tcf(c_19712,plain,
! [X0: $i] : subset(X0,set_union2(empty_set,X0)),
inference(superposition,[status(thm)],[c_264,c_19593]) ).
tcf(c_19715,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_145,c_19593]) ).
tcf(c_19725,plain,
! [X0: $i,X1: $i] : ~ empty(unordered_pair(powerset(X0),X1)),
inference(superposition,[status(thm)],[c_19515,c_19635]) ).
tcf(c_19726,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(powerset(union(X0)),X1),X0),
inference(superposition,[status(thm)],[c_222,c_19635]) ).
tcf(c_19728,plain,
! [X0: $i,X1: $i] : ~ empty(unordered_pair(X0,powerset(X1))),
inference(superposition,[status(thm)],[c_19515,c_19636]) ).
tcf(c_19729,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(X0,powerset(union(X1))),X1),
inference(superposition,[status(thm)],[c_222,c_19636]) ).
tcf(c_19736,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X1,X0)),set_union2(X0,set_union2(X1,X0))),
inference(superposition,[status(thm)],[c_153,c_19566]) ).
tcf(c_19737,plain,
! [X0: $i] : subset(set_difference(X0,empty_set),set_union2(X0,empty_set)),
inference(superposition,[status(thm)],[c_263,c_19566]) ).
tcf(c_19738,plain,
! [X0: $i] : subset(set_difference(empty_set,X0),set_union2(empty_set,X0)),
inference(superposition,[status(thm)],[c_264,c_19566]) ).
tcf(c_19739,plain,
! [X0: $i] : subset(set_difference(X0,empty_set),set_union2(X0,X0)),
inference(superposition,[status(thm)],[c_4095,c_19566]) ).
tcf(c_19741,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_145,c_19566]) ).
tcf(c_19742,plain,
! [X0: $i] : subset(set_difference(X0,set_difference(empty_set,X0)),X0),
inference(superposition,[status(thm)],[c_244,c_19566]) ).
tcf(c_19743,plain,
! [X0: $i] : subset(set_difference(X0,set_difference(X0,X0)),X0),
inference(superposition,[status(thm)],[c_245,c_19566]) ).
tcf(c_19744,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X1,X0)),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_255,c_19566]) ).
tcf(c_19745,plain,
! [X0: $i] : subset(set_difference(empty_set,set_difference(X0,empty_set)),X0),
inference(superposition,[status(thm)],[c_19599,c_19566]) ).
tcf(c_19746,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(X0,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_19566,c_188]) ).
tcf(c_19782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( X1 = X2 )
| ( unordered_pair(X0,X1) != unordered_pair(X2,X3) ) ),
inference(superposition,[status(thm)],[c_351,c_74]) ).
tcf(c_19785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_351,c_129]) ).
tcf(c_19786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_351,c_128]) ).
tcf(c_19788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(superposition,[status(thm)],[c_351,c_129]) ).
tcf(c_19789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(superposition,[status(thm)],[c_351,c_128]) ).
tcf(c_19813,plain,
! [X0: $i] :
( subset(relation_rng(empty_set),X0)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_19422,c_78]) ).
tcf(c_19814,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ proper_subset(X0,relation_rng(relation_rng_restriction(X0,X1))) ),
inference(superposition,[status(thm)],[c_78,c_188]) ).
tcf(c_19815,plain,
! [X0: $i] :
( ( relation_rng(relation_rng_restriction(empty_set,X0)) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_78,c_152]) ).
tcf(c_19816,plain,
! [X0: $i] :
( subset(empty_set,X0)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_19813,c_187]) ).
tcf(c_19827,plain,
! [X0: $i] :
( subset(relation_image(empty_set,X0),empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_187,c_94]) ).
tcf(c_19828,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(identity_relation(X0),X1),X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_204,c_94]) ).
tcf(c_19829,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ proper_subset(relation_rng(X0),relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_94,c_188]) ).
tcf(c_19830,plain,
! [X0: $i] : subset(relation_image(empty_set,X0),empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_19827,c_231]) ).
tcf(c_19833,plain,
! [X0: $i,X1: $i] : subset(relation_image(identity_relation(X0),X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_19828,c_422]) ).
tcf(c_19837,plain,
! [X0: $i] : ~ proper_subset(empty_set,relation_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_19830,c_188]) ).
tcf(c_19838,plain,
! [X0: $i] : relation_image(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_19830,c_152]) ).
tcf(c_19842,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,relation_image(identity_relation(X0),X1)),
inference(superposition,[status(thm)],[c_19833,c_188]) ).
tcf(c_19843,plain,
! [X0: $i] : relation_image(identity_relation(empty_set),X0) = empty_set,
inference(superposition,[status(thm)],[c_19833,c_152]) ).
tcf(c_19847,plain,
( subset(empty_set,relation_rng(empty_set))
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_19838,c_94]) ).
tcf(c_19849,plain,
! [X0: $i] : ~ subset(sK2(powerset(union(powerset(X0)))),X0),
inference(superposition,[status(thm)],[c_289,c_19702]) ).
tcf(c_19850,plain,
! [X0: $i] : ~ in(sK2(powerset(X0)),powerset(X0)),
inference(superposition,[status(thm)],[c_225,c_19702]) ).
tcf(c_19852,plain,
! [X0: $i] : ~ subset(sK54(powerset(union(powerset(X0)))),X0),
inference(superposition,[status(thm)],[c_289,c_19705]) ).
tcf(c_19853,plain,
! [X0: $i] : ~ in(sK54(powerset(X0)),powerset(X0)),
inference(superposition,[status(thm)],[c_225,c_19705]) ).
tcf(c_19855,plain,
( subset(empty_set,relation_rng(identity_relation(empty_set)))
| ~ relation(identity_relation(empty_set)) ),
inference(superposition,[status(thm)],[c_19843,c_94]) ).
tcf(c_19862,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,sK1(X0,X1)) ),
inference(superposition,[status(thm)],[c_6708,c_243]) ).
tcf(c_19864,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| element(sK1(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_6708,c_276]) ).
tcf(c_19866,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| subset(sK1(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_6708,c_290]) ).
tcf(c_19879,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_341,c_19211]) ).
tcf(c_19880,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_359,c_19211]) ).
tcf(c_19881,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_432,c_19211]) ).
tcf(c_19896,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_341,c_19212]) ).
tcf(c_19897,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_359,c_19212]) ).
tcf(c_19898,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_432,c_19212]) ).
tcf(c_19912,plain,
relation_inverse(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_232,c_19213]) ).
tcf(c_19913,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_341,c_19213]) ).
tcf(c_19914,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_359,c_19213]) ).
tcf(c_19915,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_432,c_19213]) ).
tcf(c_19929,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ~ proper_subset(X0,sK18(powerset(X0),X1)) ),
inference(superposition,[status(thm)],[c_19652,c_188]) ).
tcf(c_19930,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| ( sK18(powerset(empty_set),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_19652,c_152]) ).
tcf(c_19941,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(identity_relation(X0),X1),X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_203,c_105]) ).
tcf(c_19942,plain,
! [X0: $i] :
( subset(relation_inverse_image(empty_set,X0),empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_186,c_105]) ).
tcf(c_19943,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ proper_subset(relation_dom(X0),relation_inverse_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_105,c_188]) ).
tcf(c_19944,plain,
! [X0: $i] : subset(relation_inverse_image(empty_set,X0),empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_19942,c_231]) ).
tcf(c_19947,plain,
! [X0: $i,X1: $i] : subset(relation_inverse_image(identity_relation(X0),X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_19941,c_422]) ).
tcf(c_19955,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| ~ in(empty_set,X0) ),
inference(superposition,[status(thm)],[c_111,c_140]) ).
tcf(c_19956,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ proper_subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_140,c_188]) ).
tcf(c_19958,plain,
! [X0: $i] : ~ in(powerset(X0),X0),
inference(superposition,[status(thm)],[c_140,c_19635]) ).
tcf(c_19971,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,union(X2))
| ~ in(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_222,c_143]) ).
tcf(c_19972,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(unordered_pair(X0,X1),X2)),
inference(superposition,[status(thm)],[c_209,c_143]) ).
tcf(c_19974,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(X1,unordered_pair(X0,X2))),
inference(superposition,[status(thm)],[c_19598,c_143]) ).
tcf(c_19976,plain,
! [X0: $i] :
( in(empty_set,X0)
| ~ subset(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_111,c_143]) ).
tcf(c_19991,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,union(X2))
| ~ in(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_222,c_144]) ).
tcf(c_19992,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(unordered_pair(X1,X0),X2)),
inference(superposition,[status(thm)],[c_209,c_144]) ).
tcf(c_19994,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(X1,unordered_pair(X2,X0))),
inference(superposition,[status(thm)],[c_19598,c_144]) ).
tcf(c_20005,plain,
! [X0: $i] : ~ proper_subset(empty_set,relation_inverse_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_19944,c_188]) ).
tcf(c_20006,plain,
! [X0: $i] : relation_inverse_image(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_19944,c_152]) ).
tcf(c_20010,plain,
! [X0: $i] : ~ subset(powerset(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_289,c_19958]) ).
tcf(c_20012,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,relation_inverse_image(identity_relation(X0),X1)),
inference(superposition,[status(thm)],[c_19947,c_188]) ).
tcf(c_20013,plain,
! [X0: $i] : relation_inverse_image(identity_relation(empty_set),X0) = empty_set,
inference(superposition,[status(thm)],[c_19947,c_152]) ).
tcf(c_20017,plain,
( subset(empty_set,relation_dom(empty_set))
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_20006,c_105]) ).
tcf(c_20019,plain,
! [X0: $i] : ~ empty(powerset(powerset(X0))),
inference(superposition,[status(thm)],[c_19515,c_20010]) ).
tcf(c_20020,plain,
! [X0: $i] : ~ in(powerset(powerset(union(X0))),X0),
inference(superposition,[status(thm)],[c_222,c_20010]) ).
tcf(c_20028,plain,
! [X0: $i] : in(empty_set,set_union2(powerset(empty_set),X0)),
inference(superposition,[status(thm)],[c_111,c_19972]) ).
tcf(c_20030,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(unordered_pair(X0,X1),X2),X0),
inference(superposition,[status(thm)],[c_19972,c_243]) ).
tcf(c_20031,plain,
! [X0: $i,X1: $i,X2: $i] : ~ empty(set_union2(unordered_pair(X0,X1),X2)),
inference(superposition,[status(thm)],[c_19972,c_471]) ).
tcf(c_20032,plain,
! [X0: $i,X1: $i,X2: $i] : element(X0,set_union2(unordered_pair(X0,X1),X2)),
inference(superposition,[status(thm)],[c_19972,c_276]) ).
tcf(c_20041,plain,
! [X0: $i] : in(empty_set,set_union2(X0,powerset(empty_set))),
inference(superposition,[status(thm)],[c_255,c_20028]) ).
tcf(c_20042,plain,
! [X0: $i] : ~ in(set_union2(powerset(empty_set),X0),empty_set),
inference(superposition,[status(thm)],[c_20028,c_243]) ).
tcf(c_20043,plain,
! [X0: $i] : ~ empty(set_union2(powerset(empty_set),X0)),
inference(superposition,[status(thm)],[c_20028,c_471]) ).
tcf(c_20044,plain,
! [X0: $i] : element(empty_set,set_union2(powerset(empty_set),X0)),
inference(superposition,[status(thm)],[c_20028,c_276]) ).
tcf(c_20052,plain,
! [X0: $i] : ~ in(set_union2(X0,powerset(empty_set)),empty_set),
inference(superposition,[status(thm)],[c_20041,c_243]) ).
tcf(c_20053,plain,
! [X0: $i] : ~ empty(set_union2(X0,powerset(empty_set))),
inference(superposition,[status(thm)],[c_20041,c_471]) ).
tcf(c_20054,plain,
! [X0: $i] : element(empty_set,set_union2(X0,powerset(empty_set))),
inference(superposition,[status(thm)],[c_20041,c_276]) ).
tcf(c_20077,plain,
! [X0: $i,X1: $i] :
( subset(X0,powerset(X1))
| ~ subset(sK18(X0,powerset(X1)),X1) ),
inference(superposition,[status(thm)],[c_289,c_240]) ).
tcf(c_20091,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_252,c_243]) ).
tcf(c_20092,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_252,c_471]) ).
tcf(c_20093,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_252,c_276]) ).
tcf(c_20094,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_union2(X1,X2))
| ~ in(sK18(X0,set_union2(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_252,c_240]) ).
tcf(c_20095,plain,
! [X0: $i,X1: $i] : ~ in(sK2(set_union2(X0,X1)),X0),
inference(superposition,[status(thm)],[c_252,c_19526]) ).
tcf(c_20096,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(set_union2(X0,X1),X2),X0),
inference(superposition,[status(thm)],[c_252,c_19532]) ).
tcf(c_20097,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,set_union2(X1,X2)),X1),
inference(superposition,[status(thm)],[c_252,c_19533]) ).
tcf(c_20098,plain,
! [X0: $i,X1: $i] : ~ in(sK54(set_union2(X0,X1)),X0),
inference(superposition,[status(thm)],[c_252,c_19534]) ).
tcf(c_20099,plain,
! [X0: $i,X1: $i] : ~ in(sK2(powerset(union(set_union2(X0,X1)))),X0),
inference(superposition,[status(thm)],[c_252,c_19702]) ).
tcf(c_20100,plain,
! [X0: $i,X1: $i] : ~ in(sK54(powerset(union(set_union2(X0,X1)))),X0),
inference(superposition,[status(thm)],[c_252,c_19705]) ).
tcf(c_20101,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),X0),
inference(superposition,[status(thm)],[c_252,c_19958]) ).
tcf(c_20122,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_145,c_253]) ).
tcf(c_20127,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_253,c_243]) ).
tcf(c_20128,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_253,c_471]) ).
tcf(c_20129,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_253,c_276]) ).
tcf(c_20130,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_union2(X1,X2))
| ~ in(sK18(X0,set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_253,c_240]) ).
tcf(c_20131,plain,
! [X0: $i,X1: $i] : ~ in(sK2(set_union2(X0,X1)),X1),
inference(superposition,[status(thm)],[c_253,c_19526]) ).
tcf(c_20132,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(set_union2(X0,X1),X2),X1),
inference(superposition,[status(thm)],[c_253,c_19532]) ).
tcf(c_20133,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(unordered_pair(X0,set_union2(X1,X2)),X2),
inference(superposition,[status(thm)],[c_253,c_19533]) ).
tcf(c_20134,plain,
! [X0: $i,X1: $i] : ~ in(sK54(set_union2(X0,X1)),X1),
inference(superposition,[status(thm)],[c_253,c_19534]) ).
tcf(c_20135,plain,
! [X0: $i,X1: $i] : ~ in(sK2(powerset(union(set_union2(X0,X1)))),X1),
inference(superposition,[status(thm)],[c_253,c_19702]) ).
tcf(c_20136,plain,
! [X0: $i,X1: $i] : ~ in(sK54(powerset(union(set_union2(X0,X1)))),X1),
inference(superposition,[status(thm)],[c_253,c_19705]) ).
tcf(c_20137,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),X1),
inference(superposition,[status(thm)],[c_253,c_19958]) ).
tcf(c_20164,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(X0,unordered_pair(X1,X2)),X1),
inference(superposition,[status(thm)],[c_19974,c_243]) ).
tcf(c_20165,plain,
! [X0: $i,X1: $i,X2: $i] : ~ empty(set_union2(X0,unordered_pair(X1,X2))),
inference(superposition,[status(thm)],[c_19974,c_471]) ).
tcf(c_20166,plain,
! [X0: $i,X1: $i,X2: $i] : element(X0,set_union2(X1,unordered_pair(X0,X2))),
inference(superposition,[status(thm)],[c_19974,c_276]) ).
tcf(c_20178,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(unordered_pair(X0,X1),X2),X1),
inference(superposition,[status(thm)],[c_19992,c_243]) ).
tcf(c_20180,plain,
! [X0: $i,X1: $i,X2: $i] : element(X0,set_union2(unordered_pair(X1,X0),X2)),
inference(superposition,[status(thm)],[c_19992,c_276]) ).
tcf(c_20188,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(set_union2(X0,unordered_pair(X1,X2)),X2),
inference(superposition,[status(thm)],[c_19994,c_243]) ).
tcf(c_20190,plain,
! [X0: $i,X1: $i,X2: $i] : element(X0,set_union2(X1,unordered_pair(X2,X0))),
inference(superposition,[status(thm)],[c_19994,c_276]) ).
tcf(c_20191,plain,
( subset(empty_set,relation_dom(identity_relation(empty_set)))
| ~ relation(identity_relation(empty_set)) ),
inference(superposition,[status(thm)],[c_20013,c_105]) ).
tcf(c_20194,plain,
! [X0: $i,X1: $i] : ~ in(powerset(powerset(union(set_union2(X0,X1)))),X0),
inference(superposition,[status(thm)],[c_252,c_20020]) ).
tcf(c_20195,plain,
! [X0: $i,X1: $i] : ~ in(powerset(powerset(union(set_union2(X0,X1)))),X1),
inference(superposition,[status(thm)],[c_253,c_20020]) ).
tcf(c_20196,plain,
! [X0: $i] : ~ subset(powerset(powerset(union(powerset(X0)))),X0),
inference(superposition,[status(thm)],[c_289,c_20020]) ).
tcf(c_20197,plain,
! [X0: $i] : ~ in(powerset(powerset(X0)),powerset(X0)),
inference(superposition,[status(thm)],[c_225,c_20020]) ).
tcf(c_20216,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(sK2(set_union2(set_union2(X0,X1),X2)),X0),
inference(superposition,[status(thm)],[c_252,c_20095]) ).
tcf(c_20217,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(sK2(set_union2(set_union2(X0,X1),X2)),X1),
inference(superposition,[status(thm)],[c_253,c_20095]) ).
tcf(c_20218,plain,
! [X0: $i,X1: $i] : ~ subset(sK2(set_union2(powerset(X0),X1)),X0),
inference(superposition,[status(thm)],[c_289,c_20095]) ).
tcf(c_20224,plain,
! [X0: $i] : ~ in(sK2(X0),empty_set),
inference(superposition,[status(thm)],[c_19599,c_20095]) ).
tcf(c_20227,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(sK54(set_union2(set_union2(X0,X1),X2)),X0),
inference(superposition,[status(thm)],[c_252,c_20098]) ).
tcf(c_20228,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(sK54(set_union2(set_union2(X0,X1),X2)),X1),
inference(superposition,[status(thm)],[c_253,c_20098]) ).
tcf(c_20229,plain,
! [X0: $i,X1: $i] : ~ subset(sK54(set_union2(powerset(X0),X1)),X0),
inference(superposition,[status(thm)],[c_289,c_20098]) ).
tcf(c_20235,plain,
! [X0: $i] : ~ in(sK54(X0),empty_set),
inference(superposition,[status(thm)],[c_19599,c_20098]) ).
tcf(c_20238,plain,
! [X0: $i] : subset(set_difference(X0,empty_set),set_union2(empty_set,X0)),
inference(superposition,[status(thm)],[c_264,c_19715]) ).
tcf(c_20239,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),X1),set_union2(X1,set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_153,c_19715]) ).
tcf(c_20242,plain,
! [X0: $i] : subset(set_difference(empty_set,X0),set_union2(X0,X0)),
inference(superposition,[status(thm)],[c_4095,c_19715]) ).
tcf(c_20244,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_145,c_19715]) ).
tcf(c_20245,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,X0),X0),X0),
inference(superposition,[status(thm)],[c_244,c_19715]) ).
tcf(c_20246,plain,
! [X0: $i] : subset(set_difference(set_difference(X0,X0),X0),X0),
inference(superposition,[status(thm)],[c_245,c_19715]) ).
tcf(c_20247,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),X1),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_255,c_19715]) ).
tcf(c_20248,plain,
! [X0: $i] : subset(set_difference(set_difference(X0,empty_set),empty_set),X0),
inference(superposition,[status(thm)],[c_19599,c_19715]) ).
tcf(c_20249,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0)),
inference(superposition,[status(thm)],[c_19715,c_188]) ).
tcf(c_20262,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),X2)
| in(sK1(set_difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_6708,c_269]) ).
tcf(c_20263,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,X1),X2)
| in(sK8(set_difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_149,c_269]) ).
tcf(c_20264,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_difference(X1,X2))
| in(sK8(X0,set_difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_150,c_269]) ).
tcf(c_20265,plain,
! [X0: $i,X1: $i] :
( in(sK16(set_difference(X0,X1)),X0)
| ( set_difference(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_233,c_269]) ).
tcf(c_20266,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),X2)
| in(sK18(set_difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_241,c_269]) ).
tcf(c_20267,plain,
! [X0: $i,X1: $i] :
( relation(set_difference(X0,X1))
| in(sK38(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_314,c_269]) ).
tcf(c_20268,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_153,c_269]) ).
tcf(c_20296,plain,
! [X0: $i] :
( empty(X0)
| empty(powerset(X0))
| in(sK22(X0),powerset(X0)) ),
inference(superposition,[status(thm)],[c_279,c_283]) ).
tcf(c_20297,plain,
! [X0: $i] :
( empty(X0)
| in(sK23(X0),X0) ),
inference(superposition,[status(thm)],[c_281,c_283]) ).
tcf(c_20298,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(X0,powerset(X0)) ),
inference(superposition,[status(thm)],[c_4010,c_283]) ).
tcf(c_20299,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(empty_set,powerset(X0)) ),
inference(superposition,[status(thm)],[c_19225,c_283]) ).
tcf(c_20310,plain,
! [X0: $i] : in(empty_set,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_20299,c_286]) ).
tcf(c_20311,plain,
! [X0: $i] : in(X0,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_20298,c_286]) ).
tcf(c_20312,plain,
! [X0: $i] :
( empty(X0)
| in(sK22(X0),powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20296,c_286]) ).
tcf(c_20329,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_273,c_285]) ).
tcf(c_20331,plain,
! [X0: $i] :
( empty(sK23(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_281,c_285]) ).
tcf(c_20336,plain,
! [X0: $i] :
( relation(X0)
| empty(sK38(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19315,c_285]) ).
tcf(c_20349,plain,
! [X0: $i] : ~ in(powerset(X0),empty_set),
inference(superposition,[status(thm)],[c_20310,c_243]) ).
tcf(c_20361,plain,
( empty(powerset(empty_set))
| in(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_19669,c_20297]) ).
tcf(c_20362,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK23(X0)) ),
inference(superposition,[status(thm)],[c_20297,c_243]) ).
tcf(c_20366,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X0,X1))
| in(sK23(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_20297,c_269]) ).
tcf(c_20378,plain,
! [X0: $i] :
( ( relation_inverse(sK23(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20331,c_19213]) ).
tcf(c_20379,plain,
! [X0: $i] :
( ( relation_rng(sK23(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20331,c_19212]) ).
tcf(c_20380,plain,
! [X0: $i] :
( ( relation_dom(sK23(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20331,c_19211]) ).
tcf(c_20381,plain,
! [X0: $i] :
( ( sK23(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20331,c_229]) ).
tcf(c_20382,plain,
! [X0: $i] :
( one_to_one(sK23(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20331,c_6826]) ).
tcf(c_20383,plain,
! [X0: $i] :
( relation(sK23(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20331,c_478]) ).
tcf(c_20384,plain,
! [X0: $i] :
( function(sK23(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20331,c_331]) ).
tcf(c_20421,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(set_union2(X0,X1),X2)),X0),
inference(superposition,[status(thm)],[c_252,c_20101]) ).
tcf(c_20422,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(set_union2(X0,X1),X2)),X1),
inference(superposition,[status(thm)],[c_253,c_20101]) ).
tcf(c_20423,plain,
! [X0: $i,X1: $i] : ~ subset(powerset(set_union2(powerset(X0),X1)),X0),
inference(superposition,[status(thm)],[c_289,c_20101]) ).
tcf(c_20432,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(sK2(set_union2(X0,set_union2(X1,X2))),X1),
inference(superposition,[status(thm)],[c_252,c_20131]) ).
tcf(c_20433,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(sK2(set_union2(X0,set_union2(X1,X2))),X2),
inference(superposition,[status(thm)],[c_253,c_20131]) ).
tcf(c_20434,plain,
! [X0: $i,X1: $i] : ~ subset(sK2(set_union2(X0,powerset(X1))),X1),
inference(superposition,[status(thm)],[c_289,c_20131]) ).
tcf(c_20436,plain,
! [X0: $i,X1: $i] : ~ in(sK2(set_union2(X0,X1)),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_145,c_20131]) ).
tcf(c_20444,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(sK54(set_union2(X0,set_union2(X1,X2))),X1),
inference(superposition,[status(thm)],[c_252,c_20134]) ).
tcf(c_20445,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(sK54(set_union2(X0,set_union2(X1,X2))),X2),
inference(superposition,[status(thm)],[c_253,c_20134]) ).
tcf(c_20446,plain,
! [X0: $i,X1: $i] : ~ subset(sK54(set_union2(X0,powerset(X1))),X1),
inference(superposition,[status(thm)],[c_289,c_20134]) ).
tcf(c_20448,plain,
! [X0: $i,X1: $i] : ~ in(sK54(set_union2(X0,X1)),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_145,c_20134]) ).
tcf(c_20456,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(X0,set_union2(X1,X2))),X1),
inference(superposition,[status(thm)],[c_252,c_20137]) ).
tcf(c_20457,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(powerset(set_union2(X0,set_union2(X1,X2))),X2),
inference(superposition,[status(thm)],[c_253,c_20137]) ).
tcf(c_20458,plain,
! [X0: $i,X1: $i] : ~ subset(powerset(set_union2(X0,powerset(X1))),X1),
inference(superposition,[status(thm)],[c_289,c_20137]) ).
tcf(c_20460,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_145,c_20137]) ).
tcf(c_20476,plain,
! [X0: $i] : subset(set_difference(empty_set,set_difference(X0,empty_set)),set_union2(empty_set,X0)),
inference(superposition,[status(thm)],[c_264,c_19741]) ).
tcf(c_20477,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_union2(X0,set_union2(X1,X0))),
inference(superposition,[status(thm)],[c_153,c_19741]) ).
tcf(c_20480,plain,
! [X0: $i] : subset(set_difference(X0,set_difference(empty_set,X0)),set_union2(X0,X0)),
inference(superposition,[status(thm)],[c_4095,c_19741]) ).
tcf(c_20482,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_145,c_19741]) ).
tcf(c_20483,plain,
! [X0: $i] : subset(set_difference(X0,set_difference(set_difference(empty_set,X0),X0)),X0),
inference(superposition,[status(thm)],[c_244,c_19741]) ).
tcf(c_20484,plain,
! [X0: $i] : subset(set_difference(X0,set_difference(set_difference(X0,X0),X0)),X0),
inference(superposition,[status(thm)],[c_245,c_19741]) ).
tcf(c_20485,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_255,c_19741]) ).
tcf(c_20486,plain,
! [X0: $i] : subset(set_difference(empty_set,set_difference(set_difference(X0,empty_set),empty_set)),X0),
inference(superposition,[status(thm)],[c_19599,c_19741]) ).
tcf(c_20487,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(X0,set_difference(set_difference(X1,X0),X0))),
inference(superposition,[status(thm)],[c_19741,c_188]) ).
tcf(c_20509,plain,
! [X0: $i] :
( empty(identity_relation(X0))
| ~ empty(X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_203,c_343]) ).
tcf(c_20511,plain,
! [X0: $i] :
( empty(identity_relation(X0))
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20509,c_422]) ).
tcf(c_20528,plain,
relation_inverse(relation_inverse(sK5)) = sK5,
inference(superposition,[status(thm)],[c_96,c_429]) ).
tcf(c_20529,plain,
! [X0: $i] : relation_inverse(relation_inverse(identity_relation(X0))) = identity_relation(X0),
inference(superposition,[status(thm)],[c_422,c_429]) ).
tcf(c_20530,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(relation_dom_restriction(X0,X1))) = relation_dom_restriction(X0,X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_334,c_429]) ).
tcf(c_20531,plain,
relation_inverse(relation_inverse(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_231,c_429]) ).
tcf(c_20532,plain,
relation_inverse(relation_inverse(sK47)) = sK47,
inference(superposition,[status(thm)],[c_329,c_429]) ).
tcf(c_20533,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(X0))) = relation_dom(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_342,c_429]) ).
tcf(c_20534,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(relation_rng_restriction(X1,X0))) = relation_rng_restriction(X1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_352,c_429]) ).
tcf(c_20535,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(X0))) = relation_rng(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_360,c_429]) ).
tcf(c_20536,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(X0))) = relation_inverse(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_434,c_429]) ).
tcf(c_20537,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(X0))) = relation_inverse(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_433,c_429]) ).
tcf(c_20538,plain,
relation_inverse(relation_inverse(sK75)) = sK75,
inference(superposition,[status(thm)],[c_456,c_429]) ).
tcf(c_20539,plain,
relation_inverse(relation_inverse(sK79)) = sK79,
inference(superposition,[status(thm)],[c_474,c_429]) ).
tcf(c_20540,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK23(X0))) = sK23(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20383,c_429]) ).
tcf(c_20568,plain,
! [X0: $i] :
( ( relation_inverse(identity_relation(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20511,c_19213]) ).
tcf(c_20569,plain,
! [X0: $i] :
( ( relation_rng(identity_relation(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20511,c_19212]) ).
tcf(c_20570,plain,
! [X0: $i] :
( ( relation_dom(identity_relation(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20511,c_19211]) ).
tcf(c_20571,plain,
! [X0: $i] :
( ( identity_relation(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20511,c_229]) ).
tcf(c_20572,plain,
! [X0: $i] :
( one_to_one(identity_relation(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20511,c_6826]) ).
tcf(c_20591,plain,
( one_to_one(sK5)
| ~ empty(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20528,c_19173]) ).
tcf(c_20594,plain,
( empty(sK5)
| ~ empty(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20528,c_432]) ).
tcf(c_20600,plain,
( one_to_one(sK47)
| ~ empty(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_20532,c_19173]) ).
tcf(c_20603,plain,
( empty(sK47)
| ~ empty(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_20532,c_432]) ).
tcf(c_20612,plain,
( empty(sK75)
| ~ empty(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_20538,c_432]) ).
tcf(c_20619,plain,
( one_to_one(sK5)
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_432,c_20591]) ).
tcf(c_20631,plain,
( empty(sK79)
| ~ empty(relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_20539,c_432]) ).
tcf(c_20632,plain,
~ empty(relation_inverse(sK79)),
inference(forward_subsumption_resolution,[status(thm)],[c_20631,c_473]) ).
tcf(c_20642,plain,
( one_to_one(sK47)
| ~ empty(sK47) ),
inference(superposition,[status(thm)],[c_432,c_20600]) ).
tcf(c_20646,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X1,X0)),set_union2(set_union2(X1,X0),X0)),
inference(superposition,[status(thm)],[c_153,c_19744]) ).
tcf(c_20648,plain,
! [X0: $i] : subset(set_difference(empty_set,X0),set_union2(X0,empty_set)),
inference(superposition,[status(thm)],[c_264,c_19744]) ).
tcf(c_20651,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_145,c_19744]) ).
tcf(c_20656,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(X1,set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_19744,c_188]) ).
tcf(c_20666,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(function_inverse(X0))) = function_inverse(X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_465,c_429]) ).
tcf(c_20682,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ~ empty(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_19395,c_51]) ).
tcf(c_20685,plain,
! [X0: $i] :
( in(empty_set,unordered_pair(X0,X0))
| ~ in(X0,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_19442,c_51]) ).
tcf(c_20686,plain,
! [X0: $i] :
( ~ in(empty_set,X0)
| ~ disjoint(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_111,c_51]) ).
tcf(c_20695,plain,
( subset(relation_rng(empty_set),relation_rng(empty_set))
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_19422,c_80]) ).
tcf(c_20696,plain,
! [X0: $i] :
( subset(relation_rng(relation_rng_restriction(X0,empty_set)),empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_187,c_80]) ).
tcf(c_20697,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X1,identity_relation(X0))),X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_204,c_80]) ).
tcf(c_20698,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ proper_subset(relation_rng(X0),relation_rng(relation_rng_restriction(X1,X0))) ),
inference(superposition,[status(thm)],[c_80,c_188]) ).
tcf(c_20703,plain,
! [X0: $i,X1: $i] : subset(relation_rng(relation_rng_restriction(X0,identity_relation(X1))),X1),
inference(forward_subsumption_resolution,[status(thm)],[c_20697,c_422]) ).
tcf(c_20748,plain,
! [X0: $i] :
( empty(X0)
| ~ in(powerset(X0),sK22(X0)) ),
inference(superposition,[status(thm)],[c_20312,c_243]) ).
tcf(c_20758,plain,
( empty(powerset(empty_set))
| ~ in(powerset(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_19669,c_20362]) ).
tcf(c_20759,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,relation_rng(relation_rng_restriction(X1,identity_relation(X0)))),
inference(superposition,[status(thm)],[c_20703,c_188]) ).
tcf(c_20760,plain,
! [X0: $i] : relation_rng(relation_rng_restriction(X0,identity_relation(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_20703,c_152]) ).
tcf(c_20768,plain,
! [X0: $i,X1: $i] :
( in(X1,unordered_pair(X0,X0))
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_19372,c_51]) ).
tcf(c_20777,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| empty(sK8(X0,X1))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19396,c_285]) ).
tcf(c_20787,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| empty(sK8(X1,X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19408,c_285]) ).
tcf(c_20794,plain,
! [X0: $i] : ~ proper_subset(X0,set_difference(X0,empty_set)),
inference(superposition,[status(thm)],[c_244,c_19484]) ).
tcf(c_20795,plain,
! [X0: $i] : ~ proper_subset(X0,set_difference(X0,X0)),
inference(superposition,[status(thm)],[c_245,c_19484]) ).
tcf(c_20797,plain,
! [X0: $i] : ~ proper_subset(X0,set_difference(empty_set,X0)),
inference(superposition,[status(thm)],[c_19599,c_19484]) ).
tcf(c_20798,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(set_union2(X0,X1),X1),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_153,c_19484]) ).
tcf(c_20799,plain,
! [X0: $i] : ~ proper_subset(set_union2(empty_set,X0),empty_set),
inference(superposition,[status(thm)],[c_263,c_19484]) ).
tcf(c_20800,plain,
! [X0: $i] : ~ proper_subset(set_union2(X0,empty_set),X0),
inference(superposition,[status(thm)],[c_264,c_19484]) ).
tcf(c_20801,plain,
! [X0: $i] : ~ proper_subset(set_union2(X0,X0),empty_set),
inference(superposition,[status(thm)],[c_4095,c_19484]) ).
tcf(c_20813,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ~ proper_subset(X0,sK1(powerset(X0),X1)) ),
inference(superposition,[status(thm)],[c_19866,c_188]) ).
tcf(c_20814,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| ( sK1(powerset(empty_set),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_19866,c_152]) ).
tcf(c_20826,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19515,c_85]) ).
tcf(c_20827,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,union(X1)) = union(X1) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_222,c_85]) ).
tcf(c_20828,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_rng(relation_rng_restriction(X1,X0)),X1) = X1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_78,c_85]) ).
tcf(c_20829,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_rng_restriction(X1,X0),X0) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_79,c_85]) ).
tcf(c_20830,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_rng(relation_rng_restriction(X1,X0)),relation_rng(X0)) = relation_rng(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_80,c_85]) ).
tcf(c_20831,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_image(X0,X1),relation_rng(X0)) = relation_rng(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_94,c_85]) ).
tcf(c_20832,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_inverse_image(X0,X1),relation_dom(X0)) = relation_dom(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_105,c_85]) ).
tcf(c_20834,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),X0) = X0,
inference(superposition,[status(thm)],[c_135,c_85]) ).
tcf(c_20835,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_union2(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_209,c_85]) ).
tcf(c_20836,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_dom_restriction(X0,X1),X0) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_215,c_85]) ).
tcf(c_20838,plain,
! [X0: $i] :
( empty(X0)
| ( set_union2(sK22(X0),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_19616,c_85]) ).
tcf(c_20839,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_union2(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_19485,c_85]) ).
tcf(c_20840,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_difference(X1,X0)),set_union2(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_19566,c_85]) ).
tcf(c_20841,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_union2(X1,X0)) = set_union2(X1,X0),
inference(superposition,[status(thm)],[c_19593,c_85]) ).
tcf(c_20842,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_union2(X1,X0)) = set_union2(X1,X0),
inference(superposition,[status(thm)],[c_19598,c_85]) ).
tcf(c_20843,plain,
! [X0: $i] : set_union2(sK23(powerset(X0)),X0) = X0,
inference(superposition,[status(thm)],[c_19617,c_85]) ).
tcf(c_20844,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( set_union2(sK18(powerset(X0),X1),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_19652,c_85]) ).
tcf(c_20845,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0)) = set_union2(X1,X0),
inference(superposition,[status(thm)],[c_19715,c_85]) ).
tcf(c_20846,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_difference(X1,X0)),set_union2(X1,X0)) = set_union2(X1,X0),
inference(superposition,[status(thm)],[c_19744,c_85]) ).
tcf(c_20847,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_union2(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_19741,c_85]) ).
tcf(c_20848,plain,
! [X0: $i,X1: $i] : set_union2(relation_image(identity_relation(X0),X1),X0) = X0,
inference(superposition,[status(thm)],[c_19833,c_85]) ).
tcf(c_20849,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( set_union2(sK1(powerset(X0),X1),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_19866,c_85]) ).
tcf(c_20850,plain,
! [X0: $i,X1: $i] : set_union2(relation_inverse_image(identity_relation(X0),X1),X0) = X0,
inference(superposition,[status(thm)],[c_19947,c_85]) ).
tcf(c_20851,plain,
! [X0: $i,X1: $i] : set_union2(relation_rng(relation_rng_restriction(X0,identity_relation(X1))),X1) = X1,
inference(superposition,[status(thm)],[c_20703,c_85]) ).
tcf(c_20895,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,sK2(X0))
| ~ in(sK2(X0),powerset(X1)) ),
inference(superposition,[status(thm)],[c_88,c_243]) ).
tcf(c_20896,plain,
! [X0: $i,X1: $i] :
( ~ empty(sK2(X1))
| ~ in(X0,sK2(X1)) ),
inference(superposition,[status(thm)],[c_88,c_471]) ).
tcf(c_20897,plain,
! [X0: $i,X1: $i] :
( element(powerset(X0),sK2(X1))
| ~ in(X0,sK2(X1)) ),
inference(superposition,[status(thm)],[c_88,c_276]) ).
tcf(c_20898,plain,
! [X0: $i] : ~ in(sK2(X0),sK2(X0)),
inference(superposition,[status(thm)],[c_88,c_19958]) ).
tcf(c_20899,plain,
! [X0: $i] : ~ in(powerset(union(sK2(X0))),sK2(X0)),
inference(superposition,[status(thm)],[c_88,c_20020]) ).
tcf(c_20900,plain,
! [X0: $i,X1: $i] : ~ in(set_union2(sK2(X0),X1),sK2(X0)),
inference(superposition,[status(thm)],[c_88,c_20101]) ).
tcf(c_20901,plain,
! [X0: $i,X1: $i] : ~ in(set_union2(X0,sK2(X1)),sK2(X1)),
inference(superposition,[status(thm)],[c_88,c_20137]) ).
tcf(c_20916,plain,
! [X0: $i] :
( subset(identity_relation(X0),cartesian_product2(X0,relation_rng(identity_relation(X0))))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_203,c_117]) ).
tcf(c_20917,plain,
( subset(empty_set,cartesian_product2(empty_set,relation_rng(empty_set)))
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_186,c_117]) ).
tcf(c_20918,plain,
( subset(empty_set,cartesian_product2(relation_dom(empty_set),empty_set))
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_187,c_117]) ).
tcf(c_20919,plain,
! [X0: $i] :
( subset(identity_relation(X0),cartesian_product2(relation_dom(identity_relation(X0)),X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_204,c_117]) ).
tcf(c_20920,plain,
! [X0: $i] :
( ( set_union2(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) = cartesian_product2(relation_dom(X0),relation_rng(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_117,c_85]) ).
tcf(c_20921,plain,
! [X0: $i] :
( ~ relation(X0)
| ~ proper_subset(cartesian_product2(relation_dom(X0),relation_rng(X0)),X0) ),
inference(superposition,[status(thm)],[c_117,c_188]) ).
tcf(c_20922,plain,
! [X0: $i,X1: $i] :
( in(X1,cartesian_product2(relation_dom(unordered_pair(X0,X1)),relation_rng(unordered_pair(X0,X1))))
| ~ relation(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_117,c_144]) ).
tcf(c_20923,plain,
! [X0: $i,X1: $i] :
( in(X0,cartesian_product2(relation_dom(unordered_pair(X0,X1)),relation_rng(unordered_pair(X0,X1))))
| ~ relation(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_117,c_143]) ).
tcf(c_20924,plain,
( subset(empty_set,cartesian_product2(empty_set,empty_set))
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_20918,c_186]) ).
tcf(c_20928,plain,
! [X0: $i] :
( subset(identity_relation(X0),cartesian_product2(X0,X0))
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_20919,c_203]) ).
tcf(c_20929,plain,
! [X0: $i] : subset(identity_relation(X0),cartesian_product2(X0,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_20928,c_422]) ).
tcf(c_20946,plain,
relation_dom(relation_inverse(sK5)) = relation_rng(sK5),
inference(superposition,[status(thm)],[c_96,c_136]) ).
tcf(c_20947,plain,
! [X0: $i] : relation_dom(relation_inverse(identity_relation(X0))) = relation_rng(identity_relation(X0)),
inference(superposition,[status(thm)],[c_422,c_136]) ).
tcf(c_20948,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(function_inverse(X0))) = relation_rng(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_465,c_136]) ).
tcf(c_20949,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(relation_dom_restriction(X0,X1))) = relation_rng(relation_dom_restriction(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_334,c_136]) ).
tcf(c_20950,plain,
relation_dom(relation_inverse(empty_set)) = relation_rng(empty_set),
inference(superposition,[status(thm)],[c_231,c_136]) ).
tcf(c_20951,plain,
relation_dom(relation_inverse(sK47)) = relation_rng(sK47),
inference(superposition,[status(thm)],[c_329,c_136]) ).
tcf(c_20952,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(X0))) = relation_rng(relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_342,c_136]) ).
tcf(c_20953,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(relation_rng_restriction(X1,X0))) = relation_rng(relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_352,c_136]) ).
tcf(c_20954,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(X0))) = relation_rng(relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_360,c_136]) ).
tcf(c_20955,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(X0))) = relation_rng(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_434,c_136]) ).
tcf(c_20956,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(X0))) = relation_rng(relation_inverse(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_433,c_136]) ).
tcf(c_20957,plain,
relation_dom(relation_inverse(sK75)) = relation_rng(sK75),
inference(superposition,[status(thm)],[c_456,c_136]) ).
tcf(c_20958,plain,
relation_dom(relation_inverse(sK79)) = relation_rng(sK79),
inference(superposition,[status(thm)],[c_474,c_136]) ).
tcf(c_20959,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK23(X0))) = relation_rng(sK23(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20383,c_136]) ).
tcf(c_20961,plain,
! [X0: $i] : relation_dom(relation_inverse(identity_relation(X0))) = X0,
inference(light_normalisation,[status(thm)],[c_20947,c_204]) ).
tcf(c_20988,plain,
! [X0: $i] : set_union2(identity_relation(X0),cartesian_product2(X0,X0)) = cartesian_product2(X0,X0),
inference(superposition,[status(thm)],[c_20929,c_85]) ).
tcf(c_20989,plain,
! [X0: $i] : ~ proper_subset(cartesian_product2(X0,X0),identity_relation(X0)),
inference(superposition,[status(thm)],[c_20929,c_188]) ).
tcf(c_20992,plain,
( subset(relation_inverse(sK5),cartesian_product2(relation_rng(sK5),relation_rng(relation_inverse(sK5))))
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20946,c_117]) ).
tcf(c_20993,plain,
( empty(relation_inverse(sK5))
| ~ empty(relation_rng(sK5))
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20946,c_343]) ).
tcf(c_20994,plain,
! [X0: $i] :
( subset(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20946,c_105]) ).
tcf(c_20995,plain,
( function(relation_rng(sK5))
| ~ empty(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20946,c_19131]) ).
tcf(c_20996,plain,
( one_to_one(relation_rng(sK5))
| ~ empty(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20946,c_19129]) ).
tcf(c_20997,plain,
( relation(relation_rng(sK5))
| ~ empty(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20946,c_342]) ).
tcf(c_20998,plain,
( empty(relation_rng(sK5))
| ~ empty(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20946,c_341]) ).
tcf(c_21015,plain,
( subset(relation_inverse(sK47),cartesian_product2(relation_rng(sK47),relation_rng(relation_inverse(sK47))))
| ~ relation(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_20951,c_117]) ).
tcf(c_21016,plain,
( empty(relation_inverse(sK47))
| ~ empty(relation_rng(sK47))
| ~ relation(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_20951,c_343]) ).
tcf(c_21017,plain,
! [X0: $i] :
( subset(relation_inverse_image(relation_inverse(sK47),X0),relation_rng(sK47))
| ~ relation(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_20951,c_105]) ).
tcf(c_21018,plain,
( function(relation_rng(sK47))
| ~ empty(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_20951,c_19131]) ).
tcf(c_21019,plain,
( one_to_one(relation_rng(sK47))
| ~ empty(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_20951,c_19129]) ).
tcf(c_21020,plain,
( relation(relation_rng(sK47))
| ~ empty(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_20951,c_342]) ).
tcf(c_21021,plain,
( empty(relation_rng(sK47))
| ~ empty(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_20951,c_341]) ).
tcf(c_21042,plain,
( function(relation_rng(sK5))
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_432,c_20995]) ).
tcf(c_21049,plain,
( one_to_one(relation_rng(sK5))
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_432,c_20996]) ).
tcf(c_21056,plain,
( relation(relation_rng(sK5))
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_432,c_20997]) ).
tcf(c_21064,plain,
( empty(relation_rng(sK5))
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_432,c_20998]) ).
tcf(c_21073,plain,
( empty(relation_inverse(sK5))
| ~ relation(sK5)
| ~ empty(relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_434,c_20993]) ).
tcf(c_21078,plain,
( empty(relation_inverse(sK5))
| ~ empty(relation_rng(sK5)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21073,c_96]) ).
tcf(c_21087,plain,
( empty(relation_inverse(sK5))
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_359,c_21078]) ).
tcf(c_21095,plain,
! [X0: $i] :
( ( set_union2(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)) = relation_rng(sK5) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20994,c_85]) ).
tcf(c_21096,plain,
! [X0: $i] :
( ~ relation(relation_inverse(sK5))
| ~ proper_subset(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_20994,c_188]) ).
tcf(c_21109,plain,
! [X0: $i,X1: $i] :
( subset(X0,powerset(X1))
| ~ empty(sK18(X0,powerset(X1))) ),
inference(superposition,[status(thm)],[c_19515,c_20077]) ).
tcf(c_21110,plain,
! [X0: $i,X1: $i] :
( subset(X0,powerset(union(X1)))
| ~ in(sK18(X0,powerset(union(X1))),X1) ),
inference(superposition,[status(thm)],[c_222,c_20077]) ).
tcf(c_21111,plain,
! [X0: $i] : subset(powerset(X0),powerset(X0)),
inference(superposition,[status(thm)],[c_19652,c_20077]) ).
tcf(c_21123,plain,
relation_rng(relation_inverse(sK5)) = relation_dom(sK5),
inference(superposition,[status(thm)],[c_96,c_137]) ).
tcf(c_21124,plain,
! [X0: $i] : relation_rng(relation_inverse(identity_relation(X0))) = relation_dom(identity_relation(X0)),
inference(superposition,[status(thm)],[c_422,c_137]) ).
tcf(c_21125,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(function_inverse(X0))) = relation_dom(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_465,c_137]) ).
tcf(c_21126,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(relation_dom_restriction(X0,X1))) = relation_dom(relation_dom_restriction(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_334,c_137]) ).
tcf(c_21127,plain,
relation_rng(relation_inverse(empty_set)) = relation_dom(empty_set),
inference(superposition,[status(thm)],[c_231,c_137]) ).
tcf(c_21128,plain,
relation_rng(relation_inverse(sK47)) = relation_dom(sK47),
inference(superposition,[status(thm)],[c_329,c_137]) ).
tcf(c_21129,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(X0))) = relation_dom(relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_342,c_137]) ).
tcf(c_21130,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(relation_rng_restriction(X1,X0))) = relation_dom(relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_352,c_137]) ).
tcf(c_21131,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(X0))) = relation_dom(relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_360,c_137]) ).
tcf(c_21132,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(X0))) = relation_dom(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_434,c_137]) ).
tcf(c_21133,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(X0))) = relation_dom(relation_inverse(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_433,c_137]) ).
tcf(c_21134,plain,
relation_rng(relation_inverse(sK75)) = relation_dom(sK75),
inference(superposition,[status(thm)],[c_456,c_137]) ).
tcf(c_21135,plain,
relation_rng(relation_inverse(sK79)) = relation_dom(sK79),
inference(superposition,[status(thm)],[c_474,c_137]) ).
tcf(c_21136,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK23(X0))) = relation_dom(sK23(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20383,c_137]) ).
tcf(c_21138,plain,
! [X0: $i] : relation_rng(relation_inverse(identity_relation(X0))) = X0,
inference(light_normalisation,[status(thm)],[c_21124,c_203]) ).
tcf(c_21194,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X0,X0),X1) = empty_set )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_140,c_138]) ).
tcf(c_21195,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19515,c_138]) ).
tcf(c_21196,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,union(X1)) = empty_set )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_222,c_138]) ).
tcf(c_21197,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,X0)),X1) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_78,c_138]) ).
tcf(c_21198,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng_restriction(X1,X0),X0) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_79,c_138]) ).
tcf(c_21199,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,X0)),relation_rng(X0)) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_80,c_138]) ).
tcf(c_21200,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_image(X0,X1),relation_rng(X0)) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_94,c_138]) ).
tcf(c_21201,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_inverse_image(X0,X1),relation_dom(X0)) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_105,c_138]) ).
tcf(c_21202,plain,
! [X0: $i] :
( ( set_difference(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_117,c_138]) ).
tcf(c_21204,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),X0) = empty_set,
inference(superposition,[status(thm)],[c_135,c_138]) ).
tcf(c_21205,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_209,c_138]) ).
tcf(c_21206,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom_restriction(X0,X1),X0) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_215,c_138]) ).
tcf(c_21208,plain,
! [X0: $i] :
( empty(X0)
| ( set_difference(sK22(X0),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_19616,c_138]) ).
tcf(c_21209,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_19485,c_138]) ).
tcf(c_21210,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X1,X0)),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_19566,c_138]) ).
tcf(c_21211,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_union2(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_19593,c_138]) ).
tcf(c_21212,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_union2(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_19598,c_138]) ).
tcf(c_21213,plain,
! [X0: $i] : set_difference(sK23(powerset(X0)),X0) = empty_set,
inference(superposition,[status(thm)],[c_19617,c_138]) ).
tcf(c_21214,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( set_difference(sK18(powerset(X0),X1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_19652,c_138]) ).
tcf(c_21215,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_19715,c_138]) ).
tcf(c_21216,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X1,X0)),set_union2(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_19744,c_138]) ).
tcf(c_21217,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_19741,c_138]) ).
tcf(c_21218,plain,
! [X0: $i,X1: $i] : set_difference(relation_image(identity_relation(X0),X1),X0) = empty_set,
inference(superposition,[status(thm)],[c_19833,c_138]) ).
tcf(c_21219,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( set_difference(sK1(powerset(X0),X1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_19866,c_138]) ).
tcf(c_21220,plain,
! [X0: $i,X1: $i] : set_difference(relation_inverse_image(identity_relation(X0),X1),X0) = empty_set,
inference(superposition,[status(thm)],[c_19947,c_138]) ).
tcf(c_21221,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_rng_restriction(X0,identity_relation(X1))),X1) = empty_set,
inference(superposition,[status(thm)],[c_20703,c_138]) ).
tcf(c_21222,plain,
! [X0: $i] : set_difference(identity_relation(X0),cartesian_product2(X0,X0)) = empty_set,
inference(superposition,[status(thm)],[c_20929,c_138]) ).
tcf(c_21223,plain,
! [X0: $i] :
( ( set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)) = empty_set )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20994,c_138]) ).
tcf(c_21304,plain,
! [X0: $i,X1: $i] :
( subset(set_union2(X0,X1),X1)
| ( set_difference(X0,X1) != empty_set ) ),
inference(superposition,[status(thm)],[c_153,c_139]) ).
tcf(c_21306,plain,
! [X0: $i] :
( subset(X0,empty_set)
| ( X0 != empty_set ) ),
inference(superposition,[status(thm)],[c_264,c_139]) ).
tcf(c_21317,plain,
! [X0: $i,X1: $i] :
( disjoint(set_union2(X0,X1),X1)
| ( set_union2(X0,X1) != set_difference(X0,X1) ) ),
inference(superposition,[status(thm)],[c_153,c_210]) ).
tcf(c_21320,plain,
! [X0: $i] :
( disjoint(X0,X0)
| ( X0 != empty_set ) ),
inference(superposition,[status(thm)],[c_4095,c_210]) ).
tcf(c_21330,plain,
( subset(relation_inverse(sK5),cartesian_product2(relation_dom(relation_inverse(sK5)),relation_dom(sK5)))
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21123,c_117]) ).
tcf(c_21331,plain,
! [X0: $i] :
( subset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21123,c_80]) ).
tcf(c_21332,plain,
( empty(relation_inverse(sK5))
| ~ empty(relation_dom(sK5))
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21123,c_361]) ).
tcf(c_21333,plain,
! [X0: $i] :
( subset(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21123,c_94]) ).
tcf(c_21334,plain,
( function(relation_dom(sK5))
| ~ empty(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21123,c_19156]) ).
tcf(c_21335,plain,
( one_to_one(relation_dom(sK5))
| ~ empty(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21123,c_19154]) ).
tcf(c_21336,plain,
( relation(relation_dom(sK5))
| ~ empty(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21123,c_360]) ).
tcf(c_21337,plain,
( empty(relation_dom(sK5))
| ~ empty(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21123,c_359]) ).
tcf(c_21353,plain,
( subset(relation_inverse(sK5),cartesian_product2(relation_rng(sK5),relation_dom(sK5)))
| ~ relation(relation_inverse(sK5)) ),
inference(light_normalisation,[status(thm)],[c_21330,c_20946]) ).
tcf(c_21370,plain,
( function(relation_dom(sK5))
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_432,c_21334]) ).
tcf(c_21377,plain,
( one_to_one(relation_dom(sK5))
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_432,c_21335]) ).
tcf(c_21384,plain,
( relation(relation_dom(sK5))
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_432,c_21336]) ).
tcf(c_21391,plain,
( empty(relation_dom(sK5))
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_432,c_21337]) ).
tcf(c_21403,plain,
( empty(relation_inverse(sK5))
| ~ relation(sK5)
| ~ empty(relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_434,c_21332]) ).
tcf(c_21408,plain,
( empty(relation_inverse(sK5))
| ~ empty(relation_dom(sK5)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21403,c_96]) ).
tcf(c_21422,plain,
! [X0: $i] :
( ( set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)) = empty_set )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21333,c_138]) ).
tcf(c_21423,plain,
! [X0: $i] :
( ( set_union2(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)) = relation_dom(sK5) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21333,c_85]) ).
tcf(c_21424,plain,
! [X0: $i] :
( ~ relation(relation_inverse(sK5))
| ~ proper_subset(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_21333,c_188]) ).
tcf(c_21454,plain,
! [X0: $i,X1: $i] : ~ empty(sK2(set_union2(powerset(X0),X1))),
inference(superposition,[status(thm)],[c_19515,c_20218]) ).
tcf(c_21455,plain,
! [X0: $i,X1: $i] : ~ in(sK2(set_union2(powerset(union(X0)),X1)),X0),
inference(superposition,[status(thm)],[c_222,c_20218]) ).
tcf(c_21466,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(unordered_pair(X0,X0),X1) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_52,c_211]) ).
tcf(c_21467,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19395,c_211]) ).
tcf(c_21468,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,X0) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19407,c_211]) ).
tcf(c_21471,plain,
! [X0: $i] :
( in(empty_set,X0)
| ( set_difference(powerset(empty_set),X0) = powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_19371,c_211]) ).
tcf(c_21473,plain,
! [X0: $i] :
( in(empty_set,X0)
| ( set_difference(X0,powerset(empty_set)) = X0 ) ),
inference(superposition,[status(thm)],[c_19442,c_211]) ).
tcf(c_21492,plain,
! [X0: $i] :
( subset(relation_rng(relation_dom_restriction(empty_set,X0)),empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_187,c_224]) ).
tcf(c_21493,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_dom_restriction(identity_relation(X0),X1)),X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_204,c_224]) ).
tcf(c_21494,plain,
! [X0: $i] :
( subset(relation_rng(relation_dom_restriction(relation_inverse(sK5),X0)),relation_dom(sK5))
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21123,c_224]) ).
tcf(c_21495,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_dom_restriction(X0,X1)),relation_rng(X0)) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_224,c_138]) ).
tcf(c_21496,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_rng(relation_dom_restriction(X0,X1)),relation_rng(X0)) = relation_rng(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_224,c_85]) ).
tcf(c_21497,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ proper_subset(relation_rng(X0),relation_rng(relation_dom_restriction(X0,X1))) ),
inference(superposition,[status(thm)],[c_224,c_188]) ).
tcf(c_21501,plain,
! [X0: $i,X1: $i] : subset(relation_rng(relation_dom_restriction(identity_relation(X0),X1)),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_21493,c_422]) ).
tcf(c_21517,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ( sK1(unordered_pair(X0,X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_6708,c_239]) ).
tcf(c_21518,plain,
! [X0: $i,X1: $i] :
( disjoint(unordered_pair(X0,X0),X1)
| ( sK8(unordered_pair(X0,X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_149,c_239]) ).
tcf(c_21519,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,unordered_pair(X1,X1))
| ( sK8(X0,unordered_pair(X1,X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_150,c_239]) ).
tcf(c_21520,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = empty_set )
| ( sK16(unordered_pair(X0,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_233,c_239]) ).
tcf(c_21521,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ( sK18(unordered_pair(X0,X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_241,c_239]) ).
tcf(c_21522,plain,
! [X0: $i] :
( relation(unordered_pair(X0,X0))
| ( sK38(unordered_pair(X0,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_314,c_239]) ).
tcf(c_21525,plain,
! [X0: $i] :
( empty(unordered_pair(X0,X0))
| ( sK23(unordered_pair(X0,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_20297,c_239]) ).
tcf(c_21526,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ in(X0,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_111,c_239]) ).
tcf(c_21529,plain,
! [X0: $i] : sK23(unordered_pair(X0,X0)) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_21525,c_344]) ).
tcf(c_21534,plain,
! [X0: $i] : sK16(unordered_pair(X0,X0)) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_21520,c_49]) ).
tcf(c_21571,plain,
! [X0: $i,X1: $i] :
( relation(set_union2(X1,X0))
| ~ relation(X1)
| ~ relation(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_145,c_248]) ).
tcf(c_21574,plain,
! [X0: $i,X1: $i] :
( relation(set_union2(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_255,c_248]) ).
tcf(c_21576,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(set_union2(X0,X1))) = relation_dom(set_union2(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_248,c_137]) ).
tcf(c_21577,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(set_union2(X0,X1))) = relation_rng(set_union2(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_248,c_136]) ).
tcf(c_21578,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(set_union2(X0,X1))) = set_union2(X0,X1) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_248,c_429]) ).
tcf(c_21601,plain,
! [X0: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)) = empty_set )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21331,c_138]) ).
tcf(c_21602,plain,
! [X0: $i] :
( ( set_union2(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)) = relation_dom(sK5) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21331,c_85]) ).
tcf(c_21603,plain,
! [X0: $i] :
( ~ relation(relation_inverse(sK5))
| ~ proper_subset(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_21331,c_188]) ).
tcf(c_21617,plain,
( ( set_difference(relation_inverse(sK5),cartesian_product2(relation_rng(sK5),relation_dom(sK5))) = empty_set )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21353,c_138]) ).
tcf(c_21618,plain,
( ( set_union2(relation_inverse(sK5),cartesian_product2(relation_rng(sK5),relation_dom(sK5))) = cartesian_product2(relation_rng(sK5),relation_dom(sK5)) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21353,c_85]) ).
tcf(c_21619,plain,
( ~ relation(relation_inverse(sK5))
| ~ proper_subset(cartesian_product2(relation_rng(sK5),relation_dom(sK5)),relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21353,c_188]) ).
tcf(c_21630,plain,
! [X0: $i] :
( ( set_difference(relation_rng(relation_dom_restriction(relation_inverse(sK5),X0)),relation_dom(sK5)) = empty_set )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21494,c_138]) ).
tcf(c_21631,plain,
! [X0: $i] :
( ( set_union2(relation_rng(relation_dom_restriction(relation_inverse(sK5),X0)),relation_dom(sK5)) = relation_dom(sK5) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21494,c_85]) ).
tcf(c_21632,plain,
! [X0: $i] :
( ~ relation(relation_inverse(sK5))
| ~ proper_subset(relation_dom(sK5),relation_rng(relation_dom_restriction(relation_inverse(sK5),X0))) ),
inference(superposition,[status(thm)],[c_21494,c_188]) ).
tcf(c_21673,plain,
! [X0: $i,X1: $i] : ~ empty(sK54(set_union2(powerset(X0),X1))),
inference(superposition,[status(thm)],[c_19515,c_20229]) ).
tcf(c_21674,plain,
! [X0: $i,X1: $i] : ~ in(sK54(set_union2(powerset(union(X0)),X1)),X0),
inference(superposition,[status(thm)],[c_222,c_20229]) ).
tcf(c_21685,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),X2)
| ~ in(sK1(set_difference(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_6708,c_270]) ).
tcf(c_21686,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,X1),X2)
| ~ in(sK8(set_difference(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_149,c_270]) ).
tcf(c_21687,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_difference(X1,X2))
| ~ in(sK8(X0,set_difference(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_150,c_270]) ).
tcf(c_21688,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = empty_set )
| ~ in(sK16(set_difference(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_233,c_270]) ).
tcf(c_21689,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),X2)
| ~ in(sK18(set_difference(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_241,c_270]) ).
tcf(c_21690,plain,
! [X0: $i,X1: $i] :
( relation(set_difference(X0,X1))
| ~ in(sK38(set_difference(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_314,c_270]) ).
tcf(c_21691,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X0,X1))
| ~ in(sK23(set_difference(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_20297,c_270]) ).
tcf(c_21722,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,union(X0))
| ~ in(sK27(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_296,c_243]) ).
tcf(c_21723,plain,
! [X0: $i,X1: $i] :
( ~ empty(sK27(X1,X0))
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_296,c_471]) ).
tcf(c_21724,plain,
! [X0: $i,X1: $i] :
( element(X0,sK27(X1,X0))
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_296,c_276]) ).
tcf(c_21738,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,union(X0))
| ~ in(X0,sK27(X0,X1)) ),
inference(superposition,[status(thm)],[c_297,c_243]) ).
tcf(c_21739,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_297,c_471]) ).
tcf(c_21740,plain,
! [X0: $i,X1: $i] :
( element(sK27(X1,X0),X1)
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_297,c_276]) ).
tcf(c_21741,plain,
! [X0: $i] : ~ in(X0,union(empty_set)),
inference(superposition,[status(thm)],[c_297,c_234]) ).
tcf(c_21742,plain,
! [X0: $i,X1: $i] :
( ( sK27(unordered_pair(X1,X1),X0) = X1 )
| ~ in(X0,union(unordered_pair(X1,X1))) ),
inference(superposition,[status(thm)],[c_297,c_239]) ).
tcf(c_21743,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,union(set_difference(X0,X1)))
| ~ in(sK27(set_difference(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_297,c_270]) ).
tcf(c_21744,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK27(set_difference(X1,X2),X0),X1)
| ~ in(X0,union(set_difference(X1,X2))) ),
inference(superposition,[status(thm)],[c_297,c_269]) ).
tcf(c_21745,plain,
! [X0: $i,X1: $i] :
( subset(sK27(powerset(X1),X0),X1)
| ~ in(X0,union(powerset(X1))) ),
inference(superposition,[status(thm)],[c_297,c_290]) ).
tcf(c_21787,plain,
! [X0: $i] : disjoint(union(empty_set),X0),
inference(superposition,[status(thm)],[c_149,c_21741]) ).
tcf(c_21788,plain,
! [X0: $i] : disjoint(X0,union(empty_set)),
inference(superposition,[status(thm)],[c_150,c_21741]) ).
tcf(c_21789,plain,
union(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_233,c_21741]) ).
tcf(c_21790,plain,
! [X0: $i] : subset(union(empty_set),X0),
inference(superposition,[status(thm)],[c_241,c_21741]) ).
tcf(c_21791,plain,
! [X0: $i] : ~ in(X0,union(union(empty_set))),
inference(superposition,[status(thm)],[c_297,c_21741]) ).
tcf(c_21792,plain,
relation(union(empty_set)),
inference(superposition,[status(thm)],[c_314,c_21741]) ).
tcf(c_21793,plain,
empty(union(empty_set)),
inference(superposition,[status(thm)],[c_20297,c_21741]) ).
tcf(c_21830,plain,
! [X0: $i] :
( ( set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)) = empty_set )
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_434,c_21223]) ).
tcf(c_21834,plain,
! [X0: $i] : set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_21830,c_96]) ).
tcf(c_21836,plain,
! [X0: $i] :
( disjoint(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))
| ( relation_inverse_image(relation_inverse(sK5),X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_21834,c_210]) ).
tcf(c_21837,plain,
! [X0: $i] : subset(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21834,c_139]) ).
tcf(c_21838,plain,
! [X0: $i] : ~ proper_subset(set_union2(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_21834,c_19484]) ).
tcf(c_21839,plain,
! [X0: $i] : subset(set_difference(empty_set,relation_rng(sK5)),set_union2(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_21834,c_19715]) ).
tcf(c_21840,plain,
! [X0: $i] : subset(empty_set,set_union2(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_21834,c_19593]) ).
tcf(c_21841,plain,
! [X0: $i] : subset(empty_set,set_union2(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_21834,c_19485]) ).
tcf(c_21842,plain,
! [X0: $i] : ~ proper_subset(relation_inverse_image(relation_inverse(sK5),X0),empty_set),
inference(superposition,[status(thm)],[c_21834,c_19457]) ).
tcf(c_21843,plain,
! [X0: $i] : subset(empty_set,relation_inverse_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_21834,c_135]) ).
tcf(c_21846,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),empty_set),set_union2(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_21834,c_19744]) ).
tcf(c_21847,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),set_difference(empty_set,relation_rng(sK5))),set_union2(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_21834,c_19741]) ).
tcf(c_21848,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),empty_set),set_union2(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_21834,c_19566]) ).
tcf(c_21849,plain,
! [X0: $i] : set_union2(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)) = set_union2(relation_rng(sK5),empty_set),
inference(superposition,[status(thm)],[c_21834,c_145]) ).
tcf(c_21860,plain,
! [X0: $i] : set_union2(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)) = relation_rng(sK5),
inference(superposition,[status(thm)],[c_21837,c_85]) ).
tcf(c_21861,plain,
! [X0: $i] : ~ proper_subset(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_21837,c_188]) ).
tcf(c_21864,plain,
subset(set_difference(empty_set,relation_rng(sK5)),set_union2(relation_rng(sK5),empty_set)),
inference(light_normalisation,[status(thm)],[c_21839,c_21849]) ).
tcf(c_21865,plain,
subset(empty_set,relation_rng(sK5)),
inference(demodulation,[status(thm)],[c_21864,c_244,c_263]) ).
tcf(c_21866,plain,
subset(set_difference(relation_rng(sK5),empty_set),relation_rng(sK5)),
inference(light_normalisation,[status(thm)],[c_21846,c_21860]) ).
tcf(c_21867,plain,
subset(relation_rng(sK5),relation_rng(sK5)),
inference(demodulation,[status(thm)],[c_21866,c_264]) ).
tcf(c_21868,plain,
subset(set_difference(relation_rng(sK5),empty_set),set_union2(relation_rng(sK5),empty_set)),
inference(light_normalisation,[status(thm)],[c_21848,c_21849]) ).
tcf(c_21870,plain,
! [X0: $i] : set_union2(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)) = relation_rng(sK5),
inference(demodulation,[status(thm)],[c_21849,c_244]) ).
tcf(c_21872,plain,
! [X0: $i] : ~ proper_subset(relation_rng(sK5),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_21870,c_19484]) ).
tcf(c_21873,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),set_difference(set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),relation_rng(sK5))),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_19741]) ).
tcf(c_21874,plain,
! [X0: $i] : ~ in(powerset(relation_rng(sK5)),relation_inverse_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_21870,c_20137]) ).
tcf(c_21875,plain,
! [X0: $i] : ~ in(sK54(relation_rng(sK5)),relation_inverse_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_21870,c_20134]) ).
tcf(c_21876,plain,
! [X0: $i] : ~ in(sK2(relation_rng(sK5)),relation_inverse_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_21870,c_20131]) ).
tcf(c_21877,plain,
~ in(powerset(relation_rng(sK5)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_20101]) ).
tcf(c_21878,plain,
~ in(sK54(relation_rng(sK5)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_20098]) ).
tcf(c_21879,plain,
~ in(sK2(relation_rng(sK5)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_20095]) ).
tcf(c_21880,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_19566]) ).
tcf(c_21882,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_19485]) ).
tcf(c_21883,plain,
~ proper_subset(relation_rng(sK5),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_19458]) ).
tcf(c_21885,plain,
! [X0: $i] :
( empty(relation_inverse_image(relation_inverse(sK5),X0))
| ~ empty(relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_21870,c_246]) ).
tcf(c_21887,plain,
! [X0: $i] : subset(set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_19744]) ).
tcf(c_21888,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_19715]) ).
tcf(c_21889,plain,
! [X0: $i] : subset(set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_19593]) ).
tcf(c_21892,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(sK5))
| ~ in(X0,relation_inverse_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_21870,c_253]) ).
tcf(c_21898,plain,
subset(set_difference(empty_set,relation_rng(sK5)),relation_rng(sK5)),
inference(light_normalisation,[status(thm)],[c_21888,c_21834]) ).
tcf(c_21900,plain,
subset(set_difference(relation_rng(sK5),set_difference(empty_set,relation_rng(sK5))),relation_rng(sK5)),
inference(light_normalisation,[status(thm)],[c_21873,c_21834]) ).
tcf(c_21914,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_composition(X1,X0)) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_402,c_19213]) ).
tcf(c_21915,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X1,X0)) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_402,c_19212]) ).
tcf(c_21916,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(X1,X0)) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_402,c_19211]) ).
tcf(c_21917,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X1,X0) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_402,c_229]) ).
tcf(c_21918,plain,
! [X0: $i,X1: $i] :
( one_to_one(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_402,c_6826]) ).
tcf(c_21920,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_402,c_331]) ).
tcf(c_21951,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(relation_composition(X1,X0))) = relation_dom(relation_composition(X1,X0)) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_403,c_137]) ).
tcf(c_21952,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(relation_composition(X1,X0))) = relation_rng(relation_composition(X1,X0)) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_403,c_136]) ).
tcf(c_21953,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(relation_composition(X1,X0))) = relation_composition(X1,X0) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_403,c_429]) ).
tcf(c_21991,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_composition(X0,X1)) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_406,c_19213]) ).
tcf(c_21992,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X0,X1)) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_406,c_19212]) ).
tcf(c_21993,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(X0,X1)) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_406,c_19211]) ).
tcf(c_21994,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(X0,X1) = empty_set )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_406,c_229]) ).
tcf(c_21995,plain,
! [X0: $i,X1: $i] :
( one_to_one(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_406,c_6826]) ).
tcf(c_21997,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_406,c_331]) ).
tcf(c_22045,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(relation_composition(X0,X1))) = relation_dom(relation_composition(X0,X1)) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_407,c_137]) ).
tcf(c_22046,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(relation_composition(X0,X1))) = relation_rng(relation_composition(X0,X1)) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_407,c_136]) ).
tcf(c_22047,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(relation_composition(X0,X1))) = relation_composition(X0,X1) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_407,c_429]) ).
tcf(c_22060,plain,
~ in(powerset(powerset(empty_set)),empty_set),
inference(superposition,[status(thm)],[c_21789,c_20020]) ).
tcf(c_22061,plain,
~ in(sK54(powerset(empty_set)),empty_set),
inference(superposition,[status(thm)],[c_21789,c_19705]) ).
tcf(c_22062,plain,
~ in(sK2(powerset(empty_set)),empty_set),
inference(superposition,[status(thm)],[c_21789,c_19702]) ).
tcf(c_22075,plain,
! [X0: $i] :
( ( set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)) = empty_set )
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_434,c_21422]) ).
tcf(c_22079,plain,
! [X0: $i] : set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_22075,c_96]) ).
tcf(c_22081,plain,
! [X0: $i] :
( disjoint(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))
| ( relation_image(relation_inverse(sK5),X0) != empty_set ) ),
inference(superposition,[status(thm)],[c_22079,c_210]) ).
tcf(c_22082,plain,
! [X0: $i] : subset(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22079,c_139]) ).
tcf(c_22083,plain,
! [X0: $i] : ~ proper_subset(set_union2(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_22079,c_19484]) ).
tcf(c_22084,plain,
! [X0: $i] : subset(set_difference(empty_set,relation_dom(sK5)),set_union2(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22079,c_19715]) ).
tcf(c_22085,plain,
! [X0: $i] : subset(empty_set,set_union2(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22079,c_19593]) ).
tcf(c_22086,plain,
! [X0: $i] : subset(empty_set,set_union2(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_22079,c_19485]) ).
tcf(c_22087,plain,
! [X0: $i] : ~ proper_subset(relation_image(relation_inverse(sK5),X0),empty_set),
inference(superposition,[status(thm)],[c_22079,c_19457]) ).
tcf(c_22088,plain,
! [X0: $i] : subset(empty_set,relation_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_22079,c_135]) ).
tcf(c_22091,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),empty_set),set_union2(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_22079,c_19744]) ).
tcf(c_22092,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),set_difference(empty_set,relation_dom(sK5))),set_union2(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22079,c_19741]) ).
tcf(c_22093,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),empty_set),set_union2(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22079,c_19566]) ).
tcf(c_22094,plain,
! [X0: $i] : set_union2(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)) = set_union2(relation_dom(sK5),empty_set),
inference(superposition,[status(thm)],[c_22079,c_145]) ).
tcf(c_22105,plain,
! [X0: $i] : set_union2(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)) = relation_dom(sK5),
inference(superposition,[status(thm)],[c_22082,c_85]) ).
tcf(c_22106,plain,
! [X0: $i] : ~ proper_subset(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_22082,c_188]) ).
tcf(c_22109,plain,
! [X0: $i] : subset(set_difference(set_difference(X0,empty_set),empty_set),set_union2(empty_set,X0)),
inference(superposition,[status(thm)],[c_264,c_20244]) ).
tcf(c_22111,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_union2(X1,set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_153,c_20244]) ).
tcf(c_22114,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,X0),X0),set_union2(X0,X0)),
inference(superposition,[status(thm)],[c_4095,c_20244]) ).
tcf(c_22115,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,relation_rng(sK5)),relation_rng(sK5)),set_union2(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_21834,c_20244]) ).
tcf(c_22116,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5)),set_union2(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22079,c_20244]) ).
tcf(c_22118,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),X1),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_145,c_20244]) ).
tcf(c_22119,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(empty_set,X0),X0),X0),X0),
inference(superposition,[status(thm)],[c_244,c_20244]) ).
tcf(c_22120,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(X0,X0),X0),X0),X0),
inference(superposition,[status(thm)],[c_245,c_20244]) ).
tcf(c_22121,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_255,c_20244]) ).
tcf(c_22122,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(X0,empty_set),empty_set),empty_set),X0),
inference(superposition,[status(thm)],[c_19599,c_20244]) ).
tcf(c_22123,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_20244]) ).
tcf(c_22124,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_union2(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_20244,c_138]) ).
tcf(c_22125,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_union2(X1,X0)) = set_union2(X1,X0),
inference(superposition,[status(thm)],[c_20244,c_85]) ).
tcf(c_22126,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(set_difference(set_difference(X1,X0),X0),X0)),
inference(superposition,[status(thm)],[c_20244,c_188]) ).
tcf(c_22132,plain,
subset(set_difference(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5)),set_union2(relation_dom(sK5),empty_set)),
inference(light_normalisation,[status(thm)],[c_22116,c_22094]) ).
tcf(c_22133,plain,
subset(set_difference(set_difference(empty_set,relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),
inference(light_normalisation,[status(thm)],[c_22115,c_21870]) ).
tcf(c_22146,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(relation_composition(X0,X1))) = relation_dom(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_408,c_137]) ).
tcf(c_22147,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(relation_composition(X0,X1))) = relation_rng(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_408,c_136]) ).
tcf(c_22148,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(relation_composition(X0,X1))) = relation_composition(X0,X1) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_408,c_429]) ).
tcf(c_22168,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_341,c_470]) ).
tcf(c_22169,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_359,c_470]) ).
tcf(c_22170,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X0,X1) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_406,c_470]) ).
tcf(c_22171,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(X1,X0) = X2 )
| ~ empty(X2)
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_402,c_470]) ).
tcf(c_22172,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_432,c_470]) ).
tcf(c_22173,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20511,c_470]) ).
tcf(c_22174,plain,
! [X0: $i,X1: $i] :
( ( sK23(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20331,c_470]) ).
tcf(c_22243,plain,
! [X0: $i,X1: $i] :
( subset(subset_complement(X1,X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_6701,c_274]) ).
tcf(c_22244,plain,
! [X0: $i,X1: $i] :
( empty(subset_complement(X1,X0))
| ~ empty(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_6701,c_285]) ).
tcf(c_22245,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| in(subset_complement(X1,X0),powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_6701,c_283]) ).
tcf(c_22248,plain,
! [X0: $i,X1: $i] :
( in(subset_complement(X1,X0),powerset(X1))
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22245,c_286]) ).
tcf(c_22257,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_81,c_138]) ).
tcf(c_22258,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) = cartesian_product2(X1,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_81,c_85]) ).
tcf(c_22259,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X2,X0)
| ~ proper_subset(cartesian_product2(X0,X1),cartesian_product2(X2,X1)) ),
inference(superposition,[status(thm)],[c_81,c_188]) ).
tcf(c_22269,plain,
( subset(relation_inverse(sK75),cartesian_product2(relation_rng(sK75),relation_rng(relation_inverse(sK75))))
| ~ relation(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_20957,c_117]) ).
tcf(c_22270,plain,
( empty(relation_inverse(sK75))
| ~ empty(relation_rng(sK75))
| ~ relation(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_20957,c_343]) ).
tcf(c_22271,plain,
! [X0: $i] :
( subset(relation_inverse_image(relation_inverse(sK75),X0),relation_rng(sK75))
| ~ relation(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_20957,c_105]) ).
tcf(c_22272,plain,
( function(relation_rng(sK75))
| ~ empty(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_20957,c_19131]) ).
tcf(c_22273,plain,
( one_to_one(relation_rng(sK75))
| ~ empty(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_20957,c_19129]) ).
tcf(c_22274,plain,
( relation(relation_rng(sK75))
| ~ empty(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_20957,c_342]) ).
tcf(c_22275,plain,
( empty(relation_rng(sK75))
| ~ empty(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_20957,c_341]) ).
tcf(c_22289,plain,
( subset(relation_inverse(sK75),cartesian_product2(relation_rng(sK75),relation_dom(sK75)))
| ~ relation(relation_inverse(sK75)) ),
inference(light_normalisation,[status(thm)],[c_22269,c_21134]) ).
tcf(c_22293,plain,
( subset(relation_inverse(sK79),cartesian_product2(relation_rng(sK79),relation_rng(relation_inverse(sK79))))
| ~ relation(relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_20958,c_117]) ).
tcf(c_22294,plain,
( empty(relation_inverse(sK79))
| ~ empty(relation_rng(sK79))
| ~ relation(relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_20958,c_343]) ).
tcf(c_22295,plain,
! [X0: $i] :
( subset(relation_inverse_image(relation_inverse(sK79),X0),relation_rng(sK79))
| ~ relation(relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_20958,c_105]) ).
tcf(c_22302,plain,
( ~ empty(relation_rng(sK79))
| ~ relation(relation_inverse(sK79)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22294,c_20632]) ).
tcf(c_22305,plain,
( subset(relation_inverse(sK79),cartesian_product2(relation_rng(sK79),relation_dom(sK79)))
| ~ relation(relation_inverse(sK79)) ),
inference(light_normalisation,[status(thm)],[c_22293,c_21135]) ).
tcf(c_22309,plain,
! [X0: $i] :
( subset(relation_inverse(identity_relation(X0)),cartesian_product2(X0,relation_rng(relation_inverse(identity_relation(X0)))))
| ~ relation(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_20961,c_117]) ).
tcf(c_22310,plain,
! [X0: $i] :
( empty(relation_inverse(identity_relation(X0)))
| ~ empty(X0)
| ~ relation(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_20961,c_343]) ).
tcf(c_22311,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(relation_inverse(identity_relation(X0)),X1),X0)
| ~ relation(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_20961,c_105]) ).
tcf(c_22312,plain,
! [X0: $i] :
( function(X0)
| ~ empty(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_20961,c_19131]) ).
tcf(c_22313,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_20961,c_19129]) ).
tcf(c_22314,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_20961,c_342]) ).
tcf(c_22315,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_20961,c_341]) ).
tcf(c_22329,plain,
! [X0: $i] :
( subset(relation_inverse(identity_relation(X0)),cartesian_product2(X0,X0))
| ~ relation(relation_inverse(identity_relation(X0))) ),
inference(light_normalisation,[status(thm)],[c_22309,c_21138]) ).
tcf(c_22335,plain,
subset(set_difference(empty_set,relation_dom(sK5)),set_union2(relation_dom(sK5),empty_set)),
inference(light_normalisation,[status(thm)],[c_22084,c_22094]) ).
tcf(c_22336,plain,
subset(empty_set,relation_dom(sK5)),
inference(demodulation,[status(thm)],[c_22335,c_244,c_263]) ).
tcf(c_22337,plain,
subset(set_difference(relation_dom(sK5),empty_set),relation_dom(sK5)),
inference(light_normalisation,[status(thm)],[c_22091,c_22105]) ).
tcf(c_22338,plain,
subset(relation_dom(sK5),relation_dom(sK5)),
inference(demodulation,[status(thm)],[c_22337,c_264]) ).
tcf(c_22339,plain,
subset(set_difference(relation_dom(sK5),empty_set),set_union2(relation_dom(sK5),empty_set)),
inference(light_normalisation,[status(thm)],[c_22093,c_22094]) ).
tcf(c_22341,plain,
! [X0: $i] : set_union2(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)) = relation_dom(sK5),
inference(demodulation,[status(thm)],[c_22094,c_244]) ).
tcf(c_22343,plain,
! [X0: $i] : ~ proper_subset(relation_dom(sK5),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22341,c_19484]) ).
tcf(c_22344,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),set_difference(set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),relation_dom(sK5))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_19741]) ).
tcf(c_22345,plain,
! [X0: $i] : ~ in(powerset(relation_dom(sK5)),relation_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_22341,c_20137]) ).
tcf(c_22346,plain,
! [X0: $i] : ~ in(sK54(relation_dom(sK5)),relation_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_22341,c_20134]) ).
tcf(c_22347,plain,
! [X0: $i] : ~ in(sK2(relation_dom(sK5)),relation_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_22341,c_20131]) ).
tcf(c_22348,plain,
~ in(powerset(relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_20101]) ).
tcf(c_22349,plain,
~ in(sK54(relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_20098]) ).
tcf(c_22350,plain,
~ in(sK2(relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_20095]) ).
tcf(c_22351,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_19566]) ).
tcf(c_22353,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_19485]) ).
tcf(c_22354,plain,
~ proper_subset(relation_dom(sK5),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_19458]) ).
tcf(c_22356,plain,
! [X0: $i] :
( empty(relation_image(relation_inverse(sK5),X0))
| ~ empty(relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_22341,c_246]) ).
tcf(c_22358,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_20244]) ).
tcf(c_22359,plain,
! [X0: $i] : subset(set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_19744]) ).
tcf(c_22360,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_19715]) ).
tcf(c_22361,plain,
! [X0: $i] : subset(set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_19593]) ).
tcf(c_22364,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(sK5))
| ~ in(X0,relation_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_22341,c_253]) ).
tcf(c_22370,plain,
subset(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5)),
inference(light_normalisation,[status(thm)],[c_22360,c_22079]) ).
tcf(c_22372,plain,
subset(set_difference(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),
inference(light_normalisation,[status(thm)],[c_22358,c_22079]) ).
tcf(c_22373,plain,
subset(set_difference(relation_dom(sK5),set_difference(empty_set,relation_dom(sK5))),relation_dom(sK5)),
inference(light_normalisation,[status(thm)],[c_22344,c_22079]) ).
tcf(c_22389,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),X1),set_union2(set_union2(X0,X1),X1)),
inference(superposition,[status(thm)],[c_153,c_20247]) ).
tcf(c_22393,plain,
! [X0: $i] : subset(set_difference(empty_set,relation_rng(sK5)),set_union2(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_21834,c_20247]) ).
tcf(c_22394,plain,
! [X0: $i] : subset(set_difference(empty_set,relation_dom(sK5)),set_union2(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_22079,c_20247]) ).
tcf(c_22396,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_145,c_20247]) ).
tcf(c_22401,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_20247]) ).
tcf(c_22402,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_20247]) ).
tcf(c_22403,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),X1),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_20247,c_138]) ).
tcf(c_22404,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(set_difference(X0,X1),X1),set_union2(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_20247,c_85]) ).
tcf(c_22405,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(set_difference(X0,X1),X1)),
inference(superposition,[status(thm)],[c_20247,c_188]) ).
tcf(c_22450,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_138]) ).
tcf(c_22451,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) = cartesian_product2(X2,X1) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_85]) ).
tcf(c_22452,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X2,X1)
| ~ proper_subset(cartesian_product2(X0,X1),cartesian_product2(X0,X2)) ),
inference(superposition,[status(thm)],[c_82,c_188]) ).
tcf(c_22463,plain,
relation_image(sK5,relation_dom(sK5)) = relation_rng(sK5),
inference(superposition,[status(thm)],[c_96,c_99]) ).
tcf(c_22464,plain,
! [X0: $i] : relation_image(identity_relation(X0),relation_dom(identity_relation(X0))) = relation_rng(identity_relation(X0)),
inference(superposition,[status(thm)],[c_422,c_99]) ).
tcf(c_22465,plain,
! [X0: $i] :
( ( relation_image(function_inverse(X0),relation_dom(function_inverse(X0))) = relation_rng(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_465,c_99]) ).
tcf(c_22466,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_dom_restriction(X0,X1),relation_dom(relation_dom_restriction(X0,X1))) = relation_rng(relation_dom_restriction(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_334,c_99]) ).
tcf(c_22467,plain,
relation_image(empty_set,relation_dom(empty_set)) = relation_rng(empty_set),
inference(superposition,[status(thm)],[c_231,c_99]) ).
tcf(c_22468,plain,
! [X0: $i,X1: $i] :
( ( relation_image(set_union2(X0,X1),relation_dom(set_union2(X0,X1))) = relation_rng(set_union2(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_248,c_99]) ).
tcf(c_22469,plain,
relation_image(sK47,relation_dom(sK47)) = relation_rng(sK47),
inference(superposition,[status(thm)],[c_329,c_99]) ).
tcf(c_22470,plain,
! [X0: $i] :
( ( relation_image(relation_dom(X0),relation_dom(relation_dom(X0))) = relation_rng(relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_342,c_99]) ).
tcf(c_22471,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_rng_restriction(X1,X0),relation_dom(relation_rng_restriction(X1,X0))) = relation_rng(relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_352,c_99]) ).
tcf(c_22472,plain,
! [X0: $i] :
( ( relation_image(relation_rng(X0),relation_dom(relation_rng(X0))) = relation_rng(relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_360,c_99]) ).
tcf(c_22473,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_composition(X0,X1),relation_dom(relation_composition(X0,X1))) = relation_rng(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_408,c_99]) ).
tcf(c_22474,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_composition(X0,X1),relation_dom(relation_composition(X0,X1))) = relation_rng(relation_composition(X0,X1)) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_407,c_99]) ).
tcf(c_22475,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_composition(X1,X0),relation_dom(relation_composition(X1,X0))) = relation_rng(relation_composition(X1,X0)) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_403,c_99]) ).
tcf(c_22476,plain,
! [X0: $i] :
( ( relation_image(relation_inverse(X0),relation_dom(relation_inverse(X0))) = relation_rng(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_434,c_99]) ).
tcf(c_22477,plain,
! [X0: $i] :
( ( relation_image(relation_inverse(X0),relation_dom(relation_inverse(X0))) = relation_rng(relation_inverse(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_433,c_99]) ).
tcf(c_22478,plain,
relation_image(sK75,relation_dom(sK75)) = relation_rng(sK75),
inference(superposition,[status(thm)],[c_456,c_99]) ).
tcf(c_22479,plain,
relation_image(sK79,relation_dom(sK79)) = relation_rng(sK79),
inference(superposition,[status(thm)],[c_474,c_99]) ).
tcf(c_22480,plain,
! [X0: $i] :
( ( relation_image(sK23(X0),relation_dom(sK23(X0))) = relation_rng(sK23(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20383,c_99]) ).
tcf(c_22481,plain,
relation_image(empty_set,empty_set) = empty_set,
inference(light_normalisation,[status(thm)],[c_22467,c_186,c_187]) ).
tcf(c_22482,plain,
! [X0: $i] : relation_image(identity_relation(X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_22464,c_203,c_204]) ).
tcf(c_22552,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(unordered_pair(X0,X0),X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_140,c_110]) ).
tcf(c_22553,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ empty(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_19515,c_110]) ).
tcf(c_22554,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ in(X2,X0)
| ~ subset(union(X0),X1) ),
inference(superposition,[status(thm)],[c_222,c_110]) ).
tcf(c_22555,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_rng_restriction(X0,X2)),X1)
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_78,c_110]) ).
tcf(c_22556,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng_restriction(X2,X0),X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_79,c_110]) ).
tcf(c_22557,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_rng_restriction(X2,X0)),X1)
| ~ relation(X0)
| ~ subset(relation_rng(X0),X1) ),
inference(superposition,[status(thm)],[c_80,c_110]) ).
tcf(c_22558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X3,X1),X2)
| ~ subset(X3,X0)
| ~ subset(cartesian_product2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_81,c_110]) ).
tcf(c_22559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X0,X3),X2)
| ~ subset(X3,X1)
| ~ subset(cartesian_product2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_82,c_110]) ).
tcf(c_22560,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_image(X0,X2),X1)
| ~ relation(X0)
| ~ subset(relation_rng(X0),X1) ),
inference(superposition,[status(thm)],[c_94,c_110]) ).
tcf(c_22561,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X0,X2),X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_105,c_110]) ).
tcf(c_22562,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ relation(X0)
| ~ subset(cartesian_product2(relation_dom(X0),relation_rng(X0)),X1) ),
inference(superposition,[status(thm)],[c_117,c_110]) ).
tcf(c_22563,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_124,c_110]) ).
tcf(c_22564,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_135,c_110]) ).
tcf(c_22565,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_209,c_110]) ).
tcf(c_22566,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom_restriction(X0,X2),X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_215,c_110]) ).
tcf(c_22567,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_dom_restriction(X0,X2)),X1)
| ~ relation(X0)
| ~ subset(relation_rng(X0),X1) ),
inference(superposition,[status(thm)],[c_224,c_110]) ).
tcf(c_22569,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| subset(sK22(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_19616,c_110]) ).
tcf(c_22570,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19485,c_110]) ).
tcf(c_22571,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X1,X0)),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19566,c_110]) ).
tcf(c_22572,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X1,X0),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19593,c_110]) ).
tcf(c_22573,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X1,X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19598,c_110]) ).
tcf(c_22574,plain,
! [X0: $i,X1: $i] :
( subset(sK23(powerset(X0)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_19617,c_110]) ).
tcf(c_22575,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(powerset(X0),X2)
| subset(sK18(powerset(X0),X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_19652,c_110]) ).
tcf(c_22576,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(X1,X0),X0),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19715,c_110]) ).
tcf(c_22577,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X1,set_difference(X0,X1)),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19744,c_110]) ).
tcf(c_22578,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(set_difference(X1,X0),X0)),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19741,c_110]) ).
tcf(c_22579,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_image(identity_relation(X0),X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_19833,c_110]) ).
tcf(c_22580,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(powerset(X0),X2)
| subset(sK1(powerset(X0),X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_19866,c_110]) ).
tcf(c_22581,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(identity_relation(X0),X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_19947,c_110]) ).
tcf(c_22582,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(X0,X1),X1),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_20247,c_110]) ).
tcf(c_22583,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(set_difference(X1,X0),X0),X0),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_20244,c_110]) ).
tcf(c_22584,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_rng_restriction(X2,identity_relation(X0))),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_20703,c_110]) ).
tcf(c_22585,plain,
! [X0: $i,X1: $i] :
( subset(identity_relation(X0),X1)
| ~ subset(cartesian_product2(X0,X0),X1) ),
inference(superposition,[status(thm)],[c_20929,c_110]) ).
tcf(c_22586,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(relation_inverse(sK5),X1),X0)
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_21837,c_110]) ).
tcf(c_22587,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),X0)
| ~ relation(relation_inverse(sK5))
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_21331,c_110]) ).
tcf(c_22588,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(relation_inverse(sK5),X1),X0)
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_22082,c_110]) ).
tcf(c_22589,plain,
! [X0: $i] :
( subset(relation_inverse(sK5),X0)
| ~ relation(relation_inverse(sK5))
| ~ subset(cartesian_product2(relation_rng(sK5),relation_dom(sK5)),X0) ),
inference(superposition,[status(thm)],[c_21353,c_110]) ).
tcf(c_22590,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_dom_restriction(relation_inverse(sK5),X1)),X0)
| ~ relation(relation_inverse(sK5))
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_21494,c_110]) ).
tcf(c_22769,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),set_difference(X2,X1))
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_153,c_127]) ).
tcf(c_22770,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X0,X1))
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_263,c_127]) ).
tcf(c_22771,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(X1,empty_set))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_264,c_127]) ).
tcf(c_22772,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X1,X0))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4095,c_127]) ).
tcf(c_22773,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X1,relation_rng(sK5)))
| ~ subset(relation_inverse_image(relation_inverse(sK5),X0),X1) ),
inference(superposition,[status(thm)],[c_21834,c_127]) ).
tcf(c_22774,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X1,relation_dom(sK5)))
| ~ subset(relation_image(relation_inverse(sK5),X0),X1) ),
inference(superposition,[status(thm)],[c_22079,c_127]) ).
tcf(c_22775,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_153,c_127]) ).
tcf(c_22776,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,X1),empty_set)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_263,c_127]) ).
tcf(c_22777,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,empty_set),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_264,c_127]) ).
tcf(c_22778,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,X1),empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4095,c_127]) ).
tcf(c_22779,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,relation_rng(sK5)),empty_set)
| ~ subset(X0,relation_inverse_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_21834,c_127]) ).
tcf(c_22780,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,relation_dom(sK5)),empty_set)
| ~ subset(X0,relation_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_22079,c_127]) ).
tcf(c_22781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_difference(X3,X1),X2)
| ~ subset(X3,X0)
| ~ subset(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_127,c_110]) ).
tcf(c_22782,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X0,X2),set_difference(X1,X2)) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_127,c_138]) ).
tcf(c_22783,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(set_difference(X0,X2),set_difference(X1,X2)) = set_difference(X1,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_127,c_85]) ).
tcf(c_22784,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X2,X0)
| ~ proper_subset(set_difference(X0,X1),set_difference(X2,X1)) ),
inference(superposition,[status(thm)],[c_127,c_188]) ).
tcf(c_22838,plain,
( function(relation_rng(sK47))
| ~ empty(sK47) ),
inference(superposition,[status(thm)],[c_432,c_21018]) ).
tcf(c_22856,plain,
( one_to_one(relation_rng(sK47))
| ~ empty(sK47) ),
inference(superposition,[status(thm)],[c_432,c_21019]) ).
tcf(c_22859,plain,
( subset(relation_rng(sK5),relation_rng(sK5))
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_22463,c_94]) ).
tcf(c_22865,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(unordered_pair(X0,X0),relation_rng(sK5)),empty_set)
| ~ in(X0,relation_inverse_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_140,c_22779]) ).
tcf(c_22866,plain,
! [X0: $i] :
( subset(set_difference(X0,relation_rng(sK5)),empty_set)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19515,c_22779]) ).
tcf(c_22867,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng(relation_rng_restriction(relation_inverse_image(relation_inverse(sK5),X1),X0)),relation_rng(sK5)),empty_set)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_78,c_22779]) ).
tcf(c_22868,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng_restriction(X1,relation_inverse_image(relation_inverse(sK5),X0)),relation_rng(sK5)),empty_set)
| ~ relation(relation_inverse_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_79,c_22779]) ).
tcf(c_22869,plain,
subset(set_difference(empty_set,relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_124,c_22779]) ).
tcf(c_22870,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(relation_inverse_image(relation_inverse(sK5),X0),X1),relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_135,c_22779]) ).
tcf(c_22871,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_dom_restriction(relation_inverse_image(relation_inverse(sK5),X0),X1),relation_rng(sK5)),empty_set)
| ~ relation(relation_inverse_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_215,c_22779]) ).
tcf(c_22872,plain,
! [X0: $i] : subset(set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_262,c_22779]) ).
tcf(c_22873,plain,
! [X0: $i] :
( empty(relation_inverse_image(relation_inverse(sK5),X0))
| subset(set_difference(sK22(relation_inverse_image(relation_inverse(sK5),X0)),relation_rng(sK5)),empty_set) ),
inference(superposition,[status(thm)],[c_19616,c_22779]) ).
tcf(c_22874,plain,
! [X0: $i] : subset(set_difference(sK23(powerset(relation_inverse_image(relation_inverse(sK5),X0))),relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_19617,c_22779]) ).
tcf(c_22875,plain,
! [X0: $i,X1: $i] :
( subset(powerset(relation_inverse_image(relation_inverse(sK5),X0)),X1)
| subset(set_difference(sK18(powerset(relation_inverse_image(relation_inverse(sK5),X0)),X1),relation_rng(sK5)),empty_set) ),
inference(superposition,[status(thm)],[c_19652,c_22779]) ).
tcf(c_22876,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_image(identity_relation(relation_inverse_image(relation_inverse(sK5),X0)),X1),relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_19833,c_22779]) ).
tcf(c_22877,plain,
! [X0: $i,X1: $i] :
( subset(powerset(relation_inverse_image(relation_inverse(sK5),X0)),X1)
| subset(set_difference(sK1(powerset(relation_inverse_image(relation_inverse(sK5),X0)),X1),relation_rng(sK5)),empty_set) ),
inference(superposition,[status(thm)],[c_19866,c_22779]) ).
tcf(c_22878,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_inverse_image(identity_relation(relation_inverse_image(relation_inverse(sK5),X0)),X1),relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_19947,c_22779]) ).
tcf(c_22879,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_rng(relation_rng_restriction(X0,identity_relation(relation_inverse_image(relation_inverse(sK5),X1)))),relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_20703,c_22779]) ).
tcf(c_22925,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(unordered_pair(X0,X0),relation_dom(sK5)),empty_set)
| ~ in(X0,relation_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_140,c_22780]) ).
tcf(c_22926,plain,
! [X0: $i] :
( subset(set_difference(X0,relation_dom(sK5)),empty_set)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19515,c_22780]) ).
tcf(c_22927,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng(relation_rng_restriction(relation_image(relation_inverse(sK5),X1),X0)),relation_dom(sK5)),empty_set)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_78,c_22780]) ).
tcf(c_22928,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng_restriction(X1,relation_image(relation_inverse(sK5),X0)),relation_dom(sK5)),empty_set)
| ~ relation(relation_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_79,c_22780]) ).
tcf(c_22929,plain,
subset(set_difference(empty_set,relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_124,c_22780]) ).
tcf(c_22930,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(relation_image(relation_inverse(sK5),X0),X1),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_135,c_22780]) ).
tcf(c_22931,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_dom_restriction(relation_image(relation_inverse(sK5),X0),X1),relation_dom(sK5)),empty_set)
| ~ relation(relation_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_215,c_22780]) ).
tcf(c_22932,plain,
! [X0: $i] : subset(set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_262,c_22780]) ).
tcf(c_22933,plain,
! [X0: $i] :
( empty(relation_image(relation_inverse(sK5),X0))
| subset(set_difference(sK22(relation_image(relation_inverse(sK5),X0)),relation_dom(sK5)),empty_set) ),
inference(superposition,[status(thm)],[c_19616,c_22780]) ).
tcf(c_22934,plain,
! [X0: $i] : subset(set_difference(sK23(powerset(relation_image(relation_inverse(sK5),X0))),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_19617,c_22780]) ).
tcf(c_22935,plain,
! [X0: $i,X1: $i] :
( subset(powerset(relation_image(relation_inverse(sK5),X0)),X1)
| subset(set_difference(sK18(powerset(relation_image(relation_inverse(sK5),X0)),X1),relation_dom(sK5)),empty_set) ),
inference(superposition,[status(thm)],[c_19652,c_22780]) ).
tcf(c_22936,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_image(identity_relation(relation_image(relation_inverse(sK5),X0)),X1),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_19833,c_22780]) ).
tcf(c_22937,plain,
! [X0: $i,X1: $i] :
( subset(powerset(relation_image(relation_inverse(sK5),X0)),X1)
| subset(set_difference(sK1(powerset(relation_image(relation_inverse(sK5),X0)),X1),relation_dom(sK5)),empty_set) ),
inference(superposition,[status(thm)],[c_19866,c_22780]) ).
tcf(c_22938,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_inverse_image(identity_relation(relation_image(relation_inverse(sK5),X0)),X1),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_19947,c_22780]) ).
tcf(c_22939,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_rng(relation_rng_restriction(X0,identity_relation(relation_image(relation_inverse(sK5),X1)))),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_20703,c_22780]) ).
tcf(c_23008,plain,
( subset(empty_set,empty_set)
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_263,c_22866]) ).
tcf(c_23009,plain,
( subset(empty_set,empty_set)
| ~ empty(relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_4095,c_22866]) ).
tcf(c_23010,plain,
! [X0: $i] :
( subset(empty_set,empty_set)
| ~ empty(relation_inverse_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_21834,c_22866]) ).
tcf(c_23011,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X1,relation_rng(sK5)),X0)
| ~ empty(X1)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22866,c_110]) ).
tcf(c_23026,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,relation_rng(sK5)),X1)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23011,c_124]) ).
tcf(c_23037,plain,
( subset(empty_set,empty_set)
| ~ empty(relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_4095,c_22926]) ).
tcf(c_23038,plain,
! [X0: $i] :
( subset(empty_set,empty_set)
| ~ empty(relation_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_22079,c_22926]) ).
tcf(c_23039,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X1,relation_dom(sK5)),X0)
| ~ empty(X1)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22926,c_110]) ).
tcf(c_23054,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,relation_dom(sK5)),X1)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23039,c_124]) ).
tcf(c_23060,plain,
! [X0: $i,X1: $i] : ~ empty(powerset(set_union2(powerset(X0),X1))),
inference(superposition,[status(thm)],[c_19515,c_20423]) ).
tcf(c_23061,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(powerset(union(X0)),X1)),X0),
inference(superposition,[status(thm)],[c_222,c_20423]) ).
tcf(c_23072,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( apply(identity_relation(X0),sK1(X0,X1)) = sK1(X0,X1) ) ),
inference(superposition,[status(thm)],[c_6708,c_134]) ).
tcf(c_23073,plain,
! [X0: $i] : apply(identity_relation(sK2(X0)),X0) = X0,
inference(superposition,[status(thm)],[c_86,c_134]) ).
tcf(c_23074,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK2(X1)),powerset(X0)) = powerset(X0) )
| ~ in(X0,sK2(X1)) ),
inference(superposition,[status(thm)],[c_88,c_134]) ).
tcf(c_23075,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( apply(identity_relation(X0),sK8(X0,X1)) = sK8(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149,c_134]) ).
tcf(c_23076,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ( apply(identity_relation(X0),sK8(X1,X0)) = sK8(X1,X0) ) ),
inference(superposition,[status(thm)],[c_150,c_134]) ).
tcf(c_23077,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( apply(identity_relation(X0),sK16(X0)) = sK16(X0) ) ),
inference(superposition,[status(thm)],[c_233,c_134]) ).
tcf(c_23078,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( apply(identity_relation(X0),sK18(X0,X1)) = sK18(X0,X1) ) ),
inference(superposition,[status(thm)],[c_241,c_134]) ).
tcf(c_23079,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(set_union2(X1,X2)),X0) = X0 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_252,c_134]) ).
tcf(c_23080,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(set_union2(X2,X1)),X0) = X0 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_253,c_134]) ).
tcf(c_23081,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(powerset(X1)),X0) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_289,c_134]) ).
tcf(c_23082,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK27(X1,X0)),X0) = X0 )
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_296,c_134]) ).
tcf(c_23083,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),sK27(X1,X0)) = sK27(X1,X0) )
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_297,c_134]) ).
tcf(c_23084,plain,
! [X0: $i] :
( relation(X0)
| ( apply(identity_relation(X0),sK38(X0)) = sK38(X0) ) ),
inference(superposition,[status(thm)],[c_314,c_134]) ).
tcf(c_23085,plain,
! [X0: $i,X1: $i] : apply(identity_relation(unordered_pair(X0,X1)),X0) = X0,
inference(superposition,[status(thm)],[c_348,c_134]) ).
tcf(c_23086,plain,
! [X0: $i,X1: $i] : apply(identity_relation(unordered_pair(X0,X1)),X1) = X1,
inference(superposition,[status(thm)],[c_349,c_134]) ).
tcf(c_23087,plain,
! [X0: $i] : apply(identity_relation(sK54(X0)),X0) = X0,
inference(superposition,[status(thm)],[c_372,c_134]) ).
tcf(c_23088,plain,
! [X0: $i,X1: $i,X2: $i] : apply(identity_relation(set_union2(unordered_pair(X0,X1),X2)),X0) = X0,
inference(superposition,[status(thm)],[c_19972,c_134]) ).
tcf(c_23089,plain,
! [X0: $i,X1: $i,X2: $i] : apply(identity_relation(set_union2(X0,unordered_pair(X1,X2))),X1) = X1,
inference(superposition,[status(thm)],[c_19974,c_134]) ).
tcf(c_23090,plain,
! [X0: $i,X1: $i,X2: $i] : apply(identity_relation(set_union2(unordered_pair(X0,X1),X2)),X1) = X1,
inference(superposition,[status(thm)],[c_19992,c_134]) ).
tcf(c_23091,plain,
! [X0: $i,X1: $i,X2: $i] : apply(identity_relation(set_union2(X0,unordered_pair(X1,X2))),X2) = X2,
inference(superposition,[status(thm)],[c_19994,c_134]) ).
tcf(c_23092,plain,
! [X0: $i] : apply(identity_relation(set_union2(powerset(empty_set),X0)),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_20028,c_134]) ).
tcf(c_23093,plain,
! [X0: $i] : apply(identity_relation(set_union2(X0,powerset(empty_set))),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_20041,c_134]) ).
tcf(c_23094,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(powerset(X0)),sK22(X0)) = sK22(X0) ) ),
inference(superposition,[status(thm)],[c_20312,c_134]) ).
tcf(c_23095,plain,
! [X0: $i] :
( empty(X0)
| ( apply(identity_relation(X0),sK23(X0)) = sK23(X0) ) ),
inference(superposition,[status(thm)],[c_20297,c_134]) ).
tcf(c_23096,plain,
! [X0: $i] : apply(identity_relation(powerset(X0)),X0) = X0,
inference(superposition,[status(thm)],[c_20311,c_134]) ).
tcf(c_23097,plain,
! [X0: $i] : apply(identity_relation(powerset(X0)),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_20310,c_134]) ).
tcf(c_23179,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(unordered_pair(X0,X0),X2)
| ~ disjoint(X1,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_140,c_190]) ).
tcf(c_23180,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,X1)
| ~ empty(X2)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_19515,c_190]) ).
tcf(c_23181,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,X1)
| ~ in(X2,X0)
| ~ disjoint(union(X0),X1) ),
inference(superposition,[status(thm)],[c_222,c_190]) ).
tcf(c_23182,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(relation_rng_restriction(X0,X2)),X1)
| ~ relation(X2)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_78,c_190]) ).
tcf(c_23183,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng_restriction(X2,X0),X1)
| ~ relation(X0)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_79,c_190]) ).
tcf(c_23184,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(relation_rng_restriction(X2,X0)),X1)
| ~ relation(X0)
| ~ disjoint(relation_rng(X0),X1) ),
inference(superposition,[status(thm)],[c_80,c_190]) ).
tcf(c_23185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(cartesian_product2(X3,X1),X2)
| ~ subset(X3,X0)
| ~ disjoint(cartesian_product2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_81,c_190]) ).
tcf(c_23186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(cartesian_product2(X0,X3),X2)
| ~ subset(X3,X1)
| ~ disjoint(cartesian_product2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_82,c_190]) ).
tcf(c_23187,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_image(X0,X2),X1)
| ~ relation(X0)
| ~ disjoint(relation_rng(X0),X1) ),
inference(superposition,[status(thm)],[c_94,c_190]) ).
tcf(c_23188,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_inverse_image(X0,X2),X1)
| ~ relation(X0)
| ~ disjoint(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_105,c_190]) ).
tcf(c_23189,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ relation(X0)
| ~ disjoint(cartesian_product2(relation_dom(X0),relation_rng(X0)),X1) ),
inference(superposition,[status(thm)],[c_117,c_190]) ).
tcf(c_23190,plain,
! [X0: $i,X1: $i] :
( disjoint(empty_set,X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_124,c_190]) ).
tcf(c_23191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(set_difference(X3,X1),X2)
| ~ subset(X3,X0)
| ~ disjoint(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_127,c_190]) ).
tcf(c_23192,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,X2),X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_135,c_190]) ).
tcf(c_23193,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_209,c_190]) ).
tcf(c_23194,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_dom_restriction(X0,X2),X1)
| ~ relation(X0)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_215,c_190]) ).
tcf(c_23195,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(relation_dom_restriction(X0,X2)),X1)
| ~ relation(X0)
| ~ disjoint(relation_rng(X0),X1) ),
inference(superposition,[status(thm)],[c_224,c_190]) ).
tcf(c_23197,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| disjoint(sK22(X0),X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_19616,c_190]) ).
tcf(c_23198,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,X1),X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19485,c_190]) ).
tcf(c_23199,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,set_difference(X1,X0)),X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19566,c_190]) ).
tcf(c_23200,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X1,X0),X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19593,c_190]) ).
tcf(c_23201,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X1,X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19598,c_190]) ).
tcf(c_23202,plain,
! [X0: $i,X1: $i] :
( disjoint(sK23(powerset(X0)),X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_19617,c_190]) ).
tcf(c_23203,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(powerset(X0),X2)
| disjoint(sK18(powerset(X0),X2),X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_19652,c_190]) ).
tcf(c_23204,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(set_difference(X1,X0),X0),X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19715,c_190]) ).
tcf(c_23205,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X1,set_difference(X0,X1)),X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19744,c_190]) ).
tcf(c_23206,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,set_difference(set_difference(X1,X0),X0)),X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_19741,c_190]) ).
tcf(c_23207,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_image(identity_relation(X0),X2),X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_19833,c_190]) ).
tcf(c_23208,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(powerset(X0),X2)
| disjoint(sK1(powerset(X0),X2),X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_19866,c_190]) ).
tcf(c_23209,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_inverse_image(identity_relation(X0),X2),X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_19947,c_190]) ).
tcf(c_23210,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(set_difference(X0,X1),X1),X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_20247,c_190]) ).
tcf(c_23211,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(set_difference(set_difference(X1,X0),X0),X0),X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_20244,c_190]) ).
tcf(c_23212,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(relation_rng_restriction(X2,identity_relation(X0))),X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_20703,c_190]) ).
tcf(c_23213,plain,
! [X0: $i,X1: $i] :
( disjoint(identity_relation(X0),X1)
| ~ disjoint(cartesian_product2(X0,X0),X1) ),
inference(superposition,[status(thm)],[c_20929,c_190]) ).
tcf(c_23214,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_inverse_image(relation_inverse(sK5),X1),X0)
| ~ disjoint(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_21837,c_190]) ).
tcf(c_23215,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),X0)
| ~ relation(relation_inverse(sK5))
| ~ disjoint(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_21331,c_190]) ).
tcf(c_23216,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_image(relation_inverse(sK5),X1),X0)
| ~ disjoint(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_22082,c_190]) ).
tcf(c_23217,plain,
! [X0: $i] :
( disjoint(relation_inverse(sK5),X0)
| ~ relation(relation_inverse(sK5))
| ~ disjoint(cartesian_product2(relation_rng(sK5),relation_dom(sK5)),X0) ),
inference(superposition,[status(thm)],[c_21353,c_190]) ).
tcf(c_23218,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_rng(relation_dom_restriction(relation_inverse(sK5),X1)),X0)
| ~ relation(relation_inverse(sK5))
| ~ disjoint(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_21494,c_190]) ).
tcf(c_23401,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),X1) = X1 )
| ( set_difference(X0,unordered_pair(X1,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_195,c_134]) ).
tcf(c_23402,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,unordered_pair(X1,X1)) = X0 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_195,c_243]) ).
tcf(c_23403,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,unordered_pair(X1,X1)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_195,c_471]) ).
tcf(c_23404,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| ( set_difference(X0,unordered_pair(X1,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_195,c_276]) ).
tcf(c_23405,plain,
! [X0: $i] : set_difference(empty_set,unordered_pair(X0,X0)) = empty_set,
inference(superposition,[status(thm)],[c_195,c_234]) ).
tcf(c_23406,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( set_difference(unordered_pair(X0,X0),unordered_pair(X1,X1)) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_195,c_239]) ).
tcf(c_23407,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ( set_difference(X0,unordered_pair(sK18(X1,X0),sK18(X1,X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_195,c_240]) ).
tcf(c_23408,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X2,X1),unordered_pair(X0,X0)) = set_difference(X2,X1) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_195,c_270]) ).
tcf(c_23409,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( set_difference(set_difference(X0,X1),unordered_pair(X2,X2)) = set_difference(X0,X1) ) ),
inference(superposition,[status(thm)],[c_195,c_269]) ).
tcf(c_23410,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ( set_difference(powerset(X0),unordered_pair(X1,X1)) = powerset(X0) ) ),
inference(superposition,[status(thm)],[c_195,c_290]) ).
tcf(c_23411,plain,
! [X0: $i] : set_difference(X0,unordered_pair(sK2(X0),sK2(X0))) = X0,
inference(superposition,[status(thm)],[c_195,c_19526]) ).
tcf(c_23412,plain,
! [X0: $i] :
( relation(X0)
| ( set_difference(sK38(X0),unordered_pair(X0,X0)) = sK38(X0) ) ),
inference(superposition,[status(thm)],[c_195,c_19531]) ).
tcf(c_23413,plain,
! [X0: $i,X1: $i] : set_difference(X0,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1))) = X0,
inference(superposition,[status(thm)],[c_195,c_19532]) ).
tcf(c_23414,plain,
! [X0: $i,X1: $i] : set_difference(X0,unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X0))) = X0,
inference(superposition,[status(thm)],[c_195,c_19533]) ).
tcf(c_23415,plain,
! [X0: $i] : set_difference(X0,unordered_pair(sK54(X0),sK54(X0))) = X0,
inference(superposition,[status(thm)],[c_195,c_19534]) ).
tcf(c_23416,plain,
! [X0: $i] : set_difference(X0,unordered_pair(sK2(powerset(union(X0))),sK2(powerset(union(X0))))) = X0,
inference(superposition,[status(thm)],[c_195,c_19702]) ).
tcf(c_23417,plain,
! [X0: $i] : set_difference(X0,unordered_pair(sK54(powerset(union(X0))),sK54(powerset(union(X0))))) = X0,
inference(superposition,[status(thm)],[c_195,c_19705]) ).
tcf(c_23418,plain,
! [X0: $i] : set_difference(X0,unordered_pair(powerset(X0),powerset(X0))) = X0,
inference(superposition,[status(thm)],[c_195,c_19958]) ).
tcf(c_23419,plain,
! [X0: $i] : set_difference(X0,unordered_pair(powerset(powerset(union(X0))),powerset(powerset(union(X0))))) = X0,
inference(superposition,[status(thm)],[c_195,c_20020]) ).
tcf(c_23420,plain,
! [X0: $i,X1: $i] : set_difference(X0,unordered_pair(sK2(set_union2(X0,X1)),sK2(set_union2(X0,X1)))) = X0,
inference(superposition,[status(thm)],[c_195,c_20095]) ).
tcf(c_23421,plain,
! [X0: $i,X1: $i] : set_difference(X0,unordered_pair(sK54(set_union2(X0,X1)),sK54(set_union2(X0,X1)))) = X0,
inference(superposition,[status(thm)],[c_195,c_20098]) ).
tcf(c_23422,plain,
! [X0: $i,X1: $i] : set_difference(X0,unordered_pair(powerset(set_union2(X0,X1)),powerset(set_union2(X0,X1)))) = X0,
inference(superposition,[status(thm)],[c_195,c_20101]) ).
tcf(c_23423,plain,
! [X0: $i,X1: $i] : set_difference(X0,unordered_pair(sK2(set_union2(X1,X0)),sK2(set_union2(X1,X0)))) = X0,
inference(superposition,[status(thm)],[c_195,c_20131]) ).
tcf(c_23424,plain,
! [X0: $i,X1: $i] : set_difference(X0,unordered_pair(sK54(set_union2(X1,X0)),sK54(set_union2(X1,X0)))) = X0,
inference(superposition,[status(thm)],[c_195,c_20134]) ).
tcf(c_23425,plain,
! [X0: $i,X1: $i] : set_difference(X0,unordered_pair(powerset(set_union2(X1,X0)),powerset(set_union2(X1,X0)))) = X0,
inference(superposition,[status(thm)],[c_195,c_20137]) ).
tcf(c_23426,plain,
! [X0: $i] :
( empty(X0)
| ( set_difference(sK23(X0),unordered_pair(X0,X0)) = sK23(X0) ) ),
inference(superposition,[status(thm)],[c_195,c_20362]) ).
tcf(c_23427,plain,
! [X0: $i] : set_difference(sK2(X0),unordered_pair(sK2(X0),sK2(X0))) = sK2(X0),
inference(superposition,[status(thm)],[c_195,c_20898]) ).
tcf(c_23510,plain,
( relation(relation_rng(sK47))
| ~ empty(sK47) ),
inference(superposition,[status(thm)],[c_432,c_21020]) ).
tcf(c_23521,plain,
( empty(relation_rng(sK47))
| ~ empty(sK47) ),
inference(superposition,[status(thm)],[c_432,c_21021]) ).
tcf(c_23528,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(relation_inverse(sK5),X2),X1)
| ~ subset(X0,X1)
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_22586,c_110]) ).
tcf(c_23529,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_inverse_image(relation_inverse(sK5),X1),X0) = empty_set )
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_22586,c_138]) ).
tcf(c_23530,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_inverse_image(relation_inverse(sK5),X1),X0) = X0 )
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_22586,c_85]) ).
tcf(c_23531,plain,
! [X0: $i,X1: $i] :
( ~ subset(relation_rng(sK5),X0)
| ~ proper_subset(X0,relation_inverse_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_22586,c_188]) ).
tcf(c_23532,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_inverse_image(relation_inverse(sK5),X2),X1)
| ~ disjoint(X0,X1)
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_22586,c_190]) ).
tcf(c_23533,plain,
! [X0: $i] :
( ( relation_inverse_image(relation_inverse(sK5),X0) = empty_set )
| ~ subset(relation_rng(sK5),empty_set) ),
inference(superposition,[status(thm)],[c_22586,c_152]) ).
tcf(c_23534,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_inverse_image(relation_inverse(sK5),X1),relation_rng(sK5)),empty_set)
| ~ subset(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_22586,c_22779]) ).
tcf(c_23535,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_inverse_image(relation_inverse(sK5),X1),relation_dom(sK5)),empty_set)
| ~ subset(relation_rng(sK5),relation_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_22586,c_22780]) ).
tcf(c_23609,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_image(relation_inverse(sK5),X2),X1)
| ~ subset(X0,X1)
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_22588,c_110]) ).
tcf(c_23610,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_image(relation_inverse(sK5),X1),X0) = empty_set )
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_22588,c_138]) ).
tcf(c_23611,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_image(relation_inverse(sK5),X1),X0) = X0 )
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_22588,c_85]) ).
tcf(c_23612,plain,
! [X0: $i,X1: $i] :
( ~ subset(relation_dom(sK5),X0)
| ~ proper_subset(X0,relation_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_22588,c_188]) ).
tcf(c_23613,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_image(relation_inverse(sK5),X2),X1)
| ~ disjoint(X0,X1)
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_22588,c_190]) ).
tcf(c_23614,plain,
! [X0: $i] :
( ( relation_image(relation_inverse(sK5),X0) = empty_set )
| ~ subset(relation_dom(sK5),empty_set) ),
inference(superposition,[status(thm)],[c_22588,c_152]) ).
tcf(c_23615,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_image(relation_inverse(sK5),X1),relation_rng(sK5)),empty_set)
| ~ subset(relation_dom(sK5),relation_inverse_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_22588,c_22779]) ).
tcf(c_23616,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_image(relation_inverse(sK5),X1),relation_dom(sK5)),empty_set)
| ~ subset(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_22588,c_22780]) ).
tcf(c_23645,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(relation_inverse_image(relation_inverse(sK5),X1),X2),relation_rng(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22870,c_110]) ).
tcf(c_23649,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(set_difference(relation_inverse_image(relation_inverse(sK5),X1),X2),relation_rng(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22870,c_190]) ).
tcf(c_23652,plain,
! [X0: $i,X1: $i,X2: $i] : subset(set_difference(set_difference(relation_inverse_image(relation_inverse(sK5),X0),X1),relation_rng(sK5)),X2),
inference(forward_subsumption_resolution,[status(thm)],[c_23645,c_124]) ).
tcf(c_23653,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(sK23(powerset(relation_inverse_image(relation_inverse(sK5),X1))),relation_rng(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22874,c_110]) ).
tcf(c_23657,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(sK23(powerset(relation_inverse_image(relation_inverse(sK5),X1))),relation_rng(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22874,c_190]) ).
tcf(c_23660,plain,
! [X0: $i,X1: $i] : subset(set_difference(sK23(powerset(relation_inverse_image(relation_inverse(sK5),X0))),relation_rng(sK5)),X1),
inference(forward_subsumption_resolution,[status(thm)],[c_23653,c_124]) ).
tcf(c_23664,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(relation_image(relation_inverse(sK5),X1),X2),relation_dom(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22930,c_110]) ).
tcf(c_23668,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(set_difference(relation_image(relation_inverse(sK5),X1),X2),relation_dom(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22930,c_190]) ).
tcf(c_23671,plain,
! [X0: $i,X1: $i,X2: $i] : subset(set_difference(set_difference(relation_image(relation_inverse(sK5),X0),X1),relation_dom(sK5)),X2),
inference(forward_subsumption_resolution,[status(thm)],[c_23664,c_124]) ).
tcf(c_23672,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(sK23(powerset(relation_image(relation_inverse(sK5),X1))),relation_dom(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22934,c_110]) ).
tcf(c_23676,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(sK23(powerset(relation_image(relation_inverse(sK5),X1))),relation_dom(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22934,c_190]) ).
tcf(c_23679,plain,
! [X0: $i,X1: $i] : subset(set_difference(sK23(powerset(relation_image(relation_inverse(sK5),X0))),relation_dom(sK5)),X1),
inference(forward_subsumption_resolution,[status(thm)],[c_23672,c_124]) ).
tcf(c_23684,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_inverse_image(relation_inverse(sK5),X1),X0) = relation_inverse_image(relation_inverse(sK5),X1) )
| ~ disjoint(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_23214,c_211]) ).
tcf(c_23685,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,relation_inverse_image(relation_inverse(sK5),X1))
| ~ disjoint(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_23214,c_256]) ).
tcf(c_23692,plain,
! [X0: $i,X1: $i] : ~ empty(sK2(set_union2(X0,powerset(X1)))),
inference(superposition,[status(thm)],[c_19515,c_20434]) ).
tcf(c_23693,plain,
! [X0: $i,X1: $i] : ~ in(sK2(set_union2(X0,powerset(union(X1)))),X1),
inference(superposition,[status(thm)],[c_222,c_20434]) ).
tcf(c_23705,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK1(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_6708,c_242]) ).
tcf(c_23706,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ( set_difference(X0,unordered_pair(X2,X2)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_195,c_242]) ).
tcf(c_23707,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ subset(sK2(X0),X1) ),
inference(superposition,[status(thm)],[c_86,c_242]) ).
tcf(c_23708,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(powerset(X0),X2)
| ~ subset(sK2(X1),X2)
| ~ in(X0,sK2(X1)) ),
inference(superposition,[status(thm)],[c_88,c_242]) ).
tcf(c_23709,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| in(sK8(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_149,c_242]) ).
tcf(c_23710,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,X0)
| in(sK8(X2,X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_150,c_242]) ).
tcf(c_23711,plain,
! [X0: $i,X1: $i] :
( in(sK16(X0),X1)
| ( X0 = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_233,c_242]) ).
tcf(c_23712,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK18(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_241,c_242]) ).
tcf(c_23713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| ~ in(X3,X0)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_252,c_242]) ).
tcf(c_23714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| ~ in(X3,X1)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_253,c_242]) ).
tcf(c_23715,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ subset(X2,X0)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_289,c_242]) ).
tcf(c_23716,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ~ in(X1,union(X0))
| ~ subset(sK27(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_296,c_242]) ).
tcf(c_23717,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK27(X1,X0),X2)
| ~ subset(X1,X2)
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_297,c_242]) ).
tcf(c_23718,plain,
! [X0: $i,X1: $i] :
( relation(X0)
| in(sK38(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_314,c_242]) ).
tcf(c_23721,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ subset(sK54(X0),X1) ),
inference(superposition,[status(thm)],[c_372,c_242]) ).
tcf(c_23722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ subset(set_union2(unordered_pair(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_19972,c_242]) ).
tcf(c_23723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ subset(set_union2(X0,unordered_pair(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_19974,c_242]) ).
tcf(c_23724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ subset(set_union2(unordered_pair(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_19992,c_242]) ).
tcf(c_23725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,X3)
| ~ subset(set_union2(X0,unordered_pair(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_19994,c_242]) ).
tcf(c_23726,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X1)
| ~ subset(set_union2(powerset(empty_set),X0),X1) ),
inference(superposition,[status(thm)],[c_20028,c_242]) ).
tcf(c_23727,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X1)
| ~ subset(set_union2(X0,powerset(empty_set)),X1) ),
inference(superposition,[status(thm)],[c_20041,c_242]) ).
tcf(c_23728,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK22(X0),X1)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_20312,c_242]) ).
tcf(c_23729,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK23(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_20297,c_242]) ).
tcf(c_23730,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_20311,c_242]) ).
tcf(c_23731,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X1)
| ~ subset(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_20310,c_242]) ).
tcf(c_23814,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,X1)),X2)
| in(sK1(set_difference(X0,set_difference(X0,X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_6708,c_370]) ).
tcf(c_23815,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ( set_difference(set_difference(X0,set_difference(X0,X1)),unordered_pair(X2,X2)) = set_difference(X0,set_difference(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_195,c_370]) ).
tcf(c_23816,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,set_difference(X0,X1)),X2)
| in(sK8(set_difference(X0,set_difference(X0,X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_149,c_370]) ).
tcf(c_23817,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_difference(X1,set_difference(X1,X2)))
| in(sK8(X0,set_difference(X1,set_difference(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_150,c_370]) ).
tcf(c_23818,plain,
! [X0: $i,X1: $i] :
( in(sK16(set_difference(X0,set_difference(X0,X1))),X1)
| ( set_difference(X0,set_difference(X0,X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_233,c_370]) ).
tcf(c_23819,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,X1)),X2)
| in(sK18(set_difference(X0,set_difference(X0,X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_241,c_370]) ).
tcf(c_23820,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK27(set_difference(X1,set_difference(X1,X2)),X0),X2)
| ~ in(X0,union(set_difference(X1,set_difference(X1,X2)))) ),
inference(superposition,[status(thm)],[c_297,c_370]) ).
tcf(c_23821,plain,
! [X0: $i,X1: $i] :
( relation(set_difference(X0,set_difference(X0,X1)))
| in(sK38(set_difference(X0,set_difference(X0,X1))),X1) ),
inference(superposition,[status(thm)],[c_314,c_370]) ).
tcf(c_23822,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X0,set_difference(X0,X1)))
| in(sK23(set_difference(X0,set_difference(X0,X1))),X1) ),
inference(superposition,[status(thm)],[c_20297,c_370]) ).
tcf(c_23824,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_difference(set_union2(X1,X2),set_difference(X1,X2))) ),
inference(superposition,[status(thm)],[c_153,c_370]) ).
tcf(c_23826,plain,
! [X0: $i,X1: $i] :
( in(X0,empty_set)
| ~ in(X0,set_difference(X1,X1)) ),
inference(superposition,[status(thm)],[c_264,c_370]) ).
tcf(c_23827,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_4095,c_370]) ).
tcf(c_23828,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(sK5))
| ~ in(X0,set_difference(relation_inverse_image(relation_inverse(sK5),X1),empty_set)) ),
inference(superposition,[status(thm)],[c_21834,c_370]) ).
tcf(c_23829,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(sK5))
| ~ in(X0,set_difference(relation_image(relation_inverse(sK5),X1),empty_set)) ),
inference(superposition,[status(thm)],[c_22079,c_370]) ).
tcf(c_23832,plain,
! [X0: $i,X1: $i] : ~ in(X0,set_difference(X1,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_23826,c_234]) ).
tcf(c_23891,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK55(X1,X0),X2)
| ~ subset(sK54(X1),X2)
| ~ in(X0,sK54(X1)) ),
inference(superposition,[status(thm)],[c_374,c_242]) ).
tcf(c_23892,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(sK54(X1)),sK55(X1,X0)) = sK55(X1,X0) )
| ~ in(X0,sK54(X1)) ),
inference(superposition,[status(thm)],[c_374,c_134]) ).
tcf(c_23893,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,sK54(X0))
| ~ in(sK54(X0),sK55(X0,X1)) ),
inference(superposition,[status(thm)],[c_374,c_243]) ).
tcf(c_23894,plain,
! [X0: $i,X1: $i] :
( ~ empty(sK54(X1))
| ~ in(X0,sK54(X1)) ),
inference(superposition,[status(thm)],[c_374,c_471]) ).
tcf(c_23895,plain,
! [X0: $i,X1: $i] :
( element(sK55(X1,X0),sK54(X1))
| ~ in(X0,sK54(X1)) ),
inference(superposition,[status(thm)],[c_374,c_276]) ).
tcf(c_23915,plain,
! [X0: $i,X1: $i] :
( proper_subset(unordered_pair(X0,X0),X1)
| ( unordered_pair(X0,X0) = X1 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_140,c_468]) ).
tcf(c_23916,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,X1)
| ( X0 = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19515,c_468]) ).
tcf(c_23917,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,union(X1))
| ( union(X1) = X0 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_222,c_468]) ).
tcf(c_23918,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_rng(relation_rng_restriction(X1,X0)),X1)
| ( relation_rng(relation_rng_restriction(X1,X0)) = X1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_78,c_468]) ).
tcf(c_23919,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_rng_restriction(X1,X0),X0)
| ( relation_rng_restriction(X1,X0) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_79,c_468]) ).
tcf(c_23920,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_rng(relation_rng_restriction(X1,X0)),relation_rng(X0))
| ( relation_rng(relation_rng_restriction(X1,X0)) = relation_rng(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_80,c_468]) ).
tcf(c_23921,plain,
! [X0: $i,X1: $i,X2: $i] :
( proper_subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ( cartesian_product2(X0,X2) = cartesian_product2(X1,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_81,c_468]) ).
tcf(c_23922,plain,
! [X0: $i,X1: $i,X2: $i] :
( proper_subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ( cartesian_product2(X2,X0) = cartesian_product2(X2,X1) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_468]) ).
tcf(c_23923,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_image(X0,X1),relation_rng(X0))
| ( relation_image(X0,X1) = relation_rng(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_94,c_468]) ).
tcf(c_23924,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_inverse_image(X0,X1),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_dom(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_105,c_468]) ).
tcf(c_23925,plain,
! [X0: $i] :
( proper_subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ( cartesian_product2(relation_dom(X0),relation_rng(X0)) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_117,c_468]) ).
tcf(c_23926,plain,
! [X0: $i] :
( proper_subset(empty_set,X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_124,c_468]) ).
tcf(c_23927,plain,
! [X0: $i,X1: $i,X2: $i] :
( proper_subset(set_difference(X0,X2),set_difference(X1,X2))
| ( set_difference(X0,X2) = set_difference(X1,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_127,c_468]) ).
tcf(c_23928,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(X0,X1),X0)
| ( set_difference(X0,X1) = X0 ) ),
inference(superposition,[status(thm)],[c_135,c_468]) ).
tcf(c_23929,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,set_union2(X0,X1))
| ( set_union2(X0,X1) = X0 ) ),
inference(superposition,[status(thm)],[c_209,c_468]) ).
tcf(c_23930,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_dom_restriction(X0,X1),X0)
| ( relation_dom_restriction(X0,X1) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_215,c_468]) ).
tcf(c_23931,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_rng(relation_dom_restriction(X0,X1)),relation_rng(X0))
| ( relation_rng(relation_dom_restriction(X0,X1)) = relation_rng(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_224,c_468]) ).
tcf(c_23933,plain,
! [X0: $i] :
( empty(X0)
| proper_subset(sK22(X0),X0)
| ( sK22(X0) = X0 ) ),
inference(superposition,[status(thm)],[c_19616,c_468]) ).
tcf(c_23934,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(X0,X1),set_union2(X0,X1))
| ( set_union2(X0,X1) = set_difference(X0,X1) ) ),
inference(superposition,[status(thm)],[c_19485,c_468]) ).
tcf(c_23935,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(X0,set_difference(X1,X0)),set_union2(X0,X1))
| ( set_difference(X0,set_difference(X1,X0)) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_19566,c_468]) ).
tcf(c_23936,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(X1,X0),set_union2(X0,X1))
| ( set_union2(X0,X1) = set_difference(X1,X0) ) ),
inference(superposition,[status(thm)],[c_19593,c_468]) ).
tcf(c_23937,plain,
! [X0: $i,X1: $i] :
( proper_subset(X1,set_union2(X0,X1))
| ( set_union2(X0,X1) = X1 ) ),
inference(superposition,[status(thm)],[c_19598,c_468]) ).
tcf(c_23938,plain,
! [X0: $i] :
( proper_subset(sK23(powerset(X0)),X0)
| ( sK23(powerset(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_19617,c_468]) ).
tcf(c_23939,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| proper_subset(sK18(powerset(X0),X1),X0)
| ( sK18(powerset(X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_19652,c_468]) ).
tcf(c_23940,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0))
| ( set_difference(set_difference(X0,X1),X1) = set_union2(X1,X0) ) ),
inference(superposition,[status(thm)],[c_19715,c_468]) ).
tcf(c_23941,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(X0,set_difference(X1,X0)),set_union2(X1,X0))
| ( set_difference(X0,set_difference(X1,X0)) = set_union2(X1,X0) ) ),
inference(superposition,[status(thm)],[c_19744,c_468]) ).
tcf(c_23942,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_union2(X0,X1))
| ( set_difference(X0,set_difference(set_difference(X1,X0),X0)) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_19741,c_468]) ).
tcf(c_23943,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_image(identity_relation(X0),X1),X0)
| ( relation_image(identity_relation(X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_19833,c_468]) ).
tcf(c_23944,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| proper_subset(sK1(powerset(X0),X1),X0)
| ( sK1(powerset(X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_19866,c_468]) ).
tcf(c_23945,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_inverse_image(identity_relation(X0),X1),X0)
| ( relation_inverse_image(identity_relation(X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_19947,c_468]) ).
tcf(c_23946,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(set_difference(X0,X1),X1),set_union2(X0,X1))
| ( set_difference(set_difference(X0,X1),X1) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_20247,c_468]) ).
tcf(c_23947,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_union2(X1,X0))
| ( set_difference(set_difference(set_difference(X0,X1),X1),X1) = set_union2(X1,X0) ) ),
inference(superposition,[status(thm)],[c_20244,c_468]) ).
tcf(c_23948,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_rng(relation_rng_restriction(X0,identity_relation(X1))),X1)
| ( relation_rng(relation_rng_restriction(X0,identity_relation(X1))) = X1 ) ),
inference(superposition,[status(thm)],[c_20703,c_468]) ).
tcf(c_23949,plain,
! [X0: $i] :
( proper_subset(identity_relation(X0),cartesian_product2(X0,X0))
| ( cartesian_product2(X0,X0) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_20929,c_468]) ).
tcf(c_23950,plain,
! [X0: $i] :
( proper_subset(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))
| ( relation_inverse_image(relation_inverse(sK5),X0) = relation_rng(sK5) ) ),
inference(superposition,[status(thm)],[c_21837,c_468]) ).
tcf(c_23951,plain,
! [X0: $i] :
( proper_subset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))
| ( relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))) = relation_dom(sK5) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21331,c_468]) ).
tcf(c_23952,plain,
! [X0: $i] :
( proper_subset(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))
| ( relation_image(relation_inverse(sK5),X0) = relation_dom(sK5) ) ),
inference(superposition,[status(thm)],[c_22082,c_468]) ).
tcf(c_23953,plain,
( proper_subset(relation_inverse(sK5),cartesian_product2(relation_rng(sK5),relation_dom(sK5)))
| ( cartesian_product2(relation_rng(sK5),relation_dom(sK5)) = relation_inverse(sK5) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21353,c_468]) ).
tcf(c_23954,plain,
! [X0: $i] :
( proper_subset(relation_rng(relation_dom_restriction(relation_inverse(sK5),X0)),relation_dom(sK5))
| ( relation_rng(relation_dom_restriction(relation_inverse(sK5),X0)) = relation_dom(sK5) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21494,c_468]) ).
tcf(c_23955,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_inverse_image(relation_inverse(sK5),X1),X0)
| ( relation_inverse_image(relation_inverse(sK5),X1) = X0 )
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_22586,c_468]) ).
tcf(c_23956,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_image(relation_inverse(sK5),X1),X0)
| ( relation_image(relation_inverse(sK5),X1) = X0 )
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_22588,c_468]) ).
tcf(c_24118,plain,
! [X0: $i] :
( subset(relation_rng(relation_dom_restriction(relation_inverse(sK47),X0)),relation_dom(sK47))
| ~ relation(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_21128,c_224]) ).
tcf(c_24119,plain,
( subset(relation_inverse(sK47),cartesian_product2(relation_dom(relation_inverse(sK47)),relation_dom(sK47)))
| ~ relation(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_21128,c_117]) ).
tcf(c_24120,plain,
! [X0: $i] :
( subset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK47))),relation_dom(sK47))
| ~ relation(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_21128,c_80]) ).
tcf(c_24121,plain,
( empty(relation_inverse(sK47))
| ~ empty(relation_dom(sK47))
| ~ relation(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_21128,c_361]) ).
tcf(c_24122,plain,
! [X0: $i] :
( subset(relation_image(relation_inverse(sK47),X0),relation_dom(sK47))
| ~ relation(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_21128,c_94]) ).
tcf(c_24123,plain,
( function(relation_dom(sK47))
| ~ empty(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_21128,c_19156]) ).
tcf(c_24124,plain,
( one_to_one(relation_dom(sK47))
| ~ empty(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_21128,c_19154]) ).
tcf(c_24125,plain,
( relation(relation_dom(sK47))
| ~ empty(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_21128,c_360]) ).
tcf(c_24126,plain,
( empty(relation_dom(sK47))
| ~ empty(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_21128,c_359]) ).
tcf(c_24144,plain,
( subset(relation_inverse(sK47),cartesian_product2(relation_rng(sK47),relation_dom(sK47)))
| ~ relation(relation_inverse(sK47)) ),
inference(light_normalisation,[status(thm)],[c_24119,c_20951]) ).
tcf(c_24177,plain,
! [X0: $i] :
( subset(relation_rng(relation_dom_restriction(relation_inverse(sK75),X0)),relation_dom(sK75))
| ~ relation(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_21134,c_224]) ).
tcf(c_24178,plain,
( subset(relation_inverse(sK75),cartesian_product2(relation_dom(relation_inverse(sK75)),relation_dom(sK75)))
| ~ relation(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_21134,c_117]) ).
tcf(c_24179,plain,
! [X0: $i] :
( subset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK75))),relation_dom(sK75))
| ~ relation(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_21134,c_80]) ).
tcf(c_24180,plain,
( empty(relation_inverse(sK75))
| ~ empty(relation_dom(sK75))
| ~ relation(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_21134,c_361]) ).
tcf(c_24181,plain,
! [X0: $i] :
( subset(relation_image(relation_inverse(sK75),X0),relation_dom(sK75))
| ~ relation(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_21134,c_94]) ).
tcf(c_24182,plain,
( function(relation_dom(sK75))
| ~ empty(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_21134,c_19156]) ).
tcf(c_24183,plain,
( one_to_one(relation_dom(sK75))
| ~ empty(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_21134,c_19154]) ).
tcf(c_24184,plain,
( relation(relation_dom(sK75))
| ~ empty(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_21134,c_360]) ).
tcf(c_24185,plain,
( empty(relation_dom(sK75))
| ~ empty(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_21134,c_359]) ).
tcf(c_24207,plain,
! [X0: $i] :
( subset(relation_rng(relation_dom_restriction(relation_inverse(sK79),X0)),relation_dom(sK79))
| ~ relation(relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_21135,c_224]) ).
tcf(c_24208,plain,
( subset(relation_inverse(sK79),cartesian_product2(relation_dom(relation_inverse(sK79)),relation_dom(sK79)))
| ~ relation(relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_21135,c_117]) ).
tcf(c_24209,plain,
! [X0: $i] :
( subset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK79))),relation_dom(sK79))
| ~ relation(relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_21135,c_80]) ).
tcf(c_24210,plain,
( empty(relation_inverse(sK79))
| ~ empty(relation_dom(sK79))
| ~ relation(relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_21135,c_361]) ).
tcf(c_24211,plain,
! [X0: $i] :
( subset(relation_image(relation_inverse(sK79),X0),relation_dom(sK79))
| ~ relation(relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_21135,c_94]) ).
tcf(c_24218,plain,
( ~ empty(relation_dom(sK79))
| ~ relation(relation_inverse(sK79)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24210,c_20632]) ).
tcf(c_24245,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_image(relation_inverse(sK5),X1),X0) = relation_image(relation_inverse(sK5),X1) )
| ~ disjoint(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_23216,c_211]) ).
tcf(c_24246,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,relation_image(relation_inverse(sK5),X1))
| ~ disjoint(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_23216,c_256]) ).
tcf(c_24256,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(relation_image(identity_relation(relation_inverse_image(relation_inverse(sK5),X1)),X2),relation_rng(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22876,c_110]) ).
tcf(c_24260,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(relation_image(identity_relation(relation_inverse_image(relation_inverse(sK5),X1)),X2),relation_rng(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22876,c_190]) ).
tcf(c_24263,plain,
! [X0: $i,X1: $i,X2: $i] : subset(set_difference(relation_image(identity_relation(relation_inverse_image(relation_inverse(sK5),X0)),X1),relation_rng(sK5)),X2),
inference(forward_subsumption_resolution,[status(thm)],[c_24256,c_124]) ).
tcf(c_24265,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(relation_inverse_image(identity_relation(relation_inverse_image(relation_inverse(sK5),X1)),X2),relation_rng(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22878,c_110]) ).
tcf(c_24269,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(relation_inverse_image(identity_relation(relation_inverse_image(relation_inverse(sK5),X1)),X2),relation_rng(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22878,c_190]) ).
tcf(c_24272,plain,
! [X0: $i,X1: $i,X2: $i] : subset(set_difference(relation_inverse_image(identity_relation(relation_inverse_image(relation_inverse(sK5),X0)),X1),relation_rng(sK5)),X2),
inference(forward_subsumption_resolution,[status(thm)],[c_24265,c_124]) ).
tcf(c_24274,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(relation_image(identity_relation(relation_image(relation_inverse(sK5),X1)),X2),relation_dom(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22936,c_110]) ).
tcf(c_24278,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(relation_image(identity_relation(relation_image(relation_inverse(sK5),X1)),X2),relation_dom(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22936,c_190]) ).
tcf(c_24281,plain,
! [X0: $i,X1: $i,X2: $i] : subset(set_difference(relation_image(identity_relation(relation_image(relation_inverse(sK5),X0)),X1),relation_dom(sK5)),X2),
inference(forward_subsumption_resolution,[status(thm)],[c_24274,c_124]) ).
tcf(c_24283,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(relation_inverse_image(identity_relation(relation_image(relation_inverse(sK5),X1)),X2),relation_dom(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22938,c_110]) ).
tcf(c_24287,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(relation_inverse_image(identity_relation(relation_image(relation_inverse(sK5),X1)),X2),relation_dom(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22938,c_190]) ).
tcf(c_24290,plain,
! [X0: $i,X1: $i,X2: $i] : subset(set_difference(relation_inverse_image(identity_relation(relation_image(relation_inverse(sK5),X0)),X1),relation_dom(sK5)),X2),
inference(forward_subsumption_resolution,[status(thm)],[c_24283,c_124]) ).
tcf(c_24292,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(relation_rng(relation_rng_restriction(X1,identity_relation(relation_inverse_image(relation_inverse(sK5),X2)))),relation_rng(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22879,c_110]) ).
tcf(c_24296,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(relation_rng(relation_rng_restriction(X1,identity_relation(relation_inverse_image(relation_inverse(sK5),X2)))),relation_rng(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22879,c_190]) ).
tcf(c_24299,plain,
! [X0: $i,X1: $i,X2: $i] : subset(set_difference(relation_rng(relation_rng_restriction(X0,identity_relation(relation_inverse_image(relation_inverse(sK5),X1)))),relation_rng(sK5)),X2),
inference(forward_subsumption_resolution,[status(thm)],[c_24292,c_124]) ).
tcf(c_24300,plain,
! [X0: $i,X1: $i] : ~ empty(sK54(set_union2(X0,powerset(X1)))),
inference(superposition,[status(thm)],[c_19515,c_20446]) ).
tcf(c_24301,plain,
! [X0: $i,X1: $i] : ~ in(sK54(set_union2(X0,powerset(union(X1)))),X1),
inference(superposition,[status(thm)],[c_222,c_20446]) ).
tcf(c_24311,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),X1)) = unordered_pair(X0,X0) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_140,c_123]) ).
tcf(c_24312,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19515,c_123]) ).
tcf(c_24313,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,union(X1))) = X0 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_222,c_123]) ).
tcf(c_24314,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,X0)),set_difference(relation_rng(relation_rng_restriction(X1,X0)),X1)) = relation_rng(relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_78,c_123]) ).
tcf(c_24315,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng_restriction(X1,X0),set_difference(relation_rng_restriction(X1,X0),X0)) = relation_rng_restriction(X1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_79,c_123]) ).
tcf(c_24316,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,X0)),set_difference(relation_rng(relation_rng_restriction(X1,X0)),relation_rng(X0))) = relation_rng(relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_80,c_123]) ).
tcf(c_24317,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(cartesian_product2(X0,X2),set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X2))) = cartesian_product2(X0,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_81,c_123]) ).
tcf(c_24318,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(cartesian_product2(X2,X0),set_difference(cartesian_product2(X2,X0),cartesian_product2(X2,X1))) = cartesian_product2(X2,X0) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_123]) ).
tcf(c_24319,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_image(X0,X1),set_difference(relation_image(X0,X1),relation_rng(X0))) = relation_image(X0,X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_94,c_123]) ).
tcf(c_24320,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_inverse_image(X0,X1),set_difference(relation_inverse_image(X0,X1),relation_dom(X0))) = relation_inverse_image(X0,X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_105,c_123]) ).
tcf(c_24321,plain,
! [X0: $i] :
( ( set_difference(X0,set_difference(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_117,c_123]) ).
tcf(c_24322,plain,
! [X0: $i] : set_difference(empty_set,set_difference(empty_set,X0)) = empty_set,
inference(superposition,[status(thm)],[c_124,c_123]) ).
tcf(c_24323,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X0,X2),set_difference(set_difference(X0,X2),set_difference(X1,X2))) = set_difference(X0,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_127,c_123]) ).
tcf(c_24324,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_difference(set_difference(X0,X1),X0)) = set_difference(X0,X1),
inference(superposition,[status(thm)],[c_135,c_123]) ).
tcf(c_24325,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,set_union2(X0,X1))) = X0,
inference(superposition,[status(thm)],[c_209,c_123]) ).
tcf(c_24326,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom_restriction(X0,X1),set_difference(relation_dom_restriction(X0,X1),X0)) = relation_dom_restriction(X0,X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_215,c_123]) ).
tcf(c_24327,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_dom_restriction(X0,X1)),set_difference(relation_rng(relation_dom_restriction(X0,X1)),relation_rng(X0))) = relation_rng(relation_dom_restriction(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_224,c_123]) ).
tcf(c_24328,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,X0)) = X0,
inference(superposition,[status(thm)],[c_262,c_123]) ).
tcf(c_24329,plain,
! [X0: $i] :
( empty(X0)
| ( set_difference(sK22(X0),set_difference(sK22(X0),X0)) = sK22(X0) ) ),
inference(superposition,[status(thm)],[c_19616,c_123]) ).
tcf(c_24330,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_difference(set_difference(X0,X1),set_union2(X0,X1))) = set_difference(X0,X1),
inference(superposition,[status(thm)],[c_19485,c_123]) ).
tcf(c_24331,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(set_difference(X0,set_difference(X1,X0)),set_union2(X0,X1))) = set_difference(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_19566,c_123]) ).
tcf(c_24332,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_difference(set_difference(X0,X1),set_union2(X1,X0))) = set_difference(X0,X1),
inference(superposition,[status(thm)],[c_19593,c_123]) ).
tcf(c_24333,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,set_union2(X1,X0))) = X0,
inference(superposition,[status(thm)],[c_19598,c_123]) ).
tcf(c_24334,plain,
! [X0: $i] : set_difference(sK23(powerset(X0)),set_difference(sK23(powerset(X0)),X0)) = sK23(powerset(X0)),
inference(superposition,[status(thm)],[c_19617,c_123]) ).
tcf(c_24335,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( set_difference(sK18(powerset(X0),X1),set_difference(sK18(powerset(X0),X1),X0)) = sK18(powerset(X0),X1) ) ),
inference(superposition,[status(thm)],[c_19652,c_123]) ).
tcf(c_24336,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),X1),set_difference(set_difference(set_difference(X0,X1),X1),set_union2(X1,X0))) = set_difference(set_difference(X0,X1),X1),
inference(superposition,[status(thm)],[c_19715,c_123]) ).
tcf(c_24337,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(set_difference(X0,set_difference(X1,X0)),set_union2(X1,X0))) = set_difference(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_19744,c_123]) ).
tcf(c_24338,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_difference(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_union2(X0,X1))) = set_difference(X0,set_difference(set_difference(X1,X0),X0)),
inference(superposition,[status(thm)],[c_19741,c_123]) ).
tcf(c_24339,plain,
! [X0: $i,X1: $i] : set_difference(relation_image(identity_relation(X0),X1),set_difference(relation_image(identity_relation(X0),X1),X0)) = relation_image(identity_relation(X0),X1),
inference(superposition,[status(thm)],[c_19833,c_123]) ).
tcf(c_24340,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( set_difference(sK1(powerset(X0),X1),set_difference(sK1(powerset(X0),X1),X0)) = sK1(powerset(X0),X1) ) ),
inference(superposition,[status(thm)],[c_19866,c_123]) ).
tcf(c_24341,plain,
! [X0: $i,X1: $i] : set_difference(relation_inverse_image(identity_relation(X0),X1),set_difference(relation_inverse_image(identity_relation(X0),X1),X0)) = relation_inverse_image(identity_relation(X0),X1),
inference(superposition,[status(thm)],[c_19947,c_123]) ).
tcf(c_24342,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),X1),set_difference(set_difference(set_difference(X0,X1),X1),set_union2(X0,X1))) = set_difference(set_difference(X0,X1),X1),
inference(superposition,[status(thm)],[c_20247,c_123]) ).
tcf(c_24343,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_union2(X1,X0))) = set_difference(set_difference(set_difference(X0,X1),X1),X1),
inference(superposition,[status(thm)],[c_20244,c_123]) ).
tcf(c_24344,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_rng_restriction(X0,identity_relation(X1))),set_difference(relation_rng(relation_rng_restriction(X0,identity_relation(X1))),X1)) = relation_rng(relation_rng_restriction(X0,identity_relation(X1))),
inference(superposition,[status(thm)],[c_20703,c_123]) ).
tcf(c_24345,plain,
! [X0: $i] : set_difference(identity_relation(X0),set_difference(identity_relation(X0),cartesian_product2(X0,X0))) = identity_relation(X0),
inference(superposition,[status(thm)],[c_20929,c_123]) ).
tcf(c_24346,plain,
! [X0: $i] : set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))) = relation_inverse_image(relation_inverse(sK5),X0),
inference(superposition,[status(thm)],[c_21837,c_123]) ).
tcf(c_24347,plain,
! [X0: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))) = relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21331,c_123]) ).
tcf(c_24348,plain,
! [X0: $i] : set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))) = relation_image(relation_inverse(sK5),X0),
inference(superposition,[status(thm)],[c_22082,c_123]) ).
tcf(c_24349,plain,
( ( set_difference(relation_inverse(sK5),set_difference(relation_inverse(sK5),cartesian_product2(relation_rng(sK5),relation_dom(sK5)))) = relation_inverse(sK5) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21353,c_123]) ).
tcf(c_24350,plain,
! [X0: $i] :
( ( set_difference(relation_rng(relation_dom_restriction(relation_inverse(sK5),X0)),set_difference(relation_rng(relation_dom_restriction(relation_inverse(sK5),X0)),relation_dom(sK5))) = relation_rng(relation_dom_restriction(relation_inverse(sK5),X0)) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21494,c_123]) ).
tcf(c_24351,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_inverse_image(relation_inverse(sK5),X1),set_difference(relation_inverse_image(relation_inverse(sK5),X1),X0)) = relation_inverse_image(relation_inverse(sK5),X1) )
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_22586,c_123]) ).
tcf(c_24352,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_image(relation_inverse(sK5),X1),set_difference(relation_image(relation_inverse(sK5),X1),X0)) = relation_image(relation_inverse(sK5),X1) )
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_22588,c_123]) ).
tcf(c_24354,plain,
set_difference(empty_set,empty_set) = empty_set,
inference(light_normalisation,[status(thm)],[c_24322,c_263]) ).
tcf(c_24359,plain,
! [X0: $i] : set_difference(identity_relation(X0),empty_set) = identity_relation(X0),
inference(light_normalisation,[status(thm)],[c_24345,c_21222]) ).
tcf(c_24364,plain,
! [X0: $i] : set_difference(sK23(powerset(X0)),empty_set) = sK23(powerset(X0)),
inference(light_normalisation,[status(thm)],[c_24334,c_21213]) ).
tcf(c_24365,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),empty_set) = set_difference(X0,X1),
inference(light_normalisation,[status(thm)],[c_24324,c_21204]) ).
tcf(c_24370,plain,
! [X0: $i,X1: $i] : set_difference(relation_inverse_image(identity_relation(X0),X1),empty_set) = relation_inverse_image(identity_relation(X0),X1),
inference(light_normalisation,[status(thm)],[c_24341,c_21220]) ).
tcf(c_24371,plain,
! [X0: $i,X1: $i] : set_difference(relation_image(identity_relation(X0),X1),empty_set) = relation_image(identity_relation(X0),X1),
inference(light_normalisation,[status(thm)],[c_24339,c_21218]) ).
tcf(c_24376,plain,
! [X0: $i] : set_difference(relation_image(relation_inverse(sK5),X0),empty_set) = relation_image(relation_inverse(sK5),X0),
inference(light_normalisation,[status(thm)],[c_24348,c_22079]) ).
tcf(c_24377,plain,
! [X0: $i] : set_difference(relation_inverse_image(relation_inverse(sK5),X0),empty_set) = relation_inverse_image(relation_inverse(sK5),X0),
inference(light_normalisation,[status(thm)],[c_24346,c_21834]) ).
tcf(c_24386,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_rng_restriction(X0,identity_relation(X1))),empty_set) = relation_rng(relation_rng_restriction(X0,identity_relation(X1))),
inference(light_normalisation,[status(thm)],[c_24344,c_21221]) ).
tcf(c_24407,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),X1),empty_set) = set_difference(set_difference(X0,X1),X1),
inference(light_normalisation,[status(thm)],[c_24342,c_22403]) ).
tcf(c_24408,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X1,X0)),empty_set) = set_difference(X0,set_difference(X1,X0)),
inference(light_normalisation,[status(thm)],[c_24337,c_21216]) ).
tcf(c_24415,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),empty_set) = set_difference(set_difference(set_difference(X0,X1),X1),X1),
inference(light_normalisation,[status(thm)],[c_24343,c_22124]) ).
tcf(c_24416,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(set_difference(X1,X0),X0)),empty_set) = set_difference(X0,set_difference(set_difference(X1,X0),X0)),
inference(light_normalisation,[status(thm)],[c_24338,c_21217]) ).
tcf(c_24461,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X1)
| ~ disjoint(X0,X2)
| ~ in(sK1(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6708,c_151]) ).
tcf(c_24462,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X2,unordered_pair(X0,X0)) = X2 )
| ~ disjoint(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_195,c_151]) ).
tcf(c_24463,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ~ disjoint(sK2(X0),X1) ),
inference(superposition,[status(thm)],[c_86,c_151]) ).
tcf(c_24464,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(sK2(X2),X1)
| ~ in(X0,sK2(X2))
| ~ in(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_88,c_151]) ).
tcf(c_24465,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X1)
| ~ disjoint(X0,X2)
| ~ in(sK8(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_149,c_151]) ).
tcf(c_24466,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X1)
| ~ disjoint(X1,X2)
| ~ in(sK8(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_150,c_151]) ).
tcf(c_24467,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ~ disjoint(X0,X1)
| ~ in(sK16(X0),X1) ),
inference(superposition,[status(thm)],[c_233,c_151]) ).
tcf(c_24468,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X1)
| ~ disjoint(X0,X2)
| ~ in(sK18(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_241,c_151]) ).
tcf(c_24469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_252,c_151]) ).
tcf(c_24470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_253,c_151]) ).
tcf(c_24471,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X2,X0)
| ~ in(X2,X1)
| ~ disjoint(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_289,c_151]) ).
tcf(c_24472,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X1,X2)
| ~ in(X1,union(X0))
| ~ disjoint(sK27(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_296,c_151]) ).
tcf(c_24473,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X0,X2)
| ~ in(X1,union(X0))
| ~ in(sK27(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_297,c_151]) ).
tcf(c_24474,plain,
! [X0: $i,X1: $i] :
( relation(X0)
| ~ disjoint(X0,X1)
| ~ in(sK38(X0),X1) ),
inference(superposition,[status(thm)],[c_314,c_151]) ).
tcf(c_24475,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ disjoint(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_348,c_151]) ).
tcf(c_24476,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X1,X2)
| ~ disjoint(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_349,c_151]) ).
tcf(c_24477,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ~ disjoint(sK54(X0),X1) ),
inference(superposition,[status(thm)],[c_372,c_151]) ).
tcf(c_24478,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(sK54(X0),X2)
| ~ in(X1,sK54(X0))
| ~ in(sK55(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_374,c_151]) ).
tcf(c_24479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X0,X3)
| ~ disjoint(set_union2(unordered_pair(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_19972,c_151]) ).
tcf(c_24480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X1,X3)
| ~ disjoint(set_union2(X0,unordered_pair(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_19974,c_151]) ).
tcf(c_24481,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X1,X3)
| ~ disjoint(set_union2(unordered_pair(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_19992,c_151]) ).
tcf(c_24482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X2,X3)
| ~ disjoint(set_union2(X0,unordered_pair(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_19994,c_151]) ).
tcf(c_24483,plain,
! [X0: $i,X1: $i] :
( ~ in(empty_set,X1)
| ~ disjoint(set_union2(powerset(empty_set),X0),X1) ),
inference(superposition,[status(thm)],[c_20028,c_151]) ).
tcf(c_24484,plain,
! [X0: $i,X1: $i] :
( ~ in(empty_set,X1)
| ~ disjoint(set_union2(X0,powerset(empty_set)),X1) ),
inference(superposition,[status(thm)],[c_20041,c_151]) ).
tcf(c_24485,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ disjoint(powerset(X0),X1)
| ~ in(sK22(X0),X1) ),
inference(superposition,[status(thm)],[c_20312,c_151]) ).
tcf(c_24486,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ disjoint(X0,X1)
| ~ in(sK23(X0),X1) ),
inference(superposition,[status(thm)],[c_20297,c_151]) ).
tcf(c_24487,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ~ disjoint(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_20311,c_151]) ).
tcf(c_24488,plain,
! [X0: $i,X1: $i] :
( ~ in(empty_set,X1)
| ~ disjoint(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_20310,c_151]) ).
tcf(c_24594,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_union2(unordered_pair(sK1(X0,X1),sK1(X0,X1)),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_6708,c_161]) ).
tcf(c_24595,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,unordered_pair(X0,X0)) = X1 )
| ( set_union2(unordered_pair(X0,X0),X1) = X1 ) ),
inference(superposition,[status(thm)],[c_195,c_161]) ).
tcf(c_24596,plain,
! [X0: $i] : set_union2(unordered_pair(X0,X0),sK2(X0)) = sK2(X0),
inference(superposition,[status(thm)],[c_86,c_161]) ).
tcf(c_24597,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(powerset(X0),powerset(X0)),sK2(X1)) = sK2(X1) )
| ~ in(X0,sK2(X1)) ),
inference(superposition,[status(thm)],[c_88,c_161]) ).
tcf(c_24598,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_union2(unordered_pair(sK8(X0,X1),sK8(X0,X1)),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_149,c_161]) ).
tcf(c_24599,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_union2(unordered_pair(sK8(X0,X1),sK8(X0,X1)),X1) = X1 ) ),
inference(superposition,[status(thm)],[c_150,c_161]) ).
tcf(c_24600,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( set_union2(unordered_pair(sK16(X0),sK16(X0)),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_233,c_161]) ).
tcf(c_24601,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_union2(unordered_pair(sK18(X0,X1),sK18(X0,X1)),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_241,c_161]) ).
tcf(c_24602,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(X0,X0),set_union2(X1,X2)) = set_union2(X1,X2) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_252,c_161]) ).
tcf(c_24603,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(X0,X0),set_union2(X2,X1)) = set_union2(X2,X1) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_253,c_161]) ).
tcf(c_24604,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(X0,X0),powerset(X1)) = powerset(X1) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_289,c_161]) ).
tcf(c_24605,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(X0,X0),sK27(X1,X0)) = sK27(X1,X0) )
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_296,c_161]) ).
tcf(c_24606,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(sK27(X1,X0),sK27(X1,X0)),X1) = X1 )
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_297,c_161]) ).
tcf(c_24607,plain,
! [X0: $i] :
( relation(X0)
| ( set_union2(unordered_pair(sK38(X0),sK38(X0)),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_314,c_161]) ).
tcf(c_24608,plain,
! [X0: $i,X1: $i] : set_union2(unordered_pair(X0,X0),unordered_pair(X0,X1)) = unordered_pair(X0,X1),
inference(superposition,[status(thm)],[c_348,c_161]) ).
tcf(c_24609,plain,
! [X0: $i,X1: $i] : set_union2(unordered_pair(X0,X0),unordered_pair(X1,X0)) = unordered_pair(X1,X0),
inference(superposition,[status(thm)],[c_349,c_161]) ).
tcf(c_24610,plain,
! [X0: $i] : set_union2(unordered_pair(X0,X0),sK54(X0)) = sK54(X0),
inference(superposition,[status(thm)],[c_372,c_161]) ).
tcf(c_24611,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(sK55(X1,X0),sK55(X1,X0)),sK54(X1)) = sK54(X1) )
| ~ in(X0,sK54(X1)) ),
inference(superposition,[status(thm)],[c_374,c_161]) ).
tcf(c_24612,plain,
! [X0: $i,X1: $i,X2: $i] : set_union2(unordered_pair(X0,X0),set_union2(unordered_pair(X0,X1),X2)) = set_union2(unordered_pair(X0,X1),X2),
inference(superposition,[status(thm)],[c_19972,c_161]) ).
tcf(c_24613,plain,
! [X0: $i,X1: $i,X2: $i] : set_union2(unordered_pair(X0,X0),set_union2(X1,unordered_pair(X0,X2))) = set_union2(X1,unordered_pair(X0,X2)),
inference(superposition,[status(thm)],[c_19974,c_161]) ).
tcf(c_24614,plain,
! [X0: $i,X1: $i,X2: $i] : set_union2(unordered_pair(X0,X0),set_union2(unordered_pair(X1,X0),X2)) = set_union2(unordered_pair(X1,X0),X2),
inference(superposition,[status(thm)],[c_19992,c_161]) ).
tcf(c_24615,plain,
! [X0: $i,X1: $i,X2: $i] : set_union2(unordered_pair(X0,X0),set_union2(X1,unordered_pair(X2,X0))) = set_union2(X1,unordered_pair(X2,X0)),
inference(superposition,[status(thm)],[c_19994,c_161]) ).
tcf(c_24616,plain,
! [X0: $i] : set_union2(unordered_pair(empty_set,empty_set),set_union2(powerset(empty_set),X0)) = set_union2(powerset(empty_set),X0),
inference(superposition,[status(thm)],[c_20028,c_161]) ).
tcf(c_24617,plain,
! [X0: $i] : set_union2(unordered_pair(empty_set,empty_set),set_union2(X0,powerset(empty_set))) = set_union2(X0,powerset(empty_set)),
inference(superposition,[status(thm)],[c_20041,c_161]) ).
tcf(c_24618,plain,
! [X0: $i] :
( empty(X0)
| ( set_union2(unordered_pair(sK22(X0),sK22(X0)),powerset(X0)) = powerset(X0) ) ),
inference(superposition,[status(thm)],[c_20312,c_161]) ).
tcf(c_24619,plain,
! [X0: $i] :
( empty(X0)
| ( set_union2(unordered_pair(sK23(X0),sK23(X0)),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_20297,c_161]) ).
tcf(c_24620,plain,
! [X0: $i] : set_union2(unordered_pair(X0,X0),powerset(X0)) = powerset(X0),
inference(superposition,[status(thm)],[c_20311,c_161]) ).
tcf(c_24621,plain,
! [X0: $i] : set_union2(unordered_pair(empty_set,empty_set),powerset(X0)) = powerset(X0),
inference(superposition,[status(thm)],[c_20310,c_161]) ).
tcf(c_24622,plain,
! [X0: $i] : set_union2(powerset(empty_set),powerset(X0)) = powerset(X0),
inference(light_normalisation,[status(thm)],[c_24621,c_111]) ).
tcf(c_24629,plain,
! [X0: $i] : set_union2(powerset(empty_set),set_union2(X0,powerset(empty_set))) = set_union2(X0,powerset(empty_set)),
inference(light_normalisation,[status(thm)],[c_24617,c_111]) ).
tcf(c_24630,plain,
! [X0: $i] : set_union2(powerset(empty_set),set_union2(powerset(empty_set),X0)) = set_union2(powerset(empty_set),X0),
inference(light_normalisation,[status(thm)],[c_24616,c_111]) ).
tcf(c_24705,plain,
! [X0: $i,X1: $i] :
( disjoint(set_union2(X0,X1),X1)
| in(sK9(set_union2(X0,X1),X1),set_difference(set_union2(X0,X1),set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_153,c_165]) ).
tcf(c_24708,plain,
! [X0: $i] :
( disjoint(X0,X0)
| in(sK9(X0,X0),set_difference(X0,empty_set)) ),
inference(superposition,[status(thm)],[c_4095,c_165]) ).
tcf(c_24709,plain,
! [X0: $i] :
( disjoint(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))
| in(sK9(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),set_difference(relation_inverse_image(relation_inverse(sK5),X0),empty_set)) ),
inference(superposition,[status(thm)],[c_21834,c_165]) ).
tcf(c_24710,plain,
! [X0: $i] :
( disjoint(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))
| in(sK9(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),set_difference(relation_image(relation_inverse(sK5),X0),empty_set)) ),
inference(superposition,[status(thm)],[c_22079,c_165]) ).
tcf(c_24711,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_union2(unordered_pair(sK9(X0,X1),sK9(X0,X1)),set_difference(X0,set_difference(X0,X1))) = set_difference(X0,set_difference(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_165,c_161]) ).
tcf(c_24712,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X1)
| ~ in(sK9(X0,X1),X2)
| ~ disjoint(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_165,c_151]) ).
tcf(c_24713,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X1)
| in(sK9(X0,X1),X2)
| ~ subset(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_165,c_242]) ).
tcf(c_24714,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( apply(identity_relation(set_difference(X0,set_difference(X0,X1))),sK9(X0,X1)) = sK9(X0,X1) ) ),
inference(superposition,[status(thm)],[c_165,c_134]) ).
tcf(c_24715,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ in(set_difference(X0,set_difference(X0,X1)),sK9(X0,X1)) ),
inference(superposition,[status(thm)],[c_165,c_243]) ).
tcf(c_24716,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ empty(set_difference(X0,set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_165,c_471]) ).
tcf(c_24717,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| element(sK9(X0,X1),set_difference(X0,set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_165,c_276]) ).
tcf(c_24718,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK9(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_165,c_370]) ).
tcf(c_24719,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ in(sK9(X0,X1),set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_165,c_270]) ).
tcf(c_24720,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK9(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_165,c_269]) ).
tcf(c_24727,plain,
! [X0: $i] :
( disjoint(X0,X0)
| in(sK9(X0,X0),X0) ),
inference(light_normalisation,[status(thm)],[c_24708,c_264]) ).
tcf(c_24774,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_dom_restriction(relation_inverse(identity_relation(X0)),X1)),X0)
| ~ relation(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_21138,c_224]) ).
tcf(c_24775,plain,
! [X0: $i] :
( subset(relation_inverse(identity_relation(X0)),cartesian_product2(relation_dom(relation_inverse(identity_relation(X0))),X0))
| ~ relation(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_21138,c_117]) ).
tcf(c_24776,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X1,relation_inverse(identity_relation(X0)))),X0)
| ~ relation(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_21138,c_80]) ).
tcf(c_24778,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(relation_inverse(identity_relation(X0)),X1),X0)
| ~ relation(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_21138,c_94]) ).
tcf(c_24793,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_dom_restriction(identity_relation(X0),X1)),set_difference(relation_rng(relation_dom_restriction(identity_relation(X0),X1)),X0)) = relation_rng(relation_dom_restriction(identity_relation(X0),X1)),
inference(superposition,[status(thm)],[c_21501,c_123]) ).
tcf(c_24794,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_rng(relation_dom_restriction(identity_relation(X0),X1)),X0)
| ( relation_rng(relation_dom_restriction(identity_relation(X0),X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_21501,c_468]) ).
tcf(c_24795,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_dom_restriction(identity_relation(X0),X2)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_21501,c_110]) ).
tcf(c_24796,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_dom_restriction(identity_relation(X0),X1)),X0) = empty_set,
inference(superposition,[status(thm)],[c_21501,c_138]) ).
tcf(c_24797,plain,
! [X0: $i,X1: $i] : set_union2(relation_rng(relation_dom_restriction(identity_relation(X0),X1)),X0) = X0,
inference(superposition,[status(thm)],[c_21501,c_85]) ).
tcf(c_24798,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,relation_rng(relation_dom_restriction(identity_relation(X0),X1))),
inference(superposition,[status(thm)],[c_21501,c_188]) ).
tcf(c_24799,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(relation_dom_restriction(identity_relation(X0),X2)),X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_21501,c_190]) ).
tcf(c_24800,plain,
! [X0: $i] : relation_rng(relation_dom_restriction(identity_relation(empty_set),X0)) = empty_set,
inference(superposition,[status(thm)],[c_21501,c_152]) ).
tcf(c_24801,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_rng(relation_dom_restriction(identity_relation(relation_inverse_image(relation_inverse(sK5),X0)),X1)),relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_21501,c_22779]) ).
tcf(c_24802,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_rng(relation_dom_restriction(identity_relation(relation_image(relation_inverse(sK5),X0)),X1)),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_21501,c_22780]) ).
tcf(c_24842,plain,
! [X0: $i] :
( empty(unordered_pair(X0,X0))
| ~ in(unordered_pair(X0,X0),X0) ),
inference(superposition,[status(thm)],[c_21529,c_20362]) ).
tcf(c_24843,plain,
! [X0: $i] :
( function(X0)
| ~ empty(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_21529,c_20384]) ).
tcf(c_24844,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_21529,c_20383]) ).
tcf(c_24845,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_21529,c_20382]) ).
tcf(c_24846,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_21529,c_20331]) ).
tcf(c_24847,plain,
! [X0: $i] :
( empty(unordered_pair(X0,X0))
| in(X0,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_21529,c_20297]) ).
tcf(c_24848,plain,
! [X0: $i] : element(X0,unordered_pair(X0,X0)),
inference(superposition,[status(thm)],[c_21529,c_281]) ).
tcf(c_24849,plain,
sK16(powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_111,c_21534]) ).
tcf(c_24850,plain,
! [X0: $i] :
( in(X0,unordered_pair(X0,X0))
| ( unordered_pair(X0,X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_21534,c_233]) ).
tcf(c_24928,plain,
! [X0: $i] :
( disjoint(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))
| in(sK9(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),relation_inverse_image(relation_inverse(sK5),X0)) ),
inference(demodulation,[status(thm)],[c_24709,c_264]) ).
tcf(c_24935,plain,
! [X0: $i] :
( disjoint(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))
| ( set_union2(unordered_pair(sK9(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),sK9(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))),relation_inverse_image(relation_inverse(sK5),X0)) = relation_inverse_image(relation_inverse(sK5),X0) ) ),
inference(superposition,[status(thm)],[c_24928,c_161]) ).
tcf(c_24936,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))
| ~ disjoint(relation_inverse_image(relation_inverse(sK5),X0),X1)
| ~ in(sK9(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),X1) ),
inference(superposition,[status(thm)],[c_24928,c_151]) ).
tcf(c_24937,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))
| in(sK9(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),X1)
| ~ subset(relation_inverse_image(relation_inverse(sK5),X0),X1) ),
inference(superposition,[status(thm)],[c_24928,c_242]) ).
tcf(c_24938,plain,
! [X0: $i] :
( disjoint(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))
| ( apply(identity_relation(relation_inverse_image(relation_inverse(sK5),X0)),sK9(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))) = sK9(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)) ) ),
inference(superposition,[status(thm)],[c_24928,c_134]) ).
tcf(c_24939,plain,
! [X0: $i] :
( disjoint(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))
| ~ in(relation_inverse_image(relation_inverse(sK5),X0),sK9(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_24928,c_243]) ).
tcf(c_24940,plain,
! [X0: $i] :
( disjoint(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))
| ~ empty(relation_inverse_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_24928,c_471]) ).
tcf(c_24941,plain,
! [X0: $i] :
( disjoint(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))
| element(sK9(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),relation_inverse_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_24928,c_276]) ).
tcf(c_24965,plain,
! [X0: $i] :
( disjoint(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))
| in(sK9(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),relation_image(relation_inverse(sK5),X0)) ),
inference(demodulation,[status(thm)],[c_24710,c_264]) ).
tcf(c_24972,plain,
! [X0: $i] :
( disjoint(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))
| ( set_union2(unordered_pair(sK9(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),sK9(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))),relation_image(relation_inverse(sK5),X0)) = relation_image(relation_inverse(sK5),X0) ) ),
inference(superposition,[status(thm)],[c_24965,c_161]) ).
tcf(c_24973,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))
| ~ disjoint(relation_image(relation_inverse(sK5),X0),X1)
| ~ in(sK9(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),X1) ),
inference(superposition,[status(thm)],[c_24965,c_151]) ).
tcf(c_24974,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))
| in(sK9(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),X1)
| ~ subset(relation_image(relation_inverse(sK5),X0),X1) ),
inference(superposition,[status(thm)],[c_24965,c_242]) ).
tcf(c_24975,plain,
! [X0: $i] :
( disjoint(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))
| ( apply(identity_relation(relation_image(relation_inverse(sK5),X0)),sK9(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))) = sK9(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)) ) ),
inference(superposition,[status(thm)],[c_24965,c_134]) ).
tcf(c_24976,plain,
! [X0: $i] :
( disjoint(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))
| ~ in(relation_image(relation_inverse(sK5),X0),sK9(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))) ),
inference(superposition,[status(thm)],[c_24965,c_243]) ).
tcf(c_24977,plain,
! [X0: $i] :
( disjoint(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))
| ~ empty(relation_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_24965,c_471]) ).
tcf(c_24978,plain,
! [X0: $i] :
( disjoint(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))
| element(sK9(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),relation_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_24965,c_276]) ).
tcf(c_25004,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(relation_rng(relation_rng_restriction(X1,identity_relation(relation_image(relation_inverse(sK5),X2)))),relation_dom(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22939,c_110]) ).
tcf(c_25008,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(relation_rng(relation_rng_restriction(X1,identity_relation(relation_image(relation_inverse(sK5),X2)))),relation_dom(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_22939,c_190]) ).
tcf(c_25011,plain,
! [X0: $i,X1: $i,X2: $i] : subset(set_difference(relation_rng(relation_rng_restriction(X0,identity_relation(relation_image(relation_inverse(sK5),X1)))),relation_dom(sK5)),X2),
inference(forward_subsumption_resolution,[status(thm)],[c_25004,c_124]) ).
tcf(c_25026,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(relation_rng(relation_dom_restriction(identity_relation(relation_inverse_image(relation_inverse(sK5),X1)),X2)),relation_rng(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_24801,c_110]) ).
tcf(c_25030,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(relation_rng(relation_dom_restriction(identity_relation(relation_inverse_image(relation_inverse(sK5),X1)),X2)),relation_rng(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_24801,c_190]) ).
tcf(c_25033,plain,
! [X0: $i,X1: $i,X2: $i] : subset(set_difference(relation_rng(relation_dom_restriction(identity_relation(relation_inverse_image(relation_inverse(sK5),X0)),X1)),relation_rng(sK5)),X2),
inference(forward_subsumption_resolution,[status(thm)],[c_25026,c_124]) ).
tcf(c_25036,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(relation_rng(relation_dom_restriction(identity_relation(relation_image(relation_inverse(sK5),X1)),X2)),relation_dom(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_24802,c_110]) ).
tcf(c_25040,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(relation_rng(relation_dom_restriction(identity_relation(relation_image(relation_inverse(sK5),X1)),X2)),relation_dom(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_24802,c_190]) ).
tcf(c_25043,plain,
! [X0: $i,X1: $i,X2: $i] : subset(set_difference(relation_rng(relation_dom_restriction(identity_relation(relation_image(relation_inverse(sK5),X0)),X1)),relation_dom(sK5)),X2),
inference(forward_subsumption_resolution,[status(thm)],[c_25036,c_124]) ).
tcf(c_25052,plain,
! [X0: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)) = empty_set )
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_434,c_21601]) ).
tcf(c_25056,plain,
! [X0: $i] : set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_25052,c_96]) ).
tcf(c_25058,plain,
! [X0: $i,X1: $i] : ~ empty(powerset(set_union2(X0,powerset(X1)))),
inference(superposition,[status(thm)],[c_19515,c_20458]) ).
tcf(c_25059,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,powerset(union(X1)))),X1),
inference(superposition,[status(thm)],[c_222,c_20458]) ).
tcf(c_25070,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X0,set_difference(X0,X1)),unordered_pair(X2,X2)) = set_difference(X0,set_difference(X0,X1)) )
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_195,c_166]) ).
tcf(c_25071,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,set_difference(X0,X1)),X2)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_149,c_166]) ).
tcf(c_25072,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,set_difference(X0,set_difference(X0,X1)))
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_150,c_166]) ).
tcf(c_25075,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,X1)),X2)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_241,c_166]) ).
tcf(c_25076,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,union(set_difference(X1,set_difference(X1,X2)))) ),
inference(superposition,[status(thm)],[c_297,c_166]) ).
tcf(c_25077,plain,
! [X0: $i,X1: $i] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_314,c_166]) ).
tcf(c_25078,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X0,set_difference(X0,X1)))
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_20297,c_166]) ).
tcf(c_25080,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(set_union2(X1,X2),X2)
| ~ in(X0,set_difference(set_union2(X1,X2),set_difference(X1,X2))) ),
inference(superposition,[status(thm)],[c_153,c_166]) ).
tcf(c_25081,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(empty_set,X1)
| ~ in(X0,set_difference(empty_set,empty_set)) ),
inference(superposition,[status(thm)],[c_263,c_166]) ).
tcf(c_25082,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(X1,empty_set)
| ~ in(X0,set_difference(X1,X1)) ),
inference(superposition,[status(thm)],[c_264,c_166]) ).
tcf(c_25083,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(X1,X1)
| ~ in(X0,set_difference(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_4095,c_166]) ).
tcf(c_25084,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(relation_inverse_image(relation_inverse(sK5),X1),relation_rng(sK5))
| ~ in(X0,set_difference(relation_inverse_image(relation_inverse(sK5),X1),empty_set)) ),
inference(superposition,[status(thm)],[c_21834,c_166]) ).
tcf(c_25085,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(relation_image(relation_inverse(sK5),X1),relation_dom(sK5))
| ~ in(X0,set_difference(relation_image(relation_inverse(sK5),X1),empty_set)) ),
inference(superposition,[status(thm)],[c_22079,c_166]) ).
tcf(c_25089,plain,
! [X0: $i] : ~ in(X0,set_difference(empty_set,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_25081,c_19397]) ).
tcf(c_25152,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_19515,c_201]) ).
tcf(c_25154,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(powerset(empty_set),unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_111,c_201]) ).
tcf(c_25155,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(unordered_pair(X0,X0),powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_111,c_201]) ).
tcf(c_25160,plain,
( in(empty_set,powerset(empty_set))
| ( powerset(empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_24849,c_233]) ).
tcf(c_25166,plain,
( function(relation_rng(sK75))
| ~ empty(sK75) ),
inference(superposition,[status(thm)],[c_432,c_22272]) ).
tcf(c_25169,plain,
! [X0: $i] :
( disjoint(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))
| in(sK9(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)),set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),empty_set)) ),
inference(superposition,[status(thm)],[c_25056,c_165]) ).
tcf(c_25170,plain,
! [X0: $i] : subset(set_difference(empty_set,relation_dom(sK5)),set_union2(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_25056,c_20247]) ).
tcf(c_25171,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5)),set_union2(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),
inference(superposition,[status(thm)],[c_25056,c_20244]) ).
tcf(c_25172,plain,
! [X0: $i] :
( disjoint(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))
| ( relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))) != empty_set ) ),
inference(superposition,[status(thm)],[c_25056,c_210]) ).
tcf(c_25173,plain,
! [X0: $i] : subset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_25056,c_139]) ).
tcf(c_25174,plain,
! [X0: $i] : ~ proper_subset(set_union2(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_25056,c_19484]) ).
tcf(c_25175,plain,
! [X0: $i] : subset(set_difference(empty_set,relation_dom(sK5)),set_union2(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),
inference(superposition,[status(thm)],[c_25056,c_19715]) ).
tcf(c_25176,plain,
! [X0: $i] : subset(empty_set,set_union2(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),
inference(superposition,[status(thm)],[c_25056,c_19593]) ).
tcf(c_25177,plain,
! [X0: $i] : subset(empty_set,set_union2(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_25056,c_19485]) ).
tcf(c_25178,plain,
! [X0: $i] : ~ proper_subset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),empty_set),
inference(superposition,[status(thm)],[c_25056,c_19457]) ).
tcf(c_25179,plain,
! [X0: $i] : subset(empty_set,relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),
inference(superposition,[status(thm)],[c_25056,c_135]) ).
tcf(c_25180,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),relation_dom(sK5))
| ~ in(X0,set_difference(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),empty_set)) ),
inference(superposition,[status(thm)],[c_25056,c_166]) ).
tcf(c_25181,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(sK5))
| ~ in(X0,set_difference(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),empty_set)) ),
inference(superposition,[status(thm)],[c_25056,c_370]) ).
tcf(c_25182,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,relation_dom(sK5)),empty_set)
| ~ subset(X0,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_25056,c_127]) ).
tcf(c_25185,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X1,relation_dom(sK5)))
| ~ subset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1) ),
inference(superposition,[status(thm)],[c_25056,c_127]) ).
tcf(c_25186,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),empty_set),set_union2(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_25056,c_19744]) ).
tcf(c_25187,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),set_difference(empty_set,relation_dom(sK5))),set_union2(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),
inference(superposition,[status(thm)],[c_25056,c_19741]) ).
tcf(c_25188,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),empty_set),set_union2(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),
inference(superposition,[status(thm)],[c_25056,c_19566]) ).
tcf(c_25189,plain,
! [X0: $i] : set_union2(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))) = set_union2(relation_dom(sK5),empty_set),
inference(superposition,[status(thm)],[c_25056,c_145]) ).
tcf(c_25228,plain,
! [X0: $i] : set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))) = relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),
inference(superposition,[status(thm)],[c_25173,c_123]) ).
tcf(c_25229,plain,
! [X0: $i] :
( proper_subset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))
| ( relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))) = relation_dom(sK5) ) ),
inference(superposition,[status(thm)],[c_25173,c_468]) ).
tcf(c_25230,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),X0)
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_25173,c_110]) ).
tcf(c_25232,plain,
! [X0: $i] : set_union2(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)) = relation_dom(sK5),
inference(superposition,[status(thm)],[c_25173,c_85]) ).
tcf(c_25233,plain,
! [X0: $i] : ~ proper_subset(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),
inference(superposition,[status(thm)],[c_25173,c_188]) ).
tcf(c_25234,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),X0)
| ~ disjoint(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_25173,c_190]) ).
tcf(c_25241,plain,
! [X0: $i] : set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),empty_set) = relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),
inference(light_normalisation,[status(thm)],[c_25228,c_25056]) ).
tcf(c_25255,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(sK5))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5)))) ),
inference(demodulation,[status(thm)],[c_25181,c_264]) ).
tcf(c_25262,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1)
| in(sK1(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_6708,c_25255]) ).
tcf(c_25263,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(sK5))
| ( set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),unordered_pair(X1,X1)) = relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))) ) ),
inference(superposition,[status(thm)],[c_195,c_25255]) ).
tcf(c_25264,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1)
| in(sK8(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_149,c_25255]) ).
tcf(c_25265,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))))
| in(sK8(X0,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5)))),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_150,c_25255]) ).
tcf(c_25266,plain,
! [X0: $i] :
( in(sK16(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_dom(sK5))
| ( relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))) = empty_set ) ),
inference(superposition,[status(thm)],[c_233,c_25255]) ).
tcf(c_25267,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1)
| in(sK18(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_241,c_25255]) ).
tcf(c_25268,plain,
! [X0: $i,X1: $i] :
( in(sK27(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),X0),relation_dom(sK5))
| ~ in(X0,union(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))))) ),
inference(superposition,[status(thm)],[c_297,c_25255]) ).
tcf(c_25269,plain,
! [X0: $i] :
( relation(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))
| in(sK38(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_314,c_25255]) ).
tcf(c_25270,plain,
! [X0: $i] :
( empty(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))
| in(sK23(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_20297,c_25255]) ).
tcf(c_25302,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(unordered_pair(X0,X0),relation_dom(sK5)),empty_set)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_140,c_25182]) ).
tcf(c_25304,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng(relation_rng_restriction(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),X0)),relation_dom(sK5)),empty_set)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_78,c_25182]) ).
tcf(c_25305,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng_restriction(X1,relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_dom(sK5)),empty_set)
| ~ relation(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_79,c_25182]) ).
tcf(c_25306,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng(relation_rng_restriction(X1,relation_rng_restriction(X0,relation_inverse(sK5)))),relation_dom(sK5)),empty_set)
| ~ relation(relation_rng_restriction(X0,relation_inverse(sK5))) ),
inference(superposition,[status(thm)],[c_80,c_25182]) ).
tcf(c_25307,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_image(relation_rng_restriction(X0,relation_inverse(sK5)),X1),relation_dom(sK5)),empty_set)
| ~ relation(relation_rng_restriction(X0,relation_inverse(sK5))) ),
inference(superposition,[status(thm)],[c_94,c_25182]) ).
tcf(c_25309,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_135,c_25182]) ).
tcf(c_25310,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_dom_restriction(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1),relation_dom(sK5)),empty_set)
| ~ relation(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_215,c_25182]) ).
tcf(c_25311,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,relation_inverse(sK5)),X1)),relation_dom(sK5)),empty_set)
| ~ relation(relation_rng_restriction(X0,relation_inverse(sK5))) ),
inference(superposition,[status(thm)],[c_224,c_25182]) ).
tcf(c_25312,plain,
! [X0: $i] : subset(set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_262,c_25182]) ).
tcf(c_25313,plain,
! [X0: $i] :
( empty(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))
| subset(set_difference(sK22(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_dom(sK5)),empty_set) ),
inference(superposition,[status(thm)],[c_19616,c_25182]) ).
tcf(c_25314,plain,
! [X0: $i] : subset(set_difference(sK23(powerset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_19617,c_25182]) ).
tcf(c_25315,plain,
! [X0: $i,X1: $i] :
( subset(powerset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),X1)
| subset(set_difference(sK18(powerset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),X1),relation_dom(sK5)),empty_set) ),
inference(superposition,[status(thm)],[c_19652,c_25182]) ).
tcf(c_25316,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_image(identity_relation(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),X1),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_19833,c_25182]) ).
tcf(c_25317,plain,
! [X0: $i,X1: $i] :
( subset(powerset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),X1)
| subset(set_difference(sK1(powerset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),X1),relation_dom(sK5)),empty_set) ),
inference(superposition,[status(thm)],[c_19866,c_25182]) ).
tcf(c_25318,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_inverse_image(identity_relation(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),X1),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_19947,c_25182]) ).
tcf(c_25319,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_rng(relation_rng_restriction(X0,identity_relation(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5)))))),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_20703,c_25182]) ).
tcf(c_25320,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_rng(relation_dom_restriction(identity_relation(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),X1)),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_21501,c_25182]) ).
tcf(c_25321,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_inverse_image(relation_inverse(sK5),X1),relation_dom(sK5)),empty_set)
| ~ subset(relation_rng(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_22586,c_25182]) ).
tcf(c_25322,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_image(relation_inverse(sK5),X1),relation_dom(sK5)),empty_set)
| ~ subset(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_22588,c_25182]) ).
tcf(c_25396,plain,
! [X0: $i] : subset(set_difference(empty_set,set_difference(set_difference(X0,empty_set),empty_set)),set_union2(empty_set,X0)),
inference(superposition,[status(thm)],[c_264,c_20482]) ).
tcf(c_25398,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)),set_union2(X0,set_union2(X1,X0))),
inference(superposition,[status(thm)],[c_153,c_20482]) ).
tcf(c_25401,plain,
! [X0: $i] : subset(set_difference(X0,set_difference(set_difference(empty_set,X0),X0)),set_union2(X0,X0)),
inference(superposition,[status(thm)],[c_4095,c_20482]) ).
tcf(c_25402,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),set_difference(set_difference(empty_set,relation_rng(sK5)),relation_rng(sK5))),set_union2(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_21834,c_20482]) ).
tcf(c_25403,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),set_difference(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5))),set_union2(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22079,c_20482]) ).
tcf(c_25404,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),set_difference(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5))),set_union2(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),
inference(superposition,[status(thm)],[c_25056,c_20482]) ).
tcf(c_25406,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(set_difference(set_difference(set_difference(X1,X0),X0),X0),X0)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_145,c_20482]) ).
tcf(c_25407,plain,
! [X0: $i] : subset(set_difference(X0,set_difference(set_difference(set_difference(empty_set,X0),X0),X0)),X0),
inference(superposition,[status(thm)],[c_244,c_20482]) ).
tcf(c_25408,plain,
! [X0: $i] : subset(set_difference(X0,set_difference(set_difference(set_difference(X0,X0),X0),X0)),X0),
inference(superposition,[status(thm)],[c_245,c_20482]) ).
tcf(c_25409,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_255,c_20482]) ).
tcf(c_25410,plain,
! [X0: $i] : subset(set_difference(empty_set,set_difference(set_difference(set_difference(X0,empty_set),empty_set),empty_set)),X0),
inference(superposition,[status(thm)],[c_19599,c_20482]) ).
tcf(c_25411,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),set_difference(set_difference(set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5))),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_20482]) ).
tcf(c_25412,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),set_difference(set_difference(set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_20482]) ).
tcf(c_25413,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)),set_difference(set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)),set_union2(X0,X1))) = set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)),
inference(superposition,[status(thm)],[c_20482,c_123]) ).
tcf(c_25414,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)),set_union2(X0,X1))
| ( set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_20482,c_468]) ).
tcf(c_25415,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_20482,c_110]) ).
tcf(c_25416,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_20482,c_138]) ).
tcf(c_25417,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)),set_union2(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_20482,c_85]) ).
tcf(c_25418,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0))),
inference(superposition,[status(thm)],[c_20482,c_188]) ).
tcf(c_25419,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)),X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_20482,c_190]) ).
tcf(c_25430,plain,
subset(set_difference(relation_dom(sK5),set_difference(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5))),relation_dom(sK5)),
inference(light_normalisation,[status(thm)],[c_25403,c_22341]) ).
tcf(c_25431,plain,
subset(set_difference(relation_rng(sK5),set_difference(set_difference(empty_set,relation_rng(sK5)),relation_rng(sK5))),relation_rng(sK5)),
inference(light_normalisation,[status(thm)],[c_25402,c_21870]) ).
tcf(c_25434,plain,
subset(set_difference(relation_dom(sK5),set_difference(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5))),set_union2(relation_dom(sK5),empty_set)),
inference(light_normalisation,[status(thm)],[c_25404,c_25189]) ).
tcf(c_25464,plain,
! [X0: $i] : relation_composition(identity_relation(X0),sK5) = relation_dom_restriction(sK5,X0),
inference(superposition,[status(thm)],[c_96,c_223]) ).
tcf(c_25465,plain,
! [X0: $i,X1: $i] : relation_composition(identity_relation(X0),identity_relation(X1)) = relation_dom_restriction(identity_relation(X1),X0),
inference(superposition,[status(thm)],[c_422,c_223]) ).
tcf(c_25466,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X1),function_inverse(X0)) = relation_dom_restriction(function_inverse(X0),X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_465,c_223]) ).
tcf(c_25467,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(identity_relation(X1),relation_dom_restriction(X0,X2)) = relation_dom_restriction(relation_dom_restriction(X0,X2),X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_334,c_223]) ).
tcf(c_25468,plain,
! [X0: $i] : relation_composition(identity_relation(X0),empty_set) = relation_dom_restriction(empty_set,X0),
inference(superposition,[status(thm)],[c_231,c_223]) ).
tcf(c_25469,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(identity_relation(X2),set_union2(X0,X1)) = relation_dom_restriction(set_union2(X0,X1),X2) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_248,c_223]) ).
tcf(c_25470,plain,
! [X0: $i] : relation_composition(identity_relation(X0),sK47) = relation_dom_restriction(sK47,X0),
inference(superposition,[status(thm)],[c_329,c_223]) ).
tcf(c_25471,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X1),relation_dom(X0)) = relation_dom_restriction(relation_dom(X0),X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_342,c_223]) ).
tcf(c_25472,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(identity_relation(X1),relation_rng_restriction(X2,X0)) = relation_dom_restriction(relation_rng_restriction(X2,X0),X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_352,c_223]) ).
tcf(c_25473,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X1),relation_rng(X0)) = relation_dom_restriction(relation_rng(X0),X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_360,c_223]) ).
tcf(c_25474,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(identity_relation(X2),relation_composition(X0,X1)) = relation_dom_restriction(relation_composition(X0,X1),X2) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_408,c_223]) ).
tcf(c_25475,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(identity_relation(X2),relation_composition(X0,X1)) = relation_dom_restriction(relation_composition(X0,X1),X2) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_407,c_223]) ).
tcf(c_25476,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(identity_relation(X2),relation_composition(X1,X0)) = relation_dom_restriction(relation_composition(X1,X0),X2) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_403,c_223]) ).
tcf(c_25477,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X1),relation_inverse(X0)) = relation_dom_restriction(relation_inverse(X0),X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_434,c_223]) ).
tcf(c_25478,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X1),relation_inverse(X0)) = relation_dom_restriction(relation_inverse(X0),X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_433,c_223]) ).
tcf(c_25479,plain,
! [X0: $i] : relation_composition(identity_relation(X0),sK75) = relation_dom_restriction(sK75,X0),
inference(superposition,[status(thm)],[c_456,c_223]) ).
tcf(c_25480,plain,
! [X0: $i] : relation_composition(identity_relation(X0),sK79) = relation_dom_restriction(sK79,X0),
inference(superposition,[status(thm)],[c_474,c_223]) ).
tcf(c_25481,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X1),sK23(X0)) = relation_dom_restriction(sK23(X0),X1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20383,c_223]) ).
tcf(c_25482,plain,
! [X0: $i] : relation_composition(identity_relation(X0),empty_set) = empty_set,
inference(light_normalisation,[status(thm)],[c_25468,c_19477]) ).
tcf(c_25566,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_union2(X0,X1),X2)
| in(sK1(set_union2(X0,X1),X2),X1)
| in(sK1(set_union2(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_6708,c_254]) ).
tcf(c_25567,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| in(X2,X0)
| ( set_difference(set_union2(X0,X1),unordered_pair(X2,X2)) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_195,c_254]) ).
tcf(c_25568,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_union2(X0,X1),X2)
| in(sK8(set_union2(X0,X1),X2),X1)
| in(sK8(set_union2(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_149,c_254]) ).
tcf(c_25569,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_union2(X1,X2))
| in(sK8(X0,set_union2(X1,X2)),X2)
| in(sK8(X0,set_union2(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_150,c_254]) ).
tcf(c_25570,plain,
! [X0: $i,X1: $i] :
( in(sK16(set_union2(X0,X1)),X1)
| in(sK16(set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_233,c_254]) ).
tcf(c_25571,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_union2(X0,X1),X2)
| in(sK18(set_union2(X0,X1),X2),X1)
| in(sK18(set_union2(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_241,c_254]) ).
tcf(c_25574,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK27(set_union2(X1,X2),X0),X2)
| in(sK27(set_union2(X1,X2),X0),X1)
| ~ in(X0,union(set_union2(X1,X2))) ),
inference(superposition,[status(thm)],[c_297,c_254]) ).
tcf(c_25575,plain,
! [X0: $i,X1: $i] :
( relation(set_union2(X0,X1))
| in(sK38(set_union2(X0,X1)),X1)
| in(sK38(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_314,c_254]) ).
tcf(c_25580,plain,
! [X0: $i] :
( in(empty_set,X0)
| in(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_20028,c_254]) ).
tcf(c_25582,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,X1))
| in(sK23(set_union2(X0,X1)),X1)
| in(sK23(set_union2(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_20297,c_254]) ).
tcf(c_25584,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| in(X0,set_difference(X2,X1))
| ~ in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_145,c_254]) ).
tcf(c_25635,plain,
! [X0: $i,X1: $i] :
( disjoint(set_union2(X0,X1),X1)
| ( set_difference(set_union2(X0,X1),set_difference(X0,X1)) != empty_set ) ),
inference(superposition,[status(thm)],[c_153,c_257]) ).
tcf(c_25638,plain,
! [X0: $i] :
( disjoint(X0,X0)
| ( set_difference(X0,empty_set) != empty_set ) ),
inference(superposition,[status(thm)],[c_4095,c_257]) ).
tcf(c_25639,plain,
! [X0: $i] :
( disjoint(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))
| ( set_difference(relation_inverse_image(relation_inverse(sK5),X0),empty_set) != empty_set ) ),
inference(superposition,[status(thm)],[c_21834,c_257]) ).
tcf(c_25640,plain,
! [X0: $i] :
( disjoint(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))
| ( set_difference(relation_image(relation_inverse(sK5),X0),empty_set) != empty_set ) ),
inference(superposition,[status(thm)],[c_22079,c_257]) ).
tcf(c_25641,plain,
! [X0: $i] :
( disjoint(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))
| ( set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),empty_set) != empty_set ) ),
inference(superposition,[status(thm)],[c_25056,c_257]) ).
tcf(c_25665,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_52,c_258]) ).
tcf(c_25666,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19395,c_258]) ).
tcf(c_25667,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,set_difference(X1,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19407,c_258]) ).
tcf(c_25669,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_19409,c_258]) ).
tcf(c_25670,plain,
! [X0: $i] :
( in(empty_set,X0)
| ( set_difference(powerset(empty_set),set_difference(powerset(empty_set),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_19371,c_258]) ).
tcf(c_25671,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( set_difference(X0,set_difference(X0,unordered_pair(X1,X1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_19372,c_258]) ).
tcf(c_25672,plain,
! [X0: $i] :
( in(empty_set,X0)
| ( set_difference(X0,set_difference(X0,powerset(empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_19442,c_258]) ).
tcf(c_25673,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_inverse_image(relation_inverse(sK5),X1),set_difference(relation_inverse_image(relation_inverse(sK5),X1),X0)) = empty_set )
| ~ disjoint(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_23214,c_258]) ).
tcf(c_25674,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_image(relation_inverse(sK5),X1),set_difference(relation_image(relation_inverse(sK5),X1),X0)) = empty_set )
| ~ disjoint(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_23216,c_258]) ).
tcf(c_25714,plain,
( one_to_one(relation_rng(sK75))
| ~ empty(sK75) ),
inference(superposition,[status(thm)],[c_432,c_22273]) ).
tcf(c_25721,plain,
( relation(relation_rng(sK75))
| ~ empty(sK75) ),
inference(superposition,[status(thm)],[c_432,c_22274]) ).
tcf(c_25724,plain,
! [X0: $i] :
( relation(relation_dom_restriction(sK5,X0))
| ~ relation(sK5)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25464,c_408]) ).
tcf(c_25725,plain,
! [X0: $i] :
( relation(relation_dom_restriction(sK5,X0))
| ~ empty(sK5)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25464,c_407]) ).
tcf(c_25726,plain,
! [X0: $i] :
( empty(relation_dom_restriction(sK5,X0))
| ~ empty(sK5)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25464,c_406]) ).
tcf(c_25727,plain,
! [X0: $i] :
( relation(relation_dom_restriction(sK5,X0))
| ~ relation(sK5)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25464,c_403]) ).
tcf(c_25728,plain,
! [X0: $i] :
( empty(relation_dom_restriction(sK5,X0))
| ~ relation(sK5)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25464,c_402]) ).
tcf(c_25729,plain,
! [X0: $i] :
( empty(relation_dom_restriction(sK5,X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25728,c_96]) ).
tcf(c_25735,plain,
! [X0: $i] :
( empty(relation_dom_restriction(sK5,X0))
| ~ empty(sK5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25726,c_422]) ).
tcf(c_25741,plain,
! [X0: $i] : relation(relation_dom_restriction(sK5,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_25724,c_96,c_422]) ).
tcf(c_25745,plain,
! [X0: $i,X1: $i] : relation_composition(identity_relation(X0),relation_dom_restriction(sK5,X1)) = relation_dom_restriction(relation_dom_restriction(sK5,X1),X0),
inference(superposition,[status(thm)],[c_25741,c_223]) ).
tcf(c_25746,plain,
! [X0: $i] : relation_image(relation_dom_restriction(sK5,X0),relation_dom(relation_dom_restriction(sK5,X0))) = relation_rng(relation_dom_restriction(sK5,X0)),
inference(superposition,[status(thm)],[c_25741,c_99]) ).
tcf(c_25747,plain,
! [X0: $i] : relation_rng(relation_inverse(relation_dom_restriction(sK5,X0))) = relation_dom(relation_dom_restriction(sK5,X0)),
inference(superposition,[status(thm)],[c_25741,c_137]) ).
tcf(c_25748,plain,
! [X0: $i] : relation_dom(relation_inverse(relation_dom_restriction(sK5,X0))) = relation_rng(relation_dom_restriction(sK5,X0)),
inference(superposition,[status(thm)],[c_25741,c_136]) ).
tcf(c_25749,plain,
! [X0: $i] : relation_inverse(relation_inverse(relation_dom_restriction(sK5,X0))) = relation_dom_restriction(sK5,X0),
inference(superposition,[status(thm)],[c_25741,c_429]) ).
tcf(c_25774,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(sK5,X0) = X1 )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25729,c_470]) ).
tcf(c_25775,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25729,c_19213]) ).
tcf(c_25776,plain,
! [X0: $i] :
( ( relation_rng(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25729,c_19212]) ).
tcf(c_25777,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25729,c_19211]) ).
tcf(c_25778,plain,
! [X0: $i] :
( ( relation_dom_restriction(sK5,X0) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25729,c_229]) ).
tcf(c_25779,plain,
! [X0: $i] :
( one_to_one(relation_dom_restriction(sK5,X0))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25729,c_6826]) ).
tcf(c_25781,plain,
! [X0: $i] :
( function(relation_dom_restriction(sK5,X0))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25729,c_331]) ).
tcf(c_25811,plain,
! [X0: $i] :
( function(relation_dom_restriction(sK5,X0))
| ~ empty(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25749,c_19175]) ).
tcf(c_25812,plain,
! [X0: $i] :
( one_to_one(relation_dom_restriction(sK5,X0))
| ~ empty(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25749,c_19173]) ).
tcf(c_25815,plain,
! [X0: $i] :
( empty(relation_dom_restriction(sK5,X0))
| ~ empty(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25749,c_432]) ).
tcf(c_25829,plain,
! [X0: $i] :
( ( relation_dom_restriction(sK5,X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20511,c_25778]) ).
tcf(c_25836,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_dom_restriction(relation_inverse(relation_dom_restriction(sK5,X0)),X1)),relation_dom(relation_dom_restriction(sK5,X0)))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25747,c_224]) ).
tcf(c_25837,plain,
! [X0: $i] :
( subset(relation_inverse(relation_dom_restriction(sK5,X0)),cartesian_product2(relation_dom(relation_inverse(relation_dom_restriction(sK5,X0))),relation_dom(relation_dom_restriction(sK5,X0))))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25747,c_117]) ).
tcf(c_25838,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X1,relation_inverse(relation_dom_restriction(sK5,X0)))),relation_dom(relation_dom_restriction(sK5,X0)))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25747,c_80]) ).
tcf(c_25839,plain,
! [X0: $i] :
( empty(relation_inverse(relation_dom_restriction(sK5,X0)))
| ~ empty(relation_dom(relation_dom_restriction(sK5,X0)))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25747,c_361]) ).
tcf(c_25840,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(relation_inverse(relation_dom_restriction(sK5,X0)),X1),relation_dom(relation_dom_restriction(sK5,X0)))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25747,c_94]) ).
tcf(c_25841,plain,
! [X0: $i] :
( function(relation_dom(relation_dom_restriction(sK5,X0)))
| ~ empty(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25747,c_19156]) ).
tcf(c_25842,plain,
! [X0: $i] :
( one_to_one(relation_dom(relation_dom_restriction(sK5,X0)))
| ~ empty(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25747,c_19154]) ).
tcf(c_25843,plain,
! [X0: $i] :
( relation(relation_dom(relation_dom_restriction(sK5,X0)))
| ~ empty(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25747,c_360]) ).
tcf(c_25844,plain,
! [X0: $i] :
( empty(relation_dom(relation_dom_restriction(sK5,X0)))
| ~ empty(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25747,c_359]) ).
tcf(c_25862,plain,
! [X0: $i] :
( subset(relation_inverse(relation_dom_restriction(sK5,X0)),cartesian_product2(relation_rng(relation_dom_restriction(sK5,X0)),relation_dom(relation_dom_restriction(sK5,X0))))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(light_normalisation,[status(thm)],[c_25837,c_25748]) ).
tcf(c_25890,plain,
! [X0: $i] : subset(set_difference(empty_set,set_difference(X0,empty_set)),set_union2(X0,empty_set)),
inference(superposition,[status(thm)],[c_264,c_20485]) ).
tcf(c_25891,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_union2(set_union2(X1,X0),X0)),
inference(superposition,[status(thm)],[c_153,c_20485]) ).
tcf(c_25895,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),set_difference(empty_set,relation_rng(sK5))),set_union2(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_21834,c_20485]) ).
tcf(c_25896,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),set_difference(empty_set,relation_dom(sK5))),set_union2(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_22079,c_20485]) ).
tcf(c_25897,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),set_difference(empty_set,relation_dom(sK5))),set_union2(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_25056,c_20485]) ).
tcf(c_25899,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),set_difference(set_difference(X1,set_difference(X0,X1)),set_difference(X0,X1))),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_145,c_20485]) ).
tcf(c_25904,plain,
! [X0: $i] : subset(set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0))),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_20485]) ).
tcf(c_25905,plain,
! [X0: $i] : subset(set_difference(relation_image(relation_inverse(sK5),X0),set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_20485]) ).
tcf(c_25906,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_difference(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_union2(X1,X0))) = set_difference(X0,set_difference(set_difference(X1,X0),X0)),
inference(superposition,[status(thm)],[c_20485,c_123]) ).
tcf(c_25907,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_union2(X1,X0))
| ( set_difference(X0,set_difference(set_difference(X1,X0),X0)) = set_union2(X1,X0) ) ),
inference(superposition,[status(thm)],[c_20485,c_468]) ).
tcf(c_25908,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X1,set_difference(set_difference(X0,X1),X1)),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_20485,c_110]) ).
tcf(c_25909,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_union2(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_20485,c_138]) ).
tcf(c_25910,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_union2(X1,X0)) = set_union2(X1,X0),
inference(superposition,[status(thm)],[c_20485,c_85]) ).
tcf(c_25911,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(X1,set_difference(set_difference(X0,X1),X1))),
inference(superposition,[status(thm)],[c_20485,c_188]) ).
tcf(c_25912,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X1,set_difference(set_difference(X0,X1),X1)),X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_20485,c_190]) ).
tcf(c_25948,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X1,X1) = X0 )
| ~ in(X1,X0)
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_140,c_260]) ).
tcf(c_25949,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_19515,c_260]) ).
tcf(c_25950,plain,
! [X0: $i,X1: $i] :
( ( union(X0) = X1 )
| ~ in(X1,X0)
| ~ subset(union(X0),X1) ),
inference(superposition,[status(thm)],[c_222,c_260]) ).
tcf(c_25951,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng_restriction(X0,X1)) = X0 )
| ~ relation(X1)
| ~ subset(X0,relation_rng(relation_rng_restriction(X0,X1))) ),
inference(superposition,[status(thm)],[c_78,c_260]) ).
tcf(c_25952,plain,
! [X0: $i,X1: $i] :
( ( relation_rng_restriction(X1,X0) = X0 )
| ~ relation(X0)
| ~ subset(X0,relation_rng_restriction(X1,X0)) ),
inference(superposition,[status(thm)],[c_79,c_260]) ).
tcf(c_25953,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng_restriction(X1,X0)) = relation_rng(X0) )
| ~ relation(X0)
| ~ subset(relation_rng(X0),relation_rng(relation_rng_restriction(X1,X0))) ),
inference(superposition,[status(thm)],[c_80,c_260]) ).
tcf(c_25954,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X1) )
| ~ subset(X2,X0)
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X1)) ),
inference(superposition,[status(thm)],[c_81,c_260]) ).
tcf(c_25955,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X0,X2) )
| ~ subset(X2,X1)
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X0,X2)) ),
inference(superposition,[status(thm)],[c_82,c_260]) ).
tcf(c_25956,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,X1) = relation_rng(X0) )
| ~ relation(X0)
| ~ subset(relation_rng(X0),relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_94,c_260]) ).
tcf(c_25957,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,X1) = relation_dom(X0) )
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_inverse_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_105,c_260]) ).
tcf(c_25958,plain,
! [X0: $i] :
( ( cartesian_product2(relation_dom(X0),relation_rng(X0)) = X0 )
| ~ relation(X0)
| ~ subset(cartesian_product2(relation_dom(X0),relation_rng(X0)),X0) ),
inference(superposition,[status(thm)],[c_117,c_260]) ).
tcf(c_25960,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,X1) = set_difference(X2,X1) )
| ~ subset(X2,X0)
| ~ subset(set_difference(X0,X1),set_difference(X2,X1)) ),
inference(superposition,[status(thm)],[c_127,c_260]) ).
tcf(c_25961,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = X0 )
| ~ subset(X0,set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_135,c_260]) ).
tcf(c_25962,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X0 )
| ~ subset(set_union2(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_209,c_260]) ).
tcf(c_25963,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(X0,X1) = X0 )
| ~ relation(X0)
| ~ subset(X0,relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_215,c_260]) ).
tcf(c_25964,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom_restriction(X0,X1)) = relation_rng(X0) )
| ~ relation(X0)
| ~ subset(relation_rng(X0),relation_rng(relation_dom_restriction(X0,X1))) ),
inference(superposition,[status(thm)],[c_224,c_260]) ).
tcf(c_25966,plain,
! [X0: $i] :
( empty(X0)
| ( sK22(X0) = X0 )
| ~ subset(X0,sK22(X0)) ),
inference(superposition,[status(thm)],[c_19616,c_260]) ).
tcf(c_25967,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = set_difference(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_19485,c_260]) ).
tcf(c_25968,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X1,X0)) = set_union2(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(X0,set_difference(X1,X0))) ),
inference(superposition,[status(thm)],[c_19566,c_260]) ).
tcf(c_25969,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = set_difference(X1,X0) )
| ~ subset(set_union2(X0,X1),set_difference(X1,X0)) ),
inference(superposition,[status(thm)],[c_19593,c_260]) ).
tcf(c_25970,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ subset(set_union2(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_19598,c_260]) ).
tcf(c_25971,plain,
! [X0: $i] :
( ( sK23(powerset(X0)) = X0 )
| ~ subset(X0,sK23(powerset(X0))) ),
inference(superposition,[status(thm)],[c_19617,c_260]) ).
tcf(c_25972,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( sK18(powerset(X0),X1) = X0 )
| ~ subset(X0,sK18(powerset(X0),X1)) ),
inference(superposition,[status(thm)],[c_19652,c_260]) ).
tcf(c_25973,plain,
! [X0: $i,X1: $i] :
( ( set_difference(set_difference(X1,X0),X0) = set_union2(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0)) ),
inference(superposition,[status(thm)],[c_19715,c_260]) ).
tcf(c_25974,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,set_difference(X0,X1)) = set_union2(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(X1,set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_19744,c_260]) ).
tcf(c_25975,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(set_difference(X1,X0),X0)) = set_union2(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(X0,set_difference(set_difference(X1,X0),X0))) ),
inference(superposition,[status(thm)],[c_19741,c_260]) ).
tcf(c_25976,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(X0),X1) = X0 )
| ~ subset(X0,relation_image(identity_relation(X0),X1)) ),
inference(superposition,[status(thm)],[c_19833,c_260]) ).
tcf(c_25977,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( sK1(powerset(X0),X1) = X0 )
| ~ subset(X0,sK1(powerset(X0),X1)) ),
inference(superposition,[status(thm)],[c_19866,c_260]) ).
tcf(c_25978,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(identity_relation(X0),X1) = X0 )
| ~ subset(X0,relation_inverse_image(identity_relation(X0),X1)) ),
inference(superposition,[status(thm)],[c_19947,c_260]) ).
tcf(c_25979,plain,
! [X0: $i,X1: $i] :
( ( set_difference(set_difference(X0,X1),X1) = set_union2(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(set_difference(X0,X1),X1)) ),
inference(superposition,[status(thm)],[c_20247,c_260]) ).
tcf(c_25980,plain,
! [X0: $i,X1: $i] :
( ( set_difference(set_difference(set_difference(X1,X0),X0),X0) = set_union2(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(set_difference(set_difference(X1,X0),X0),X0)) ),
inference(superposition,[status(thm)],[c_20244,c_260]) ).
tcf(c_25981,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,set_difference(set_difference(X0,X1),X1)) = set_union2(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(X1,set_difference(set_difference(X0,X1),X1))) ),
inference(superposition,[status(thm)],[c_20485,c_260]) ).
tcf(c_25982,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)) = set_union2(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0))) ),
inference(superposition,[status(thm)],[c_20482,c_260]) ).
tcf(c_25983,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng_restriction(X1,identity_relation(X0))) = X0 )
| ~ subset(X0,relation_rng(relation_rng_restriction(X1,identity_relation(X0)))) ),
inference(superposition,[status(thm)],[c_20703,c_260]) ).
tcf(c_25984,plain,
! [X0: $i] :
( ( cartesian_product2(X0,X0) = identity_relation(X0) )
| ~ subset(cartesian_product2(X0,X0),identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20929,c_260]) ).
tcf(c_25985,plain,
! [X0: $i] :
( ( relation_inverse_image(relation_inverse(sK5),X0) = relation_rng(sK5) )
| ~ subset(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_21837,c_260]) ).
tcf(c_25986,plain,
! [X0: $i] :
( ( relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))) = relation_dom(sK5) )
| ~ subset(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_25173,c_260]) ).
tcf(c_25987,plain,
! [X0: $i] :
( ( relation_image(relation_inverse(sK5),X0) = relation_dom(sK5) )
| ~ subset(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_22082,c_260]) ).
tcf(c_25988,plain,
( ( cartesian_product2(relation_rng(sK5),relation_dom(sK5)) = relation_inverse(sK5) )
| ~ relation(relation_inverse(sK5))
| ~ subset(cartesian_product2(relation_rng(sK5),relation_dom(sK5)),relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21353,c_260]) ).
tcf(c_25989,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom_restriction(identity_relation(X0),X1)) = X0 )
| ~ subset(X0,relation_rng(relation_dom_restriction(identity_relation(X0),X1))) ),
inference(superposition,[status(thm)],[c_21501,c_260]) ).
tcf(c_25990,plain,
! [X0: $i] :
( ( relation_rng(relation_dom_restriction(relation_inverse(sK5),X0)) = relation_dom(sK5) )
| ~ relation(relation_inverse(sK5))
| ~ subset(relation_dom(sK5),relation_rng(relation_dom_restriction(relation_inverse(sK5),X0))) ),
inference(superposition,[status(thm)],[c_21494,c_260]) ).
tcf(c_25991,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(relation_inverse(sK5),X1) = X0 )
| ~ subset(relation_rng(sK5),X0)
| ~ subset(X0,relation_inverse_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_22586,c_260]) ).
tcf(c_25992,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_inverse(sK5),X1) = X0 )
| ~ subset(relation_dom(sK5),X0)
| ~ subset(X0,relation_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_22588,c_260]) ).
tcf(c_26258,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_153,c_268]) ).
tcf(c_26265,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ( set_union2(unordered_pair(X0,X0),set_difference(X1,X2)) = set_difference(X1,X2) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_268,c_161]) ).
tcf(c_26266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X1)
| ~ in(X3,X2)
| ~ in(X3,X0)
| ~ disjoint(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_268,c_151]) ).
tcf(c_26267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| ~ subset(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_268,c_242]) ).
tcf(c_26268,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ( apply(identity_relation(set_difference(X1,X2)),X0) = X0 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_268,c_134]) ).
tcf(c_26269,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ in(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_268,c_243]) ).
tcf(c_26270,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ empty(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_268,c_471]) ).
tcf(c_26271,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| element(X0,set_difference(X1,X2))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_268,c_276]) ).
tcf(c_26272,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(X1,X2))
| ~ disjoint(X1,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_268,c_166]) ).
tcf(c_26274,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X1,X2))
| in(sK18(X0,set_difference(X1,X2)),X2)
| ~ in(sK18(X0,set_difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_268,c_240]) ).
tcf(c_26277,plain,
! [X0: $i,X1: $i] :
( in(sK2(set_difference(X0,X1)),X1)
| ~ in(sK2(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_268,c_19526]) ).
tcf(c_26278,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(set_difference(X0,X1),X2),X1)
| ~ in(unordered_pair(set_difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_268,c_19532]) ).
tcf(c_26279,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(X0,set_difference(X1,X2)),X2)
| ~ in(unordered_pair(X0,set_difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_268,c_19533]) ).
tcf(c_26280,plain,
! [X0: $i,X1: $i] :
( in(sK54(set_difference(X0,X1)),X1)
| ~ in(sK54(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_268,c_19534]) ).
tcf(c_26281,plain,
! [X0: $i,X1: $i] :
( in(sK2(powerset(union(set_difference(X0,X1)))),X1)
| ~ in(sK2(powerset(union(set_difference(X0,X1)))),X0) ),
inference(superposition,[status(thm)],[c_268,c_19702]) ).
tcf(c_26282,plain,
! [X0: $i,X1: $i] :
( in(sK54(powerset(union(set_difference(X0,X1)))),X1)
| ~ in(sK54(powerset(union(set_difference(X0,X1)))),X0) ),
inference(superposition,[status(thm)],[c_268,c_19705]) ).
tcf(c_26283,plain,
! [X0: $i,X1: $i] :
( in(powerset(set_difference(X0,X1)),X1)
| ~ in(powerset(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_268,c_19958]) ).
tcf(c_26284,plain,
! [X0: $i,X1: $i] :
( in(powerset(powerset(union(set_difference(X0,X1)))),X1)
| ~ in(powerset(powerset(union(set_difference(X0,X1)))),X0) ),
inference(superposition,[status(thm)],[c_268,c_20020]) ).
tcf(c_26285,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_union2(set_difference(X0,X1),X2)),X1)
| ~ in(sK2(set_union2(set_difference(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_268,c_20095]) ).
tcf(c_26286,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK54(set_union2(set_difference(X0,X1),X2)),X1)
| ~ in(sK54(set_union2(set_difference(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_268,c_20098]) ).
tcf(c_26287,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(powerset(set_union2(set_difference(X0,X1),X2)),X1)
| ~ in(powerset(set_union2(set_difference(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_268,c_20101]) ).
tcf(c_26288,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(set_union2(X0,set_difference(X1,X2))),X2)
| ~ in(sK2(set_union2(X0,set_difference(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_268,c_20131]) ).
tcf(c_26289,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK54(set_union2(X0,set_difference(X1,X2))),X2)
| ~ in(sK54(set_union2(X0,set_difference(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_268,c_20134]) ).
tcf(c_26290,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(powerset(set_union2(X0,set_difference(X1,X2))),X2)
| ~ in(powerset(set_union2(X0,set_difference(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_268,c_20137]) ).
tcf(c_26379,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK1(X0,X2),union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_6708,c_295]) ).
tcf(c_26380,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,union(X1))
| ( set_difference(X0,unordered_pair(X2,X2)) = X0 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_195,c_295]) ).
tcf(c_26381,plain,
! [X0: $i,X1: $i] :
( in(X0,union(X1))
| ~ in(sK2(X0),X1) ),
inference(superposition,[status(thm)],[c_86,c_295]) ).
tcf(c_26382,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(powerset(X2),union(X1))
| ~ in(X2,sK2(X0))
| ~ in(sK2(X0),X1) ),
inference(superposition,[status(thm)],[c_88,c_295]) ).
tcf(c_26383,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| in(sK8(X0,X2),union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_149,c_295]) ).
tcf(c_26384,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,X0)
| in(sK8(X2,X0),union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_150,c_295]) ).
tcf(c_26385,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X1)
| in(sK9(X0,X1),union(X2))
| ~ in(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_165,c_295]) ).
tcf(c_26386,plain,
! [X0: $i,X1: $i] :
( in(sK16(X0),union(X1))
| ( X0 = empty_set )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_233,c_295]) ).
tcf(c_26387,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| in(sK18(X0,X2),union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_241,c_295]) ).
tcf(c_26388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,union(X2))
| ~ in(X3,X0)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_252,c_295]) ).
tcf(c_26389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,union(X2))
| ~ in(X3,X1)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_253,c_295]) ).
tcf(c_26390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X1)
| in(X3,union(X2))
| ~ in(X3,X0)
| ~ in(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_268,c_295]) ).
tcf(c_26391,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,union(X1))
| ~ subset(X2,X0)
| ~ in(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_289,c_295]) ).
tcf(c_26392,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,union(X2))
| ~ in(X1,union(X0))
| ~ in(sK27(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_296,c_295]) ).
tcf(c_26393,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK27(X1,X0),union(X2))
| ~ in(X1,X2)
| ~ in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_297,c_295]) ).
tcf(c_26394,plain,
! [X0: $i,X1: $i] :
( relation(X0)
| in(sK38(X0),union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_314,c_295]) ).
tcf(c_26397,plain,
! [X0: $i,X1: $i] :
( in(X0,union(X1))
| ~ in(sK54(X0),X1) ),
inference(superposition,[status(thm)],[c_372,c_295]) ).
tcf(c_26398,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK55(X0,X2),union(X1))
| ~ in(X2,sK54(X0))
| ~ in(sK54(X0),X1) ),
inference(superposition,[status(thm)],[c_374,c_295]) ).
tcf(c_26399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,union(X3))
| ~ in(set_union2(unordered_pair(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_19972,c_295]) ).
tcf(c_26400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,union(X3))
| ~ in(set_union2(X0,unordered_pair(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_19974,c_295]) ).
tcf(c_26401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,union(X3))
| ~ in(set_union2(unordered_pair(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_19992,c_295]) ).
tcf(c_26402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,union(X3))
| ~ in(set_union2(X0,unordered_pair(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_19994,c_295]) ).
tcf(c_26403,plain,
! [X0: $i,X1: $i] :
( in(empty_set,union(X1))
| ~ in(set_union2(powerset(empty_set),X0),X1) ),
inference(superposition,[status(thm)],[c_20028,c_295]) ).
tcf(c_26404,plain,
! [X0: $i,X1: $i] :
( in(empty_set,union(X1))
| ~ in(set_union2(X0,powerset(empty_set)),X1) ),
inference(superposition,[status(thm)],[c_20041,c_295]) ).
tcf(c_26405,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK22(X0),union(X1))
| ~ in(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_20312,c_295]) ).
tcf(c_26406,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK23(X0),union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_20297,c_295]) ).
tcf(c_26407,plain,
! [X0: $i,X1: $i] :
( in(X0,union(X1))
| ~ in(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_20311,c_295]) ).
tcf(c_26408,plain,
! [X0: $i,X1: $i] :
( in(empty_set,union(X1))
| ~ in(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_20310,c_295]) ).
tcf(c_26409,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))
| in(sK9(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),union(X1))
| ~ in(relation_inverse_image(relation_inverse(sK5),X0),X1) ),
inference(superposition,[status(thm)],[c_24928,c_295]) ).
tcf(c_26410,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))
| in(sK9(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),union(X1))
| ~ in(relation_image(relation_inverse(sK5),X0),X1) ),
inference(superposition,[status(thm)],[c_24965,c_295]) ).
tcf(c_26578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK44(X1,X2,X0),union(X3))
| ~ in(X1,X3)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_323,c_295]) ).
tcf(c_26579,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(sK44(X1,X2,X0),sK44(X1,X2,X0)),X1) = X1 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_323,c_161]) ).
tcf(c_26580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ disjoint(X0,X3)
| ~ in(X2,cartesian_product2(X0,X1))
| ~ in(sK44(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_323,c_151]) ).
tcf(c_26581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK44(X1,X2,X0),X3)
| ~ subset(X1,X3)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_323,c_242]) ).
tcf(c_26582,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X1),sK44(X1,X2,X0)) = sK44(X1,X2,X0) )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_323,c_134]) ).
tcf(c_26583,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,cartesian_product2(X0,X1))
| ~ in(X0,sK44(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_323,c_243]) ).
tcf(c_26584,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_323,c_471]) ).
tcf(c_26585,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK44(X1,X2,X0),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_323,c_276]) ).
tcf(c_26586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,cartesian_product2(set_difference(X1,set_difference(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_323,c_166]) ).
tcf(c_26587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK44(set_difference(X1,set_difference(X1,X2)),X3,X0),X2)
| ~ in(X0,cartesian_product2(set_difference(X1,set_difference(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_323,c_370]) ).
tcf(c_26588,plain,
! [X0: $i,X1: $i] : ~ in(X0,cartesian_product2(empty_set,X1)),
inference(superposition,[status(thm)],[c_323,c_234]) ).
tcf(c_26589,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK44(unordered_pair(X1,X1),X2,X0) = X1 )
| ~ in(X0,cartesian_product2(unordered_pair(X1,X1),X2)) ),
inference(superposition,[status(thm)],[c_323,c_239]) ).
tcf(c_26590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK44(set_union2(X1,X2),X3,X0),X2)
| in(sK44(set_union2(X1,X2),X3,X0),X1)
| ~ in(X0,cartesian_product2(set_union2(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_323,c_254]) ).
tcf(c_26591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X3,cartesian_product2(set_difference(X0,X1),X2))
| ~ in(sK44(set_difference(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_323,c_270]) ).
tcf(c_26592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK44(set_difference(X1,X2),X3,X0),X1)
| ~ in(X0,cartesian_product2(set_difference(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_323,c_269]) ).
tcf(c_26593,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK44(powerset(X1),X2,X0),X1)
| ~ in(X0,cartesian_product2(powerset(X1),X2)) ),
inference(superposition,[status(thm)],[c_323,c_290]) ).
tcf(c_26594,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK44(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),X2,X0),relation_dom(sK5))
| ~ in(X0,cartesian_product2(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),X2)) ),
inference(superposition,[status(thm)],[c_323,c_25255]) ).
tcf(c_26650,plain,
! [X0: $i,X1: $i] : set_difference(cartesian_product2(empty_set,X0),unordered_pair(X1,X1)) = cartesian_product2(empty_set,X0),
inference(superposition,[status(thm)],[c_195,c_26588]) ).
tcf(c_26651,plain,
! [X0: $i,X1: $i] : disjoint(cartesian_product2(empty_set,X0),X1),
inference(superposition,[status(thm)],[c_149,c_26588]) ).
tcf(c_26652,plain,
! [X0: $i,X1: $i] : disjoint(X0,cartesian_product2(empty_set,X1)),
inference(superposition,[status(thm)],[c_150,c_26588]) ).
tcf(c_26653,plain,
! [X0: $i] : cartesian_product2(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_233,c_26588]) ).
tcf(c_26654,plain,
! [X0: $i,X1: $i] : subset(cartesian_product2(empty_set,X0),X1),
inference(superposition,[status(thm)],[c_241,c_26588]) ).
tcf(c_26655,plain,
! [X0: $i,X1: $i] : ~ in(X0,union(cartesian_product2(empty_set,X1))),
inference(superposition,[status(thm)],[c_297,c_26588]) ).
tcf(c_26656,plain,
! [X0: $i] : relation(cartesian_product2(empty_set,X0)),
inference(superposition,[status(thm)],[c_314,c_26588]) ).
tcf(c_26657,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(X0,cartesian_product2(cartesian_product2(empty_set,X1),X2)),
inference(superposition,[status(thm)],[c_323,c_26588]) ).
tcf(c_26658,plain,
! [X0: $i] : empty(cartesian_product2(empty_set,X0)),
inference(superposition,[status(thm)],[c_20297,c_26588]) ).
tcf(c_26707,plain,
! [X0: $i] :
( subset(relation_inverse(relation_dom_restriction(sK5,X0)),cartesian_product2(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(relation_inverse(relation_dom_restriction(sK5,X0)))))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25748,c_117]) ).
tcf(c_26708,plain,
! [X0: $i] :
( empty(relation_inverse(relation_dom_restriction(sK5,X0)))
| ~ empty(relation_rng(relation_dom_restriction(sK5,X0)))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25748,c_343]) ).
tcf(c_26709,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(relation_inverse(relation_dom_restriction(sK5,X0)),X1),relation_rng(relation_dom_restriction(sK5,X0)))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25748,c_105]) ).
tcf(c_26710,plain,
! [X0: $i] :
( function(relation_rng(relation_dom_restriction(sK5,X0)))
| ~ empty(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25748,c_19131]) ).
tcf(c_26711,plain,
! [X0: $i] :
( one_to_one(relation_rng(relation_dom_restriction(sK5,X0)))
| ~ empty(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25748,c_19129]) ).
tcf(c_26712,plain,
! [X0: $i] :
( relation(relation_rng(relation_dom_restriction(sK5,X0)))
| ~ empty(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25748,c_342]) ).
tcf(c_26713,plain,
! [X0: $i] :
( empty(relation_rng(relation_dom_restriction(sK5,X0)))
| ~ empty(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25748,c_341]) ).
tcf(c_26751,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20511,c_25775]) ).
tcf(c_26759,plain,
! [X0: $i] :
( ( relation_rng(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20511,c_25776]) ).
tcf(c_26767,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20511,c_25777]) ).
tcf(c_26771,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))
| ~ relation(identity_relation(X1))
| ~ relation(relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_25745,c_408]) ).
tcf(c_26772,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))
| ~ relation(identity_relation(X1))
| ~ empty(relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_25745,c_407]) ).
tcf(c_26773,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))
| ~ relation(identity_relation(X1))
| ~ empty(relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_25745,c_406]) ).
tcf(c_26774,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))
| ~ empty(identity_relation(X1))
| ~ relation(relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_25745,c_403]) ).
tcf(c_26775,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))
| ~ empty(identity_relation(X1))
| ~ relation(relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_25745,c_402]) ).
tcf(c_26776,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom_restriction(relation_dom_restriction(sK5,X1),X0))
| ~ empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26775,c_25741]) ).
tcf(c_26782,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))
| ~ empty(relation_dom_restriction(sK5,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26773,c_422]) ).
tcf(c_26788,plain,
! [X0: $i,X1: $i] : relation(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_26771,c_422,c_25741]) ).
tcf(c_26809,plain,
! [X0: $i,X1: $i,X2: $i] : relation_composition(identity_relation(X0),relation_dom_restriction(relation_dom_restriction(sK5,X1),X2)) = relation_dom_restriction(relation_dom_restriction(relation_dom_restriction(sK5,X1),X2),X0),
inference(superposition,[status(thm)],[c_26788,c_223]) ).
tcf(c_26810,plain,
! [X0: $i,X1: $i] : relation_image(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1),relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))) = relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),
inference(superposition,[status(thm)],[c_26788,c_99]) ).
tcf(c_26811,plain,
! [X0: $i,X1: $i] : relation_rng(relation_inverse(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))) = relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),
inference(superposition,[status(thm)],[c_26788,c_137]) ).
tcf(c_26812,plain,
! [X0: $i,X1: $i] : relation_dom(relation_inverse(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))) = relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),
inference(superposition,[status(thm)],[c_26788,c_136]) ).
tcf(c_26813,plain,
! [X0: $i,X1: $i] : relation_inverse(relation_inverse(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))) = relation_dom_restriction(relation_dom_restriction(sK5,X0),X1),
inference(superposition,[status(thm)],[c_26788,c_429]) ).
tcf(c_26845,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(relation_dom_restriction(sK5,X2),X0) = X1 )
| ~ empty(X1)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_26776,c_470]) ).
tcf(c_26846,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_dom_restriction(relation_dom_restriction(sK5,X1),X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_26776,c_19213]) ).
tcf(c_26847,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X1),X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_26776,c_19212]) ).
tcf(c_26848,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X1),X0)) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_26776,c_19211]) ).
tcf(c_26849,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(relation_dom_restriction(sK5,X1),X0) = empty_set )
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_26776,c_229]) ).
tcf(c_26850,plain,
! [X0: $i,X1: $i] :
( one_to_one(relation_dom_restriction(relation_dom_restriction(sK5,X1),X0))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_26776,c_6826]) ).
tcf(c_26851,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(relation_dom_restriction(sK5,X1),X0))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_26776,c_478]) ).
tcf(c_26852,plain,
! [X0: $i,X1: $i] :
( function(relation_dom_restriction(relation_dom_restriction(sK5,X1),X0))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_26776,c_331]) ).
tcf(c_27097,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(sK5,X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20511,c_25774]) ).
tcf(c_27106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK45(X1,X2,X0),union(X3))
| ~ in(X2,X3)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_324,c_295]) ).
tcf(c_27107,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(sK45(X1,X2,X0),sK45(X1,X2,X0)),X2) = X2 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_324,c_161]) ).
tcf(c_27108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ disjoint(X1,X3)
| ~ in(X2,cartesian_product2(X0,X1))
| ~ in(sK45(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_324,c_151]) ).
tcf(c_27109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK45(X1,X2,X0),X3)
| ~ subset(X2,X3)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_324,c_242]) ).
tcf(c_27110,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK45(X1,X2,X0)) = sK45(X1,X2,X0) )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_324,c_134]) ).
tcf(c_27111,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,cartesian_product2(X1,X0))
| ~ in(X0,sK45(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_324,c_243]) ).
tcf(c_27112,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_324,c_471]) ).
tcf(c_27113,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK45(X1,X2,X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_324,c_276]) ).
tcf(c_27114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ disjoint(X2,X3)
| ~ in(X0,cartesian_product2(X1,set_difference(X2,set_difference(X2,X3)))) ),
inference(superposition,[status(thm)],[c_324,c_166]) ).
tcf(c_27115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK45(X1,set_difference(X2,set_difference(X2,X3)),X0),X3)
| ~ in(X0,cartesian_product2(X1,set_difference(X2,set_difference(X2,X3)))) ),
inference(superposition,[status(thm)],[c_324,c_370]) ).
tcf(c_27116,plain,
! [X0: $i,X1: $i] : ~ in(X0,cartesian_product2(X1,empty_set)),
inference(superposition,[status(thm)],[c_324,c_234]) ).
tcf(c_27117,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK45(X1,unordered_pair(X2,X2),X0) = X2 )
| ~ in(X0,cartesian_product2(X1,unordered_pair(X2,X2))) ),
inference(superposition,[status(thm)],[c_324,c_239]) ).
tcf(c_27118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK45(X1,set_union2(X2,X3),X0),X3)
| in(sK45(X1,set_union2(X2,X3),X0),X2)
| ~ in(X0,cartesian_product2(X1,set_union2(X2,X3))) ),
inference(superposition,[status(thm)],[c_324,c_254]) ).
tcf(c_27119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X3,cartesian_product2(X0,set_difference(X1,X2)))
| ~ in(sK45(X0,set_difference(X1,X2),X3),X2) ),
inference(superposition,[status(thm)],[c_324,c_270]) ).
tcf(c_27120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK45(X1,set_difference(X2,X3),X0),X2)
| ~ in(X0,cartesian_product2(X1,set_difference(X2,X3))) ),
inference(superposition,[status(thm)],[c_324,c_269]) ).
tcf(c_27121,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK45(X1,powerset(X2),X0),X2)
| ~ in(X0,cartesian_product2(X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_324,c_290]) ).
tcf(c_27122,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK45(X1,relation_rng(relation_rng_restriction(X2,relation_inverse(sK5))),X0),relation_dom(sK5))
| ~ in(X0,cartesian_product2(X1,relation_rng(relation_rng_restriction(X2,relation_inverse(sK5))))) ),
inference(superposition,[status(thm)],[c_324,c_25255]) ).
tcf(c_27174,plain,
! [X0: $i,X1: $i] :
( relation(set_difference(set_union2(X0,X1),set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_153,c_364]) ).
tcf(c_27175,plain,
! [X0: $i] :
( relation(set_difference(empty_set,empty_set))
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_263,c_364]) ).
tcf(c_27176,plain,
! [X0: $i] :
( relation(set_difference(X0,X0))
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_264,c_364]) ).
tcf(c_27177,plain,
! [X0: $i] :
( relation(set_difference(X0,empty_set))
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_4095,c_364]) ).
tcf(c_27178,plain,
! [X0: $i] :
( relation(set_difference(relation_inverse_image(relation_inverse(sK5),X0),empty_set))
| ~ relation(relation_rng(sK5))
| ~ relation(relation_inverse_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_21834,c_364]) ).
tcf(c_27179,plain,
! [X0: $i] :
( relation(set_difference(relation_image(relation_inverse(sK5),X0),empty_set))
| ~ relation(relation_dom(sK5))
| ~ relation(relation_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_22079,c_364]) ).
tcf(c_27180,plain,
! [X0: $i] :
( relation(set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),empty_set))
| ~ relation(relation_dom(sK5))
| ~ relation(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_25056,c_364]) ).
tcf(c_27181,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_composition(identity_relation(X2),set_difference(X0,set_difference(X0,X1))) = relation_dom_restriction(set_difference(X0,set_difference(X0,X1)),X2) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_364,c_223]) ).
tcf(c_27182,plain,
! [X0: $i,X1: $i] :
( ( relation_image(set_difference(X0,set_difference(X0,X1)),relation_dom(set_difference(X0,set_difference(X0,X1)))) = relation_rng(set_difference(X0,set_difference(X0,X1))) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_364,c_99]) ).
tcf(c_27183,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(set_difference(X0,set_difference(X0,X1)))) = relation_dom(set_difference(X0,set_difference(X0,X1))) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_364,c_137]) ).
tcf(c_27184,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(set_difference(X0,set_difference(X0,X1)))) = relation_rng(set_difference(X0,set_difference(X0,X1))) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_364,c_136]) ).
tcf(c_27185,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(set_difference(X0,set_difference(X0,X1)))) = set_difference(X0,set_difference(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_364,c_429]) ).
tcf(c_27188,plain,
! [X0: $i] :
( relation(set_difference(empty_set,empty_set))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27175,c_231]) ).
tcf(c_27218,plain,
( relation(set_difference(empty_set,empty_set))
| ~ relation(empty_set) ),
inference(instantiation,[status(thm)],[c_27188]) ).
tcf(c_27236,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X0,X1)) = set_difference(X1,set_difference(X1,set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_153,c_371]) ).
tcf(c_27237,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,empty_set)) = set_difference(empty_set,empty_set),
inference(superposition,[status(thm)],[c_263,c_371]) ).
tcf(c_27238,plain,
! [X0: $i] : set_difference(empty_set,set_difference(empty_set,X0)) = set_difference(X0,X0),
inference(superposition,[status(thm)],[c_264,c_371]) ).
tcf(c_27239,plain,
! [X0: $i] : set_difference(relation_rng(sK5),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))) = set_difference(relation_inverse_image(relation_inverse(sK5),X0),empty_set),
inference(superposition,[status(thm)],[c_21834,c_371]) ).
tcf(c_27240,plain,
! [X0: $i] : set_difference(relation_dom(sK5),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))) = set_difference(relation_image(relation_inverse(sK5),X0),empty_set),
inference(superposition,[status(thm)],[c_22079,c_371]) ).
tcf(c_27241,plain,
! [X0: $i] : set_difference(relation_dom(sK5),set_difference(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))) = set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),empty_set),
inference(superposition,[status(thm)],[c_25056,c_371]) ).
tcf(c_27274,plain,
! [X0: $i,X1: $i] :
( relation(set_difference(X0,set_difference(X1,set_difference(X1,X0))))
| ~ relation(X0)
| ~ relation(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_371,c_364]) ).
tcf(c_27275,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,set_difference(X0,X1))
| ( set_difference(X0,set_difference(X1,set_difference(X1,X0))) != empty_set ) ),
inference(superposition,[status(thm)],[c_371,c_257]) ).
tcf(c_27276,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,set_difference(X0,X1))
| in(sK9(X0,set_difference(X0,X1)),set_difference(X0,set_difference(X1,set_difference(X1,X0)))) ),
inference(superposition,[status(thm)],[c_371,c_165]) ).
tcf(c_27277,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,set_difference(X0,X1)),set_difference(X1,X0)),set_union2(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_371,c_20247]) ).
tcf(c_27278,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(X0,set_difference(X0,X1)),set_difference(X1,X0)),set_difference(X1,X0)),set_union2(set_difference(X1,X0),X1)),
inference(superposition,[status(thm)],[c_371,c_20244]) ).
tcf(c_27279,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,set_difference(X1,X0))
| ( set_difference(X0,set_difference(X0,X1)) != X1 ) ),
inference(superposition,[status(thm)],[c_371,c_210]) ).
tcf(c_27280,plain,
! [X0: $i,X1: $i] :
( subset(X1,set_difference(X1,X0))
| ( set_difference(X0,set_difference(X0,X1)) != empty_set ) ),
inference(superposition,[status(thm)],[c_371,c_139]) ).
tcf(c_27281,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,set_difference(X0,X1)),set_difference(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_371,c_19484]) ).
tcf(c_27282,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,set_difference(X0,X1)),set_difference(X1,X0)),set_union2(set_difference(X1,X0),X1)),
inference(superposition,[status(thm)],[c_371,c_19715]) ).
tcf(c_27283,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X0,X1)),set_union2(set_difference(X1,X0),X1)),
inference(superposition,[status(thm)],[c_371,c_19593]) ).
tcf(c_27284,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X0,X1)),set_union2(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_371,c_19485]) ).
tcf(c_27285,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,set_difference(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_371,c_19457]) ).
tcf(c_27286,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X0,X1)),X1),
inference(superposition,[status(thm)],[c_371,c_135]) ).
tcf(c_27287,plain,
! [X0: $i,X1: $i] :
( relation(set_difference(X1,set_difference(X1,X0)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_371,c_364]) ).
tcf(c_27288,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ( set_difference(X0,set_difference(X0,X1)) != empty_set ) ),
inference(superposition,[status(thm)],[c_371,c_257]) ).
tcf(c_27289,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK9(X0,X1),set_difference(X1,set_difference(X1,X0))) ),
inference(superposition,[status(thm)],[c_371,c_165]) ).
tcf(c_27290,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(X1,X2))
| in(X0,set_difference(X2,set_difference(X2,X1)))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_371,c_268]) ).
tcf(c_27291,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,set_difference(X1,X2))
| ~ in(X0,set_difference(X1,set_difference(X2,set_difference(X2,X1)))) ),
inference(superposition,[status(thm)],[c_371,c_166]) ).
tcf(c_27292,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(X1,X2))
| ~ in(X0,set_difference(X1,set_difference(X2,set_difference(X2,X1)))) ),
inference(superposition,[status(thm)],[c_371,c_370]) ).
tcf(c_27293,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X1,X2)),set_difference(X2,set_difference(X2,X1)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_371,c_127]) ).
tcf(c_27294,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,set_difference(X2,X1))
| ~ in(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(superposition,[status(thm)],[c_371,c_270]) ).
tcf(c_27296,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X2,X1)
| ~ in(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(superposition,[status(thm)],[c_371,c_166]) ).
tcf(c_27297,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(superposition,[status(thm)],[c_371,c_370]) ).
tcf(c_27298,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X2,set_difference(X2,X0)),set_difference(X1,set_difference(X0,X2)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_371,c_127]) ).
tcf(c_27299,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),set_difference(set_difference(X1,set_difference(X1,X0)),set_difference(X0,X1))),set_union2(X0,set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_371,c_20485]) ).
tcf(c_27300,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),set_difference(set_difference(set_difference(X1,set_difference(X1,X0)),set_difference(X0,X1)),set_difference(X0,X1))),set_union2(set_difference(X0,X1),X0)),
inference(superposition,[status(thm)],[c_371,c_20482]) ).
tcf(c_27301,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X1,X0))),set_union2(X0,set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_371,c_19744]) ).
tcf(c_27302,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),set_difference(set_difference(X1,set_difference(X1,X0)),set_difference(X0,X1))),set_union2(set_difference(X0,X1),X0)),
inference(superposition,[status(thm)],[c_371,c_19741]) ).
tcf(c_27303,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X1,X0))),set_union2(set_difference(X0,X1),X0)),
inference(superposition,[status(thm)],[c_371,c_19566]) ).
tcf(c_27304,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_difference(X1,set_difference(X1,X0))) = set_union2(set_difference(X0,X1),X0),
inference(superposition,[status(thm)],[c_371,c_145]) ).
tcf(c_27325,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X1,X0))),X0),
inference(light_normalisation,[status(thm)],[c_27303,c_20834]) ).
tcf(c_27332,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_difference(X1,set_difference(X1,X0))) = X0,
inference(light_normalisation,[status(thm)],[c_27304,c_20834]) ).
tcf(c_27345,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),set_difference(set_difference(X1,set_difference(X1,X0)),set_difference(X0,X1))),X0),
inference(light_normalisation,[status(thm)],[c_27302,c_20834]) ).
tcf(c_27346,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),set_difference(set_difference(set_difference(X1,set_difference(X1,X0)),set_difference(X0,X1)),set_difference(X0,X1))),X0),
inference(light_normalisation,[status(thm)],[c_27300,c_20834]) ).
tcf(c_27464,plain,
set_union2(relation_dom(sK5),relation_rng(sK5)) = relation_field(sK5),
inference(superposition,[status(thm)],[c_96,c_419]) ).
tcf(c_27465,plain,
! [X0: $i] : set_union2(relation_dom(identity_relation(X0)),relation_rng(identity_relation(X0))) = relation_field(identity_relation(X0)),
inference(superposition,[status(thm)],[c_422,c_419]) ).
tcf(c_27466,plain,
! [X0: $i] :
( ( set_union2(relation_dom(function_inverse(X0)),relation_rng(function_inverse(X0))) = relation_field(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_465,c_419]) ).
tcf(c_27467,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_dom(relation_dom_restriction(X0,X1)),relation_rng(relation_dom_restriction(X0,X1))) = relation_field(relation_dom_restriction(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_334,c_419]) ).
tcf(c_27468,plain,
set_union2(relation_dom(empty_set),relation_rng(empty_set)) = relation_field(empty_set),
inference(superposition,[status(thm)],[c_231,c_419]) ).
tcf(c_27469,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_dom(set_union2(X0,X1)),relation_rng(set_union2(X0,X1))) = relation_field(set_union2(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_248,c_419]) ).
tcf(c_27470,plain,
set_union2(relation_dom(sK47),relation_rng(sK47)) = relation_field(sK47),
inference(superposition,[status(thm)],[c_329,c_419]) ).
tcf(c_27471,plain,
! [X0: $i] :
( ( set_union2(relation_dom(relation_dom(X0)),relation_rng(relation_dom(X0))) = relation_field(relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_342,c_419]) ).
tcf(c_27472,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_dom(relation_rng_restriction(X1,X0)),relation_rng(relation_rng_restriction(X1,X0))) = relation_field(relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_352,c_419]) ).
tcf(c_27473,plain,
! [X0: $i] :
( ( set_union2(relation_dom(relation_rng(X0)),relation_rng(relation_rng(X0))) = relation_field(relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_360,c_419]) ).
tcf(c_27474,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_dom(set_difference(X0,set_difference(X0,X1))),relation_rng(set_difference(X0,set_difference(X0,X1)))) = relation_field(set_difference(X0,set_difference(X0,X1))) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_364,c_419]) ).
tcf(c_27475,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_dom(relation_composition(X0,X1)),relation_rng(relation_composition(X0,X1))) = relation_field(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_408,c_419]) ).
tcf(c_27476,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_dom(relation_composition(X0,X1)),relation_rng(relation_composition(X0,X1))) = relation_field(relation_composition(X0,X1)) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_407,c_419]) ).
tcf(c_27477,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_dom(relation_composition(X1,X0)),relation_rng(relation_composition(X1,X0))) = relation_field(relation_composition(X1,X0)) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_403,c_419]) ).
tcf(c_27478,plain,
! [X0: $i] :
( ( set_union2(relation_dom(relation_inverse(X0)),relation_rng(relation_inverse(X0))) = relation_field(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_434,c_419]) ).
tcf(c_27479,plain,
! [X0: $i] :
( ( set_union2(relation_dom(relation_inverse(X0)),relation_rng(relation_inverse(X0))) = relation_field(relation_inverse(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_433,c_419]) ).
tcf(c_27480,plain,
set_union2(relation_dom(sK75),relation_rng(sK75)) = relation_field(sK75),
inference(superposition,[status(thm)],[c_456,c_419]) ).
tcf(c_27481,plain,
set_union2(relation_dom(sK79),relation_rng(sK79)) = relation_field(sK79),
inference(superposition,[status(thm)],[c_474,c_419]) ).
tcf(c_27482,plain,
! [X0: $i] :
( ( set_union2(relation_dom(sK23(X0)),relation_rng(sK23(X0))) = relation_field(sK23(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20383,c_419]) ).
tcf(c_27483,plain,
! [X0: $i] : set_union2(relation_dom(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(sK5,X0))) = relation_field(relation_dom_restriction(sK5,X0)),
inference(superposition,[status(thm)],[c_25741,c_419]) ).
tcf(c_27484,plain,
! [X0: $i,X1: $i] : set_union2(relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))) = relation_field(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),
inference(superposition,[status(thm)],[c_26788,c_419]) ).
tcf(c_27485,plain,
set_union2(empty_set,empty_set) = relation_field(empty_set),
inference(light_normalisation,[status(thm)],[c_27468,c_186,c_187]) ).
tcf(c_27486,plain,
! [X0: $i] : relation_field(identity_relation(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_27465,c_203,c_204,c_245]) ).
tcf(c_27609,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,cartesian_product2(X0,X1))
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_26653,c_81]) ).
tcf(c_27610,plain,
! [X0: $i,X1: $i] :
( subset(cartesian_product2(X0,X1),empty_set)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_26653,c_81]) ).
tcf(c_27611,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,cartesian_product2(empty_set,X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_26653,c_82]) ).
tcf(c_27612,plain,
! [X0: $i,X1: $i] :
( subset(cartesian_product2(empty_set,X0),empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_26653,c_82]) ).
tcf(c_27614,plain,
~ proper_subset(empty_set,identity_relation(empty_set)),
inference(superposition,[status(thm)],[c_26653,c_20989]) ).
tcf(c_27615,plain,
subset(identity_relation(empty_set),empty_set),
inference(superposition,[status(thm)],[c_26653,c_20929]) ).
tcf(c_27616,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,empty_set)
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_27612,c_26653]) ).
tcf(c_27622,plain,
! [X0: $i] :
( subset(identity_relation(empty_set),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_27615,c_110]) ).
tcf(c_27626,plain,
! [X0: $i] :
( disjoint(identity_relation(empty_set),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_27615,c_190]) ).
tcf(c_27629,plain,
! [X0: $i] : subset(identity_relation(empty_set),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_27622,c_124]) ).
tcf(c_27630,plain,
subset(set_difference(relation_dom(sK5),set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5))),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_20482]) ).
tcf(c_27631,plain,
subset(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_20247]) ).
tcf(c_27632,plain,
( relation(relation_field(sK5))
| ~ relation(relation_rng(sK5))
| ~ relation(relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_27464,c_248]) ).
tcf(c_27633,plain,
~ proper_subset(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27464,c_19484]) ).
tcf(c_27634,plain,
subset(set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_19741]) ).
tcf(c_27635,plain,
~ in(powerset(relation_field(sK5)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_27464,c_20137]) ).
tcf(c_27636,plain,
~ in(sK54(relation_field(sK5)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_27464,c_20134]) ).
tcf(c_27637,plain,
~ in(sK2(relation_field(sK5)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_27464,c_20131]) ).
tcf(c_27638,plain,
~ in(powerset(relation_field(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_27464,c_20101]) ).
tcf(c_27639,plain,
~ in(sK54(relation_field(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_27464,c_20098]) ).
tcf(c_27640,plain,
~ in(sK2(relation_field(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_27464,c_20095]) ).
tcf(c_27641,plain,
subset(set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_19566]) ).
tcf(c_27642,plain,
~ proper_subset(relation_field(sK5),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_27464,c_19595]) ).
tcf(c_27643,plain,
subset(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_19485]) ).
tcf(c_27644,plain,
set_difference(relation_dom(sK5),relation_rng(sK5)) = set_difference(relation_field(sK5),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_27464,c_153]) ).
tcf(c_27645,plain,
~ proper_subset(relation_field(sK5),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_27464,c_19458]) ).
tcf(c_27646,plain,
( empty(relation_dom(sK5))
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_27464,c_247]) ).
tcf(c_27647,plain,
( empty(relation_rng(sK5))
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_27464,c_246]) ).
tcf(c_27648,plain,
subset(relation_dom(sK5),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_209]) ).
tcf(c_27649,plain,
subset(set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_20485]) ).
tcf(c_27650,plain,
subset(set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_20244]) ).
tcf(c_27651,plain,
subset(set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_19744]) ).
tcf(c_27652,plain,
subset(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_19715]) ).
tcf(c_27653,plain,
subset(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_19593]) ).
tcf(c_27654,plain,
subset(relation_rng(sK5),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_19598]) ).
tcf(c_27655,plain,
! [X0: $i] :
( in(X0,relation_rng(sK5))
| in(X0,relation_dom(sK5))
| ~ in(X0,relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_27464,c_254]) ).
tcf(c_27656,plain,
! [X0: $i] :
( in(X0,relation_field(sK5))
| ~ in(X0,relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_27464,c_252]) ).
tcf(c_27657,plain,
! [X0: $i] :
( in(X0,relation_field(sK5))
| ~ in(X0,relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_27464,c_253]) ).
tcf(c_27783,plain,
( ( relation_dom(sK5) = relation_field(sK5) )
| ~ subset(relation_field(sK5),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_27648,c_260]) ).
tcf(c_27784,plain,
set_difference(relation_dom(sK5),set_difference(relation_dom(sK5),relation_field(sK5))) = relation_dom(sK5),
inference(superposition,[status(thm)],[c_27648,c_123]) ).
tcf(c_27785,plain,
( proper_subset(relation_dom(sK5),relation_field(sK5))
| ( relation_dom(sK5) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_27648,c_468]) ).
tcf(c_27786,plain,
! [X0: $i] :
( subset(relation_dom(sK5),X0)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27648,c_110]) ).
tcf(c_27787,plain,
set_difference(relation_dom(sK5),relation_field(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_27648,c_138]) ).
tcf(c_27788,plain,
set_union2(relation_dom(sK5),relation_field(sK5)) = relation_field(sK5),
inference(superposition,[status(thm)],[c_27648,c_85]) ).
tcf(c_27790,plain,
! [X0: $i] :
( disjoint(relation_dom(sK5),X0)
| ~ disjoint(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27648,c_190]) ).
tcf(c_27801,plain,
( ( relation_rng(sK5) = relation_field(sK5) )
| ~ subset(relation_field(sK5),relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_27654,c_260]) ).
tcf(c_27802,plain,
set_difference(relation_rng(sK5),set_difference(relation_rng(sK5),relation_field(sK5))) = relation_rng(sK5),
inference(superposition,[status(thm)],[c_27654,c_123]) ).
tcf(c_27803,plain,
( proper_subset(relation_rng(sK5),relation_field(sK5))
| ( relation_rng(sK5) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_27654,c_468]) ).
tcf(c_27804,plain,
! [X0: $i] :
( subset(relation_rng(sK5),X0)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27654,c_110]) ).
tcf(c_27805,plain,
set_difference(relation_rng(sK5),relation_field(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_27654,c_138]) ).
tcf(c_27806,plain,
set_union2(relation_rng(sK5),relation_field(sK5)) = relation_field(sK5),
inference(superposition,[status(thm)],[c_27654,c_85]) ).
tcf(c_27808,plain,
! [X0: $i] :
( disjoint(relation_rng(sK5),X0)
| ~ disjoint(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27654,c_190]) ).
tcf(c_27819,plain,
set_difference(relation_rng(sK5),unordered_pair(powerset(relation_field(sK5)),powerset(relation_field(sK5)))) = relation_rng(sK5),
inference(superposition,[status(thm)],[c_195,c_27635]) ).
tcf(c_27820,plain,
set_difference(relation_rng(sK5),unordered_pair(sK54(relation_field(sK5)),sK54(relation_field(sK5)))) = relation_rng(sK5),
inference(superposition,[status(thm)],[c_195,c_27636]) ).
tcf(c_27821,plain,
set_difference(relation_rng(sK5),unordered_pair(sK2(relation_field(sK5)),sK2(relation_field(sK5)))) = relation_rng(sK5),
inference(superposition,[status(thm)],[c_195,c_27637]) ).
tcf(c_27833,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))),set_union2(X1,set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_153,c_20651]) ).
tcf(c_27835,plain,
! [X0: $i] : subset(set_difference(X0,set_difference(empty_set,X0)),set_union2(empty_set,X0)),
inference(superposition,[status(thm)],[c_264,c_20651]) ).
tcf(c_27836,plain,
! [X0: $i] : subset(set_difference(empty_set,set_difference(X0,empty_set)),set_union2(X0,X0)),
inference(superposition,[status(thm)],[c_4095,c_20651]) ).
tcf(c_27837,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,set_difference(X0,X1)),set_difference(set_difference(X1,X0),set_difference(X0,set_difference(X0,X1)))),set_union2(set_difference(X1,X0),X1)),
inference(superposition,[status(thm)],[c_371,c_20651]) ).
tcf(c_27838,plain,
! [X0: $i] : subset(set_difference(empty_set,set_difference(relation_rng(sK5),empty_set)),set_union2(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_21834,c_20651]) ).
tcf(c_27839,plain,
! [X0: $i] : subset(set_difference(empty_set,set_difference(relation_dom(sK5),empty_set)),set_union2(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22079,c_20651]) ).
tcf(c_27840,plain,
! [X0: $i] : subset(set_difference(empty_set,set_difference(relation_dom(sK5),empty_set)),set_union2(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),
inference(superposition,[status(thm)],[c_25056,c_20651]) ).
tcf(c_27842,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(X0,X1),X1),set_difference(X1,set_difference(set_difference(X0,X1),X1))),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_145,c_20651]) ).
tcf(c_27843,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,X0),set_difference(X0,set_difference(empty_set,X0))),X0),
inference(superposition,[status(thm)],[c_244,c_20651]) ).
tcf(c_27844,plain,
! [X0: $i] : subset(set_difference(set_difference(X0,X0),set_difference(X0,set_difference(X0,X0))),X0),
inference(superposition,[status(thm)],[c_245,c_20651]) ).
tcf(c_27845,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_255,c_20651]) ).
tcf(c_27846,plain,
! [X0: $i] : subset(set_difference(set_difference(X0,empty_set),set_difference(empty_set,set_difference(X0,empty_set))),X0),
inference(superposition,[status(thm)],[c_19599,c_20651]) ).
tcf(c_27847,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),set_difference(relation_rng(sK5),set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)))),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_20651]) ).
tcf(c_27848,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),set_difference(relation_dom(sK5),set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_20651]) ).
tcf(c_27849,plain,
subset(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5)))),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_20651]) ).
tcf(c_27850,plain,
! [X0: $i,X1: $i] :
( ( set_difference(set_difference(X1,X0),set_difference(X0,set_difference(X1,X0))) = set_union2(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(set_difference(X1,X0),set_difference(X0,set_difference(X1,X0)))) ),
inference(superposition,[status(thm)],[c_20651,c_260]) ).
tcf(c_27851,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))),set_difference(set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))),set_union2(X1,X0))) = set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_20651,c_123]) ).
tcf(c_27852,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))),set_union2(X1,X0))
| ( set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))) = set_union2(X1,X0) ) ),
inference(superposition,[status(thm)],[c_20651,c_468]) ).
tcf(c_27853,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(X1,X0),set_difference(X0,set_difference(X1,X0))),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_20651,c_110]) ).
tcf(c_27854,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))),set_union2(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_20651,c_138]) ).
tcf(c_27855,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))),set_union2(X1,X0)) = set_union2(X1,X0),
inference(superposition,[status(thm)],[c_20651,c_85]) ).
tcf(c_27856,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(set_difference(X1,X0),set_difference(X0,set_difference(X1,X0)))),
inference(superposition,[status(thm)],[c_20651,c_188]) ).
tcf(c_27857,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(set_difference(X1,X0),set_difference(X0,set_difference(X1,X0))),X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_20651,c_190]) ).
tcf(c_27863,plain,
subset(set_difference(empty_set,set_difference(relation_dom(sK5),empty_set)),relation_dom(sK5)),
inference(light_normalisation,[status(thm)],[c_27839,c_22341]) ).
tcf(c_27864,plain,
subset(set_difference(empty_set,set_difference(relation_rng(sK5),empty_set)),relation_rng(sK5)),
inference(light_normalisation,[status(thm)],[c_27838,c_21870]) ).
tcf(c_27865,plain,
subset(set_difference(empty_set,set_difference(relation_dom(sK5),empty_set)),set_union2(relation_dom(sK5),empty_set)),
inference(light_normalisation,[status(thm)],[c_27840,c_25189]) ).
tcf(c_27898,plain,
( function(sK79)
| ~ one_to_one(relation_inverse(sK79))
| ~ function(relation_inverse(sK79))
| ~ relation(relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_20539,c_431]) ).
tcf(c_27899,plain,
! [X0: $i] :
( function(relation_dom_restriction(sK5,X0))
| ~ one_to_one(relation_inverse(relation_dom_restriction(sK5,X0)))
| ~ function(relation_inverse(relation_dom_restriction(sK5,X0)))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25749,c_431]) ).
tcf(c_27913,plain,
! [X0: $i,X1: $i] :
( subset(union_of_subsets(X1,X0),X1)
| ~ element(X0,powerset(powerset(X1))) ),
inference(superposition,[status(thm)],[c_452,c_274]) ).
tcf(c_27914,plain,
! [X0: $i,X1: $i] :
( empty(union_of_subsets(X1,X0))
| ~ empty(powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(superposition,[status(thm)],[c_452,c_285]) ).
tcf(c_27915,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| in(union_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(superposition,[status(thm)],[c_452,c_283]) ).
tcf(c_27918,plain,
! [X0: $i,X1: $i] :
( in(union_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27915,c_286]) ).
tcf(c_27938,plain,
! [X0: $i,X1: $i] :
( subset(meet_of_subsets(X1,X0),X1)
| ~ element(X0,powerset(powerset(X1))) ),
inference(superposition,[status(thm)],[c_453,c_274]) ).
tcf(c_27939,plain,
! [X0: $i,X1: $i] :
( empty(meet_of_subsets(X1,X0))
| ~ empty(powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(superposition,[status(thm)],[c_453,c_285]) ).
tcf(c_27940,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| in(meet_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(superposition,[status(thm)],[c_453,c_283]) ).
tcf(c_27943,plain,
! [X0: $i,X1: $i] :
( in(meet_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27940,c_286]) ).
tcf(c_27952,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_140,c_6699]) ).
tcf(c_27953,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19515,c_6699]) ).
tcf(c_27954,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(union(X1),subset_complement(union(X1),X0)) = X0 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_222,c_6699]) ).
tcf(c_27955,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,relation_rng(relation_rng_restriction(X1,X0)))) = relation_rng(relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_78,c_6699]) ).
tcf(c_27956,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X0,subset_complement(X0,relation_rng_restriction(X1,X0))) = relation_rng_restriction(X1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_79,c_6699]) ).
tcf(c_27957,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(relation_rng(X0),subset_complement(relation_rng(X0),relation_rng(relation_rng_restriction(X1,X0)))) = relation_rng(relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_80,c_6699]) ).
tcf(c_27958,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_complement(cartesian_product2(X1,X2),subset_complement(cartesian_product2(X1,X2),cartesian_product2(X0,X2))) = cartesian_product2(X0,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_81,c_6699]) ).
tcf(c_27959,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_complement(cartesian_product2(X2,X1),subset_complement(cartesian_product2(X2,X1),cartesian_product2(X2,X0))) = cartesian_product2(X2,X0) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_6699]) ).
tcf(c_27960,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(relation_rng(X0),subset_complement(relation_rng(X0),relation_image(X0,X1))) = relation_image(X0,X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_94,c_6699]) ).
tcf(c_27961,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(relation_dom(X0),subset_complement(relation_dom(X0),relation_inverse_image(X0,X1))) = relation_inverse_image(X0,X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_105,c_6699]) ).
tcf(c_27962,plain,
! [X0: $i] :
( ( subset_complement(cartesian_product2(relation_dom(X0),relation_rng(X0)),subset_complement(cartesian_product2(relation_dom(X0),relation_rng(X0)),X0)) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_117,c_6699]) ).
tcf(c_27963,plain,
! [X0: $i] : subset_complement(X0,subset_complement(X0,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_124,c_6699]) ).
tcf(c_27964,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_complement(set_difference(X1,X2),subset_complement(set_difference(X1,X2),set_difference(X0,X2))) = set_difference(X0,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_127,c_6699]) ).
tcf(c_27965,plain,
! [X0: $i,X1: $i] : subset_complement(X0,subset_complement(X0,set_difference(X0,X1))) = set_difference(X0,X1),
inference(superposition,[status(thm)],[c_135,c_6699]) ).
tcf(c_27966,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),X0)) = X0,
inference(superposition,[status(thm)],[c_209,c_6699]) ).
tcf(c_27967,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X0,subset_complement(X0,relation_dom_restriction(X0,X1))) = relation_dom_restriction(X0,X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_215,c_6699]) ).
tcf(c_27968,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(relation_rng(X0),subset_complement(relation_rng(X0),relation_rng(relation_dom_restriction(X0,X1)))) = relation_rng(relation_dom_restriction(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_224,c_6699]) ).
tcf(c_27969,plain,
! [X0: $i] : subset_complement(X0,subset_complement(X0,X0)) = X0,
inference(superposition,[status(thm)],[c_262,c_6699]) ).
tcf(c_27970,plain,
! [X0: $i] :
( empty(X0)
| ( subset_complement(X0,subset_complement(X0,sK22(X0))) = sK22(X0) ) ),
inference(superposition,[status(thm)],[c_19616,c_6699]) ).
tcf(c_27971,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),set_difference(X0,X1))) = set_difference(X0,X1),
inference(superposition,[status(thm)],[c_19485,c_6699]) ).
tcf(c_27972,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),set_difference(X0,set_difference(X1,X0)))) = set_difference(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_19566,c_6699]) ).
tcf(c_27973,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),set_difference(X1,X0))) = set_difference(X1,X0),
inference(superposition,[status(thm)],[c_19593,c_6699]) ).
tcf(c_27974,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),X1)) = X1,
inference(superposition,[status(thm)],[c_19598,c_6699]) ).
tcf(c_27975,plain,
! [X0: $i] : subset_complement(X0,subset_complement(X0,sK23(powerset(X0)))) = sK23(powerset(X0)),
inference(superposition,[status(thm)],[c_19617,c_6699]) ).
tcf(c_27976,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( subset_complement(X0,subset_complement(X0,sK18(powerset(X0),X1))) = sK18(powerset(X0),X1) ) ),
inference(superposition,[status(thm)],[c_19652,c_6699]) ).
tcf(c_27977,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0))) = set_difference(set_difference(X1,X0),X0),
inference(superposition,[status(thm)],[c_19715,c_6699]) ).
tcf(c_27978,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),set_difference(X1,set_difference(X0,X1)))) = set_difference(X1,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_19744,c_6699]) ).
tcf(c_27979,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),set_difference(X0,set_difference(set_difference(X1,X0),X0)))) = set_difference(X0,set_difference(set_difference(X1,X0),X0)),
inference(superposition,[status(thm)],[c_19741,c_6699]) ).
tcf(c_27980,plain,
! [X0: $i,X1: $i] : subset_complement(X0,subset_complement(X0,relation_image(identity_relation(X0),X1))) = relation_image(identity_relation(X0),X1),
inference(superposition,[status(thm)],[c_19833,c_6699]) ).
tcf(c_27981,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( subset_complement(X0,subset_complement(X0,sK1(powerset(X0),X1))) = sK1(powerset(X0),X1) ) ),
inference(superposition,[status(thm)],[c_19866,c_6699]) ).
tcf(c_27982,plain,
! [X0: $i,X1: $i] : subset_complement(X0,subset_complement(X0,relation_inverse_image(identity_relation(X0),X1))) = relation_inverse_image(identity_relation(X0),X1),
inference(superposition,[status(thm)],[c_19947,c_6699]) ).
tcf(c_27983,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),set_difference(set_difference(X0,X1),X1))) = set_difference(set_difference(X0,X1),X1),
inference(superposition,[status(thm)],[c_20247,c_6699]) ).
tcf(c_27984,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),set_difference(set_difference(set_difference(X1,X0),X0),X0))) = set_difference(set_difference(set_difference(X1,X0),X0),X0),
inference(superposition,[status(thm)],[c_20244,c_6699]) ).
tcf(c_27985,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),set_difference(X1,set_difference(set_difference(X0,X1),X1)))) = set_difference(X1,set_difference(set_difference(X0,X1),X1)),
inference(superposition,[status(thm)],[c_20485,c_6699]) ).
tcf(c_27986,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)))) = set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0)),
inference(superposition,[status(thm)],[c_20482,c_6699]) ).
tcf(c_27987,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),set_difference(set_difference(X1,X0),set_difference(X0,set_difference(X1,X0))))) = set_difference(set_difference(X1,X0),set_difference(X0,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_20651,c_6699]) ).
tcf(c_27988,plain,
! [X0: $i,X1: $i] : subset_complement(X0,subset_complement(X0,relation_rng(relation_rng_restriction(X1,identity_relation(X0))))) = relation_rng(relation_rng_restriction(X1,identity_relation(X0))),
inference(superposition,[status(thm)],[c_20703,c_6699]) ).
tcf(c_27989,plain,
! [X0: $i] : subset_complement(cartesian_product2(X0,X0),subset_complement(cartesian_product2(X0,X0),identity_relation(X0))) = identity_relation(X0),
inference(superposition,[status(thm)],[c_20929,c_6699]) ).
tcf(c_27990,plain,
! [X0: $i] : subset_complement(relation_rng(sK5),subset_complement(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))) = relation_inverse_image(relation_inverse(sK5),X0),
inference(superposition,[status(thm)],[c_21837,c_6699]) ).
tcf(c_27991,plain,
! [X0: $i] : subset_complement(relation_dom(sK5),subset_complement(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))) = relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),
inference(superposition,[status(thm)],[c_25173,c_6699]) ).
tcf(c_27992,plain,
! [X0: $i] : subset_complement(relation_dom(sK5),subset_complement(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))) = relation_image(relation_inverse(sK5),X0),
inference(superposition,[status(thm)],[c_22082,c_6699]) ).
tcf(c_27993,plain,
( ( subset_complement(cartesian_product2(relation_rng(sK5),relation_dom(sK5)),subset_complement(cartesian_product2(relation_rng(sK5),relation_dom(sK5)),relation_inverse(sK5))) = relation_inverse(sK5) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21353,c_6699]) ).
tcf(c_27994,plain,
! [X0: $i,X1: $i] : subset_complement(X0,subset_complement(X0,relation_rng(relation_dom_restriction(identity_relation(X0),X1)))) = relation_rng(relation_dom_restriction(identity_relation(X0),X1)),
inference(superposition,[status(thm)],[c_21501,c_6699]) ).
tcf(c_27995,plain,
! [X0: $i] :
( ( subset_complement(relation_dom(sK5),subset_complement(relation_dom(sK5),relation_rng(relation_dom_restriction(relation_inverse(sK5),X0)))) = relation_rng(relation_dom_restriction(relation_inverse(sK5),X0)) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21494,c_6699]) ).
tcf(c_27996,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X0,subset_complement(X0,relation_inverse_image(relation_inverse(sK5),X1))) = relation_inverse_image(relation_inverse(sK5),X1) )
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_22586,c_6699]) ).
tcf(c_27997,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X0,subset_complement(X0,relation_image(relation_inverse(sK5),X1))) = relation_image(relation_inverse(sK5),X1) )
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_22588,c_6699]) ).
tcf(c_27998,plain,
subset_complement(relation_field(sK5),subset_complement(relation_field(sK5),relation_dom(sK5))) = relation_dom(sK5),
inference(superposition,[status(thm)],[c_27648,c_6699]) ).
tcf(c_27999,plain,
subset_complement(relation_field(sK5),subset_complement(relation_field(sK5),relation_rng(sK5))) = relation_rng(sK5),
inference(superposition,[status(thm)],[c_27654,c_6699]) ).
tcf(c_28209,plain,
! [X0: $i] : subset_complement(X0,subset_complement(X0,identity_relation(empty_set))) = identity_relation(empty_set),
inference(superposition,[status(thm)],[c_27629,c_6699]) ).
tcf(c_28210,plain,
! [X0: $i] :
( ( identity_relation(empty_set) = X0 )
| ~ subset(X0,identity_relation(empty_set)) ),
inference(superposition,[status(thm)],[c_27629,c_260]) ).
tcf(c_28211,plain,
! [X0: $i] : set_difference(identity_relation(empty_set),set_difference(identity_relation(empty_set),X0)) = identity_relation(empty_set),
inference(superposition,[status(thm)],[c_27629,c_123]) ).
tcf(c_28212,plain,
! [X0: $i] :
( proper_subset(identity_relation(empty_set),X0)
| ( identity_relation(empty_set) = X0 ) ),
inference(superposition,[status(thm)],[c_27629,c_468]) ).
tcf(c_28214,plain,
! [X0: $i] : set_difference(identity_relation(empty_set),X0) = empty_set,
inference(superposition,[status(thm)],[c_27629,c_138]) ).
tcf(c_28215,plain,
! [X0: $i] : set_union2(identity_relation(empty_set),X0) = X0,
inference(superposition,[status(thm)],[c_27629,c_85]) ).
tcf(c_28216,plain,
! [X0: $i] : ~ proper_subset(X0,identity_relation(empty_set)),
inference(superposition,[status(thm)],[c_27629,c_188]) ).
tcf(c_28217,plain,
! [X0: $i,X1: $i] :
( disjoint(identity_relation(empty_set),X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_27629,c_190]) ).
tcf(c_28218,plain,
identity_relation(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_27629,c_152]) ).
tcf(c_28219,plain,
subset(set_difference(identity_relation(empty_set),relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_27629,c_22779]) ).
tcf(c_28220,plain,
subset(set_difference(identity_relation(empty_set),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_27629,c_22780]) ).
tcf(c_28257,plain,
! [X0: $i] :
( ( relation_dom_restriction(sK5,empty_set) = X0 )
| ~ empty(empty_set)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_28218,c_25774]) ).
tcf(c_28258,plain,
! [X0: $i] : relation_dom_restriction(relation_dom_restriction(sK5,X0),empty_set) = relation_composition(empty_set,relation_dom_restriction(sK5,X0)),
inference(superposition,[status(thm)],[c_28218,c_25745]) ).
tcf(c_28259,plain,
( ( relation_dom(relation_dom_restriction(sK5,empty_set)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_28218,c_25777]) ).
tcf(c_28260,plain,
( ( relation_rng(relation_dom_restriction(sK5,empty_set)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_28218,c_25776]) ).
tcf(c_28261,plain,
( ( relation_inverse(relation_dom_restriction(sK5,empty_set)) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_28218,c_25775]) ).
tcf(c_28262,plain,
( ( relation_dom_restriction(sK5,empty_set) = empty_set )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_28218,c_25778]) ).
tcf(c_28263,plain,
relation_dom_restriction(sK5,empty_set) = relation_composition(empty_set,sK5),
inference(superposition,[status(thm)],[c_28218,c_25464]) ).
tcf(c_28264,plain,
! [X0: $i] : subset(relation_rng(relation_dom_restriction(empty_set,X0)),empty_set),
inference(superposition,[status(thm)],[c_28218,c_21501]) ).
tcf(c_28265,plain,
relation_rng(relation_inverse(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_28218,c_21138]) ).
tcf(c_28266,plain,
~ proper_subset(cartesian_product2(empty_set,empty_set),empty_set),
inference(superposition,[status(thm)],[c_28218,c_20989]) ).
tcf(c_28267,plain,
relation_dom(relation_inverse(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_28218,c_20961]) ).
tcf(c_28268,plain,
subset(empty_set,cartesian_product2(empty_set,empty_set)),
inference(superposition,[status(thm)],[c_28218,c_20929]) ).
tcf(c_28283,plain,
! [X0: $i] : subset(relation_rng(relation_rng_restriction(X0,empty_set)),empty_set),
inference(superposition,[status(thm)],[c_28218,c_20703]) ).
tcf(c_28288,plain,
relation_dom_restriction(sK5,empty_set) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_28262,c_232]) ).
tcf(c_28289,plain,
relation_inverse(relation_dom_restriction(sK5,empty_set)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_28261,c_232]) ).
tcf(c_28290,plain,
relation_rng(relation_dom_restriction(sK5,empty_set)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_28260,c_232]) ).
tcf(c_28291,plain,
relation_dom(relation_dom_restriction(sK5,empty_set)) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_28259,c_232]) ).
tcf(c_28292,plain,
! [X0: $i] :
( ( relation_dom_restriction(sK5,empty_set) = X0 )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28257,c_232]) ).
tcf(c_28296,plain,
set_difference(relation_dom(sK5),unordered_pair(powerset(relation_field(sK5)),powerset(relation_field(sK5)))) = relation_dom(sK5),
inference(superposition,[status(thm)],[c_195,c_27638]) ).
tcf(c_28303,plain,
set_difference(relation_dom(sK5),unordered_pair(sK54(relation_field(sK5)),sK54(relation_field(sK5)))) = relation_dom(sK5),
inference(superposition,[status(thm)],[c_195,c_27639]) ).
tcf(c_28304,plain,
set_difference(relation_dom(sK5),unordered_pair(sK2(relation_field(sK5)),sK2(relation_field(sK5)))) = relation_dom(sK5),
inference(superposition,[status(thm)],[c_195,c_27640]) ).
tcf(c_28313,plain,
subset_complement(relation_field(sK5),subset_complement(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5)))) = set_difference(relation_dom(sK5),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_27643,c_6699]) ).
tcf(c_28314,plain,
( ( set_difference(relation_dom(sK5),relation_rng(sK5)) = relation_field(sK5) )
| ~ subset(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_27643,c_260]) ).
tcf(c_28315,plain,
set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_field(sK5))) = set_difference(relation_dom(sK5),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_27643,c_123]) ).
tcf(c_28316,plain,
( proper_subset(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_field(sK5))
| ( set_difference(relation_dom(sK5),relation_rng(sK5)) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_27643,c_468]) ).
tcf(c_28317,plain,
! [X0: $i] :
( subset(set_difference(relation_dom(sK5),relation_rng(sK5)),X0)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27643,c_110]) ).
tcf(c_28318,plain,
set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_field(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_27643,c_138]) ).
tcf(c_28319,plain,
set_union2(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_field(sK5)) = relation_field(sK5),
inference(superposition,[status(thm)],[c_27643,c_85]) ).
tcf(c_28321,plain,
! [X0: $i] :
( disjoint(set_difference(relation_dom(sK5),relation_rng(sK5)),X0)
| ~ disjoint(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27643,c_190]) ).
tcf(c_28350,plain,
subset_complement(relation_field(sK5),subset_complement(relation_field(sK5),set_difference(relation_rng(sK5),relation_dom(sK5)))) = set_difference(relation_rng(sK5),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_27653,c_6699]) ).
tcf(c_28351,plain,
( ( set_difference(relation_rng(sK5),relation_dom(sK5)) = relation_field(sK5) )
| ~ subset(relation_field(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))) ),
inference(superposition,[status(thm)],[c_27653,c_260]) ).
tcf(c_28352,plain,
set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_field(sK5))) = set_difference(relation_rng(sK5),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_27653,c_123]) ).
tcf(c_28353,plain,
( proper_subset(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_field(sK5))
| ( set_difference(relation_rng(sK5),relation_dom(sK5)) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_27653,c_468]) ).
tcf(c_28354,plain,
! [X0: $i] :
( subset(set_difference(relation_rng(sK5),relation_dom(sK5)),X0)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27653,c_110]) ).
tcf(c_28355,plain,
set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_field(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_27653,c_138]) ).
tcf(c_28356,plain,
set_union2(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_field(sK5)) = relation_field(sK5),
inference(superposition,[status(thm)],[c_27653,c_85]) ).
tcf(c_28357,plain,
~ proper_subset(relation_field(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_27653,c_188]) ).
tcf(c_28358,plain,
! [X0: $i] :
( disjoint(set_difference(relation_rng(sK5),relation_dom(sK5)),X0)
| ~ disjoint(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27653,c_190]) ).
tcf(c_28404,plain,
relation_composition(empty_set,sK5) = empty_set,
inference(light_normalisation,[status(thm)],[c_28263,c_28288]) ).
tcf(c_28410,plain,
! [X0: $i] : subset_complement(relation_rng(sK5),subset_complement(relation_rng(sK5),set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))))) = set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_21887,c_6699]) ).
tcf(c_28411,plain,
! [X0: $i] :
( ( set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))) = relation_rng(sK5) )
| ~ subset(relation_rng(sK5),set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)))) ),
inference(superposition,[status(thm)],[c_21887,c_260]) ).
tcf(c_28412,plain,
! [X0: $i] : set_difference(set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),set_difference(set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),relation_rng(sK5))) = set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_21887,c_123]) ).
tcf(c_28413,plain,
! [X0: $i] :
( proper_subset(set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),relation_rng(sK5))
| ( set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))) = relation_rng(sK5) ) ),
inference(superposition,[status(thm)],[c_21887,c_468]) ).
tcf(c_28414,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_inverse_image(relation_inverse(sK5),X1),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X1))),X0)
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_21887,c_110]) ).
tcf(c_28415,plain,
! [X0: $i] : set_difference(set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),relation_rng(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_21887,c_138]) ).
tcf(c_28416,plain,
! [X0: $i] : set_union2(set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),relation_rng(sK5)) = relation_rng(sK5),
inference(superposition,[status(thm)],[c_21887,c_85]) ).
tcf(c_28417,plain,
! [X0: $i] : ~ proper_subset(relation_rng(sK5),set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)))),
inference(superposition,[status(thm)],[c_21887,c_188]) ).
tcf(c_28418,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(relation_inverse_image(relation_inverse(sK5),X1),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X1))),X0)
| ~ disjoint(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_21887,c_190]) ).
tcf(c_28491,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,unordered_pair(X0,X0)) = subset_complement(X1,unordered_pair(X0,X0)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_140,c_6703]) ).
tcf(c_28492,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,X0) = subset_complement(X1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19515,c_6703]) ).
tcf(c_28493,plain,
! [X0: $i,X1: $i] :
( ( set_difference(union(X1),X0) = subset_complement(union(X1),X0) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_222,c_6703]) ).
tcf(c_28494,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,relation_rng(relation_rng_restriction(X1,X0))) = subset_complement(X1,relation_rng(relation_rng_restriction(X1,X0))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_78,c_6703]) ).
tcf(c_28495,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,relation_rng_restriction(X1,X0)) = subset_complement(X0,relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_79,c_6703]) ).
tcf(c_28496,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(X0),relation_rng(relation_rng_restriction(X1,X0))) = subset_complement(relation_rng(X0),relation_rng(relation_rng_restriction(X1,X0))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_80,c_6703]) ).
tcf(c_28497,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(cartesian_product2(X1,X2),cartesian_product2(X0,X2)) = subset_complement(cartesian_product2(X1,X2),cartesian_product2(X0,X2)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_81,c_6703]) ).
tcf(c_28498,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(cartesian_product2(X2,X1),cartesian_product2(X2,X0)) = subset_complement(cartesian_product2(X2,X1),cartesian_product2(X2,X0)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_6703]) ).
tcf(c_28499,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(X0),relation_image(X0,X1)) = subset_complement(relation_rng(X0),relation_image(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_94,c_6703]) ).
tcf(c_28500,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom(X0),relation_inverse_image(X0,X1)) = subset_complement(relation_dom(X0),relation_inverse_image(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_105,c_6703]) ).
tcf(c_28501,plain,
! [X0: $i] :
( ( set_difference(cartesian_product2(relation_dom(X0),relation_rng(X0)),X0) = subset_complement(cartesian_product2(relation_dom(X0),relation_rng(X0)),X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_117,c_6703]) ).
tcf(c_28502,plain,
! [X0: $i] : set_difference(X0,empty_set) = subset_complement(X0,empty_set),
inference(superposition,[status(thm)],[c_124,c_6703]) ).
tcf(c_28503,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X1,X2),set_difference(X0,X2)) = subset_complement(set_difference(X1,X2),set_difference(X0,X2)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_127,c_6703]) ).
tcf(c_28504,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,X1)) = subset_complement(X0,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_135,c_6703]) ).
tcf(c_28505,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),X0) = subset_complement(set_union2(X0,X1),X0),
inference(superposition,[status(thm)],[c_209,c_6703]) ).
tcf(c_28506,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,relation_dom_restriction(X0,X1)) = subset_complement(X0,relation_dom_restriction(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_215,c_6703]) ).
tcf(c_28507,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(X0),relation_rng(relation_dom_restriction(X0,X1))) = subset_complement(relation_rng(X0),relation_rng(relation_dom_restriction(X0,X1))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_224,c_6703]) ).
tcf(c_28508,plain,
! [X0: $i] : set_difference(X0,X0) = subset_complement(X0,X0),
inference(superposition,[status(thm)],[c_262,c_6703]) ).
tcf(c_28509,plain,
! [X0: $i] :
( empty(X0)
| ( set_difference(X0,sK22(X0)) = subset_complement(X0,sK22(X0)) ) ),
inference(superposition,[status(thm)],[c_19616,c_6703]) ).
tcf(c_28510,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X0,X1)) = subset_complement(set_union2(X0,X1),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_19485,c_6703]) ).
tcf(c_28511,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X0,set_difference(X1,X0))) = subset_complement(set_union2(X0,X1),set_difference(X0,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_19566,c_6703]) ).
tcf(c_28512,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X1,X0)) = subset_complement(set_union2(X0,X1),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_19593,c_6703]) ).
tcf(c_28513,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),X1) = subset_complement(set_union2(X0,X1),X1),
inference(superposition,[status(thm)],[c_19598,c_6703]) ).
tcf(c_28514,plain,
! [X0: $i] : set_difference(X0,sK23(powerset(X0))) = subset_complement(X0,sK23(powerset(X0))),
inference(superposition,[status(thm)],[c_19617,c_6703]) ).
tcf(c_28515,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( set_difference(X0,sK18(powerset(X0),X1)) = subset_complement(X0,sK18(powerset(X0),X1)) ) ),
inference(superposition,[status(thm)],[c_19652,c_6703]) ).
tcf(c_28516,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0)) = subset_complement(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0)),
inference(superposition,[status(thm)],[c_19715,c_6703]) ).
tcf(c_28517,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X1,set_difference(X0,X1))) = subset_complement(set_union2(X0,X1),set_difference(X1,set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_19744,c_6703]) ).
tcf(c_28518,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X0,set_difference(set_difference(X1,X0),X0))) = subset_complement(set_union2(X0,X1),set_difference(X0,set_difference(set_difference(X1,X0),X0))),
inference(superposition,[status(thm)],[c_19741,c_6703]) ).
tcf(c_28519,plain,
! [X0: $i,X1: $i] : set_difference(X0,relation_image(identity_relation(X0),X1)) = subset_complement(X0,relation_image(identity_relation(X0),X1)),
inference(superposition,[status(thm)],[c_19833,c_6703]) ).
tcf(c_28520,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| ( set_difference(X0,sK1(powerset(X0),X1)) = subset_complement(X0,sK1(powerset(X0),X1)) ) ),
inference(superposition,[status(thm)],[c_19866,c_6703]) ).
tcf(c_28521,plain,
! [X0: $i,X1: $i] : set_difference(X0,relation_inverse_image(identity_relation(X0),X1)) = subset_complement(X0,relation_inverse_image(identity_relation(X0),X1)),
inference(superposition,[status(thm)],[c_19947,c_6703]) ).
tcf(c_28522,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(set_difference(X0,X1),X1)) = subset_complement(set_union2(X0,X1),set_difference(set_difference(X0,X1),X1)),
inference(superposition,[status(thm)],[c_20247,c_6703]) ).
tcf(c_28523,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(set_difference(set_difference(X1,X0),X0),X0)) = subset_complement(set_union2(X0,X1),set_difference(set_difference(set_difference(X1,X0),X0),X0)),
inference(superposition,[status(thm)],[c_20244,c_6703]) ).
tcf(c_28524,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X1,set_difference(set_difference(X0,X1),X1))) = subset_complement(set_union2(X0,X1),set_difference(X1,set_difference(set_difference(X0,X1),X1))),
inference(superposition,[status(thm)],[c_20485,c_6703]) ).
tcf(c_28525,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0))) = subset_complement(set_union2(X0,X1),set_difference(X0,set_difference(set_difference(set_difference(X1,X0),X0),X0))),
inference(superposition,[status(thm)],[c_20482,c_6703]) ).
tcf(c_28526,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(set_difference(X1,X0),set_difference(X0,set_difference(X1,X0)))) = subset_complement(set_union2(X0,X1),set_difference(set_difference(X1,X0),set_difference(X0,set_difference(X1,X0)))),
inference(superposition,[status(thm)],[c_20651,c_6703]) ).
tcf(c_28527,plain,
! [X0: $i,X1: $i] : set_difference(X0,relation_rng(relation_rng_restriction(X1,identity_relation(X0)))) = subset_complement(X0,relation_rng(relation_rng_restriction(X1,identity_relation(X0)))),
inference(superposition,[status(thm)],[c_20703,c_6703]) ).
tcf(c_28528,plain,
! [X0: $i] : set_difference(cartesian_product2(X0,X0),identity_relation(X0)) = subset_complement(cartesian_product2(X0,X0),identity_relation(X0)),
inference(superposition,[status(thm)],[c_20929,c_6703]) ).
tcf(c_28529,plain,
! [X0: $i] : set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)) = subset_complement(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_21837,c_6703]) ).
tcf(c_28530,plain,
! [X0: $i] : set_difference(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))) = subset_complement(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),
inference(superposition,[status(thm)],[c_25173,c_6703]) ).
tcf(c_28531,plain,
! [X0: $i] : set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)) = subset_complement(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_22082,c_6703]) ).
tcf(c_28532,plain,
( ( set_difference(cartesian_product2(relation_rng(sK5),relation_dom(sK5)),relation_inverse(sK5)) = subset_complement(cartesian_product2(relation_rng(sK5),relation_dom(sK5)),relation_inverse(sK5)) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21353,c_6703]) ).
tcf(c_28533,plain,
! [X0: $i,X1: $i] : set_difference(X0,relation_rng(relation_dom_restriction(identity_relation(X0),X1))) = subset_complement(X0,relation_rng(relation_dom_restriction(identity_relation(X0),X1))),
inference(superposition,[status(thm)],[c_21501,c_6703]) ).
tcf(c_28534,plain,
! [X0: $i] :
( ( set_difference(relation_dom(sK5),relation_rng(relation_dom_restriction(relation_inverse(sK5),X0))) = subset_complement(relation_dom(sK5),relation_rng(relation_dom_restriction(relation_inverse(sK5),X0))) )
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21494,c_6703]) ).
tcf(c_28535,plain,
! [X0: $i] : set_difference(relation_rng(sK5),set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)))) = subset_complement(relation_rng(sK5),set_difference(relation_inverse_image(relation_inverse(sK5),X0),set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)))),
inference(superposition,[status(thm)],[c_21887,c_6703]) ).
tcf(c_28536,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,relation_inverse_image(relation_inverse(sK5),X1)) = subset_complement(X0,relation_inverse_image(relation_inverse(sK5),X1)) )
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_22586,c_6703]) ).
tcf(c_28537,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,relation_image(relation_inverse(sK5),X1)) = subset_complement(X0,relation_image(relation_inverse(sK5),X1)) )
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_22588,c_6703]) ).
tcf(c_28538,plain,
set_difference(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))) = subset_complement(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27643,c_6703]) ).
tcf(c_28539,plain,
set_difference(relation_field(sK5),relation_dom(sK5)) = subset_complement(relation_field(sK5),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_27648,c_6703]) ).
tcf(c_28540,plain,
set_difference(relation_field(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))) = subset_complement(relation_field(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_27653,c_6703]) ).
tcf(c_28541,plain,
set_difference(relation_field(sK5),relation_rng(sK5)) = subset_complement(relation_field(sK5),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_27654,c_6703]) ).
tcf(c_28542,plain,
! [X0: $i] : subset_complement(X0,X0) = empty_set,
inference(light_normalisation,[status(thm)],[c_28508,c_4095]) ).
tcf(c_28543,plain,
! [X0: $i] : subset_complement(X0,empty_set) = X0,
inference(light_normalisation,[status(thm)],[c_28502,c_264]) ).
tcf(c_28546,plain,
set_difference(relation_dom(sK5),relation_rng(sK5)) = subset_complement(relation_field(sK5),relation_rng(sK5)),
inference(light_normalisation,[status(thm)],[c_28541,c_27644]) ).
tcf(c_28547,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(light_normalisation,[status(thm)],[c_28513,c_153]) ).
tcf(c_28550,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),X0) = set_difference(X1,X0),
inference(light_normalisation,[status(thm)],[c_28505,c_19594]) ).
tcf(c_28557,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),set_difference(X1,X0)) = set_difference(X0,set_difference(X1,X0)),
inference(light_normalisation,[status(thm)],[c_28512,c_19483]) ).
tcf(c_28797,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),X2)
| in(sK1(relation_rng(relation_rng_restriction(X1,X0)),X2),X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6708,c_76]) ).
tcf(c_28798,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ( set_difference(relation_rng(relation_rng_restriction(X1,X0)),unordered_pair(X2,X2)) = relation_rng(relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_195,c_76]) ).
tcf(c_28799,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(relation_rng_restriction(X1,X0)),X2)
| in(sK8(relation_rng(relation_rng_restriction(X1,X0)),X2),X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_149,c_76]) ).
tcf(c_28800,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X1,relation_rng(relation_rng_restriction(X2,X0)))
| in(sK8(X1,relation_rng(relation_rng_restriction(X2,X0))),X2)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_150,c_76]) ).
tcf(c_28801,plain,
! [X0: $i,X1: $i] :
( in(sK16(relation_rng(relation_rng_restriction(X1,X0))),X1)
| ( relation_rng(relation_rng_restriction(X1,X0)) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_233,c_76]) ).
tcf(c_28802,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),X2)
| in(sK18(relation_rng(relation_rng_restriction(X1,X0)),X2),X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_241,c_76]) ).
tcf(c_28803,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK27(relation_rng(relation_rng_restriction(X1,X2)),X0),X1)
| ~ relation(X2)
| ~ in(X0,union(relation_rng(relation_rng_restriction(X1,X2)))) ),
inference(superposition,[status(thm)],[c_297,c_76]) ).
tcf(c_28804,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng(relation_rng_restriction(X1,X0)))
| in(sK38(relation_rng(relation_rng_restriction(X1,X0))),X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_314,c_76]) ).
tcf(c_28805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK44(relation_rng(relation_rng_restriction(X1,X2)),X3,X0),X1)
| ~ relation(X2)
| ~ in(X0,cartesian_product2(relation_rng(relation_rng_restriction(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_323,c_76]) ).
tcf(c_28806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK45(X1,relation_rng(relation_rng_restriction(X2,X3)),X0),X2)
| ~ relation(X3)
| ~ in(X0,cartesian_product2(X1,relation_rng(relation_rng_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_324,c_76]) ).
tcf(c_28807,plain,
! [X0: $i,X1: $i] :
( empty(relation_rng(relation_rng_restriction(X1,X0)))
| in(sK23(relation_rng(relation_rng_restriction(X1,X0))),X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_20297,c_76]) ).
tcf(c_28808,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ relation(empty_set)
| ~ in(X0,relation_rng(empty_set)) ),
inference(superposition,[status(thm)],[c_19422,c_76]) ).
tcf(c_28809,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ relation(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_28808,c_187]) ).
tcf(c_28861,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1),X2)
| in(X0,sK2(X1))
| ~ subset(X0,sK1(sK2(X1),X2)) ),
inference(superposition,[status(thm)],[c_6708,c_87]) ).
tcf(c_28862,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X2))
| ( set_difference(sK2(X2),unordered_pair(X1,X1)) = sK2(X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_195,c_87]) ).
tcf(c_28863,plain,
! [X0: $i,X1: $i] :
( in(X0,sK2(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_86,c_87]) ).
tcf(c_28864,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(X1))
| ~ subset(X2,powerset(X0))
| ~ in(X0,sK2(X1)) ),
inference(superposition,[status(thm)],[c_88,c_87]) ).
tcf(c_28865,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(sK2(X1),X2)
| in(X0,sK2(X1))
| ~ subset(X0,sK8(sK2(X1),X2)) ),
inference(superposition,[status(thm)],[c_149,c_87]) ).
tcf(c_28866,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X1,sK2(X2))
| in(X0,sK2(X2))
| ~ subset(X0,sK8(X1,sK2(X2))) ),
inference(superposition,[status(thm)],[c_150,c_87]) ).
tcf(c_28867,plain,
! [X0: $i,X1: $i] :
( in(X0,sK2(X1))
| ( sK2(X1) = empty_set )
| ~ subset(X0,sK16(sK2(X1))) ),
inference(superposition,[status(thm)],[c_233,c_87]) ).
tcf(c_28868,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK2(X1),X2)
| in(X0,sK2(X1))
| ~ subset(X0,sK18(sK2(X1),X2)) ),
inference(superposition,[status(thm)],[c_241,c_87]) ).
tcf(c_28869,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X1))
| ~ in(X2,union(sK2(X1)))
| ~ subset(X0,sK27(sK2(X1),X2)) ),
inference(superposition,[status(thm)],[c_297,c_87]) ).
tcf(c_28870,plain,
! [X0: $i,X1: $i] :
( relation(sK2(X1))
| in(X0,sK2(X1))
| ~ subset(X0,sK38(sK2(X1))) ),
inference(superposition,[status(thm)],[c_314,c_87]) ).
tcf(c_28871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X1))
| ~ in(X3,cartesian_product2(sK2(X1),X2))
| ~ subset(X0,sK44(sK2(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_323,c_87]) ).
tcf(c_28872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X2))
| ~ in(X3,cartesian_product2(X1,sK2(X2)))
| ~ subset(X0,sK45(X1,sK2(X2),X3)) ),
inference(superposition,[status(thm)],[c_324,c_87]) ).
tcf(c_28873,plain,
! [X0: $i,X1: $i] :
( empty(sK2(X1))
| in(X0,sK2(X1))
| ~ subset(X0,sK23(sK2(X1))) ),
inference(superposition,[status(thm)],[c_20297,c_87]) ).
tcf(c_28876,plain,
! [X0: $i,X1: $i] :
( in(X0,sK2(X1))
| ~ subset(X0,sK23(sK2(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28873,c_19359]) ).
tcf(c_28948,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(unordered_pair(X2,X0),X1)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_351,c_142]) ).
tcf(c_28949,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X1,unordered_pair(X0,X2)) = subset_complement(X1,unordered_pair(X0,X2)) )
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_142,c_6703]) ).
tcf(c_28950,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_complement(X1,subset_complement(X1,unordered_pair(X0,X2))) = unordered_pair(X0,X2) )
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_142,c_6699]) ).
tcf(c_28951,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X1,X2) = X0 )
| ~ in(X2,X0)
| ~ in(X1,X0)
| ~ subset(X0,unordered_pair(X1,X2)) ),
inference(superposition,[status(thm)],[c_142,c_260]) ).
tcf(c_28952,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(unordered_pair(X0,X2),set_difference(unordered_pair(X0,X2),X1)) = unordered_pair(X0,X2) )
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_142,c_123]) ).
tcf(c_28953,plain,
! [X0: $i,X1: $i,X2: $i] :
( proper_subset(unordered_pair(X0,X2),X1)
| ( unordered_pair(X0,X2) = X1 )
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_142,c_468]) ).
tcf(c_28954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(unordered_pair(X0,X2),X3)
| ~ subset(X1,X3)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_142,c_110]) ).
tcf(c_28955,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(unordered_pair(X0,X2),X1) = empty_set )
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_142,c_138]) ).
tcf(c_28956,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(X0,X2),X1) = X1 )
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_142,c_85]) ).
tcf(c_28957,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ in(X1,X0)
| ~ proper_subset(X0,unordered_pair(X1,X2)) ),
inference(superposition,[status(thm)],[c_142,c_188]) ).
tcf(c_28958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(unordered_pair(X0,X2),X3)
| ~ disjoint(X1,X3)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_142,c_190]) ).
tcf(c_28965,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(unordered_pair(X0,X2),relation_rng(sK5)),empty_set)
| ~ in(X2,relation_inverse_image(relation_inverse(sK5),X1))
| ~ in(X0,relation_inverse_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_142,c_22779]) ).
tcf(c_28966,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(unordered_pair(X0,X2),relation_dom(sK5)),empty_set)
| ~ in(X2,relation_image(relation_inverse(sK5),X1))
| ~ in(X0,relation_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_142,c_22780]) ).
tcf(c_28967,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(unordered_pair(X0,X2),relation_dom(sK5)),empty_set)
| ~ in(X2,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_142,c_25182]) ).
tcf(c_29069,plain,
! [X0: $i,X1: $i] : set_difference(cartesian_product2(X0,empty_set),unordered_pair(X1,X1)) = cartesian_product2(X0,empty_set),
inference(superposition,[status(thm)],[c_195,c_27116]) ).
tcf(c_29070,plain,
! [X0: $i,X1: $i] : disjoint(cartesian_product2(X0,empty_set),X1),
inference(superposition,[status(thm)],[c_149,c_27116]) ).
tcf(c_29071,plain,
! [X0: $i,X1: $i] : disjoint(X0,cartesian_product2(X1,empty_set)),
inference(superposition,[status(thm)],[c_150,c_27116]) ).
tcf(c_29072,plain,
! [X0: $i] : cartesian_product2(X0,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_233,c_27116]) ).
tcf(c_29073,plain,
! [X0: $i,X1: $i] : subset(cartesian_product2(X0,empty_set),X1),
inference(superposition,[status(thm)],[c_241,c_27116]) ).
tcf(c_29074,plain,
! [X0: $i,X1: $i] : ~ in(X0,union(cartesian_product2(X1,empty_set))),
inference(superposition,[status(thm)],[c_297,c_27116]) ).
tcf(c_29075,plain,
! [X0: $i] : relation(cartesian_product2(X0,empty_set)),
inference(superposition,[status(thm)],[c_314,c_27116]) ).
tcf(c_29076,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(X0,cartesian_product2(cartesian_product2(X1,empty_set),X2)),
inference(superposition,[status(thm)],[c_323,c_27116]) ).
tcf(c_29077,plain,
! [X0: $i,X1: $i,X2: $i] : ~ in(X0,cartesian_product2(X1,cartesian_product2(X2,empty_set))),
inference(superposition,[status(thm)],[c_324,c_27116]) ).
tcf(c_29078,plain,
! [X0: $i] : empty(cartesian_product2(X0,empty_set)),
inference(superposition,[status(thm)],[c_20297,c_27116]) ).
tcf(c_29089,plain,
! [X0: $i] :
( subset(relation_dom(sK5),X0)
| in(sK1(relation_dom(sK5),X0),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_6708,c_27656]) ).
tcf(c_29090,plain,
! [X0: $i] :
( in(X0,relation_field(sK5))
| ( set_difference(relation_dom(sK5),unordered_pair(X0,X0)) = relation_dom(sK5) ) ),
inference(superposition,[status(thm)],[c_195,c_27656]) ).
tcf(c_29091,plain,
! [X0: $i] :
( disjoint(relation_dom(sK5),X0)
| in(sK8(relation_dom(sK5),X0),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_149,c_27656]) ).
tcf(c_29092,plain,
! [X0: $i] :
( disjoint(X0,relation_dom(sK5))
| in(sK8(X0,relation_dom(sK5)),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_150,c_27656]) ).
tcf(c_29093,plain,
( in(sK16(relation_dom(sK5)),relation_field(sK5))
| ( relation_dom(sK5) = empty_set ) ),
inference(superposition,[status(thm)],[c_233,c_27656]) ).
tcf(c_29094,plain,
! [X0: $i] :
( subset(relation_dom(sK5),X0)
| in(sK18(relation_dom(sK5),X0),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_241,c_27656]) ).
tcf(c_29095,plain,
! [X0: $i] :
( in(sK27(relation_dom(sK5),X0),relation_field(sK5))
| ~ in(X0,union(relation_dom(sK5))) ),
inference(superposition,[status(thm)],[c_297,c_27656]) ).
tcf(c_29096,plain,
( relation(relation_dom(sK5))
| in(sK38(relation_dom(sK5)),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_314,c_27656]) ).
tcf(c_29097,plain,
! [X0: $i,X1: $i] :
( in(sK44(relation_dom(sK5),X1,X0),relation_field(sK5))
| ~ in(X0,cartesian_product2(relation_dom(sK5),X1)) ),
inference(superposition,[status(thm)],[c_323,c_27656]) ).
tcf(c_29098,plain,
! [X0: $i,X1: $i] :
( in(sK45(X1,relation_dom(sK5),X0),relation_field(sK5))
| ~ in(X0,cartesian_product2(X1,relation_dom(sK5))) ),
inference(superposition,[status(thm)],[c_324,c_27656]) ).
tcf(c_29099,plain,
( empty(relation_dom(sK5))
| in(sK23(relation_dom(sK5)),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_20297,c_27656]) ).
tcf(c_29175,plain,
! [X0: $i] :
( subset(relation_rng(sK5),X0)
| in(sK1(relation_rng(sK5),X0),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_6708,c_27657]) ).
tcf(c_29176,plain,
! [X0: $i] :
( in(X0,relation_field(sK5))
| ( set_difference(relation_rng(sK5),unordered_pair(X0,X0)) = relation_rng(sK5) ) ),
inference(superposition,[status(thm)],[c_195,c_27657]) ).
tcf(c_29177,plain,
! [X0: $i] :
( disjoint(relation_rng(sK5),X0)
| in(sK8(relation_rng(sK5),X0),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_149,c_27657]) ).
tcf(c_29178,plain,
! [X0: $i] :
( disjoint(X0,relation_rng(sK5))
| in(sK8(X0,relation_rng(sK5)),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_150,c_27657]) ).
tcf(c_29179,plain,
( in(sK16(relation_rng(sK5)),relation_field(sK5))
| ( relation_rng(sK5) = empty_set ) ),
inference(superposition,[status(thm)],[c_233,c_27657]) ).
tcf(c_29180,plain,
! [X0: $i] :
( subset(relation_rng(sK5),X0)
| in(sK18(relation_rng(sK5),X0),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_241,c_27657]) ).
tcf(c_29181,plain,
! [X0: $i] :
( in(sK27(relation_rng(sK5),X0),relation_field(sK5))
| ~ in(X0,union(relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_297,c_27657]) ).
tcf(c_29182,plain,
( relation(relation_rng(sK5))
| in(sK38(relation_rng(sK5)),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_314,c_27657]) ).
tcf(c_29183,plain,
! [X0: $i,X1: $i] :
( in(sK44(relation_rng(sK5),X1,X0),relation_field(sK5))
| ~ in(X0,cartesian_product2(relation_rng(sK5),X1)) ),
inference(superposition,[status(thm)],[c_323,c_27657]) ).
tcf(c_29184,plain,
! [X0: $i,X1: $i] :
( in(sK45(X1,relation_rng(sK5),X0),relation_field(sK5))
| ~ in(X0,cartesian_product2(X1,relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_324,c_27657]) ).
tcf(c_29185,plain,
( empty(relation_rng(sK5))
| in(sK23(relation_rng(sK5)),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_20297,c_27657]) ).
tcf(c_29230,plain,
set_difference(relation_field(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))) = subset_complement(relation_field(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27631,c_6703]) ).
tcf(c_29231,plain,
subset_complement(relation_field(sK5),subset_complement(relation_field(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)))) = set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_27631,c_6699]) ).
tcf(c_29232,plain,
( ( set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)) = relation_field(sK5) )
| ~ subset(relation_field(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_27631,c_260]) ).
tcf(c_29233,plain,
set_difference(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),set_difference(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),relation_field(sK5))) = set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_27631,c_123]) ).
tcf(c_29234,plain,
( proper_subset(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),relation_field(sK5))
| ( set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_27631,c_468]) ).
tcf(c_29235,plain,
! [X0: $i] :
( subset(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),X0)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27631,c_110]) ).
tcf(c_29236,plain,
set_difference(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),relation_field(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_27631,c_138]) ).
tcf(c_29237,plain,
set_union2(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),relation_field(sK5)) = relation_field(sK5),
inference(superposition,[status(thm)],[c_27631,c_85]) ).
tcf(c_29238,plain,
~ proper_subset(relation_field(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27631,c_188]) ).
tcf(c_29239,plain,
! [X0: $i] :
( disjoint(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),X0)
| ~ disjoint(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27631,c_190]) ).
tcf(c_29272,plain,
( relation(relation_field(sK5))
| ~ empty(sK5)
| ~ relation(relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_360,c_27632]) ).
tcf(c_29331,plain,
set_difference(relation_field(sK5),set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5)))) = subset_complement(relation_field(sK5),set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5)))),
inference(superposition,[status(thm)],[c_27641,c_6703]) ).
tcf(c_29332,plain,
subset_complement(relation_field(sK5),subset_complement(relation_field(sK5),set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))))) = set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_27641,c_6699]) ).
tcf(c_29333,plain,
( ( set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))) = relation_field(sK5) )
| ~ subset(relation_field(sK5),set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5)))) ),
inference(superposition,[status(thm)],[c_27641,c_260]) ).
tcf(c_29334,plain,
set_difference(set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))),set_difference(set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))),relation_field(sK5))) = set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_27641,c_123]) ).
tcf(c_29335,plain,
( proper_subset(set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))),relation_field(sK5))
| ( set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_27641,c_468]) ).
tcf(c_29336,plain,
! [X0: $i] :
( subset(set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))),X0)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27641,c_110]) ).
tcf(c_29337,plain,
set_difference(set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))),relation_field(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_27641,c_138]) ).
tcf(c_29338,plain,
set_union2(set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))),relation_field(sK5)) = relation_field(sK5),
inference(superposition,[status(thm)],[c_27641,c_85]) ).
tcf(c_29339,plain,
~ proper_subset(relation_field(sK5),set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5)))),
inference(superposition,[status(thm)],[c_27641,c_188]) ).
tcf(c_29340,plain,
! [X0: $i] :
( disjoint(set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))),X0)
| ~ disjoint(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27641,c_190]) ).
tcf(c_29351,plain,
set_difference(relation_field(sK5),set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5)))) = subset_complement(relation_field(sK5),set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5)))),
inference(superposition,[status(thm)],[c_27651,c_6703]) ).
tcf(c_29352,plain,
subset_complement(relation_field(sK5),subset_complement(relation_field(sK5),set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))))) = set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27651,c_6699]) ).
tcf(c_29353,plain,
( ( set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))) = relation_field(sK5) )
| ~ subset(relation_field(sK5),set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_27651,c_260]) ).
tcf(c_29354,plain,
set_difference(set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),set_difference(set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),relation_field(sK5))) = set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27651,c_123]) ).
tcf(c_29355,plain,
( proper_subset(set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),relation_field(sK5))
| ( set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_27651,c_468]) ).
tcf(c_29356,plain,
! [X0: $i] :
( subset(set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),X0)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27651,c_110]) ).
tcf(c_29357,plain,
set_difference(set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),relation_field(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_27651,c_138]) ).
tcf(c_29358,plain,
set_union2(set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),relation_field(sK5)) = relation_field(sK5),
inference(superposition,[status(thm)],[c_27651,c_85]) ).
tcf(c_29359,plain,
~ proper_subset(relation_field(sK5),set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5)))),
inference(superposition,[status(thm)],[c_27651,c_188]) ).
tcf(c_29360,plain,
! [X0: $i] :
( disjoint(set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),X0)
| ~ disjoint(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27651,c_190]) ).
tcf(c_29381,plain,
set_difference(relation_field(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))) = subset_complement(relation_field(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_27652,c_6703]) ).
tcf(c_29382,plain,
subset_complement(relation_field(sK5),subset_complement(relation_field(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)))) = set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_27652,c_6699]) ).
tcf(c_29383,plain,
( ( set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)) = relation_field(sK5) )
| ~ subset(relation_field(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))) ),
inference(superposition,[status(thm)],[c_27652,c_260]) ).
tcf(c_29384,plain,
set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_field(sK5))) = set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_27652,c_123]) ).
tcf(c_29385,plain,
( proper_subset(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_field(sK5))
| ( set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_27652,c_468]) ).
tcf(c_29386,plain,
! [X0: $i] :
( subset(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),X0)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27652,c_110]) ).
tcf(c_29387,plain,
set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_field(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_27652,c_138]) ).
tcf(c_29388,plain,
set_union2(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_field(sK5)) = relation_field(sK5),
inference(superposition,[status(thm)],[c_27652,c_85]) ).
tcf(c_29389,plain,
~ proper_subset(relation_field(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_27652,c_188]) ).
tcf(c_29390,plain,
! [X0: $i] :
( disjoint(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),X0)
| ~ disjoint(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27652,c_190]) ).
tcf(c_29419,plain,
! [X0: $i] :
( subset(relation_dom(relation_dom_restriction(sK5,X0)),relation_dom(identity_relation(X0)))
| ~ relation(sK5)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25464,c_156]) ).
tcf(c_29420,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),relation_dom(identity_relation(X1)))
| ~ relation(identity_relation(X1))
| ~ relation(relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_25745,c_156]) ).
tcf(c_29421,plain,
( subset(relation_dom(empty_set),relation_dom(empty_set))
| ~ relation(sK5)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_28404,c_156]) ).
tcf(c_29422,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_composition(identity_relation(X0),X1)),X0)
| ~ relation(X1)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_203,c_156]) ).
tcf(c_29423,plain,
! [X0: $i] :
( subset(relation_dom(relation_composition(empty_set,X0)),empty_set)
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_186,c_156]) ).
tcf(c_29424,plain,
! [X0: $i] :
( subset(relation_dom(relation_composition(relation_inverse(sK5),X0)),relation_rng(sK5))
| ~ relation(X0)
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20946,c_156]) ).
tcf(c_29425,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_composition(relation_inverse(identity_relation(X0)),X1)),X0)
| ~ relation(X1)
| ~ relation(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_20961,c_156]) ).
tcf(c_29426,plain,
! [X0: $i] :
( subset(relation_dom(relation_composition(relation_inverse(sK47),X0)),relation_rng(sK47))
| ~ relation(X0)
| ~ relation(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_20951,c_156]) ).
tcf(c_29427,plain,
! [X0: $i] :
( subset(relation_dom(relation_composition(relation_inverse(sK75),X0)),relation_rng(sK75))
| ~ relation(X0)
| ~ relation(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_20957,c_156]) ).
tcf(c_29428,plain,
! [X0: $i] :
( subset(relation_dom(relation_composition(relation_inverse(sK79),X0)),relation_rng(sK79))
| ~ relation(X0)
| ~ relation(relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_20958,c_156]) ).
tcf(c_29429,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_composition(relation_inverse(relation_dom_restriction(sK5,X0)),X1)),relation_rng(relation_dom_restriction(sK5,X0)))
| ~ relation(X1)
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25748,c_156]) ).
tcf(c_29430,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom(X0),relation_dom(relation_composition(X0,X1))) = subset_complement(relation_dom(X0),relation_dom(relation_composition(X0,X1))) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_156,c_6703]) ).
tcf(c_29431,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(relation_dom(X0),subset_complement(relation_dom(X0),relation_dom(relation_composition(X0,X1)))) = relation_dom(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_156,c_6699]) ).
tcf(c_29432,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(X0,X1)) = relation_dom(X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_dom(relation_composition(X0,X1))) ),
inference(superposition,[status(thm)],[c_156,c_260]) ).
tcf(c_29433,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom(relation_composition(X0,X1)),set_difference(relation_dom(relation_composition(X0,X1)),relation_dom(X0))) = relation_dom(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_156,c_123]) ).
tcf(c_29434,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ( relation_dom(relation_composition(X0,X1)) = relation_dom(X0) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_156,c_468]) ).
tcf(c_29435,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(relation_composition(X0,X2)),X1)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_156,c_110]) ).
tcf(c_29436,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) = empty_set )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_156,c_138]) ).
tcf(c_29437,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) = relation_dom(X0) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_156,c_85]) ).
tcf(c_29438,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ relation(X0)
| ~ proper_subset(relation_dom(X0),relation_dom(relation_composition(X0,X1))) ),
inference(superposition,[status(thm)],[c_156,c_188]) ).
tcf(c_29439,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_dom(relation_composition(X0,X2)),X1)
| ~ relation(X2)
| ~ relation(X0)
| ~ disjoint(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_156,c_190]) ).
tcf(c_29440,plain,
( subset(empty_set,empty_set)
| ~ relation(sK5)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_29421,c_186]) ).
tcf(c_29441,plain,
! [X0: $i] :
( subset(relation_dom(relation_composition(empty_set,X0)),empty_set)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29423,c_231]) ).
tcf(c_29447,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_composition(identity_relation(X1),X0)),X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29422,c_422]) ).
tcf(c_29462,plain,
! [X0: $i] :
( subset(relation_dom(relation_dom_restriction(sK5,X0)),X0)
| ~ relation(sK5)
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_29419,c_203]) ).
tcf(c_29463,plain,
! [X0: $i] : subset(relation_dom(relation_dom_restriction(sK5,X0)),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_29462,c_96,c_422]) ).
tcf(c_29481,plain,
! [X0: $i,X1: $i] : subset(relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),relation_dom(identity_relation(X1))),
inference(forward_subsumption_resolution,[status(thm)],[c_29420,c_422,c_25741]) ).
tcf(c_29594,plain,
! [X0: $i] :
( subset(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5))
| ~ relation(sK5)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25464,c_157]) ).
tcf(c_29595,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),relation_rng(relation_dom_restriction(sK5,X0)))
| ~ relation(identity_relation(X1))
| ~ relation(relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_25745,c_157]) ).
tcf(c_29596,plain,
( subset(relation_rng(empty_set),relation_rng(sK5))
| ~ relation(sK5)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_28404,c_157]) ).
tcf(c_29597,plain,
! [X0: $i] :
( subset(relation_rng(relation_composition(X0,empty_set)),empty_set)
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_187,c_157]) ).
tcf(c_29598,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_composition(X1,identity_relation(X0))),X0)
| ~ relation(X1)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_204,c_157]) ).
tcf(c_29599,plain,
! [X0: $i] :
( subset(relation_rng(relation_composition(X0,relation_inverse(sK5))),relation_dom(sK5))
| ~ relation(X0)
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21123,c_157]) ).
tcf(c_29600,plain,
! [X0: $i] :
( subset(relation_rng(relation_composition(X0,relation_inverse(sK47))),relation_dom(sK47))
| ~ relation(X0)
| ~ relation(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_21128,c_157]) ).
tcf(c_29601,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_composition(X1,relation_inverse(identity_relation(X0)))),X0)
| ~ relation(X1)
| ~ relation(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_21138,c_157]) ).
tcf(c_29602,plain,
! [X0: $i] :
( subset(relation_rng(relation_composition(X0,relation_inverse(sK75))),relation_dom(sK75))
| ~ relation(X0)
| ~ relation(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_21134,c_157]) ).
tcf(c_29603,plain,
! [X0: $i] :
( subset(relation_rng(relation_composition(X0,relation_inverse(sK79))),relation_dom(sK79))
| ~ relation(X0)
| ~ relation(relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_21135,c_157]) ).
tcf(c_29604,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_composition(X1,relation_inverse(relation_dom_restriction(sK5,X0)))),relation_dom(relation_dom_restriction(sK5,X0)))
| ~ relation(X1)
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25747,c_157]) ).
tcf(c_29605,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(X1),relation_rng(relation_composition(X0,X1))) = subset_complement(relation_rng(X1),relation_rng(relation_composition(X0,X1))) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_157,c_6703]) ).
tcf(c_29606,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(relation_rng(X1),subset_complement(relation_rng(X1),relation_rng(relation_composition(X0,X1)))) = relation_rng(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_157,c_6699]) ).
tcf(c_29607,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X1,X0)) = relation_rng(X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_rng(X0),relation_rng(relation_composition(X1,X0))) ),
inference(superposition,[status(thm)],[c_157,c_260]) ).
tcf(c_29608,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_composition(X0,X1)),set_difference(relation_rng(relation_composition(X0,X1)),relation_rng(X1))) = relation_rng(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_157,c_123]) ).
tcf(c_29609,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ( relation_rng(relation_composition(X0,X1)) = relation_rng(X1) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_157,c_468]) ).
tcf(c_29610,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_composition(X2,X0)),X1)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_rng(X0),X1) ),
inference(superposition,[status(thm)],[c_157,c_110]) ).
tcf(c_29611,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) = empty_set )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_157,c_138]) ).
tcf(c_29612,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) = relation_rng(X1) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_157,c_85]) ).
tcf(c_29613,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ relation(X0)
| ~ proper_subset(relation_rng(X0),relation_rng(relation_composition(X1,X0))) ),
inference(superposition,[status(thm)],[c_157,c_188]) ).
tcf(c_29614,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(relation_composition(X2,X0)),X1)
| ~ relation(X2)
| ~ relation(X0)
| ~ disjoint(relation_rng(X0),X1) ),
inference(superposition,[status(thm)],[c_157,c_190]) ).
tcf(c_29615,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng(relation_composition(X1,relation_rng_restriction(X0,relation_inverse(sK5)))),relation_dom(sK5)),empty_set)
| ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,relation_inverse(sK5))) ),
inference(superposition,[status(thm)],[c_157,c_25182]) ).
tcf(c_29616,plain,
( subset(empty_set,relation_rng(sK5))
| ~ relation(sK5)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_29596,c_187]) ).
tcf(c_29617,plain,
! [X0: $i] :
( subset(relation_rng(relation_composition(X0,empty_set)),empty_set)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29597,c_231]) ).
tcf(c_29623,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_composition(X0,identity_relation(X1))),X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29598,c_422]) ).
tcf(c_29626,plain,
! [X0: $i] : subset(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5)),
inference(forward_subsumption_resolution,[status(thm)],[c_29594,c_96,c_422]) ).
tcf(c_29656,plain,
! [X0: $i,X1: $i] : subset(relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),relation_rng(relation_dom_restriction(sK5,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_29595,c_422,c_25741]) ).
tcf(c_29799,plain,
! [X0: $i] :
( ( identity_relation(X0) = empty_set )
| ~ relation(identity_relation(X0))
| ( X0 != empty_set ) ),
inference(superposition,[status(thm)],[c_203,c_191]) ).
tcf(c_29801,plain,
( ( relation_inverse(sK5) = empty_set )
| ~ relation(relation_inverse(sK5))
| ( relation_rng(sK5) != empty_set ) ),
inference(superposition,[status(thm)],[c_20946,c_191]) ).
tcf(c_29802,plain,
! [X0: $i] :
( ( relation_inverse(identity_relation(X0)) = empty_set )
| ~ relation(relation_inverse(identity_relation(X0)))
| ( X0 != empty_set ) ),
inference(superposition,[status(thm)],[c_20961,c_191]) ).
tcf(c_29803,plain,
( ( relation_inverse(sK47) = empty_set )
| ~ relation(relation_inverse(sK47))
| ( relation_rng(sK47) != empty_set ) ),
inference(superposition,[status(thm)],[c_20951,c_191]) ).
tcf(c_29804,plain,
( ( relation_inverse(sK75) = empty_set )
| ~ relation(relation_inverse(sK75))
| ( relation_rng(sK75) != empty_set ) ),
inference(superposition,[status(thm)],[c_20957,c_191]) ).
tcf(c_29805,plain,
( ( relation_inverse(sK79) = empty_set )
| ~ relation(relation_inverse(sK79))
| ( relation_rng(sK79) != empty_set ) ),
inference(superposition,[status(thm)],[c_20958,c_191]) ).
tcf(c_29806,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0)))
| ( relation_rng(relation_dom_restriction(sK5,X0)) != empty_set ) ),
inference(superposition,[status(thm)],[c_25748,c_191]) ).
tcf(c_29807,plain,
! [X0: $i] :
( ( identity_relation(X0) = empty_set )
| ( X0 != empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29799,c_422]) ).
tcf(c_29837,plain,
( ( relation_inverse(sK5) = empty_set )
| ~ relation(relation_inverse(sK5))
| ( relation_dom(sK5) != empty_set ) ),
inference(superposition,[status(thm)],[c_21123,c_192]) ).
tcf(c_29838,plain,
( ( relation_inverse(sK47) = empty_set )
| ~ relation(relation_inverse(sK47))
| ( relation_dom(sK47) != empty_set ) ),
inference(superposition,[status(thm)],[c_21128,c_192]) ).
tcf(c_29840,plain,
( ( relation_inverse(sK75) = empty_set )
| ~ relation(relation_inverse(sK75))
| ( relation_dom(sK75) != empty_set ) ),
inference(superposition,[status(thm)],[c_21134,c_192]) ).
tcf(c_29841,plain,
( ( relation_inverse(sK79) = empty_set )
| ~ relation(relation_inverse(sK79))
| ( relation_dom(sK79) != empty_set ) ),
inference(superposition,[status(thm)],[c_21135,c_192]) ).
tcf(c_29842,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0)))
| ( relation_dom(relation_dom_restriction(sK5,X0)) != empty_set ) ),
inference(superposition,[status(thm)],[c_25747,c_192]) ).
tcf(c_29860,plain,
relation_field(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_28218,c_27486]) ).
tcf(c_29861,plain,
! [X0: $i] : set_difference(X0,relation_dom(relation_dom_restriction(sK5,X0))) = subset_complement(X0,relation_dom(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_29463,c_6703]) ).
tcf(c_29862,plain,
! [X0: $i] : subset_complement(X0,subset_complement(X0,relation_dom(relation_dom_restriction(sK5,X0)))) = relation_dom(relation_dom_restriction(sK5,X0)),
inference(superposition,[status(thm)],[c_29463,c_6699]) ).
tcf(c_29863,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,X0)) = X0 )
| ~ subset(X0,relation_dom(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_29463,c_260]) ).
tcf(c_29864,plain,
! [X0: $i] : set_difference(relation_dom(relation_dom_restriction(sK5,X0)),set_difference(relation_dom(relation_dom_restriction(sK5,X0)),X0)) = relation_dom(relation_dom_restriction(sK5,X0)),
inference(superposition,[status(thm)],[c_29463,c_123]) ).
tcf(c_29865,plain,
! [X0: $i] :
( proper_subset(relation_dom(relation_dom_restriction(sK5,X0)),X0)
| ( relation_dom(relation_dom_restriction(sK5,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_29463,c_468]) ).
tcf(c_29866,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_dom_restriction(sK5,X0)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_29463,c_110]) ).
tcf(c_29867,plain,
! [X0: $i] : set_difference(relation_dom(relation_dom_restriction(sK5,X0)),X0) = empty_set,
inference(superposition,[status(thm)],[c_29463,c_138]) ).
tcf(c_29868,plain,
! [X0: $i] : set_union2(relation_dom(relation_dom_restriction(sK5,X0)),X0) = X0,
inference(superposition,[status(thm)],[c_29463,c_85]) ).
tcf(c_29869,plain,
! [X0: $i] : ~ proper_subset(X0,relation_dom(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_29463,c_188]) ).
tcf(c_29870,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_dom(relation_dom_restriction(sK5,X0)),X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_29463,c_190]) ).
tcf(c_29872,plain,
! [X0: $i] : subset(set_difference(relation_dom(relation_dom_restriction(sK5,relation_inverse_image(relation_inverse(sK5),X0))),relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_29463,c_22779]) ).
tcf(c_29873,plain,
! [X0: $i] : subset(set_difference(relation_dom(relation_dom_restriction(sK5,relation_image(relation_inverse(sK5),X0))),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_29463,c_22780]) ).
tcf(c_29874,plain,
! [X0: $i] : subset(set_difference(relation_dom(relation_dom_restriction(sK5,relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_29463,c_25182]) ).
tcf(c_29907,plain,
! [X0: $i] : set_difference(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0))) = subset_complement(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_29626,c_6703]) ).
tcf(c_29908,plain,
! [X0: $i] : subset_complement(relation_rng(sK5),subset_complement(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0)))) = relation_rng(relation_dom_restriction(sK5,X0)),
inference(superposition,[status(thm)],[c_29626,c_6699]) ).
tcf(c_29909,plain,
! [X0: $i] :
( ( relation_rng(relation_dom_restriction(sK5,X0)) = relation_rng(sK5) )
| ~ subset(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_29626,c_260]) ).
tcf(c_29910,plain,
! [X0: $i] : set_difference(relation_rng(relation_dom_restriction(sK5,X0)),set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5))) = relation_rng(relation_dom_restriction(sK5,X0)),
inference(superposition,[status(thm)],[c_29626,c_123]) ).
tcf(c_29911,plain,
! [X0: $i] :
( proper_subset(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5))
| ( relation_rng(relation_dom_restriction(sK5,X0)) = relation_rng(sK5) ) ),
inference(superposition,[status(thm)],[c_29626,c_468]) ).
tcf(c_29912,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_dom_restriction(sK5,X1)),X0)
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29626,c_110]) ).
tcf(c_29913,plain,
! [X0: $i] : set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_29626,c_138]) ).
tcf(c_29914,plain,
! [X0: $i] : set_union2(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5)) = relation_rng(sK5),
inference(superposition,[status(thm)],[c_29626,c_85]) ).
tcf(c_29915,plain,
! [X0: $i] : ~ proper_subset(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_29626,c_188]) ).
tcf(c_29916,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_rng(relation_dom_restriction(sK5,X1)),X0)
| ~ disjoint(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29626,c_190]) ).
tcf(c_29957,plain,
! [X0: $i] : subset(set_difference(empty_set,set_difference(X0,empty_set)),set_union2(X0,relation_dom(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29867,c_20651]) ).
tcf(c_29959,plain,
! [X0: $i] :
( relation(set_difference(relation_dom(relation_dom_restriction(sK5,X0)),empty_set))
| ~ relation(X0)
| ~ relation(relation_dom(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_29867,c_364]) ).
tcf(c_29960,plain,
! [X0: $i] :
( disjoint(relation_dom(relation_dom_restriction(sK5,X0)),X0)
| ( set_difference(relation_dom(relation_dom_restriction(sK5,X0)),empty_set) != empty_set ) ),
inference(superposition,[status(thm)],[c_29867,c_257]) ).
tcf(c_29961,plain,
! [X0: $i] :
( disjoint(relation_dom(relation_dom_restriction(sK5,X0)),X0)
| in(sK9(relation_dom(relation_dom_restriction(sK5,X0)),X0),set_difference(relation_dom(relation_dom_restriction(sK5,X0)),empty_set)) ),
inference(superposition,[status(thm)],[c_29867,c_165]) ).
tcf(c_29962,plain,
! [X0: $i] : subset(set_difference(empty_set,X0),set_union2(relation_dom(relation_dom_restriction(sK5,X0)),X0)),
inference(superposition,[status(thm)],[c_29867,c_20247]) ).
tcf(c_29963,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,X0),X0),set_union2(X0,relation_dom(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29867,c_20244]) ).
tcf(c_29964,plain,
! [X0: $i] :
( disjoint(relation_dom(relation_dom_restriction(sK5,X0)),X0)
| ( relation_dom(relation_dom_restriction(sK5,X0)) != empty_set ) ),
inference(superposition,[status(thm)],[c_29867,c_210]) ).
tcf(c_29966,plain,
! [X0: $i] : ~ proper_subset(set_union2(relation_dom(relation_dom_restriction(sK5,X0)),X0),empty_set),
inference(superposition,[status(thm)],[c_29867,c_19484]) ).
tcf(c_29967,plain,
! [X0: $i] : subset(set_difference(empty_set,X0),set_union2(X0,relation_dom(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29867,c_19715]) ).
tcf(c_29968,plain,
! [X0: $i] : subset(empty_set,set_union2(X0,relation_dom(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29867,c_19593]) ).
tcf(c_29969,plain,
! [X0: $i] : subset(empty_set,set_union2(relation_dom(relation_dom_restriction(sK5,X0)),X0)),
inference(superposition,[status(thm)],[c_29867,c_19485]) ).
tcf(c_29970,plain,
! [X0: $i] : ~ proper_subset(relation_dom(relation_dom_restriction(sK5,X0)),empty_set),
inference(superposition,[status(thm)],[c_29867,c_19457]) ).
tcf(c_29971,plain,
! [X0: $i] : subset(empty_set,relation_dom(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_29867,c_135]) ).
tcf(c_29972,plain,
! [X0: $i,X1: $i] :
( in(X0,empty_set)
| in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_29867,c_268]) ).
tcf(c_29973,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(relation_dom(relation_dom_restriction(sK5,X1)),X1)
| ~ in(X0,set_difference(relation_dom(relation_dom_restriction(sK5,X1)),empty_set)) ),
inference(superposition,[status(thm)],[c_29867,c_166]) ).
tcf(c_29974,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(relation_dom(relation_dom_restriction(sK5,X1)),empty_set)) ),
inference(superposition,[status(thm)],[c_29867,c_370]) ).
tcf(c_29975,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,X1),empty_set)
| ~ subset(X0,relation_dom(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_29867,c_127]) ).
tcf(c_29978,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X1,X0))
| ~ subset(relation_dom(relation_dom_restriction(sK5,X0)),X1) ),
inference(superposition,[status(thm)],[c_29867,c_127]) ).
tcf(c_29979,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,relation_dom(relation_dom_restriction(sK5,X0)))) = set_difference(relation_dom(relation_dom_restriction(sK5,X0)),empty_set),
inference(superposition,[status(thm)],[c_29867,c_371]) ).
tcf(c_29980,plain,
! [X0: $i] : subset(set_difference(X0,set_difference(empty_set,X0)),set_union2(relation_dom(relation_dom_restriction(sK5,X0)),X0)),
inference(superposition,[status(thm)],[c_29867,c_20485]) ).
tcf(c_29981,plain,
! [X0: $i] : subset(set_difference(X0,set_difference(set_difference(empty_set,X0),X0)),set_union2(X0,relation_dom(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29867,c_20482]) ).
tcf(c_29982,plain,
! [X0: $i] : subset(set_difference(X0,empty_set),set_union2(relation_dom(relation_dom_restriction(sK5,X0)),X0)),
inference(superposition,[status(thm)],[c_29867,c_19744]) ).
tcf(c_29983,plain,
! [X0: $i] : subset(set_difference(X0,set_difference(empty_set,X0)),set_union2(X0,relation_dom(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29867,c_19741]) ).
tcf(c_29984,plain,
! [X0: $i] : subset(set_difference(X0,empty_set),set_union2(X0,relation_dom(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29867,c_19566]) ).
tcf(c_29985,plain,
! [X0: $i] : set_union2(X0,relation_dom(relation_dom_restriction(sK5,X0))) = set_union2(X0,empty_set),
inference(superposition,[status(thm)],[c_29867,c_145]) ).
tcf(c_29989,plain,
! [X0: $i] : subset(X0,set_union2(X0,relation_dom(relation_dom_restriction(sK5,X0)))),
inference(light_normalisation,[status(thm)],[c_29984,c_264]) ).
tcf(c_29993,plain,
! [X0: $i] : set_union2(X0,relation_dom(relation_dom_restriction(sK5,X0))) = X0,
inference(light_normalisation,[status(thm)],[c_29985,c_244]) ).
tcf(c_30002,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(sK5,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29972,c_234]) ).
tcf(c_30033,plain,
! [X0: $i,X1: $i] : subset(relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),X1),
inference(demodulation,[status(thm)],[c_29481,c_203]) ).
tcf(c_30034,plain,
! [X0: $i,X1: $i] : set_difference(X0,relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X1),X0))) = subset_complement(X0,relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X1),X0))),
inference(superposition,[status(thm)],[c_30033,c_6703]) ).
tcf(c_30035,plain,
! [X0: $i,X1: $i] : subset_complement(X0,subset_complement(X0,relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X1),X0)))) = relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X1),X0)),
inference(superposition,[status(thm)],[c_30033,c_6699]) ).
tcf(c_30036,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X1),X0)) = X0 )
| ~ subset(X0,relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X1),X0))) ),
inference(superposition,[status(thm)],[c_30033,c_260]) ).
tcf(c_30037,plain,
! [X0: $i,X1: $i] : set_difference(relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),set_difference(relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),X1)) = relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),
inference(superposition,[status(thm)],[c_30033,c_123]) ).
tcf(c_30038,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),X1)
| ( relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_30033,c_468]) ).
tcf(c_30039,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X2),X0)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_30033,c_110]) ).
tcf(c_30040,plain,
! [X0: $i,X1: $i] : set_difference(relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),X1) = empty_set,
inference(superposition,[status(thm)],[c_30033,c_138]) ).
tcf(c_30041,plain,
! [X0: $i,X1: $i] : set_union2(relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),X1) = X1,
inference(superposition,[status(thm)],[c_30033,c_85]) ).
tcf(c_30042,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X1),X0))),
inference(superposition,[status(thm)],[c_30033,c_188]) ).
tcf(c_30043,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X2),X0)),X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_30033,c_190]) ).
tcf(c_30044,plain,
! [X0: $i] : relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_30033,c_152]) ).
tcf(c_30045,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),relation_inverse_image(relation_inverse(sK5),X1))),relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_30033,c_22779]) ).
tcf(c_30046,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),relation_image(relation_inverse(sK5),X1))),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_30033,c_22780]) ).
tcf(c_30047,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))))),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_30033,c_25182]) ).
tcf(c_30231,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,relation_dom(relation_dom_restriction(sK5,X0))) = subset_complement(X1,relation_dom(relation_dom_restriction(sK5,X0))) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_29866,c_6703]) ).
tcf(c_30232,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,relation_dom(relation_dom_restriction(sK5,X0)))) = relation_dom(relation_dom_restriction(sK5,X0)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_29866,c_6699]) ).
tcf(c_30233,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom_restriction(sK5,X1)) = X0 )
| ~ subset(X1,X0)
| ~ subset(X0,relation_dom(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_29866,c_260]) ).
tcf(c_30234,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom(relation_dom_restriction(sK5,X0)),set_difference(relation_dom(relation_dom_restriction(sK5,X0)),X1)) = relation_dom(relation_dom_restriction(sK5,X0)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_29866,c_123]) ).
tcf(c_30235,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_dom(relation_dom_restriction(sK5,X0)),X1)
| ( relation_dom(relation_dom_restriction(sK5,X0)) = X1 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_29866,c_468]) ).
tcf(c_30236,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(relation_dom_restriction(sK5,X0)),X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_29866,c_110]) ).
tcf(c_30237,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom(relation_dom_restriction(sK5,X0)),X1) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_29866,c_138]) ).
tcf(c_30238,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_dom(relation_dom_restriction(sK5,X0)),X1) = X1 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_29866,c_85]) ).
tcf(c_30239,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ proper_subset(X0,relation_dom(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_29866,c_188]) ).
tcf(c_30240,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_dom(relation_dom_restriction(sK5,X2)),X1)
| ~ subset(X2,X0)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_29866,c_190]) ).
tcf(c_30241,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_29866,c_152]) ).
tcf(c_30242,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_dom(relation_dom_restriction(sK5,X0)),relation_rng(sK5)),empty_set)
| ~ subset(X0,relation_inverse_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_29866,c_22779]) ).
tcf(c_30243,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_dom(relation_dom_restriction(sK5,X0)),relation_dom(sK5)),empty_set)
| ~ subset(X0,relation_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_29866,c_22780]) ).
tcf(c_30244,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_dom(relation_dom_restriction(sK5,X0)),relation_dom(sK5)),empty_set)
| ~ subset(X0,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_29866,c_25182]) ).
tcf(c_30286,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(X0,empty_set),empty_set),empty_set),set_union2(empty_set,X0)),
inference(superposition,[status(thm)],[c_264,c_22118]) ).
tcf(c_30290,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),X1),set_union2(X1,set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_153,c_22118]) ).
tcf(c_30293,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(empty_set,X0),X0),X0),set_union2(X0,X0)),
inference(superposition,[status(thm)],[c_4095,c_22118]) ).
tcf(c_30294,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(set_difference(X0,set_difference(X0,X1)),set_difference(X1,X0)),set_difference(X1,X0)),set_difference(X1,X0)),set_union2(set_difference(X1,X0),X1)),
inference(superposition,[status(thm)],[c_371,c_22118]) ).
tcf(c_30295,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(empty_set,relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),set_union2(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_21834,c_22118]) ).
tcf(c_30296,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),set_union2(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22079,c_22118]) ).
tcf(c_30297,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),set_union2(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),
inference(superposition,[status(thm)],[c_25056,c_22118]) ).
tcf(c_30298,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(empty_set,X0),X0),X0),set_union2(X0,relation_dom(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29867,c_22118]) ).
tcf(c_30300,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),X1),X1),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_145,c_22118]) ).
tcf(c_30301,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(set_difference(empty_set,X0),X0),X0),X0),X0),
inference(superposition,[status(thm)],[c_244,c_22118]) ).
tcf(c_30302,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(set_difference(X0,X0),X0),X0),X0),X0),
inference(superposition,[status(thm)],[c_245,c_22118]) ).
tcf(c_30303,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),X1),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_255,c_22118]) ).
tcf(c_30304,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(set_difference(X0,empty_set),empty_set),empty_set),empty_set),X0),
inference(superposition,[status(thm)],[c_19599,c_22118]) ).
tcf(c_30305,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_22118]) ).
tcf(c_30306,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_22118]) ).
tcf(c_30307,plain,
subset(set_difference(set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_22118]) ).
tcf(c_30308,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(set_difference(set_difference(set_difference(X1,X0),X0),X0),X0)) = subset_complement(set_union2(X0,X1),set_difference(set_difference(set_difference(set_difference(X1,X0),X0),X0),X0)),
inference(superposition,[status(thm)],[c_22118,c_6703]) ).
tcf(c_30309,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),set_difference(set_difference(set_difference(set_difference(X1,X0),X0),X0),X0))) = set_difference(set_difference(set_difference(set_difference(X1,X0),X0),X0),X0),
inference(superposition,[status(thm)],[c_22118,c_6699]) ).
tcf(c_30310,plain,
! [X0: $i,X1: $i] :
( ( set_difference(set_difference(set_difference(set_difference(X1,X0),X0),X0),X0) = set_union2(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(set_difference(set_difference(set_difference(X1,X0),X0),X0),X0)) ),
inference(superposition,[status(thm)],[c_22118,c_260]) ).
tcf(c_30311,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),X1),set_difference(set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),X1),set_union2(X1,X0))) = set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),X1),
inference(superposition,[status(thm)],[c_22118,c_123]) ).
tcf(c_30312,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),X1),set_union2(X1,X0))
| ( set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),X1) = set_union2(X1,X0) ) ),
inference(superposition,[status(thm)],[c_22118,c_468]) ).
tcf(c_30313,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(set_difference(set_difference(X1,X0),X0),X0),X0),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_22118,c_110]) ).
tcf(c_30314,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),X1),set_union2(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_22118,c_138]) ).
tcf(c_30315,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),X1),set_union2(X1,X0)) = set_union2(X1,X0),
inference(superposition,[status(thm)],[c_22118,c_85]) ).
tcf(c_30316,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(set_difference(set_difference(set_difference(X1,X0),X0),X0),X0)),
inference(superposition,[status(thm)],[c_22118,c_188]) ).
tcf(c_30317,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(set_difference(set_difference(set_difference(X1,X0),X0),X0),X0),X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_22118,c_190]) ).
tcf(c_30328,plain,
subset(set_difference(set_difference(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),
inference(light_normalisation,[status(thm)],[c_30296,c_22341]) ).
tcf(c_30329,plain,
subset(set_difference(set_difference(set_difference(empty_set,relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),
inference(light_normalisation,[status(thm)],[c_30295,c_21870]) ).
tcf(c_30332,plain,
subset(set_difference(set_difference(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),set_union2(relation_dom(sK5),empty_set)),
inference(light_normalisation,[status(thm)],[c_30297,c_25189]) ).
tcf(c_30414,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,set_union2(X0,unordered_pair(X1,X1)))
| ( set_union2(X0,unordered_pair(X1,X1)) != set_difference(X0,unordered_pair(X1,X1)) ) ),
inference(superposition,[status(thm)],[c_153,c_196]) ).
tcf(c_30417,plain,
! [X0: $i] :
( ~ in(X0,relation_dom(relation_dom_restriction(sK5,unordered_pair(X0,X0))))
| ( relation_dom(relation_dom_restriction(sK5,unordered_pair(X0,X0))) != empty_set ) ),
inference(superposition,[status(thm)],[c_29867,c_196]) ).
tcf(c_30418,plain,
! [X0: $i] :
( ~ in(empty_set,X0)
| ( set_difference(X0,powerset(empty_set)) != X0 ) ),
inference(superposition,[status(thm)],[c_111,c_196]) ).
tcf(c_30423,plain,
! [X0: $i,X1: $i] : set_union2(X0,unordered_pair(X1,X1)) != set_difference(X0,unordered_pair(X1,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_30414,c_19974]) ).
tcf(c_30432,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(relation_dom_restriction(X0,X1)),X2)
| in(sK1(relation_dom(relation_dom_restriction(X0,X1)),X2),X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6708,c_213]) ).
tcf(c_30433,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ( set_difference(relation_dom(relation_dom_restriction(X0,X1)),unordered_pair(X2,X2)) = relation_dom(relation_dom_restriction(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_195,c_213]) ).
tcf(c_30434,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_dom(relation_dom_restriction(X0,X1)),X2)
| in(sK8(relation_dom(relation_dom_restriction(X0,X1)),X2),X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_149,c_213]) ).
tcf(c_30435,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(sK8(X1,relation_dom(relation_dom_restriction(X0,X2))),X2)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_150,c_213]) ).
tcf(c_30436,plain,
! [X0: $i,X1: $i] :
( in(sK16(relation_dom(relation_dom_restriction(X0,X1))),X1)
| ( relation_dom(relation_dom_restriction(X0,X1)) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_233,c_213]) ).
tcf(c_30437,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(relation_dom_restriction(X0,X1)),X2)
| in(sK18(relation_dom(relation_dom_restriction(X0,X1)),X2),X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_241,c_213]) ).
tcf(c_30438,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK27(relation_dom(relation_dom_restriction(X1,X2)),X0),X2)
| ~ relation(X1)
| ~ in(X0,union(relation_dom(relation_dom_restriction(X1,X2)))) ),
inference(superposition,[status(thm)],[c_297,c_213]) ).
tcf(c_30439,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom(relation_dom_restriction(X0,X1)))
| in(sK38(relation_dom(relation_dom_restriction(X0,X1))),X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_314,c_213]) ).
tcf(c_30440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK44(relation_dom(relation_dom_restriction(X1,X2)),X3,X0),X2)
| ~ relation(X1)
| ~ in(X0,cartesian_product2(relation_dom(relation_dom_restriction(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_323,c_213]) ).
tcf(c_30441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK45(X1,relation_dom(relation_dom_restriction(X2,X3)),X0),X3)
| ~ relation(X2)
| ~ in(X0,cartesian_product2(X1,relation_dom(relation_dom_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_324,c_213]) ).
tcf(c_30442,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom(relation_dom_restriction(X0,X1)))
| in(sK23(relation_dom(relation_dom_restriction(X0,X1))),X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_20297,c_213]) ).
tcf(c_30443,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ relation(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_19477,c_213]) ).
tcf(c_30527,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_union2(X1,X0),X2)
| ~ subset(X1,X2)
| ~ subset(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_145,c_219]) ).
tcf(c_30530,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_union2(X2,X0),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_255,c_219]) ).
tcf(c_30534,plain,
! [X0: $i] :
( subset(relation_field(sK5),X0)
| ~ subset(relation_rng(sK5),X0)
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_27464,c_219]) ).
tcf(c_30535,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X1,set_union2(X0,X2)) = subset_complement(X1,set_union2(X0,X2)) )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_219,c_6703]) ).
tcf(c_30536,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_complement(X1,subset_complement(X1,set_union2(X0,X2))) = set_union2(X0,X2) )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_219,c_6699]) ).
tcf(c_30537,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X1,X2) = X0 )
| ~ subset(X2,X0)
| ~ subset(X1,X0)
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_219,c_260]) ).
tcf(c_30538,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_union2(X0,X2),set_difference(set_union2(X0,X2),X1)) = set_union2(X0,X2) )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_219,c_123]) ).
tcf(c_30539,plain,
! [X0: $i,X1: $i,X2: $i] :
( proper_subset(set_union2(X0,X2),X1)
| ( set_union2(X0,X2) = X1 )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_219,c_468]) ).
tcf(c_30540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_union2(X0,X3),X2)
| ~ subset(X3,X1)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_219,c_110]) ).
tcf(c_30541,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_union2(X0,X2),X1) = empty_set )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_219,c_138]) ).
tcf(c_30542,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(set_union2(X0,X2),X1) = X1 )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_219,c_85]) ).
tcf(c_30543,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X2,X0)
| ~ subset(X1,X0)
| ~ proper_subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_219,c_188]) ).
tcf(c_30544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(set_union2(X2,X3),X1)
| ~ subset(X3,X0)
| ~ subset(X2,X0)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_219,c_190]) ).
tcf(c_30545,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = empty_set )
| ~ subset(X1,empty_set)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_219,c_152]) ).
tcf(c_30546,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_union2(X0,X2),relation_rng(sK5)),empty_set)
| ~ subset(X2,relation_inverse_image(relation_inverse(sK5),X1))
| ~ subset(X0,relation_inverse_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_219,c_22779]) ).
tcf(c_30547,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_union2(X0,X2),relation_dom(sK5)),empty_set)
| ~ subset(X2,relation_image(relation_inverse(sK5),X1))
| ~ subset(X0,relation_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_219,c_22780]) ).
tcf(c_30548,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_union2(X0,X2),relation_dom(sK5)),empty_set)
| ~ subset(X2,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))))
| ~ subset(X0,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_219,c_25182]) ).
tcf(c_30641,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( unordered_pair(X0,X0) != powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_111,c_220]) ).
tcf(c_30642,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
inference(superposition,[status(thm)],[c_351,c_220]) ).
tcf(c_30654,plain,
! [X0: $i] :
( in(X0,empty_set)
| ~ relation(sK5)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_28288,c_213]) ).
tcf(c_30656,plain,
( subset(relation_rng(empty_set),relation_rng(sK5))
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_28288,c_224]) ).
tcf(c_30657,plain,
( subset(empty_set,sK5)
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_28288,c_215]) ).
tcf(c_30659,plain,
! [X0: $i] :
( subset(relation_dom(empty_set),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_28288,c_29866]) ).
tcf(c_30660,plain,
! [X0: $i] : subset(relation_dom(relation_dom_restriction(empty_set,X0)),X0),
inference(superposition,[status(thm)],[c_28288,c_30033]) ).
tcf(c_30661,plain,
set_difference(relation_dom(empty_set),empty_set) = empty_set,
inference(superposition,[status(thm)],[c_28288,c_29867]) ).
tcf(c_30662,plain,
~ proper_subset(relation_rng(sK5),relation_rng(empty_set)),
inference(superposition,[status(thm)],[c_28288,c_29915]) ).
tcf(c_30663,plain,
~ proper_subset(empty_set,relation_dom(empty_set)),
inference(superposition,[status(thm)],[c_28288,c_29869]) ).
tcf(c_30664,plain,
subset(relation_rng(empty_set),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_28288,c_29626]) ).
tcf(c_30665,plain,
subset(relation_dom(empty_set),empty_set),
inference(superposition,[status(thm)],[c_28288,c_29463]) ).
tcf(c_30666,plain,
! [X0: $i] : relation(relation_dom_restriction(empty_set,X0)),
inference(superposition,[status(thm)],[c_28288,c_26788]) ).
tcf(c_30674,plain,
! [X0: $i] :
( empty(relation_dom_restriction(empty_set,X0))
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_28288,c_26776]) ).
tcf(c_30680,plain,
~ proper_subset(relation_rng(sK5),empty_set),
inference(light_normalisation,[status(thm)],[c_30662,c_187]) ).
tcf(c_30683,plain,
! [X0: $i] :
( empty(empty_set)
| ~ empty(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_30674,c_19477]) ).
tcf(c_30685,plain,
( subset(empty_set,relation_rng(sK5))
| ~ relation(sK5) ),
inference(light_normalisation,[status(thm)],[c_30656,c_187]) ).
tcf(c_30689,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,cartesian_product2(X1,empty_set))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_29072,c_81]) ).
tcf(c_30690,plain,
! [X0: $i,X1: $i] :
( subset(cartesian_product2(X0,empty_set),empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_29072,c_81]) ).
tcf(c_30691,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,cartesian_product2(X1,X0))
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_29072,c_82]) ).
tcf(c_30692,plain,
! [X0: $i,X1: $i] :
( subset(cartesian_product2(X1,X0),empty_set)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_29072,c_82]) ).
tcf(c_30703,plain,
! [X0: $i] :
( disjoint(relation_dom(empty_set),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_28288,c_29870]) ).
tcf(c_30704,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom(relation_dom_restriction(sK5,X0)),set_difference(relation_dom(relation_dom_restriction(sK5,X0)),X1)) = empty_set )
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_29870,c_258]) ).
tcf(c_30705,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom(relation_dom_restriction(sK5,X0)),X1) = relation_dom(relation_dom_restriction(sK5,X0)) )
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_29870,c_211]) ).
tcf(c_30706,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,relation_dom(relation_dom_restriction(sK5,X0)))
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_29870,c_256]) ).
tcf(c_30717,plain,
set_difference(relation_rng(empty_set),relation_rng(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_28288,c_29913]) ).
tcf(c_30718,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(empty_set,relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),set_union2(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29913,c_22118]) ).
tcf(c_30719,plain,
! [X0: $i] : subset(set_difference(empty_set,set_difference(relation_rng(sK5),empty_set)),set_union2(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29913,c_20651]) ).
tcf(c_30721,plain,
! [X0: $i] :
( relation(set_difference(relation_rng(relation_dom_restriction(sK5,X0)),empty_set))
| ~ relation(relation_rng(sK5))
| ~ relation(relation_rng(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_29913,c_364]) ).
tcf(c_30722,plain,
! [X0: $i] :
( disjoint(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5))
| ( set_difference(relation_rng(relation_dom_restriction(sK5,X0)),empty_set) != empty_set ) ),
inference(superposition,[status(thm)],[c_29913,c_257]) ).
tcf(c_30723,plain,
! [X0: $i] :
( disjoint(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5))
| in(sK9(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5)),set_difference(relation_rng(relation_dom_restriction(sK5,X0)),empty_set)) ),
inference(superposition,[status(thm)],[c_29913,c_165]) ).
tcf(c_30724,plain,
! [X0: $i] : subset(set_difference(empty_set,relation_rng(sK5)),set_union2(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_29913,c_20247]) ).
tcf(c_30725,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,relation_rng(sK5)),relation_rng(sK5)),set_union2(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29913,c_20244]) ).
tcf(c_30726,plain,
! [X0: $i] :
( disjoint(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5))
| ( relation_rng(relation_dom_restriction(sK5,X0)) != empty_set ) ),
inference(superposition,[status(thm)],[c_29913,c_210]) ).
tcf(c_30728,plain,
! [X0: $i] : ~ proper_subset(set_union2(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_29913,c_19484]) ).
tcf(c_30729,plain,
! [X0: $i] : subset(set_difference(empty_set,relation_rng(sK5)),set_union2(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29913,c_19715]) ).
tcf(c_30730,plain,
! [X0: $i] : subset(empty_set,set_union2(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29913,c_19593]) ).
tcf(c_30731,plain,
! [X0: $i] : subset(empty_set,set_union2(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_29913,c_19485]) ).
tcf(c_30732,plain,
! [X0: $i] : ~ proper_subset(relation_rng(relation_dom_restriction(sK5,X0)),empty_set),
inference(superposition,[status(thm)],[c_29913,c_19457]) ).
tcf(c_30733,plain,
! [X0: $i] : subset(empty_set,relation_rng(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_29913,c_135]) ).
tcf(c_30734,plain,
! [X0: $i,X1: $i] :
( in(X0,empty_set)
| in(X0,relation_rng(sK5))
| ~ in(X0,relation_rng(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_29913,c_268]) ).
tcf(c_30735,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(relation_rng(relation_dom_restriction(sK5,X1)),relation_rng(sK5))
| ~ in(X0,set_difference(relation_rng(relation_dom_restriction(sK5,X1)),empty_set)) ),
inference(superposition,[status(thm)],[c_29913,c_166]) ).
tcf(c_30736,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(sK5))
| ~ in(X0,set_difference(relation_rng(relation_dom_restriction(sK5,X1)),empty_set)) ),
inference(superposition,[status(thm)],[c_29913,c_370]) ).
tcf(c_30737,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,relation_rng(sK5)),empty_set)
| ~ subset(X0,relation_rng(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_29913,c_127]) ).
tcf(c_30740,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X1,relation_rng(sK5)))
| ~ subset(relation_rng(relation_dom_restriction(sK5,X0)),X1) ),
inference(superposition,[status(thm)],[c_29913,c_127]) ).
tcf(c_30741,plain,
! [X0: $i] : set_difference(relation_rng(sK5),set_difference(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0)))) = set_difference(relation_rng(relation_dom_restriction(sK5,X0)),empty_set),
inference(superposition,[status(thm)],[c_29913,c_371]) ).
tcf(c_30742,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),set_difference(empty_set,relation_rng(sK5))),set_union2(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_29913,c_20485]) ).
tcf(c_30743,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),set_difference(set_difference(empty_set,relation_rng(sK5)),relation_rng(sK5))),set_union2(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29913,c_20482]) ).
tcf(c_30744,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),empty_set),set_union2(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_29913,c_19744]) ).
tcf(c_30745,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),set_difference(empty_set,relation_rng(sK5))),set_union2(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29913,c_19741]) ).
tcf(c_30746,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),empty_set),set_union2(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29913,c_19566]) ).
tcf(c_30747,plain,
! [X0: $i] : set_union2(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0))) = set_union2(relation_rng(sK5),empty_set),
inference(superposition,[status(thm)],[c_29913,c_145]) ).
tcf(c_30748,plain,
set_difference(empty_set,relation_rng(sK5)) = empty_set,
inference(light_normalisation,[status(thm)],[c_30717,c_187]) ).
tcf(c_30757,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(sK5))
| ~ in(X0,relation_rng(relation_dom_restriction(sK5,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30734,c_234]) ).
tcf(c_30850,plain,
! [X0: $i] : subset(relation_rng(relation_dom_restriction(empty_set,X0)),relation_rng(empty_set)),
inference(superposition,[status(thm)],[c_28288,c_29656]) ).
tcf(c_30852,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))) = subset_complement(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))),
inference(superposition,[status(thm)],[c_29656,c_6703]) ).
tcf(c_30853,plain,
! [X0: $i,X1: $i] : subset_complement(relation_rng(relation_dom_restriction(sK5,X0)),subset_complement(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)))) = relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),
inference(superposition,[status(thm)],[c_29656,c_6699]) ).
tcf(c_30854,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)) = relation_rng(relation_dom_restriction(sK5,X0)) )
| ~ subset(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))) ),
inference(superposition,[status(thm)],[c_29656,c_260]) ).
tcf(c_30855,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),set_difference(relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),relation_rng(relation_dom_restriction(sK5,X0)))) = relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),
inference(superposition,[status(thm)],[c_29656,c_123]) ).
tcf(c_30856,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),relation_rng(relation_dom_restriction(sK5,X0)))
| ( relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)) = relation_rng(relation_dom_restriction(sK5,X0)) ) ),
inference(superposition,[status(thm)],[c_29656,c_468]) ).
tcf(c_30857,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X2)),X1)
| ~ subset(relation_rng(relation_dom_restriction(sK5,X0)),X1) ),
inference(superposition,[status(thm)],[c_29656,c_110]) ).
tcf(c_30858,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),relation_rng(relation_dom_restriction(sK5,X0))) = empty_set,
inference(superposition,[status(thm)],[c_29656,c_138]) ).
tcf(c_30859,plain,
! [X0: $i,X1: $i] : set_union2(relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),relation_rng(relation_dom_restriction(sK5,X0))) = relation_rng(relation_dom_restriction(sK5,X0)),
inference(superposition,[status(thm)],[c_29656,c_85]) ).
tcf(c_30860,plain,
! [X0: $i,X1: $i] : ~ proper_subset(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))),
inference(superposition,[status(thm)],[c_29656,c_188]) ).
tcf(c_30861,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X2)),X1)
| ~ disjoint(relation_rng(relation_dom_restriction(sK5,X0)),X1) ),
inference(superposition,[status(thm)],[c_29656,c_190]) ).
tcf(c_30922,plain,
! [X0: $i] :
( subset(relation_rng(empty_set),X0)
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_28288,c_29912]) ).
tcf(c_30923,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,relation_rng(relation_dom_restriction(sK5,X1))) = subset_complement(X0,relation_rng(relation_dom_restriction(sK5,X1))) )
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29912,c_6703]) ).
tcf(c_30924,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X0,subset_complement(X0,relation_rng(relation_dom_restriction(sK5,X1)))) = relation_rng(relation_dom_restriction(sK5,X1)) )
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29912,c_6699]) ).
tcf(c_30925,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom_restriction(sK5,X1)) = X0 )
| ~ subset(relation_rng(sK5),X0)
| ~ subset(X0,relation_rng(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_29912,c_260]) ).
tcf(c_30926,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_dom_restriction(sK5,X1)),set_difference(relation_rng(relation_dom_restriction(sK5,X1)),X0)) = relation_rng(relation_dom_restriction(sK5,X1)) )
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29912,c_123]) ).
tcf(c_30927,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_rng(relation_dom_restriction(sK5,X1)),X0)
| ( relation_rng(relation_dom_restriction(sK5,X1)) = X0 )
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29912,c_468]) ).
tcf(c_30928,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_dom_restriction(sK5,X2)),X1)
| ~ subset(X0,X1)
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29912,c_110]) ).
tcf(c_30929,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_dom_restriction(sK5,X1)),X0) = empty_set )
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29912,c_138]) ).
tcf(c_30930,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_rng(relation_dom_restriction(sK5,X1)),X0) = X0 )
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29912,c_85]) ).
tcf(c_30931,plain,
! [X0: $i,X1: $i] :
( ~ subset(relation_rng(sK5),X0)
| ~ proper_subset(X0,relation_rng(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_29912,c_188]) ).
tcf(c_30932,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(relation_dom_restriction(sK5,X2)),X1)
| ~ disjoint(X0,X1)
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29912,c_190]) ).
tcf(c_30933,plain,
! [X0: $i] :
( ( relation_rng(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ subset(relation_rng(sK5),empty_set) ),
inference(superposition,[status(thm)],[c_29912,c_152]) ).
tcf(c_30934,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng(relation_dom_restriction(sK5,X1)),relation_rng(sK5)),empty_set)
| ~ subset(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_29912,c_22779]) ).
tcf(c_30935,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng(relation_dom_restriction(sK5,X1)),relation_dom(sK5)),empty_set)
| ~ subset(relation_rng(sK5),relation_image(relation_inverse(sK5),X0)) ),
inference(superposition,[status(thm)],[c_29912,c_22780]) ).
tcf(c_30936,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng(relation_dom_restriction(sK5,X1)),relation_dom(sK5)),empty_set)
| ~ subset(relation_rng(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_29912,c_25182]) ).
tcf(c_30937,plain,
! [X0: $i] :
( subset(empty_set,X0)
| ~ subset(relation_rng(sK5),X0) ),
inference(light_normalisation,[status(thm)],[c_30922,c_187]) ).
tcf(c_31005,plain,
! [X0: $i] :
( disjoint(relation_rng(empty_set),X0)
| ~ disjoint(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_28288,c_29916]) ).
tcf(c_31006,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_dom_restriction(sK5,X1)),set_difference(relation_rng(relation_dom_restriction(sK5,X1)),X0)) = empty_set )
| ~ disjoint(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29916,c_258]) ).
tcf(c_31007,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_dom_restriction(sK5,X1)),X0) = relation_rng(relation_dom_restriction(sK5,X1)) )
| ~ disjoint(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29916,c_211]) ).
tcf(c_31008,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,relation_rng(relation_dom_restriction(sK5,X1)))
| ~ disjoint(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29916,c_256]) ).
tcf(c_31009,plain,
! [X0: $i] :
( disjoint(empty_set,X0)
| ~ disjoint(relation_rng(sK5),X0) ),
inference(light_normalisation,[status(thm)],[c_31005,c_187]) ).
tcf(c_31027,plain,
subset(set_difference(set_difference(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),set_union2(relation_rng(sK5),relation_field(sK5))),
inference(superposition,[status(thm)],[c_27644,c_22118]) ).
tcf(c_31028,plain,
subset(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5)))),set_union2(relation_rng(sK5),relation_field(sK5))),
inference(superposition,[status(thm)],[c_27644,c_20651]) ).
tcf(c_31030,plain,
( relation(set_difference(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))))
| ~ relation(relation_field(sK5))
| ~ relation(relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_27644,c_364]) ).
tcf(c_31031,plain,
( disjoint(relation_field(sK5),relation_rng(sK5))
| ( set_difference(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))) != empty_set ) ),
inference(superposition,[status(thm)],[c_27644,c_257]) ).
tcf(c_31032,plain,
( disjoint(relation_field(sK5),relation_rng(sK5))
| in(sK9(relation_field(sK5),relation_rng(sK5)),set_difference(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_27644,c_165]) ).
tcf(c_31033,plain,
subset(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),set_union2(relation_field(sK5),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27644,c_20247]) ).
tcf(c_31034,plain,
subset(set_difference(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),set_union2(relation_rng(sK5),relation_field(sK5))),
inference(superposition,[status(thm)],[c_27644,c_20244]) ).
tcf(c_31035,plain,
( disjoint(relation_field(sK5),relation_rng(sK5))
| ( set_difference(relation_dom(sK5),relation_rng(sK5)) != relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_27644,c_210]) ).
tcf(c_31036,plain,
( subset(relation_field(sK5),relation_rng(sK5))
| ( set_difference(relation_dom(sK5),relation_rng(sK5)) != empty_set ) ),
inference(superposition,[status(thm)],[c_27644,c_139]) ).
tcf(c_31037,plain,
~ proper_subset(set_union2(relation_field(sK5),relation_rng(sK5)),set_difference(relation_dom(sK5),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27644,c_19484]) ).
tcf(c_31038,plain,
subset(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),set_union2(relation_rng(sK5),relation_field(sK5))),
inference(superposition,[status(thm)],[c_27644,c_19715]) ).
tcf(c_31039,plain,
subset(set_difference(relation_dom(sK5),relation_rng(sK5)),set_union2(relation_rng(sK5),relation_field(sK5))),
inference(superposition,[status(thm)],[c_27644,c_19593]) ).
tcf(c_31040,plain,
subset(set_difference(relation_dom(sK5),relation_rng(sK5)),set_union2(relation_field(sK5),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27644,c_19485]) ).
tcf(c_31043,plain,
! [X0: $i] :
( in(X0,relation_rng(sK5))
| in(X0,set_difference(relation_dom(sK5),relation_rng(sK5)))
| ~ in(X0,relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_27644,c_268]) ).
tcf(c_31044,plain,
! [X0: $i] :
( ~ disjoint(relation_field(sK5),relation_rng(sK5))
| ~ in(X0,set_difference(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_27644,c_166]) ).
tcf(c_31045,plain,
! [X0: $i] :
( in(X0,relation_rng(sK5))
| ~ in(X0,set_difference(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_27644,c_370]) ).
tcf(c_31046,plain,
! [X0: $i] :
( subset(set_difference(X0,relation_rng(sK5)),set_difference(relation_dom(sK5),relation_rng(sK5)))
| ~ subset(X0,relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_27644,c_127]) ).
tcf(c_31047,plain,
! [X0: $i] :
( ~ in(X0,relation_rng(sK5))
| ~ in(X0,set_difference(relation_dom(sK5),relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_27644,c_270]) ).
tcf(c_31048,plain,
! [X0: $i] :
( in(X0,relation_field(sK5))
| ~ in(X0,set_difference(relation_dom(sK5),relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_27644,c_269]) ).
tcf(c_31049,plain,
! [X0: $i] :
( subset(set_difference(relation_dom(sK5),relation_rng(sK5)),set_difference(X0,relation_rng(sK5)))
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27644,c_127]) ).
tcf(c_31050,plain,
set_difference(relation_rng(sK5),set_difference(relation_rng(sK5),relation_field(sK5))) = set_difference(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27644,c_371]) ).
tcf(c_31051,plain,
subset(set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))),set_union2(relation_field(sK5),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27644,c_20485]) ).
tcf(c_31052,plain,
subset(set_difference(relation_rng(sK5),set_difference(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5))),set_union2(relation_rng(sK5),relation_field(sK5))),
inference(superposition,[status(thm)],[c_27644,c_20482]) ).
tcf(c_31053,plain,
subset(set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),set_union2(relation_field(sK5),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27644,c_19744]) ).
tcf(c_31054,plain,
subset(set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))),set_union2(relation_rng(sK5),relation_field(sK5))),
inference(superposition,[status(thm)],[c_27644,c_19741]) ).
tcf(c_31055,plain,
subset(set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),set_union2(relation_rng(sK5),relation_field(sK5))),
inference(superposition,[status(thm)],[c_27644,c_19566]) ).
tcf(c_31056,plain,
set_union2(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))) = set_union2(relation_rng(sK5),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27644,c_145]) ).
tcf(c_31066,plain,
set_union2(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))) = relation_field(sK5),
inference(light_normalisation,[status(thm)],[c_31056,c_27806]) ).
tcf(c_31081,plain,
subset(set_difference(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),relation_field(sK5)),
inference(light_normalisation,[status(thm)],[c_31034,c_27806]) ).
tcf(c_31087,plain,
set_difference(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))) = relation_rng(sK5),
inference(light_normalisation,[status(thm)],[c_31050,c_27802]) ).
tcf(c_31090,plain,
subset(set_difference(relation_rng(sK5),set_difference(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5))),relation_field(sK5)),
inference(light_normalisation,[status(thm)],[c_31052,c_27806]) ).
tcf(c_31091,plain,
subset(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5)))),relation_field(sK5)),
inference(light_normalisation,[status(thm)],[c_31028,c_27806]) ).
tcf(c_31092,plain,
subset(set_difference(set_difference(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),relation_field(sK5)),
inference(light_normalisation,[status(thm)],[c_31027,c_27806]) ).
tcf(c_31283,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_dom(relation_dom_restriction(sK5,relation_inverse_image(relation_inverse(sK5),X1))),relation_rng(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_29872,c_110]) ).
tcf(c_31287,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(relation_dom(relation_dom_restriction(sK5,relation_inverse_image(relation_inverse(sK5),X1))),relation_rng(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_29872,c_190]) ).
tcf(c_31290,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_dom(relation_dom_restriction(sK5,relation_inverse_image(relation_inverse(sK5),X0))),relation_rng(sK5)),X1),
inference(forward_subsumption_resolution,[status(thm)],[c_31283,c_124]) ).
tcf(c_31291,plain,
! [X0: $i] : subset(set_difference(set_difference(X0,empty_set),empty_set),set_union2(X0,empty_set)),
inference(superposition,[status(thm)],[c_264,c_22121]) ).
tcf(c_31294,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_union2(set_union2(X0,X1),X1)),
inference(superposition,[status(thm)],[c_153,c_22121]) ).
tcf(c_31298,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(X0,set_difference(X0,X1)),set_difference(X1,X0)),set_difference(X1,X0)),set_union2(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_371,c_22121]) ).
tcf(c_31299,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,relation_rng(sK5)),relation_rng(sK5)),set_union2(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_21834,c_22121]) ).
tcf(c_31300,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5)),set_union2(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_22079,c_22121]) ).
tcf(c_31301,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,relation_dom(sK5)),relation_dom(sK5)),set_union2(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_25056,c_22121]) ).
tcf(c_31302,plain,
subset(set_difference(set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)),relation_rng(sK5)),set_union2(relation_field(sK5),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27644,c_22121]) ).
tcf(c_31303,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,X0),X0),set_union2(relation_dom(relation_dom_restriction(sK5,X0)),X0)),
inference(superposition,[status(thm)],[c_29867,c_22121]) ).
tcf(c_31304,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,relation_rng(sK5)),relation_rng(sK5)),set_union2(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_29913,c_22121]) ).
tcf(c_31306,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),set_difference(X1,X0)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_145,c_22121]) ).
tcf(c_31311,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_22121]) ).
tcf(c_31312,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_22121]) ).
tcf(c_31314,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(set_difference(set_difference(X0,X1),X1),X1)) = subset_complement(set_union2(X0,X1),set_difference(set_difference(set_difference(X0,X1),X1),X1)),
inference(superposition,[status(thm)],[c_22121,c_6703]) ).
tcf(c_31315,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),set_difference(set_difference(set_difference(X0,X1),X1),X1))) = set_difference(set_difference(set_difference(X0,X1),X1),X1),
inference(superposition,[status(thm)],[c_22121,c_6699]) ).
tcf(c_31316,plain,
! [X0: $i,X1: $i] :
( ( set_difference(set_difference(set_difference(X0,X1),X1),X1) = set_union2(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(set_difference(set_difference(X0,X1),X1),X1)) ),
inference(superposition,[status(thm)],[c_22121,c_260]) ).
tcf(c_31317,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_union2(X0,X1))) = set_difference(set_difference(set_difference(X0,X1),X1),X1),
inference(superposition,[status(thm)],[c_22121,c_123]) ).
tcf(c_31318,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_union2(X0,X1))
| ( set_difference(set_difference(set_difference(X0,X1),X1),X1) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_22121,c_468]) ).
tcf(c_31319,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(set_difference(X0,X1),X1),X1),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_22121,c_110]) ).
tcf(c_31320,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_22121,c_138]) ).
tcf(c_31321,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(set_difference(set_difference(X0,X1),X1),X1),set_union2(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_22121,c_85]) ).
tcf(c_31322,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(set_difference(set_difference(X0,X1),X1),X1)),
inference(superposition,[status(thm)],[c_22121,c_188]) ).
tcf(c_31323,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(set_difference(set_difference(X0,X1),X1),X1),X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_22121,c_190]) ).
tcf(c_31373,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( unordered_pair(X0,X1) != powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_111,c_226]) ).
tcf(c_31452,plain,
! [X0: $i,X1: $i] :
( ( union_of_subsets(X1,X0) = union(X0) )
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_273,c_291]) ).
tcf(c_31453,plain,
! [X0: $i] :
( empty(powerset(X0))
| ( union_of_subsets(X0,sK22(powerset(X0))) = union(sK22(powerset(X0))) ) ),
inference(superposition,[status(thm)],[c_279,c_291]) ).
tcf(c_31454,plain,
! [X0: $i] : union_of_subsets(X0,sK23(powerset(powerset(X0)))) = union(sK23(powerset(powerset(X0)))),
inference(superposition,[status(thm)],[c_281,c_291]) ).
tcf(c_31455,plain,
! [X0: $i,X1: $i] :
( ( union_of_subsets(X0,X1) = union(X1) )
| ~ empty(X1)
| ~ empty(powerset(powerset(X0))) ),
inference(superposition,[status(thm)],[c_284,c_291]) ).
tcf(c_31456,plain,
! [X0: $i,X1: $i] :
( ( union_of_subsets(X1,subset_complement(powerset(X1),X0)) = union(subset_complement(powerset(X1),X0)) )
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_6701,c_291]) ).
tcf(c_31457,plain,
! [X0: $i,X1: $i] :
( ( union_of_subsets(X1,union_of_subsets(powerset(X1),X0)) = union(union_of_subsets(powerset(X1),X0)) )
| ~ element(X0,powerset(powerset(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_452,c_291]) ).
tcf(c_31458,plain,
! [X0: $i,X1: $i] :
( ( union_of_subsets(X1,meet_of_subsets(powerset(X1),X0)) = union(meet_of_subsets(powerset(X1),X0)) )
| ~ element(X0,powerset(powerset(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_453,c_291]) ).
tcf(c_31459,plain,
! [X0: $i] : union_of_subsets(X0,powerset(X0)) = union(powerset(X0)),
inference(superposition,[status(thm)],[c_4010,c_291]) ).
tcf(c_31460,plain,
! [X0: $i] : union_of_subsets(X0,empty_set) = union(empty_set),
inference(superposition,[status(thm)],[c_19225,c_291]) ).
tcf(c_31461,plain,
! [X0: $i] :
( relation(powerset(powerset(X0)))
| ( union_of_subsets(X0,sK38(powerset(powerset(X0)))) = union(sK38(powerset(powerset(X0)))) ) ),
inference(superposition,[status(thm)],[c_19315,c_291]) ).
tcf(c_31462,plain,
! [X0: $i,X1: $i] :
( disjoint(powerset(powerset(X0)),X1)
| ( union_of_subsets(X0,sK8(powerset(powerset(X0)),X1)) = union(sK8(powerset(powerset(X0)),X1)) ) ),
inference(superposition,[status(thm)],[c_19396,c_291]) ).
tcf(c_31463,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,powerset(powerset(X0)))
| ( union_of_subsets(X0,sK8(X1,powerset(powerset(X0)))) = union(sK8(X1,powerset(powerset(X0)))) ) ),
inference(superposition,[status(thm)],[c_19408,c_291]) ).
tcf(c_31464,plain,
! [X0: $i] : union_of_subsets(X0,empty_set) = empty_set,
inference(light_normalisation,[status(thm)],[c_31460,c_21789]) ).
tcf(c_31465,plain,
! [X0: $i] : union_of_subsets(X0,powerset(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_31459,c_225]) ).
tcf(c_31468,plain,
! [X0: $i] : union_of_subsets(X0,sK22(powerset(X0))) = union(sK22(powerset(X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_31453,c_286]) ).
tcf(c_31498,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK54(X1),X2)
| in(X0,sK54(X1))
| ~ subset(X0,sK1(sK54(X1),X2)) ),
inference(superposition,[status(thm)],[c_6708,c_373]) ).
tcf(c_31499,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK54(X2))
| ( set_difference(sK54(X2),unordered_pair(X1,X1)) = sK54(X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_195,c_373]) ).
tcf(c_31500,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(sK54(X1),X2)
| in(X0,sK54(X1))
| ~ subset(X0,sK8(sK54(X1),X2)) ),
inference(superposition,[status(thm)],[c_149,c_373]) ).
tcf(c_31501,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X1,sK54(X2))
| in(X0,sK54(X2))
| ~ subset(X0,sK8(X1,sK54(X2))) ),
inference(superposition,[status(thm)],[c_150,c_373]) ).
tcf(c_31502,plain,
! [X0: $i,X1: $i] :
( in(X0,sK54(X1))
| ( sK54(X1) = empty_set )
| ~ subset(X0,sK16(sK54(X1))) ),
inference(superposition,[status(thm)],[c_233,c_373]) ).
tcf(c_31503,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK54(X1),X2)
| in(X0,sK54(X1))
| ~ subset(X0,sK18(sK54(X1),X2)) ),
inference(superposition,[status(thm)],[c_241,c_373]) ).
tcf(c_31504,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK54(X1))
| ~ in(X2,union(sK54(X1)))
| ~ subset(X0,sK27(sK54(X1),X2)) ),
inference(superposition,[status(thm)],[c_297,c_373]) ).
tcf(c_31505,plain,
! [X0: $i,X1: $i] :
( relation(sK54(X1))
| in(X0,sK54(X1))
| ~ subset(X0,sK38(sK54(X1))) ),
inference(superposition,[status(thm)],[c_314,c_373]) ).
tcf(c_31506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK54(X1))
| ~ in(X3,cartesian_product2(sK54(X1),X2))
| ~ subset(X0,sK44(sK54(X1),X2,X3)) ),
inference(superposition,[status(thm)],[c_323,c_373]) ).
tcf(c_31507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK54(X2))
| ~ in(X3,cartesian_product2(X1,sK54(X2)))
| ~ subset(X0,sK45(X1,sK54(X2),X3)) ),
inference(superposition,[status(thm)],[c_324,c_373]) ).
tcf(c_31508,plain,
! [X0: $i,X1: $i] :
( in(X0,sK54(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_372,c_373]) ).
tcf(c_31509,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK54(X1))
| ~ in(X2,sK54(X1))
| ~ subset(X0,sK55(X1,X2)) ),
inference(superposition,[status(thm)],[c_374,c_373]) ).
tcf(c_31510,plain,
! [X0: $i,X1: $i] :
( empty(sK54(X1))
| in(X0,sK54(X1))
| ~ subset(X0,sK23(sK54(X1))) ),
inference(superposition,[status(thm)],[c_20297,c_373]) ).
tcf(c_31513,plain,
! [X0: $i,X1: $i] :
( in(X0,sK54(X1))
| ~ subset(X0,sK23(sK54(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31510,c_19363]) ).
tcf(c_31581,plain,
! [X0: $i,X1: $i] :
( subset(complements_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(superposition,[status(thm)],[c_449,c_274]) ).
tcf(c_31582,plain,
! [X0: $i,X1: $i] :
( ( union_of_subsets(X1,complements_of_subsets(X1,X0)) = union(complements_of_subsets(X1,X0)) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(superposition,[status(thm)],[c_449,c_291]) ).
tcf(c_31583,plain,
! [X0: $i,X1: $i] :
( empty(complements_of_subsets(X1,X0))
| ~ empty(powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(superposition,[status(thm)],[c_449,c_285]) ).
tcf(c_31584,plain,
! [X0: $i,X1: $i] :
( empty(powerset(powerset(X1)))
| in(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(superposition,[status(thm)],[c_449,c_283]) ).
tcf(c_31587,plain,
! [X0: $i,X1: $i] :
( in(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31584,c_286]) ).
tcf(c_31600,plain,
( empty(relation_rng(sK75))
| ~ empty(sK75) ),
inference(superposition,[status(thm)],[c_432,c_22275]) ).
tcf(c_31614,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_dom(relation_dom_restriction(sK5,relation_image(relation_inverse(sK5),X1))),relation_dom(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_29873,c_110]) ).
tcf(c_31618,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(relation_dom(relation_dom_restriction(sK5,relation_image(relation_inverse(sK5),X1))),relation_dom(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_29873,c_190]) ).
tcf(c_31621,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_dom(relation_dom_restriction(sK5,relation_image(relation_inverse(sK5),X0))),relation_dom(sK5)),X1),
inference(forward_subsumption_resolution,[status(thm)],[c_31614,c_124]) ).
tcf(c_31628,plain,
! [X0: $i] :
( subset(relation_field(sK5),X0)
| in(sK1(relation_field(sK5),X0),relation_rng(sK5))
| in(sK1(relation_field(sK5),X0),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_6708,c_27655]) ).
tcf(c_31629,plain,
! [X0: $i] :
( in(X0,relation_rng(sK5))
| in(X0,relation_dom(sK5))
| ( set_difference(relation_field(sK5),unordered_pair(X0,X0)) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_195,c_27655]) ).
tcf(c_31630,plain,
! [X0: $i] :
( disjoint(relation_field(sK5),X0)
| in(sK8(relation_field(sK5),X0),relation_rng(sK5))
| in(sK8(relation_field(sK5),X0),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_149,c_27655]) ).
tcf(c_31631,plain,
! [X0: $i] :
( disjoint(X0,relation_field(sK5))
| in(sK8(X0,relation_field(sK5)),relation_rng(sK5))
| in(sK8(X0,relation_field(sK5)),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_150,c_27655]) ).
tcf(c_31632,plain,
( in(sK16(relation_field(sK5)),relation_rng(sK5))
| in(sK16(relation_field(sK5)),relation_dom(sK5))
| ( relation_field(sK5) = empty_set ) ),
inference(superposition,[status(thm)],[c_233,c_27655]) ).
tcf(c_31633,plain,
! [X0: $i] :
( subset(relation_field(sK5),X0)
| in(sK18(relation_field(sK5),X0),relation_rng(sK5))
| in(sK18(relation_field(sK5),X0),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_241,c_27655]) ).
tcf(c_31634,plain,
! [X0: $i] :
( in(sK27(relation_field(sK5),X0),relation_rng(sK5))
| in(sK27(relation_field(sK5),X0),relation_dom(sK5))
| ~ in(X0,union(relation_field(sK5))) ),
inference(superposition,[status(thm)],[c_297,c_27655]) ).
tcf(c_31635,plain,
( relation(relation_field(sK5))
| in(sK38(relation_field(sK5)),relation_rng(sK5))
| in(sK38(relation_field(sK5)),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_314,c_27655]) ).
tcf(c_31636,plain,
! [X0: $i,X1: $i] :
( in(sK44(relation_field(sK5),X1,X0),relation_rng(sK5))
| in(sK44(relation_field(sK5),X1,X0),relation_dom(sK5))
| ~ in(X0,cartesian_product2(relation_field(sK5),X1)) ),
inference(superposition,[status(thm)],[c_323,c_27655]) ).
tcf(c_31637,plain,
! [X0: $i,X1: $i] :
( in(sK45(X1,relation_field(sK5),X0),relation_rng(sK5))
| in(sK45(X1,relation_field(sK5),X0),relation_dom(sK5))
| ~ in(X0,cartesian_product2(X1,relation_field(sK5))) ),
inference(superposition,[status(thm)],[c_324,c_27655]) ).
tcf(c_31638,plain,
( empty(relation_field(sK5))
| in(sK23(relation_field(sK5)),relation_rng(sK5))
| in(sK23(relation_field(sK5)),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_20297,c_27655]) ).
tcf(c_31686,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,X0)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29865,c_19555]) ).
tcf(c_31721,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_dom(relation_dom_restriction(sK5,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))))),relation_dom(sK5)),X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_29874,c_110]) ).
tcf(c_31725,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(relation_dom(relation_dom_restriction(sK5,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))))),relation_dom(sK5)),X0)
| ~ disjoint(empty_set,X0) ),
inference(superposition,[status(thm)],[c_29874,c_190]) ).
tcf(c_31728,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_dom(relation_dom_restriction(sK5,relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),relation_dom(sK5)),X1),
inference(forward_subsumption_resolution,[status(thm)],[c_31721,c_124]) ).
tcf(c_31729,plain,
! [X0: $i] : set_union2(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))) = relation_dom(sK5),
inference(demodulation,[status(thm)],[c_25189,c_244]) ).
tcf(c_31730,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_31729,c_22121]) ).
tcf(c_31731,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),set_difference(set_difference(set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_31729,c_20482]) ).
tcf(c_31732,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_31729,c_20247]) ).
tcf(c_31734,plain,
! [X0: $i] : ~ proper_subset(relation_dom(sK5),set_difference(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),
inference(superposition,[status(thm)],[c_31729,c_19484]) ).
tcf(c_31735,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)),relation_dom(sK5))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_31729,c_19741]) ).
tcf(c_31736,plain,
! [X0: $i] : ~ in(powerset(relation_dom(sK5)),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),
inference(superposition,[status(thm)],[c_31729,c_20137]) ).
tcf(c_31737,plain,
! [X0: $i] : ~ in(sK54(relation_dom(sK5)),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),
inference(superposition,[status(thm)],[c_31729,c_20134]) ).
tcf(c_31738,plain,
! [X0: $i] : ~ in(sK2(relation_dom(sK5)),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),
inference(superposition,[status(thm)],[c_31729,c_20131]) ).
tcf(c_31742,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_31729,c_19566]) ).
tcf(c_31744,plain,
! [X0: $i] : subset(set_difference(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_31729,c_19485]) ).
tcf(c_31747,plain,
! [X0: $i] :
( empty(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))
| ~ empty(relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_31729,c_246]) ).
tcf(c_31750,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_31729,c_22118]) ).
tcf(c_31751,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)),set_difference(relation_dom(sK5),set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_31729,c_20651]) ).
tcf(c_31752,plain,
! [X0: $i] : subset(set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),set_difference(set_difference(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_31729,c_20485]) ).
tcf(c_31753,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_31729,c_20244]) ).
tcf(c_31754,plain,
! [X0: $i] : subset(set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),set_difference(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_31729,c_19744]) ).
tcf(c_31755,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_31729,c_19715]) ).
tcf(c_31756,plain,
! [X0: $i] : subset(set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_31729,c_19593]) ).
tcf(c_31789,plain,
! [X0: $i] :
( subset(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(sK5,X0)))
| ~ relation(relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_25746,c_94]) ).
tcf(c_31815,plain,
set_difference(relation_field(sK5),set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)))) = subset_complement(relation_field(sK5),set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)))),
inference(superposition,[status(thm)],[c_27634,c_6703]) ).
tcf(c_31816,plain,
subset_complement(relation_field(sK5),subset_complement(relation_field(sK5),set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))))) = set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_27634,c_6699]) ).
tcf(c_31817,plain,
( ( set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))) = relation_field(sK5) )
| ~ subset(relation_field(sK5),set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)))) ),
inference(superposition,[status(thm)],[c_27634,c_260]) ).
tcf(c_31818,plain,
set_difference(set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))),set_difference(set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))),relation_field(sK5))) = set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_27634,c_123]) ).
tcf(c_31819,plain,
( proper_subset(set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))),relation_field(sK5))
| ( set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_27634,c_468]) ).
tcf(c_31820,plain,
! [X0: $i] :
( subset(set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))),X0)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27634,c_110]) ).
tcf(c_31821,plain,
set_difference(set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))),relation_field(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_27634,c_138]) ).
tcf(c_31822,plain,
set_union2(set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))),relation_field(sK5)) = relation_field(sK5),
inference(superposition,[status(thm)],[c_27634,c_85]) ).
tcf(c_31823,plain,
~ proper_subset(relation_field(sK5),set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)))),
inference(superposition,[status(thm)],[c_27634,c_188]) ).
tcf(c_31824,plain,
! [X0: $i] :
( disjoint(set_difference(relation_dom(sK5),set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5))),X0)
| ~ disjoint(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27634,c_190]) ).
tcf(c_31939,plain,
set_difference(relation_field(sK5),set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)))) = subset_complement(relation_field(sK5),set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)))),
inference(superposition,[status(thm)],[c_27649,c_6703]) ).
tcf(c_31940,plain,
subset_complement(relation_field(sK5),subset_complement(relation_field(sK5),set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))))) = set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27649,c_6699]) ).
tcf(c_31941,plain,
( ( set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))) = relation_field(sK5) )
| ~ subset(relation_field(sK5),set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_27649,c_260]) ).
tcf(c_31942,plain,
set_difference(set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))),set_difference(set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))),relation_field(sK5))) = set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))),
inference(superposition,[status(thm)],[c_27649,c_123]) ).
tcf(c_31943,plain,
( proper_subset(set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))),relation_field(sK5))
| ( set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_27649,c_468]) ).
tcf(c_31944,plain,
! [X0: $i] :
( subset(set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))),X0)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27649,c_110]) ).
tcf(c_31945,plain,
set_difference(set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))),relation_field(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_27649,c_138]) ).
tcf(c_31946,plain,
set_union2(set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))),relation_field(sK5)) = relation_field(sK5),
inference(superposition,[status(thm)],[c_27649,c_85]) ).
tcf(c_31947,plain,
~ proper_subset(relation_field(sK5),set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5)))),
inference(superposition,[status(thm)],[c_27649,c_188]) ).
tcf(c_31948,plain,
! [X0: $i] :
( disjoint(set_difference(relation_rng(sK5),set_difference(set_difference(relation_dom(sK5),relation_rng(sK5)),relation_rng(sK5))),X0)
| ~ disjoint(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27649,c_190]) ).
tcf(c_31991,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,subset_complement(X1,X0)) = subset_complement(X1,subset_complement(X1,X0)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_22243,c_6703]) ).
tcf(c_31992,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,subset_complement(X1,X0))) = subset_complement(X1,X0) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_22243,c_6699]) ).
tcf(c_31993,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X0,X1) = X0 )
| ~ subset(X1,X0)
| ~ subset(X0,subset_complement(X0,X1)) ),
inference(superposition,[status(thm)],[c_22243,c_260]) ).
tcf(c_31994,plain,
! [X0: $i,X1: $i] :
( ( set_difference(subset_complement(X1,X0),set_difference(subset_complement(X1,X0),X1)) = subset_complement(X1,X0) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_22243,c_123]) ).
tcf(c_31995,plain,
! [X0: $i,X1: $i] :
( proper_subset(subset_complement(X1,X0),X1)
| ( subset_complement(X1,X0) = X1 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_22243,c_468]) ).
tcf(c_31996,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(subset_complement(X1,X0),X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_22243,c_110]) ).
tcf(c_31997,plain,
! [X0: $i,X1: $i] :
( ( set_difference(subset_complement(X1,X0),X1) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_22243,c_138]) ).
tcf(c_31998,plain,
! [X0: $i,X1: $i] :
( ( set_union2(subset_complement(X1,X0),X1) = X1 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_22243,c_85]) ).
tcf(c_31999,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ proper_subset(X0,subset_complement(X0,X1)) ),
inference(superposition,[status(thm)],[c_22243,c_188]) ).
tcf(c_32000,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(subset_complement(X0,X2),X1)
| ~ subset(X2,X0)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_22243,c_190]) ).
tcf(c_32001,plain,
! [X0: $i] :
( ( subset_complement(empty_set,X0) = empty_set )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_22243,c_152]) ).
tcf(c_32002,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(subset_complement(relation_inverse_image(relation_inverse(sK5),X1),X0),relation_rng(sK5)),empty_set)
| ~ subset(X0,relation_inverse_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_22243,c_22779]) ).
tcf(c_32003,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(subset_complement(relation_image(relation_inverse(sK5),X1),X0),relation_dom(sK5)),empty_set)
| ~ subset(X0,relation_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_22243,c_22780]) ).
tcf(c_32004,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(subset_complement(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),X0),relation_dom(sK5)),empty_set)
| ~ subset(X0,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_22243,c_25182]) ).
tcf(c_32121,plain,
! [X0: $i] :
( one_to_one(identity_relation(X0))
| in(sK76(identity_relation(X0)),X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_203,c_460]) ).
tcf(c_32123,plain,
( one_to_one(relation_inverse(sK5))
| in(sK76(relation_inverse(sK5)),relation_rng(sK5))
| ~ function(relation_inverse(sK5))
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20946,c_460]) ).
tcf(c_32124,plain,
! [X0: $i] :
( one_to_one(relation_inverse(identity_relation(X0)))
| in(sK76(relation_inverse(identity_relation(X0))),X0)
| ~ function(relation_inverse(identity_relation(X0)))
| ~ relation(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_20961,c_460]) ).
tcf(c_32125,plain,
( one_to_one(relation_inverse(sK47))
| in(sK76(relation_inverse(sK47)),relation_rng(sK47))
| ~ function(relation_inverse(sK47))
| ~ relation(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_20951,c_460]) ).
tcf(c_32126,plain,
( one_to_one(relation_inverse(sK75))
| in(sK76(relation_inverse(sK75)),relation_rng(sK75))
| ~ function(relation_inverse(sK75))
| ~ relation(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_20957,c_460]) ).
tcf(c_32127,plain,
( one_to_one(relation_inverse(sK79))
| in(sK76(relation_inverse(sK79)),relation_rng(sK79))
| ~ function(relation_inverse(sK79))
| ~ relation(relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_20958,c_460]) ).
tcf(c_32128,plain,
! [X0: $i] :
( one_to_one(relation_inverse(relation_dom_restriction(sK5,X0)))
| in(sK76(relation_inverse(relation_dom_restriction(sK5,X0))),relation_rng(relation_dom_restriction(sK5,X0)))
| ~ function(relation_inverse(relation_dom_restriction(sK5,X0)))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25748,c_460]) ).
tcf(c_32129,plain,
! [X0: $i,X1: $i] :
( one_to_one(X0)
| in(sK76(X0),union(X1))
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_460,c_295]) ).
tcf(c_32130,plain,
! [X0: $i] :
( one_to_one(X0)
| ( set_union2(unordered_pair(sK76(X0),sK76(X0)),relation_dom(X0)) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_460,c_161]) ).
tcf(c_32131,plain,
! [X0: $i,X1: $i] :
( one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ disjoint(relation_dom(X0),X1)
| ~ in(sK76(X0),X1) ),
inference(superposition,[status(thm)],[c_460,c_151]) ).
tcf(c_32132,plain,
! [X0: $i,X1: $i] :
( one_to_one(X0)
| in(sK76(X0),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_460,c_242]) ).
tcf(c_32133,plain,
! [X0: $i] :
( one_to_one(X0)
| ( apply(identity_relation(relation_dom(X0)),sK76(X0)) = sK76(X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_460,c_134]) ).
tcf(c_32134,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK76(X0)) ),
inference(superposition,[status(thm)],[c_460,c_243]) ).
tcf(c_32135,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_460,c_471]) ).
tcf(c_32136,plain,
! [X0: $i] :
( one_to_one(X0)
| element(sK76(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_460,c_276]) ).
tcf(c_32137,plain,
! [X0: $i,X1: $i] :
( one_to_one(relation_dom_restriction(X0,X1))
| in(sK76(relation_dom_restriction(X0,X1)),X1)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_460,c_213]) ).
tcf(c_32138,plain,
( one_to_one(sK5)
| in(sK76(sK5),relation_field(sK5))
| ~ function(sK5)
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_460,c_27656]) ).
tcf(c_32143,plain,
( one_to_one(sK5)
| in(sK76(sK5),relation_field(sK5)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32138,c_97,c_96]) ).
tcf(c_32154,plain,
! [X0: $i] :
( one_to_one(identity_relation(X0))
| in(sK76(identity_relation(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32121,c_421,c_422]) ).
tcf(c_32264,plain,
! [X0: $i] :
( one_to_one(identity_relation(X0))
| in(sK77(identity_relation(X0)),X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_203,c_461]) ).
tcf(c_32266,plain,
( one_to_one(relation_inverse(sK5))
| in(sK77(relation_inverse(sK5)),relation_rng(sK5))
| ~ function(relation_inverse(sK5))
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20946,c_461]) ).
tcf(c_32267,plain,
! [X0: $i] :
( one_to_one(relation_inverse(identity_relation(X0)))
| in(sK77(relation_inverse(identity_relation(X0))),X0)
| ~ function(relation_inverse(identity_relation(X0)))
| ~ relation(relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_20961,c_461]) ).
tcf(c_32268,plain,
( one_to_one(relation_inverse(sK47))
| in(sK77(relation_inverse(sK47)),relation_rng(sK47))
| ~ function(relation_inverse(sK47))
| ~ relation(relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_20951,c_461]) ).
tcf(c_32269,plain,
( one_to_one(relation_inverse(sK75))
| in(sK77(relation_inverse(sK75)),relation_rng(sK75))
| ~ function(relation_inverse(sK75))
| ~ relation(relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_20957,c_461]) ).
tcf(c_32270,plain,
( one_to_one(relation_inverse(sK79))
| in(sK77(relation_inverse(sK79)),relation_rng(sK79))
| ~ function(relation_inverse(sK79))
| ~ relation(relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_20958,c_461]) ).
tcf(c_32271,plain,
! [X0: $i] :
( one_to_one(relation_inverse(relation_dom_restriction(sK5,X0)))
| in(sK77(relation_inverse(relation_dom_restriction(sK5,X0))),relation_rng(relation_dom_restriction(sK5,X0)))
| ~ function(relation_inverse(relation_dom_restriction(sK5,X0)))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25748,c_461]) ).
tcf(c_32272,plain,
! [X0: $i,X1: $i] :
( one_to_one(X0)
| in(sK77(X0),union(X1))
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_461,c_295]) ).
tcf(c_32273,plain,
! [X0: $i] :
( one_to_one(X0)
| ( set_union2(unordered_pair(sK77(X0),sK77(X0)),relation_dom(X0)) = relation_dom(X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_461,c_161]) ).
tcf(c_32274,plain,
! [X0: $i,X1: $i] :
( one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ disjoint(relation_dom(X0),X1)
| ~ in(sK77(X0),X1) ),
inference(superposition,[status(thm)],[c_461,c_151]) ).
tcf(c_32275,plain,
! [X0: $i,X1: $i] :
( one_to_one(X0)
| in(sK77(X0),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_461,c_242]) ).
tcf(c_32276,plain,
! [X0: $i] :
( one_to_one(X0)
| ( apply(identity_relation(relation_dom(X0)),sK77(X0)) = sK77(X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_461,c_134]) ).
tcf(c_32277,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK77(X0)) ),
inference(superposition,[status(thm)],[c_461,c_243]) ).
tcf(c_32279,plain,
! [X0: $i] :
( one_to_one(X0)
| element(sK77(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_461,c_276]) ).
tcf(c_32280,plain,
! [X0: $i,X1: $i] :
( one_to_one(relation_dom_restriction(X0,X1))
| in(sK77(relation_dom_restriction(X0,X1)),X1)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_461,c_213]) ).
tcf(c_32281,plain,
( one_to_one(sK5)
| in(sK77(sK5),relation_field(sK5))
| ~ function(sK5)
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_461,c_27656]) ).
tcf(c_32282,plain,
( one_to_one(sK5)
| in(sK77(sK5),relation_field(sK5)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32281,c_97,c_96]) ).
tcf(c_32293,plain,
! [X0: $i] :
( one_to_one(identity_relation(X0))
| in(sK77(identity_relation(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32264,c_421,c_422]) ).
tcf(c_32439,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| ~ subset(X0,set_union2(X1,unordered_pair(X2,X2))) ),
inference(superposition,[status(thm)],[c_153,c_58]) ).
tcf(c_32441,plain,
! [X0: $i,X1: $i] :
( subset(X0,empty_set)
| in(X1,X0)
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_4095,c_58]) ).
tcf(c_32442,plain,
! [X0: $i,X1: $i] :
( subset(X0,empty_set)
| in(X1,X0)
| ~ subset(X0,relation_dom(relation_dom_restriction(sK5,unordered_pair(X1,X1)))) ),
inference(superposition,[status(thm)],[c_29867,c_58]) ).
tcf(c_32443,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X0)
| subset(X0,set_difference(X1,powerset(empty_set)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_111,c_58]) ).
tcf(c_32444,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( set_difference(set_difference(X1,unordered_pair(X2,X2)),X0) = subset_complement(set_difference(X1,unordered_pair(X2,X2)),X0) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_6703]) ).
tcf(c_32445,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( subset_complement(set_difference(X1,unordered_pair(X2,X2)),subset_complement(set_difference(X1,unordered_pair(X2,X2)),X0)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_6699]) ).
tcf(c_32446,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ( set_difference(X0,unordered_pair(X1,X1)) = X2 )
| ~ subset(X2,X0)
| ~ subset(set_difference(X0,unordered_pair(X1,X1)),X2) ),
inference(superposition,[status(thm)],[c_58,c_260]) ).
tcf(c_32447,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( set_difference(X0,set_difference(X0,set_difference(X1,unordered_pair(X2,X2)))) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_123]) ).
tcf(c_32448,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| proper_subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| ( set_difference(X1,unordered_pair(X2,X2)) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_468]) ).
tcf(c_32449,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,X2)
| in(X1,X3)
| ~ subset(X3,X0)
| ~ subset(set_difference(X0,unordered_pair(X1,X1)),X2) ),
inference(superposition,[status(thm)],[c_58,c_110]) ).
tcf(c_32450,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( set_difference(X0,set_difference(X1,unordered_pair(X2,X2))) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_138]) ).
tcf(c_32451,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( set_union2(X0,set_difference(X1,unordered_pair(X2,X2))) = set_difference(X1,unordered_pair(X2,X2)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_85]) ).
tcf(c_32452,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ~ subset(X2,X0)
| ~ proper_subset(set_difference(X0,unordered_pair(X1,X1)),X2) ),
inference(superposition,[status(thm)],[c_58,c_188]) ).
tcf(c_32453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(X3,X2)
| in(X1,X3)
| ~ subset(X3,X0)
| ~ disjoint(set_difference(X0,unordered_pair(X1,X1)),X2) ),
inference(superposition,[status(thm)],[c_58,c_190]) ).
tcf(c_32454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,unordered_pair(X0,X1))
| in(X1,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_58,c_144]) ).
tcf(c_32455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,unordered_pair(X0,X1))
| in(X0,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_58,c_143]) ).
tcf(c_32456,plain,
! [X0: $i,X1: $i] :
( in(X1,sK2(powerset(set_difference(X0,unordered_pair(X1,X1)))))
| ~ subset(sK2(powerset(set_difference(X0,unordered_pair(X1,X1)))),X0) ),
inference(superposition,[status(thm)],[c_58,c_19634]) ).
tcf(c_32457,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,unordered_pair(powerset(set_difference(X0,unordered_pair(X1,X1))),X2))
| ~ subset(unordered_pair(powerset(set_difference(X0,unordered_pair(X1,X1))),X2),X0) ),
inference(superposition,[status(thm)],[c_58,c_19635]) ).
tcf(c_32458,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,unordered_pair(X0,powerset(set_difference(X1,unordered_pair(X2,X2)))))
| ~ subset(unordered_pair(X0,powerset(set_difference(X1,unordered_pair(X2,X2)))),X1) ),
inference(superposition,[status(thm)],[c_58,c_19636]) ).
tcf(c_32459,plain,
! [X0: $i,X1: $i] :
( in(X1,sK54(powerset(set_difference(X0,unordered_pair(X1,X1)))))
| ~ subset(sK54(powerset(set_difference(X0,unordered_pair(X1,X1)))),X0) ),
inference(superposition,[status(thm)],[c_58,c_19637]) ).
tcf(c_32460,plain,
! [X0: $i,X1: $i] :
( in(X1,powerset(powerset(set_difference(X0,unordered_pair(X1,X1)))))
| ~ subset(powerset(powerset(set_difference(X0,unordered_pair(X1,X1)))),X0) ),
inference(superposition,[status(thm)],[c_58,c_20010]) ).
tcf(c_32461,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,powerset(set_difference(X1,unordered_pair(X2,X2))))
| in(X2,sK18(X0,powerset(set_difference(X1,unordered_pair(X2,X2)))))
| ~ subset(sK18(X0,powerset(set_difference(X1,unordered_pair(X2,X2)))),X1) ),
inference(superposition,[status(thm)],[c_58,c_20077]) ).
tcf(c_32462,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK2(set_union2(powerset(set_difference(X0,unordered_pair(X1,X1))),X2)))
| ~ subset(sK2(set_union2(powerset(set_difference(X0,unordered_pair(X1,X1))),X2)),X0) ),
inference(superposition,[status(thm)],[c_58,c_20218]) ).
tcf(c_32463,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK54(set_union2(powerset(set_difference(X0,unordered_pair(X1,X1))),X2)))
| ~ subset(sK54(set_union2(powerset(set_difference(X0,unordered_pair(X1,X1))),X2)),X0) ),
inference(superposition,[status(thm)],[c_58,c_20229]) ).
tcf(c_32464,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,powerset(set_union2(powerset(set_difference(X0,unordered_pair(X1,X1))),X2)))
| ~ subset(powerset(set_union2(powerset(set_difference(X0,unordered_pair(X1,X1))),X2)),X0) ),
inference(superposition,[status(thm)],[c_58,c_20423]) ).
tcf(c_32465,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK2(set_union2(X0,powerset(set_difference(X1,unordered_pair(X2,X2))))))
| ~ subset(sK2(set_union2(X0,powerset(set_difference(X1,unordered_pair(X2,X2))))),X1) ),
inference(superposition,[status(thm)],[c_58,c_20434]) ).
tcf(c_32466,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK54(set_union2(X0,powerset(set_difference(X1,unordered_pair(X2,X2))))))
| ~ subset(sK54(set_union2(X0,powerset(set_difference(X1,unordered_pair(X2,X2))))),X1) ),
inference(superposition,[status(thm)],[c_58,c_20446]) ).
tcf(c_32467,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,powerset(set_union2(X0,powerset(set_difference(X1,unordered_pair(X2,X2))))))
| ~ subset(powerset(set_union2(X0,powerset(set_difference(X1,unordered_pair(X2,X2))))),X1) ),
inference(superposition,[status(thm)],[c_58,c_20458]) ).
tcf(c_32588,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),X2)
| in(sK1(relation_rng(relation_rng_restriction(X1,X0)),X2),relation_rng(X0))
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6708,c_77]) ).
tcf(c_32589,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,relation_rng(X0))
| ( set_difference(relation_rng(relation_rng_restriction(X1,X0)),unordered_pair(X2,X2)) = relation_rng(relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_195,c_77]) ).
tcf(c_32590,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(relation_rng_restriction(X1,X0)),X2)
| in(sK8(relation_rng(relation_rng_restriction(X1,X0)),X2),relation_rng(X0))
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_149,c_77]) ).
tcf(c_32591,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X1,relation_rng(relation_rng_restriction(X2,X0)))
| in(sK8(X1,relation_rng(relation_rng_restriction(X2,X0))),relation_rng(X0))
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_150,c_77]) ).
tcf(c_32592,plain,
! [X0: $i,X1: $i] :
( in(sK16(relation_rng(relation_rng_restriction(X1,X0))),relation_rng(X0))
| ( relation_rng(relation_rng_restriction(X1,X0)) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_233,c_77]) ).
tcf(c_32593,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),X2)
| in(sK18(relation_rng(relation_rng_restriction(X1,X0)),X2),relation_rng(X0))
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_241,c_77]) ).
tcf(c_32594,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK27(relation_rng(relation_rng_restriction(X1,X2)),X0),relation_rng(X2))
| ~ relation(X2)
| ~ in(X0,union(relation_rng(relation_rng_restriction(X1,X2)))) ),
inference(superposition,[status(thm)],[c_297,c_77]) ).
tcf(c_32595,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng(relation_rng_restriction(X1,X0)))
| in(sK38(relation_rng(relation_rng_restriction(X1,X0))),relation_rng(X0))
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_314,c_77]) ).
tcf(c_32596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK44(relation_rng(relation_rng_restriction(X1,X2)),X3,X0),relation_rng(X2))
| ~ relation(X2)
| ~ in(X0,cartesian_product2(relation_rng(relation_rng_restriction(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_323,c_77]) ).
tcf(c_32597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK45(X1,relation_rng(relation_rng_restriction(X2,X3)),X0),relation_rng(X3))
| ~ relation(X3)
| ~ in(X0,cartesian_product2(X1,relation_rng(relation_rng_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_324,c_77]) ).
tcf(c_32598,plain,
! [X0: $i,X1: $i] :
( empty(relation_rng(relation_rng_restriction(X1,X0)))
| in(sK23(relation_rng(relation_rng_restriction(X1,X0))),relation_rng(X0))
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_20297,c_77]) ).
tcf(c_32686,plain,
! [X0: $i] :
( subset(X0,relation_rng(identity_relation(X0)))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_22482,c_94]) ).
tcf(c_32689,plain,
! [X0: $i] :
( subset(X0,X0)
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_32686,c_204]) ).
tcf(c_32694,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK76(sK5),union(X0))
| ~ in(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_32143,c_295]) ).
tcf(c_32695,plain,
( one_to_one(sK5)
| ( set_union2(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5)) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_32143,c_161]) ).
tcf(c_32696,plain,
! [X0: $i] :
( one_to_one(sK5)
| ~ disjoint(relation_field(sK5),X0)
| ~ in(sK76(sK5),X0) ),
inference(superposition,[status(thm)],[c_32143,c_151]) ).
tcf(c_32697,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK76(sK5),X0)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_32143,c_242]) ).
tcf(c_32698,plain,
( one_to_one(sK5)
| ( apply(identity_relation(relation_field(sK5)),sK76(sK5)) = sK76(sK5) ) ),
inference(superposition,[status(thm)],[c_32143,c_134]) ).
tcf(c_32699,plain,
( one_to_one(sK5)
| ~ in(relation_field(sK5),sK76(sK5)) ),
inference(superposition,[status(thm)],[c_32143,c_243]) ).
tcf(c_32700,plain,
( one_to_one(sK5)
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_32143,c_471]) ).
tcf(c_32701,plain,
( one_to_one(sK5)
| element(sK76(sK5),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_32143,c_276]) ).
tcf(c_32702,plain,
( one_to_one(sK5)
| in(sK76(sK5),relation_rng(sK5))
| in(sK76(sK5),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_32143,c_27655]) ).
tcf(c_32802,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK77(sK5),union(X0))
| ~ in(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_32282,c_295]) ).
tcf(c_32803,plain,
( one_to_one(sK5)
| ( set_union2(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5)) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_32282,c_161]) ).
tcf(c_32804,plain,
! [X0: $i] :
( one_to_one(sK5)
| ~ disjoint(relation_field(sK5),X0)
| ~ in(sK77(sK5),X0) ),
inference(superposition,[status(thm)],[c_32282,c_151]) ).
tcf(c_32805,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK77(sK5),X0)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_32282,c_242]) ).
tcf(c_32806,plain,
( one_to_one(sK5)
| ( apply(identity_relation(relation_field(sK5)),sK77(sK5)) = sK77(sK5) ) ),
inference(superposition,[status(thm)],[c_32282,c_134]) ).
tcf(c_32807,plain,
( one_to_one(sK5)
| ~ in(relation_field(sK5),sK77(sK5)) ),
inference(superposition,[status(thm)],[c_32282,c_243]) ).
tcf(c_32809,plain,
( one_to_one(sK5)
| element(sK77(sK5),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_32282,c_276]) ).
tcf(c_32810,plain,
( one_to_one(sK5)
| in(sK77(sK5),relation_rng(sK5))
| in(sK77(sK5),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_32282,c_27655]) ).
tcf(c_32842,plain,
( one_to_one(sK5)
| empty(sK76(sK5))
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_32701,c_285]) ).
tcf(c_32843,plain,
( one_to_one(sK5)
| empty(relation_field(sK5))
| in(sK76(sK5),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_32701,c_283]) ).
tcf(c_32854,plain,
( one_to_one(sK5)
| empty(sK77(sK5))
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_32809,c_285]) ).
tcf(c_32855,plain,
( one_to_one(sK5)
| empty(relation_field(sK5))
| in(sK77(sK5),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_32809,c_283]) ).
tcf(c_32866,plain,
( one_to_one(sK5)
| ( set_difference(sK76(sK5),unordered_pair(relation_field(sK5),relation_field(sK5))) = sK76(sK5) ) ),
inference(superposition,[status(thm)],[c_195,c_32699]) ).
tcf(c_32873,plain,
( one_to_one(sK5)
| ( set_difference(sK77(sK5),unordered_pair(relation_field(sK5),relation_field(sK5))) = sK77(sK5) ) ),
inference(superposition,[status(thm)],[c_195,c_32807]) ).
tcf(c_32882,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK76(sK5),X0)
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_19515,c_32697]) ).
tcf(c_32883,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK5)
| in(X1,relation_field(sK5))
| in(sK76(sK5),set_difference(X0,unordered_pair(X1,X1)))
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_58,c_32697]) ).
tcf(c_32885,plain,
( one_to_one(sK5)
| in(sK76(sK5),cartesian_product2(relation_dom(relation_field(sK5)),relation_rng(relation_field(sK5))))
| ~ relation(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_117,c_32697]) ).
tcf(c_32886,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK76(sK5),set_union2(relation_field(sK5),X0)) ),
inference(superposition,[status(thm)],[c_209,c_32697]) ).
tcf(c_32888,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK76(sK5),set_union2(X0,relation_field(sK5))) ),
inference(superposition,[status(thm)],[c_19598,c_32697]) ).
tcf(c_32918,plain,
! [X0: $i] : set_difference(relation_dom(sK5),set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)))) = subset_complement(relation_dom(sK5),set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)))),
inference(superposition,[status(thm)],[c_22359,c_6703]) ).
tcf(c_32919,plain,
! [X0: $i] : subset_complement(relation_dom(sK5),subset_complement(relation_dom(sK5),set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))))) = set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22359,c_6699]) ).
tcf(c_32920,plain,
! [X0: $i] :
( ( set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))) = relation_dom(sK5) )
| ~ subset(relation_dom(sK5),set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)))) ),
inference(superposition,[status(thm)],[c_22359,c_260]) ).
tcf(c_32921,plain,
! [X0: $i] : set_difference(set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),set_difference(set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),relation_dom(sK5))) = set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22359,c_123]) ).
tcf(c_32922,plain,
! [X0: $i] :
( proper_subset(set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),relation_dom(sK5))
| ( set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))) = relation_dom(sK5) ) ),
inference(superposition,[status(thm)],[c_22359,c_468]) ).
tcf(c_32923,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_image(relation_inverse(sK5),X1),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X1))),X0)
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_22359,c_110]) ).
tcf(c_32924,plain,
! [X0: $i] : set_difference(set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),relation_dom(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_22359,c_138]) ).
tcf(c_32925,plain,
! [X0: $i] : set_union2(set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),relation_dom(sK5)) = relation_dom(sK5),
inference(superposition,[status(thm)],[c_22359,c_85]) ).
tcf(c_32926,plain,
! [X0: $i] : ~ proper_subset(relation_dom(sK5),set_difference(relation_image(relation_inverse(sK5),X0),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)))),
inference(superposition,[status(thm)],[c_22359,c_188]) ).
tcf(c_32927,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(relation_image(relation_inverse(sK5),X1),set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X1))),X0)
| ~ disjoint(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_22359,c_190]) ).
tcf(c_32993,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,relation_inverse_image(empty_set,X1))
| ~ relation(empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_20006,c_107]) ).
tcf(c_32994,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(empty_set,X0),empty_set)
| ~ relation(empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_20006,c_107]) ).
tcf(c_32995,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_inverse_image(X2,X1),relation_inverse_image(X2,X0)) = subset_complement(relation_inverse_image(X2,X1),relation_inverse_image(X2,X0)) )
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_6703]) ).
tcf(c_32996,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_complement(relation_inverse_image(X2,X1),subset_complement(relation_inverse_image(X2,X1),relation_inverse_image(X2,X0))) = relation_inverse_image(X2,X0) )
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_6699]) ).
tcf(c_32997,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X1) = relation_inverse_image(X0,X2) )
| ~ relation(X0)
| ~ subset(X2,X1)
| ~ subset(relation_inverse_image(X0,X1),relation_inverse_image(X0,X2)) ),
inference(superposition,[status(thm)],[c_107,c_260]) ).
tcf(c_32998,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_inverse_image(X2,X0),set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))) = relation_inverse_image(X2,X0) )
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_123]) ).
tcf(c_32999,plain,
! [X0: $i,X1: $i,X2: $i] :
( proper_subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ( relation_inverse_image(X2,X0) = relation_inverse_image(X2,X1) )
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_468]) ).
tcf(c_33000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(relation_inverse_image(X0,X3),X2)
| ~ relation(X0)
| ~ subset(X3,X1)
| ~ subset(relation_inverse_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_107,c_110]) ).
tcf(c_33001,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) = empty_set )
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_138]) ).
tcf(c_33002,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) = relation_inverse_image(X2,X1) )
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_85]) ).
tcf(c_33003,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X0)
| ~ subset(X2,X1)
| ~ proper_subset(relation_inverse_image(X0,X1),relation_inverse_image(X0,X2)) ),
inference(superposition,[status(thm)],[c_107,c_188]) ).
tcf(c_33004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(relation_inverse_image(X0,X3),X2)
| ~ relation(X0)
| ~ subset(X3,X1)
| ~ disjoint(relation_inverse_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_107,c_190]) ).
tcf(c_33005,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5)),empty_set)
| ~ relation(relation_inverse(sK5))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_107,c_22779]) ).
tcf(c_33006,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,empty_set)
| ~ relation(empty_set)
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_32994,c_20006]) ).
tcf(c_33010,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,empty_set)
| ~ relation(relation_inverse(sK5))
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_33005,c_21834]) ).
tcf(c_33057,plain,
! [X0: $i] :
( ( relation_dom(identity_relation(X0)) = empty_set )
| ~ relation(identity_relation(X0))
| ( X0 != empty_set ) ),
inference(superposition,[status(thm)],[c_204,c_193]) ).
tcf(c_33058,plain,
( ( relation_dom(relation_inverse(sK5)) = empty_set )
| ~ relation(relation_inverse(sK5))
| ( relation_dom(sK5) != empty_set ) ),
inference(superposition,[status(thm)],[c_21123,c_193]) ).
tcf(c_33059,plain,
( ( relation_dom(relation_inverse(sK47)) = empty_set )
| ~ relation(relation_inverse(sK47))
| ( relation_dom(sK47) != empty_set ) ),
inference(superposition,[status(thm)],[c_21128,c_193]) ).
tcf(c_33060,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(identity_relation(X0))) = empty_set )
| ~ relation(relation_inverse(identity_relation(X0)))
| ( X0 != empty_set ) ),
inference(superposition,[status(thm)],[c_21138,c_193]) ).
tcf(c_33061,plain,
( ( relation_dom(relation_inverse(sK75)) = empty_set )
| ~ relation(relation_inverse(sK75))
| ( relation_dom(sK75) != empty_set ) ),
inference(superposition,[status(thm)],[c_21134,c_193]) ).
tcf(c_33062,plain,
( ( relation_dom(relation_inverse(sK79)) = empty_set )
| ~ relation(relation_inverse(sK79))
| ( relation_dom(sK79) != empty_set ) ),
inference(superposition,[status(thm)],[c_21135,c_193]) ).
tcf(c_33063,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom_restriction(sK5,X0))) = empty_set )
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0)))
| ( relation_dom(relation_dom_restriction(sK5,X0)) != empty_set ) ),
inference(superposition,[status(thm)],[c_25747,c_193]) ).
tcf(c_33065,plain,
( ( relation_rng(sK79) = empty_set )
| ~ relation(relation_inverse(sK79))
| ( relation_dom(sK79) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_33062,c_20958]) ).
tcf(c_33069,plain,
( ( relation_rng(sK75) = empty_set )
| ~ relation(relation_inverse(sK75))
| ( relation_dom(sK75) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_33061,c_20957]) ).
tcf(c_33073,plain,
( ( relation_rng(sK47) = empty_set )
| ~ relation(relation_inverse(sK47))
| ( relation_dom(sK47) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_33059,c_20951]) ).
tcf(c_33077,plain,
( ( relation_rng(sK5) = empty_set )
| ~ relation(relation_inverse(sK5))
| ( relation_dom(sK5) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_33058,c_20946]) ).
tcf(c_33082,plain,
! [X0: $i] :
( ( relation_rng(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0)))
| ( relation_dom(relation_dom_restriction(sK5,X0)) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_33063,c_25748]) ).
tcf(c_33092,plain,
! [X0: $i] :
( ( relation_rng(identity_relation(X0)) = empty_set )
| ~ relation(identity_relation(X0))
| ( X0 != empty_set ) ),
inference(superposition,[status(thm)],[c_203,c_194]) ).
tcf(c_33094,plain,
( ( relation_rng(relation_inverse(sK5)) = empty_set )
| ~ relation(relation_inverse(sK5))
| ( relation_rng(sK5) != empty_set ) ),
inference(superposition,[status(thm)],[c_20946,c_194]) ).
tcf(c_33095,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(identity_relation(X0))) = empty_set )
| ~ relation(relation_inverse(identity_relation(X0)))
| ( X0 != empty_set ) ),
inference(superposition,[status(thm)],[c_20961,c_194]) ).
tcf(c_33096,plain,
( ( relation_rng(relation_inverse(sK47)) = empty_set )
| ~ relation(relation_inverse(sK47))
| ( relation_rng(sK47) != empty_set ) ),
inference(superposition,[status(thm)],[c_20951,c_194]) ).
tcf(c_33097,plain,
( ( relation_rng(relation_inverse(sK75)) = empty_set )
| ~ relation(relation_inverse(sK75))
| ( relation_rng(sK75) != empty_set ) ),
inference(superposition,[status(thm)],[c_20957,c_194]) ).
tcf(c_33098,plain,
( ( relation_rng(relation_inverse(sK79)) = empty_set )
| ~ relation(relation_inverse(sK79))
| ( relation_rng(sK79) != empty_set ) ),
inference(superposition,[status(thm)],[c_20958,c_194]) ).
tcf(c_33099,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom_restriction(sK5,X0))) = empty_set )
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0)))
| ( relation_rng(relation_dom_restriction(sK5,X0)) != empty_set ) ),
inference(superposition,[status(thm)],[c_25748,c_194]) ).
tcf(c_33101,plain,
( ( relation_dom(sK79) = empty_set )
| ~ relation(relation_inverse(sK79))
| ( relation_rng(sK79) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_33098,c_21135]) ).
tcf(c_33105,plain,
( ( relation_dom(sK75) = empty_set )
| ~ relation(relation_inverse(sK75))
| ( relation_rng(sK75) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_33097,c_21134]) ).
tcf(c_33109,plain,
( ( relation_dom(sK47) = empty_set )
| ~ relation(relation_inverse(sK47))
| ( relation_rng(sK47) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_33096,c_21128]) ).
tcf(c_33113,plain,
( ( relation_dom(sK5) = empty_set )
| ~ relation(relation_inverse(sK5))
| ( relation_rng(sK5) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_33094,c_21123]) ).
tcf(c_33118,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0)))
| ( relation_rng(relation_dom_restriction(sK5,X0)) != empty_set ) ),
inference(light_normalisation,[status(thm)],[c_33099,c_25747]) ).
tcf(c_33151,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(relation_dom_restriction(X0,X1)),X2)
| in(sK1(relation_dom(relation_dom_restriction(X0,X1)),X2),relation_dom(X0))
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6708,c_214]) ).
tcf(c_33152,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,relation_dom(X0))
| ( set_difference(relation_dom(relation_dom_restriction(X0,X1)),unordered_pair(X2,X2)) = relation_dom(relation_dom_restriction(X0,X1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_195,c_214]) ).
tcf(c_33153,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_dom(relation_dom_restriction(X0,X1)),X2)
| in(sK8(relation_dom(relation_dom_restriction(X0,X1)),X2),relation_dom(X0))
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_149,c_214]) ).
tcf(c_33154,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(sK8(X1,relation_dom(relation_dom_restriction(X0,X2))),relation_dom(X0))
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_150,c_214]) ).
tcf(c_33155,plain,
! [X0: $i,X1: $i] :
( in(sK16(relation_dom(relation_dom_restriction(X0,X1))),relation_dom(X0))
| ( relation_dom(relation_dom_restriction(X0,X1)) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_233,c_214]) ).
tcf(c_33156,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(relation_dom_restriction(X0,X1)),X2)
| in(sK18(relation_dom(relation_dom_restriction(X0,X1)),X2),relation_dom(X0))
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_241,c_214]) ).
tcf(c_33157,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK27(relation_dom(relation_dom_restriction(X1,X2)),X0),relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,union(relation_dom(relation_dom_restriction(X1,X2)))) ),
inference(superposition,[status(thm)],[c_297,c_214]) ).
tcf(c_33158,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom(relation_dom_restriction(X0,X1)))
| in(sK38(relation_dom(relation_dom_restriction(X0,X1))),relation_dom(X0))
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_314,c_214]) ).
tcf(c_33159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK44(relation_dom(relation_dom_restriction(X1,X2)),X3,X0),relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,cartesian_product2(relation_dom(relation_dom_restriction(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_323,c_214]) ).
tcf(c_33160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK45(X1,relation_dom(relation_dom_restriction(X2,X3)),X0),relation_dom(X2))
| ~ relation(X2)
| ~ in(X0,cartesian_product2(X1,relation_dom(relation_dom_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_324,c_214]) ).
tcf(c_33161,plain,
! [X0: $i,X1: $i] :
( one_to_one(relation_dom_restriction(X0,X1))
| in(sK76(relation_dom_restriction(X0,X1)),relation_dom(X0))
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_460,c_214]) ).
tcf(c_33162,plain,
! [X0: $i,X1: $i] :
( one_to_one(relation_dom_restriction(X0,X1))
| in(sK77(relation_dom_restriction(X0,X1)),relation_dom(X0))
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_461,c_214]) ).
tcf(c_33163,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom(relation_dom_restriction(X0,X1)))
| in(sK23(relation_dom(relation_dom_restriction(X0,X1))),relation_dom(X0))
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_20297,c_214]) ).
tcf(c_33165,plain,
! [X0: $i] :
( in(X0,relation_dom(sK5))
| ~ relation(sK5)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_28288,c_214]) ).
tcf(c_33166,plain,
! [X0: $i] :
( in(X0,relation_dom(sK5))
| ~ relation(sK5)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_33165,c_186]) ).
tcf(c_33300,plain,
( function(relation_dom(sK47))
| ~ empty(sK47) ),
inference(superposition,[status(thm)],[c_432,c_24123]) ).
tcf(c_33307,plain,
( one_to_one(relation_dom(sK47))
| ~ empty(sK47) ),
inference(superposition,[status(thm)],[c_432,c_24124]) ).
tcf(c_33316,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK77(sK5),X0)
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_19515,c_32805]) ).
tcf(c_33317,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK5)
| in(X1,relation_field(sK5))
| in(sK77(sK5),set_difference(X0,unordered_pair(X1,X1)))
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_58,c_32805]) ).
tcf(c_33319,plain,
( one_to_one(sK5)
| in(sK77(sK5),cartesian_product2(relation_dom(relation_field(sK5)),relation_rng(relation_field(sK5))))
| ~ relation(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_117,c_32805]) ).
tcf(c_33320,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK77(sK5),set_union2(relation_field(sK5),X0)) ),
inference(superposition,[status(thm)],[c_209,c_32805]) ).
tcf(c_33322,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK77(sK5),set_union2(X0,relation_field(sK5))) ),
inference(superposition,[status(thm)],[c_19598,c_32805]) ).
tcf(c_33387,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK76(sK5),X0)
| ~ in(relation_field(sK5),powerset(X0)) ),
inference(superposition,[status(thm)],[c_225,c_32694]) ).
tcf(c_33388,plain,
( one_to_one(sK5)
| in(sK76(sK5),empty_set)
| ~ in(relation_field(sK5),empty_set) ),
inference(superposition,[status(thm)],[c_21789,c_32694]) ).
tcf(c_33389,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK5)
| in(sK76(sK5),union(X1))
| ~ in(relation_field(sK5),X0)
| ~ in(union(X0),X1) ),
inference(superposition,[status(thm)],[c_32694,c_295]) ).
tcf(c_33390,plain,
! [X0: $i] :
( one_to_one(sK5)
| ( set_union2(unordered_pair(sK76(sK5),sK76(sK5)),union(X0)) = union(X0) )
| ~ in(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_32694,c_161]) ).
tcf(c_33391,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK5)
| ~ in(sK76(sK5),X1)
| ~ in(relation_field(sK5),X0)
| ~ disjoint(union(X0),X1) ),
inference(superposition,[status(thm)],[c_32694,c_151]) ).
tcf(c_33392,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK5)
| in(sK76(sK5),X1)
| ~ in(relation_field(sK5),X0)
| ~ subset(union(X0),X1) ),
inference(superposition,[status(thm)],[c_32694,c_242]) ).
tcf(c_33393,plain,
! [X0: $i] :
( one_to_one(sK5)
| ( apply(identity_relation(union(X0)),sK76(sK5)) = sK76(sK5) )
| ~ in(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_32694,c_134]) ).
tcf(c_33394,plain,
! [X0: $i] :
( one_to_one(sK5)
| ~ in(relation_field(sK5),X0)
| ~ in(union(X0),sK76(sK5)) ),
inference(superposition,[status(thm)],[c_32694,c_243]) ).
tcf(c_33395,plain,
! [X0: $i] :
( one_to_one(sK5)
| ~ empty(union(X0))
| ~ in(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_32694,c_471]) ).
tcf(c_33396,plain,
! [X0: $i] :
( one_to_one(sK5)
| element(sK76(sK5),union(X0))
| ~ in(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_32694,c_276]) ).
tcf(c_33469,plain,
! [X0: $i] :
( one_to_one(sK5)
| ~ empty(X0)
| ~ in(sK76(sK5),X0) ),
inference(superposition,[status(thm)],[c_19407,c_32696]) ).
tcf(c_33470,plain,
( one_to_one(sK5)
| ~ in(sK76(sK5),empty_set) ),
inference(superposition,[status(thm)],[c_19409,c_32696]) ).
tcf(c_33471,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(X0,relation_field(sK5))
| ~ in(sK76(sK5),unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_19372,c_32696]) ).
tcf(c_33472,plain,
( one_to_one(sK5)
| in(empty_set,relation_field(sK5))
| ~ in(sK76(sK5),powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_19442,c_32696]) ).
tcf(c_33536,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK76(sK5),relation_dom(sK5))
| in(sK76(sK5),union(X0))
| ~ in(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_32702,c_295]) ).
tcf(c_33537,plain,
( one_to_one(sK5)
| in(sK76(sK5),relation_dom(sK5))
| ( set_union2(unordered_pair(sK76(sK5),sK76(sK5)),relation_rng(sK5)) = relation_rng(sK5) ) ),
inference(superposition,[status(thm)],[c_32702,c_161]) ).
tcf(c_33538,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK76(sK5),relation_dom(sK5))
| ~ disjoint(relation_rng(sK5),X0)
| ~ in(sK76(sK5),X0) ),
inference(superposition,[status(thm)],[c_32702,c_151]) ).
tcf(c_33539,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK76(sK5),X0)
| in(sK76(sK5),relation_dom(sK5))
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_32702,c_242]) ).
tcf(c_33540,plain,
( one_to_one(sK5)
| in(sK76(sK5),relation_dom(sK5))
| ( apply(identity_relation(relation_rng(sK5)),sK76(sK5)) = sK76(sK5) ) ),
inference(superposition,[status(thm)],[c_32702,c_134]) ).
tcf(c_33541,plain,
( one_to_one(sK5)
| in(sK76(sK5),relation_dom(sK5))
| ~ in(relation_rng(sK5),sK76(sK5)) ),
inference(superposition,[status(thm)],[c_32702,c_243]) ).
tcf(c_33542,plain,
( one_to_one(sK5)
| in(sK76(sK5),relation_dom(sK5))
| ~ empty(relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_32702,c_471]) ).
tcf(c_33543,plain,
( one_to_one(sK5)
| element(sK76(sK5),relation_rng(sK5))
| in(sK76(sK5),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_32702,c_276]) ).
tcf(c_33650,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK77(sK5),X0)
| ~ in(relation_field(sK5),powerset(X0)) ),
inference(superposition,[status(thm)],[c_225,c_32802]) ).
tcf(c_33651,plain,
( one_to_one(sK5)
| in(sK77(sK5),empty_set)
| ~ in(relation_field(sK5),empty_set) ),
inference(superposition,[status(thm)],[c_21789,c_32802]) ).
tcf(c_33652,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK5)
| in(sK77(sK5),union(X1))
| ~ in(relation_field(sK5),X0)
| ~ in(union(X0),X1) ),
inference(superposition,[status(thm)],[c_32802,c_295]) ).
tcf(c_33653,plain,
! [X0: $i] :
( one_to_one(sK5)
| ( set_union2(unordered_pair(sK77(sK5),sK77(sK5)),union(X0)) = union(X0) )
| ~ in(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_32802,c_161]) ).
tcf(c_33654,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK5)
| ~ in(sK77(sK5),X1)
| ~ in(relation_field(sK5),X0)
| ~ disjoint(union(X0),X1) ),
inference(superposition,[status(thm)],[c_32802,c_151]) ).
tcf(c_33655,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK5)
| in(sK77(sK5),X1)
| ~ in(relation_field(sK5),X0)
| ~ subset(union(X0),X1) ),
inference(superposition,[status(thm)],[c_32802,c_242]) ).
tcf(c_33656,plain,
! [X0: $i] :
( one_to_one(sK5)
| ( apply(identity_relation(union(X0)),sK77(sK5)) = sK77(sK5) )
| ~ in(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_32802,c_134]) ).
tcf(c_33657,plain,
! [X0: $i] :
( one_to_one(sK5)
| ~ in(relation_field(sK5),X0)
| ~ in(union(X0),sK77(sK5)) ),
inference(superposition,[status(thm)],[c_32802,c_243]) ).
tcf(c_33659,plain,
! [X0: $i] :
( one_to_one(sK5)
| element(sK77(sK5),union(X0))
| ~ in(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_32802,c_276]) ).
tcf(c_33701,plain,
! [X0: $i] :
( one_to_one(sK5)
| ~ empty(X0)
| ~ in(sK77(sK5),X0) ),
inference(superposition,[status(thm)],[c_19407,c_32804]) ).
tcf(c_33702,plain,
( one_to_one(sK5)
| ~ in(sK77(sK5),empty_set) ),
inference(superposition,[status(thm)],[c_19409,c_32804]) ).
tcf(c_33703,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(X0,relation_field(sK5))
| ~ in(sK77(sK5),unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_19372,c_32804]) ).
tcf(c_33704,plain,
( one_to_one(sK5)
| in(empty_set,relation_field(sK5))
| ~ in(sK77(sK5),powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_19442,c_32804]) ).
tcf(c_33763,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X2,X0),X2)
| in(sK15(X2,X0),union(X1))
| ( X0 = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_228,c_295]) ).
tcf(c_33764,plain,
! [X0: $i,X1: $i] :
( in(sK15(X0,X1),X0)
| ( X0 = X1 )
| ( set_union2(unordered_pair(sK15(X0,X1),sK15(X0,X1)),X1) = X1 ) ),
inference(superposition,[status(thm)],[c_228,c_161]) ).
tcf(c_33765,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X0,X1),X0)
| ( X0 = X1 )
| ~ disjoint(X1,X2)
| ~ in(sK15(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_228,c_151]) ).
tcf(c_33766,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X2,X0),X2)
| in(sK15(X2,X0),X1)
| ( X0 = X2 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_228,c_242]) ).
tcf(c_33767,plain,
! [X0: $i,X1: $i] :
( in(sK15(X1,X0),X1)
| ( X0 = X1 )
| ( apply(identity_relation(X0),sK15(X1,X0)) = sK15(X1,X0) ) ),
inference(superposition,[status(thm)],[c_228,c_134]) ).
tcf(c_33768,plain,
! [X0: $i,X1: $i] :
( in(sK15(X1,X0),X1)
| ( X0 = X1 )
| ~ in(X0,sK15(X1,X0)) ),
inference(superposition,[status(thm)],[c_228,c_243]) ).
tcf(c_33769,plain,
! [X0: $i,X1: $i] :
( in(sK15(X1,X0),X1)
| ( X0 = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_228,c_471]) ).
tcf(c_33770,plain,
! [X0: $i,X1: $i] :
( element(sK15(X0,X1),X1)
| in(sK15(X0,X1),X0)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_228,c_276]) ).
tcf(c_33771,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X2,relation_dom(relation_dom_restriction(X0,X1))),X2)
| in(sK15(X2,relation_dom(relation_dom_restriction(X0,X1))),relation_dom(X0))
| ( relation_dom(relation_dom_restriction(X0,X1)) = X2 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_228,c_214]) ).
tcf(c_33772,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X2,relation_dom(relation_dom_restriction(X0,X1))),X2)
| in(sK15(X2,relation_dom(relation_dom_restriction(X0,X1))),X1)
| ( relation_dom(relation_dom_restriction(X0,X1)) = X2 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_228,c_213]) ).
tcf(c_33773,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X2,relation_rng(relation_rng_restriction(X1,X0))),X2)
| in(sK15(X2,relation_rng(relation_rng_restriction(X1,X0))),relation_rng(X0))
| ( relation_rng(relation_rng_restriction(X1,X0)) = X2 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_228,c_77]) ).
tcf(c_33774,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X2,relation_rng(relation_rng_restriction(X1,X0))),X2)
| in(sK15(X2,relation_rng(relation_rng_restriction(X1,X0))),X1)
| ( relation_rng(relation_rng_restriction(X1,X0)) = X2 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_228,c_76]) ).
tcf(c_33775,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X2))
| in(sK15(X1,sK2(X2)),X1)
| ( sK2(X2) = X1 )
| ~ subset(X0,sK15(X1,sK2(X2))) ),
inference(superposition,[status(thm)],[c_228,c_87]) ).
tcf(c_33776,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X2,set_difference(X0,set_difference(X0,X1))),X2)
| ( set_difference(X0,set_difference(X0,X1)) = X2 )
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_228,c_166]) ).
tcf(c_33777,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X2,set_difference(X0,set_difference(X0,X1))),X2)
| in(sK15(X2,set_difference(X0,set_difference(X0,X1))),X1)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_228,c_370]) ).
tcf(c_33778,plain,
! [X0: $i] :
( in(sK15(X0,empty_set),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_228,c_234]) ).
tcf(c_33779,plain,
! [X0: $i,X1: $i] :
( in(sK15(X0,unordered_pair(X1,X1)),X0)
| ( unordered_pair(X1,X1) = X0 )
| ( sK15(X0,unordered_pair(X1,X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_228,c_239]) ).
tcf(c_33780,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X2,set_union2(X0,X1)),X2)
| in(sK15(X2,set_union2(X0,X1)),X1)
| in(sK15(X2,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_228,c_254]) ).
tcf(c_33781,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X0,set_difference(X1,X2)),X0)
| ( set_difference(X1,X2) = X0 )
| ~ in(sK15(X0,set_difference(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_228,c_270]) ).
tcf(c_33782,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X2,set_difference(X0,X1)),X2)
| in(sK15(X2,set_difference(X0,X1)),X0)
| ( set_difference(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_228,c_269]) ).
tcf(c_33783,plain,
! [X0: $i,X1: $i] :
( subset(sK15(X1,powerset(X0)),X0)
| in(sK15(X1,powerset(X0)),X1)
| ( powerset(X0) = X1 ) ),
inference(superposition,[status(thm)],[c_228,c_290]) ).
tcf(c_33784,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK54(X2))
| in(sK15(X1,sK54(X2)),X1)
| ( sK54(X2) = X1 )
| ~ subset(X0,sK15(X1,sK54(X2))) ),
inference(superposition,[status(thm)],[c_228,c_373]) ).
tcf(c_33785,plain,
! [X0: $i] :
( in(sK15(X0,relation_rng(sK5)),X0)
| in(sK15(X0,relation_rng(sK5)),relation_field(sK5))
| ( relation_rng(sK5) = X0 ) ),
inference(superposition,[status(thm)],[c_228,c_27657]) ).
tcf(c_33786,plain,
! [X0: $i] :
( in(sK15(X0,relation_dom(sK5)),X0)
| in(sK15(X0,relation_dom(sK5)),relation_field(sK5))
| ( relation_dom(sK5) = X0 ) ),
inference(superposition,[status(thm)],[c_228,c_27656]) ).
tcf(c_33787,plain,
! [X0: $i,X1: $i] :
( in(sK15(X1,relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),X1)
| in(sK15(X1,relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_dom(sK5))
| ( relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))) = X1 ) ),
inference(superposition,[status(thm)],[c_228,c_25255]) ).
tcf(c_33788,plain,
! [X0: $i] :
( in(sK15(X0,relation_field(sK5)),X0)
| in(sK15(X0,relation_field(sK5)),relation_rng(sK5))
| in(sK15(X0,relation_field(sK5)),relation_dom(sK5))
| ( relation_field(sK5) = X0 ) ),
inference(superposition,[status(thm)],[c_228,c_27655]) ).
tcf(c_33789,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X0,X2),X2)
| in(sK15(X0,X2),union(X1))
| ( X0 = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_228,c_295]) ).
tcf(c_33790,plain,
! [X0: $i,X1: $i] :
( in(sK15(X0,X1),X1)
| ( X0 = X1 )
| ( set_union2(unordered_pair(sK15(X0,X1),sK15(X0,X1)),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_228,c_161]) ).
tcf(c_33791,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X0,X1),X1)
| ( X0 = X1 )
| ~ disjoint(X0,X2)
| ~ in(sK15(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_228,c_151]) ).
tcf(c_33792,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X0,X2),X2)
| in(sK15(X0,X2),X1)
| ( X0 = X2 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_228,c_242]) ).
tcf(c_33793,plain,
! [X0: $i,X1: $i] :
( in(sK15(X0,X1),X1)
| ( X0 = X1 )
| ( apply(identity_relation(X0),sK15(X0,X1)) = sK15(X0,X1) ) ),
inference(superposition,[status(thm)],[c_228,c_134]) ).
tcf(c_33794,plain,
! [X0: $i,X1: $i] :
( in(sK15(X0,X1),X1)
| ( X0 = X1 )
| ~ in(X0,sK15(X0,X1)) ),
inference(superposition,[status(thm)],[c_228,c_243]) ).
tcf(c_33795,plain,
! [X0: $i,X1: $i] :
( in(sK15(X0,X1),X1)
| ( X0 = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_228,c_471]) ).
tcf(c_33796,plain,
! [X0: $i,X1: $i] :
( element(sK15(X0,X1),X0)
| in(sK15(X0,X1),X1)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_228,c_276]) ).
tcf(c_33797,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(relation_dom(relation_dom_restriction(X0,X1)),X2),X2)
| in(sK15(relation_dom(relation_dom_restriction(X0,X1)),X2),relation_dom(X0))
| ( relation_dom(relation_dom_restriction(X0,X1)) = X2 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_228,c_214]) ).
tcf(c_33798,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(relation_dom(relation_dom_restriction(X0,X1)),X2),X2)
| in(sK15(relation_dom(relation_dom_restriction(X0,X1)),X2),X1)
| ( relation_dom(relation_dom_restriction(X0,X1)) = X2 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_228,c_213]) ).
tcf(c_33799,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(relation_rng(relation_rng_restriction(X1,X0)),X2),X2)
| in(sK15(relation_rng(relation_rng_restriction(X1,X0)),X2),relation_rng(X0))
| ( relation_rng(relation_rng_restriction(X1,X0)) = X2 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_228,c_77]) ).
tcf(c_33800,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(relation_rng(relation_rng_restriction(X1,X0)),X2),X2)
| in(sK15(relation_rng(relation_rng_restriction(X1,X0)),X2),X1)
| ( relation_rng(relation_rng_restriction(X1,X0)) = X2 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_228,c_76]) ).
tcf(c_33801,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X1))
| in(sK15(sK2(X1),X2),X2)
| ( sK2(X1) = X2 )
| ~ subset(X0,sK15(sK2(X1),X2)) ),
inference(superposition,[status(thm)],[c_228,c_87]) ).
tcf(c_33802,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(set_difference(X0,set_difference(X0,X1)),X2),X2)
| ( set_difference(X0,set_difference(X0,X1)) = X2 )
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_228,c_166]) ).
tcf(c_33803,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(set_difference(X0,set_difference(X0,X1)),X2),X2)
| in(sK15(set_difference(X0,set_difference(X0,X1)),X2),X1)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_228,c_370]) ).
tcf(c_33804,plain,
! [X0: $i] :
( in(sK15(empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_228,c_234]) ).
tcf(c_33805,plain,
! [X0: $i,X1: $i] :
( in(sK15(unordered_pair(X0,X0),X1),X1)
| ( unordered_pair(X0,X0) = X1 )
| ( sK15(unordered_pair(X0,X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_228,c_239]) ).
tcf(c_33806,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(set_union2(X0,X1),X2),X2)
| in(sK15(set_union2(X0,X1),X2),X1)
| in(sK15(set_union2(X0,X1),X2),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_228,c_254]) ).
tcf(c_33807,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(set_difference(X0,X1),X2),X2)
| ( set_difference(X0,X1) = X2 )
| ~ in(sK15(set_difference(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_228,c_270]) ).
tcf(c_33808,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(set_difference(X0,X1),X2),X2)
| in(sK15(set_difference(X0,X1),X2),X0)
| ( set_difference(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_228,c_269]) ).
tcf(c_33809,plain,
! [X0: $i,X1: $i] :
( subset(sK15(powerset(X0),X1),X0)
| in(sK15(powerset(X0),X1),X1)
| ( powerset(X0) = X1 ) ),
inference(superposition,[status(thm)],[c_228,c_290]) ).
tcf(c_33810,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK54(X1))
| in(sK15(sK54(X1),X2),X2)
| ( sK54(X1) = X2 )
| ~ subset(X0,sK15(sK54(X1),X2)) ),
inference(superposition,[status(thm)],[c_228,c_373]) ).
tcf(c_33811,plain,
! [X0: $i] :
( in(sK15(relation_rng(sK5),X0),X0)
| in(sK15(relation_rng(sK5),X0),relation_field(sK5))
| ( relation_rng(sK5) = X0 ) ),
inference(superposition,[status(thm)],[c_228,c_27657]) ).
tcf(c_33812,plain,
! [X0: $i] :
( in(sK15(relation_dom(sK5),X0),X0)
| in(sK15(relation_dom(sK5),X0),relation_field(sK5))
| ( relation_dom(sK5) = X0 ) ),
inference(superposition,[status(thm)],[c_228,c_27656]) ).
tcf(c_33813,plain,
! [X0: $i,X1: $i] :
( in(sK15(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1),X1)
| in(sK15(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1),relation_dom(sK5))
| ( relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))) = X1 ) ),
inference(superposition,[status(thm)],[c_228,c_25255]) ).
tcf(c_33814,plain,
! [X0: $i] :
( in(sK15(relation_field(sK5),X0),X0)
| in(sK15(relation_field(sK5),X0),relation_rng(sK5))
| in(sK15(relation_field(sK5),X0),relation_dom(sK5))
| ( relation_field(sK5) = X0 ) ),
inference(superposition,[status(thm)],[c_228,c_27655]) ).
tcf(c_34247,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X2)
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != sK38(X2) ) ),
inference(superposition,[status(thm)],[c_351,c_315]) ).
tcf(c_34250,plain,
! [X0: $i] :
( relation(X0)
| ( unordered_pair(powerset(empty_set),powerset(empty_set)) != sK38(X0) ) ),
inference(superposition,[status(thm)],[c_111,c_315]) ).
tcf(c_34251,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X2)
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)) != sK38(X2) ) ),
inference(superposition,[status(thm)],[c_351,c_315]) ).
tcf(c_34252,plain,
! [X0: $i,X1: $i] :
( relation(X1)
| ( unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)) != sK38(X1) ) ),
inference(superposition,[status(thm)],[c_111,c_315]) ).
tcf(c_34283,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(unordered_pair(X0,X1),X2)
| ( sK1(unordered_pair(X0,X1),X2) = X1 )
| ( sK1(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_6708,c_350]) ).
tcf(c_34284,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = X2 )
| ( set_difference(unordered_pair(X0,X1),unordered_pair(X2,X2)) = unordered_pair(X0,X1) ) ),
inference(superposition,[status(thm)],[c_195,c_350]) ).
tcf(c_34285,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(unordered_pair(X0,X1),X2)
| ( sK8(unordered_pair(X0,X1),X2) = X1 )
| ( sK8(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_149,c_350]) ).
tcf(c_34286,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,unordered_pair(X1,X2))
| ( sK8(X0,unordered_pair(X1,X2)) = X2 )
| ( sK8(X0,unordered_pair(X1,X2)) = X1 ) ),
inference(superposition,[status(thm)],[c_150,c_350]) ).
tcf(c_34287,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X0,unordered_pair(X1,X2)),X0)
| ( unordered_pair(X1,X2) = X0 )
| ( sK15(X0,unordered_pair(X1,X2)) = X2 )
| ( sK15(X0,unordered_pair(X1,X2)) = X1 ) ),
inference(superposition,[status(thm)],[c_228,c_350]) ).
tcf(c_34288,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(unordered_pair(X0,X1),X2),X2)
| ( unordered_pair(X0,X1) = X2 )
| ( sK15(unordered_pair(X0,X1),X2) = X1 )
| ( sK15(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_228,c_350]) ).
tcf(c_34289,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X1) = empty_set )
| ( sK16(unordered_pair(X0,X1)) = X1 )
| ( sK16(unordered_pair(X0,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_233,c_350]) ).
tcf(c_34290,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(unordered_pair(X0,X1),X2)
| ( sK18(unordered_pair(X0,X1),X2) = X1 )
| ( sK18(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_241,c_350]) ).
tcf(c_34291,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK27(unordered_pair(X1,X2),X0) = X2 )
| ( sK27(unordered_pair(X1,X2),X0) = X1 )
| ~ in(X0,union(unordered_pair(X1,X2))) ),
inference(superposition,[status(thm)],[c_297,c_350]) ).
tcf(c_34292,plain,
! [X0: $i,X1: $i] :
( relation(unordered_pair(X0,X1))
| ( sK38(unordered_pair(X0,X1)) = X1 )
| ( sK38(unordered_pair(X0,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_314,c_350]) ).
tcf(c_34293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK44(unordered_pair(X1,X2),X3,X0) = X2 )
| ( sK44(unordered_pair(X1,X2),X3,X0) = X1 )
| ~ in(X0,cartesian_product2(unordered_pair(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_323,c_350]) ).
tcf(c_34294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK45(X1,unordered_pair(X2,X3),X0) = X3 )
| ( sK45(X1,unordered_pair(X2,X3),X0) = X2 )
| ~ in(X0,cartesian_product2(X1,unordered_pair(X2,X3))) ),
inference(superposition,[status(thm)],[c_324,c_350]) ).
tcf(c_34297,plain,
! [X0: $i,X1: $i] :
( empty(unordered_pair(X0,X1))
| ( sK23(unordered_pair(X0,X1)) = X1 )
| ( sK23(unordered_pair(X0,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_20297,c_350]) ).
tcf(c_34301,plain,
! [X0: $i,X1: $i] :
( ( sK23(unordered_pair(X0,X1)) = X1 )
| ( sK23(unordered_pair(X0,X1)) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34297,c_344]) ).
tcf(c_34411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,union(X2))
| ~ subset(X3,X1)
| ~ in(X1,sK54(X0))
| ~ in(sK55(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_375,c_295]) ).
tcf(c_34412,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(X2,X2),sK55(X1,X0)) = sK55(X1,X0) )
| ~ subset(X2,X0)
| ~ in(X0,sK54(X1)) ),
inference(superposition,[status(thm)],[c_375,c_161]) ).
tcf(c_34413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ subset(X3,X1)
| ~ in(X3,X2)
| ~ in(X1,sK54(X0))
| ~ disjoint(sK55(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_375,c_151]) ).
tcf(c_34414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| ~ subset(X3,X1)
| ~ in(X1,sK54(X0))
| ~ subset(sK55(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_375,c_242]) ).
tcf(c_34415,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(sK55(X1,X0)),X2) = X2 )
| ~ subset(X2,X0)
| ~ in(X0,sK54(X1)) ),
inference(superposition,[status(thm)],[c_375,c_134]) ).
tcf(c_34416,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X2,X1)
| ~ in(X1,sK54(X0))
| ~ in(sK55(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_375,c_243]) ).
tcf(c_34417,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X2,X0)
| ~ empty(sK55(X1,X0))
| ~ in(X0,sK54(X1)) ),
inference(superposition,[status(thm)],[c_375,c_471]) ).
tcf(c_34418,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,sK55(X1,X0))
| ~ subset(X2,X0)
| ~ in(X0,sK54(X1)) ),
inference(superposition,[status(thm)],[c_375,c_276]) ).
tcf(c_34419,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,sK55(X1,X2))
| ~ in(X2,sK54(X1))
| ~ subset(sK18(X0,sK55(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_375,c_240]) ).
tcf(c_34420,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,sK54(X0))
| ~ subset(sK2(sK55(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_375,c_19526]) ).
tcf(c_34421,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X1,sK54(X0))
| ~ subset(unordered_pair(sK55(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_375,c_19532]) ).
tcf(c_34422,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,sK54(X1))
| ~ subset(unordered_pair(X0,sK55(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_375,c_19533]) ).
tcf(c_34423,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,sK54(X0))
| ~ subset(sK54(sK55(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_375,c_19534]) ).
tcf(c_34424,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,sK54(X0))
| ~ subset(sK2(powerset(union(sK55(X0,X1)))),X1) ),
inference(superposition,[status(thm)],[c_375,c_19702]) ).
tcf(c_34425,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,sK54(X0))
| ~ subset(sK54(powerset(union(sK55(X0,X1)))),X1) ),
inference(superposition,[status(thm)],[c_375,c_19705]) ).
tcf(c_34426,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,sK54(X0))
| ~ subset(powerset(sK55(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_375,c_19958]) ).
tcf(c_34427,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,sK54(X0))
| ~ subset(powerset(powerset(union(sK55(X0,X1)))),X1) ),
inference(superposition,[status(thm)],[c_375,c_20020]) ).
tcf(c_34428,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X1,sK54(X0))
| ~ subset(sK2(set_union2(sK55(X0,X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_375,c_20095]) ).
tcf(c_34429,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X1,sK54(X0))
| ~ subset(sK54(set_union2(sK55(X0,X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_375,c_20098]) ).
tcf(c_34430,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X1,sK54(X0))
| ~ subset(powerset(set_union2(sK55(X0,X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_375,c_20101]) ).
tcf(c_34431,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,sK54(X1))
| ~ subset(sK2(set_union2(X0,sK55(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_375,c_20131]) ).
tcf(c_34432,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,sK54(X1))
| ~ subset(sK54(set_union2(X0,sK55(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_375,c_20134]) ).
tcf(c_34433,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,sK54(X1))
| ~ subset(powerset(set_union2(X0,sK55(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_375,c_20137]) ).
tcf(c_34565,plain,
( relation(relation_dom(sK47))
| ~ empty(sK47) ),
inference(superposition,[status(thm)],[c_432,c_24125]) ).
tcf(c_34617,plain,
( empty(relation_dom(sK47))
| ~ empty(sK47) ),
inference(superposition,[status(thm)],[c_432,c_24126]) ).
tcf(c_34626,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK77(sK5),relation_dom(sK5))
| in(sK77(sK5),union(X0))
| ~ in(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_32810,c_295]) ).
tcf(c_34627,plain,
( one_to_one(sK5)
| in(sK77(sK5),relation_dom(sK5))
| ( set_union2(unordered_pair(sK77(sK5),sK77(sK5)),relation_rng(sK5)) = relation_rng(sK5) ) ),
inference(superposition,[status(thm)],[c_32810,c_161]) ).
tcf(c_34628,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK77(sK5),relation_dom(sK5))
| ~ disjoint(relation_rng(sK5),X0)
| ~ in(sK77(sK5),X0) ),
inference(superposition,[status(thm)],[c_32810,c_151]) ).
tcf(c_34629,plain,
! [X0: $i] :
( one_to_one(sK5)
| in(sK77(sK5),X0)
| in(sK77(sK5),relation_dom(sK5))
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_32810,c_242]) ).
tcf(c_34630,plain,
( one_to_one(sK5)
| in(sK77(sK5),relation_dom(sK5))
| ( apply(identity_relation(relation_rng(sK5)),sK77(sK5)) = sK77(sK5) ) ),
inference(superposition,[status(thm)],[c_32810,c_134]) ).
tcf(c_34631,plain,
( one_to_one(sK5)
| in(sK77(sK5),relation_dom(sK5))
| ~ in(relation_rng(sK5),sK77(sK5)) ),
inference(superposition,[status(thm)],[c_32810,c_243]) ).
tcf(c_34632,plain,
( one_to_one(sK5)
| in(sK77(sK5),relation_dom(sK5))
| ~ empty(relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_32810,c_471]) ).
tcf(c_34633,plain,
( one_to_one(sK5)
| element(sK77(sK5),relation_rng(sK5))
| in(sK77(sK5),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_32810,c_276]) ).
tcf(c_34665,plain,
set_difference(relation_field(sK5),set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5))) = subset_complement(relation_field(sK5),set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_27650,c_6703]) ).
tcf(c_34666,plain,
subset_complement(relation_field(sK5),subset_complement(relation_field(sK5),set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)))) = set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_27650,c_6699]) ).
tcf(c_34667,plain,
( ( set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)) = relation_field(sK5) )
| ~ subset(relation_field(sK5),set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5))) ),
inference(superposition,[status(thm)],[c_27650,c_260]) ).
tcf(c_34668,plain,
set_difference(set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),set_difference(set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),relation_field(sK5))) = set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_27650,c_123]) ).
tcf(c_34669,plain,
( proper_subset(set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),relation_field(sK5))
| ( set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_27650,c_468]) ).
tcf(c_34670,plain,
! [X0: $i] :
( subset(set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),X0)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27650,c_110]) ).
tcf(c_34671,plain,
set_difference(set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),relation_field(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_27650,c_138]) ).
tcf(c_34672,plain,
set_union2(set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),relation_field(sK5)) = relation_field(sK5),
inference(superposition,[status(thm)],[c_27650,c_85]) ).
tcf(c_34673,plain,
~ proper_subset(relation_field(sK5),set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5))),
inference(superposition,[status(thm)],[c_27650,c_188]) ).
tcf(c_34674,plain,
! [X0: $i] :
( disjoint(set_difference(set_difference(set_difference(relation_rng(sK5),relation_dom(sK5)),relation_dom(sK5)),relation_dom(sK5)),X0)
| ~ disjoint(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27650,c_190]) ).
tcf(c_34738,plain,
set_difference(empty_set,relation_dom(empty_set)) = subset_complement(empty_set,relation_dom(empty_set)),
inference(superposition,[status(thm)],[c_28288,c_29861]) ).
tcf(c_34739,plain,
! [X0: $i] :
( subset(set_difference(X0,relation_dom(relation_dom_restriction(sK5,X0))),X0)
| ~ subset(relation_dom(relation_dom_restriction(sK5,X0)),X0) ),
inference(superposition,[status(thm)],[c_29861,c_22243]) ).
tcf(c_34740,plain,
! [X0: $i] :
( element(set_difference(X0,relation_dom(relation_dom_restriction(sK5,X0))),powerset(X0))
| ~ subset(relation_dom(relation_dom_restriction(sK5,X0)),X0) ),
inference(superposition,[status(thm)],[c_29861,c_6701]) ).
tcf(c_34741,plain,
set_difference(empty_set,empty_set) = subset_complement(empty_set,empty_set),
inference(light_normalisation,[status(thm)],[c_34738,c_186]) ).
tcf(c_34742,plain,
! [X0: $i] : element(set_difference(X0,relation_dom(relation_dom_restriction(sK5,X0))),powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_34740,c_29463]) ).
tcf(c_34745,plain,
element(set_difference(empty_set,relation_dom(empty_set)),powerset(empty_set)),
inference(superposition,[status(thm)],[c_28288,c_34742]) ).
tcf(c_34746,plain,
! [X0: $i] : subset(set_difference(X0,relation_dom(relation_dom_restriction(sK5,X0))),X0),
inference(superposition,[status(thm)],[c_34742,c_274]) ).
tcf(c_34747,plain,
! [X0: $i] : union_of_subsets(X0,set_difference(powerset(X0),relation_dom(relation_dom_restriction(sK5,powerset(X0))))) = union(set_difference(powerset(X0),relation_dom(relation_dom_restriction(sK5,powerset(X0))))),
inference(superposition,[status(thm)],[c_34742,c_291]) ).
tcf(c_34749,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(set_difference(X0,relation_dom(relation_dom_restriction(sK5,X0))),powerset(X0)) ),
inference(superposition,[status(thm)],[c_34742,c_283]) ).
tcf(c_34750,plain,
element(set_difference(empty_set,empty_set),powerset(empty_set)),
inference(light_normalisation,[status(thm)],[c_34745,c_186]) ).
tcf(c_34751,plain,
! [X0: $i] : in(set_difference(X0,relation_dom(relation_dom_restriction(sK5,X0))),powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_34749,c_286]) ).
tcf(c_34754,plain,
! [X0: $i] : subset_complement(X0,set_difference(X0,relation_dom(relation_dom_restriction(sK5,X0)))) = relation_dom(relation_dom_restriction(sK5,X0)),
inference(light_normalisation,[status(thm)],[c_29862,c_29861]) ).
tcf(c_34759,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ in(X0,relation_dom(relation_dom_restriction(sK5,unordered_pair(X0,X0)))) ),
inference(superposition,[status(thm)],[c_140,c_29863]) ).
tcf(c_34762,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom_restriction(sK5,unordered_pair(X0,X1))) = unordered_pair(X0,X1) )
| ~ in(X1,relation_dom(relation_dom_restriction(sK5,unordered_pair(X0,X1))))
| ~ in(X0,relation_dom(relation_dom_restriction(sK5,unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_142,c_29863]) ).
tcf(c_34763,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom_restriction(sK5,set_union2(X0,X1))) = set_union2(X0,X1) )
| ~ subset(X1,relation_dom(relation_dom_restriction(sK5,set_union2(X0,X1))))
| ~ subset(X0,relation_dom(relation_dom_restriction(sK5,set_union2(X0,X1)))) ),
inference(superposition,[status(thm)],[c_219,c_29863]) ).
tcf(c_34764,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,relation_inverse_image(relation_inverse(sK5),X0))) = relation_inverse_image(relation_inverse(sK5),X0) )
| ~ subset(relation_rng(sK5),relation_dom(relation_dom_restriction(sK5,relation_inverse_image(relation_inverse(sK5),X0)))) ),
inference(superposition,[status(thm)],[c_22586,c_29863]) ).
tcf(c_34765,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,relation_image(relation_inverse(sK5),X0))) = relation_image(relation_inverse(sK5),X0) )
| ~ subset(relation_dom(sK5),relation_dom(relation_dom_restriction(sK5,relation_image(relation_inverse(sK5),X0)))) ),
inference(superposition,[status(thm)],[c_22588,c_29863]) ).
tcf(c_34766,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,relation_dom(relation_dom_restriction(sK5,X0)))) = relation_dom(relation_dom_restriction(sK5,X0)) )
| ~ subset(X0,relation_dom(relation_dom_restriction(sK5,relation_dom(relation_dom_restriction(sK5,X0))))) ),
inference(superposition,[status(thm)],[c_29866,c_29863]) ).
tcf(c_34767,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,relation_rng(relation_dom_restriction(sK5,X0)))) = relation_rng(relation_dom_restriction(sK5,X0)) )
| ~ subset(relation_rng(sK5),relation_dom(relation_dom_restriction(sK5,relation_rng(relation_dom_restriction(sK5,X0))))) ),
inference(superposition,[status(thm)],[c_29912,c_29863]) ).
tcf(c_34797,plain,
! [X0: $i] :
( subset(relation_field(sK5),X0)
| ~ empty(relation_rng(sK5))
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_19515,c_30534]) ).
tcf(c_34798,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(sK5))
| subset(relation_field(sK5),set_difference(X0,unordered_pair(X1,X1)))
| ~ subset(relation_rng(sK5),X0)
| ~ subset(relation_dom(sK5),set_difference(X0,unordered_pair(X1,X1))) ),
inference(superposition,[status(thm)],[c_58,c_30534]) ).
tcf(c_34799,plain,
! [X0: $i] :
( subset(relation_field(sK5),union(X0))
| ~ in(relation_rng(sK5),X0)
| ~ subset(relation_dom(sK5),union(X0)) ),
inference(superposition,[status(thm)],[c_222,c_30534]) ).
tcf(c_34800,plain,
( subset(relation_field(sK5),cartesian_product2(relation_dom(relation_rng(sK5)),relation_rng(relation_rng(sK5))))
| ~ relation(relation_rng(sK5))
| ~ subset(relation_dom(sK5),cartesian_product2(relation_dom(relation_rng(sK5)),relation_rng(relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_117,c_30534]) ).
tcf(c_34801,plain,
! [X0: $i] :
( subset(relation_field(sK5),set_union2(relation_rng(sK5),X0))
| ~ subset(relation_dom(sK5),set_union2(relation_rng(sK5),X0)) ),
inference(superposition,[status(thm)],[c_209,c_30534]) ).
tcf(c_34802,plain,
( subset(relation_field(sK5),relation_rng(sK5))
| ~ subset(relation_dom(sK5),relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_262,c_30534]) ).
tcf(c_34803,plain,
! [X0: $i] :
( subset(relation_field(sK5),set_union2(X0,relation_rng(sK5)))
| ~ subset(relation_dom(sK5),set_union2(X0,relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_19598,c_30534]) ).
tcf(c_34804,plain,
( subset(relation_field(sK5),relation_field(sK5))
| ~ subset(relation_dom(sK5),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_27654,c_30534]) ).
tcf(c_34829,plain,
( one_to_one(sK5)
| ( set_union2(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5))) = relation_field(sK5) ) ),
inference(demodulation,[status(thm)],[c_32695,c_255]) ).
tcf(c_34850,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),set_union2(X0,set_union2(X1,X0))),
inference(superposition,[status(thm)],[c_153,c_22396]) ).
tcf(c_34852,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,X0),X0),set_union2(empty_set,X0)),
inference(superposition,[status(thm)],[c_264,c_22396]) ).
tcf(c_34853,plain,
! [X0: $i] : subset(set_difference(set_difference(X0,empty_set),empty_set),set_union2(X0,X0)),
inference(superposition,[status(thm)],[c_4095,c_22396]) ).
tcf(c_34854,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X1,X0))),set_difference(X1,set_difference(X1,X0))),set_union2(set_difference(X0,X1),X0)),
inference(superposition,[status(thm)],[c_371,c_22396]) ).
tcf(c_34855,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_rng(sK5),empty_set),empty_set),set_union2(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_21834,c_22396]) ).
tcf(c_34856,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_dom(sK5),empty_set),empty_set),set_union2(relation_dom(sK5),relation_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22079,c_22396]) ).
tcf(c_34857,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_dom(sK5),empty_set),empty_set),set_union2(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))))),
inference(superposition,[status(thm)],[c_25056,c_22396]) ).
tcf(c_34858,plain,
subset(set_difference(set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),set_difference(relation_dom(sK5),relation_rng(sK5))),set_union2(relation_rng(sK5),relation_field(sK5))),
inference(superposition,[status(thm)],[c_27644,c_22396]) ).
tcf(c_34859,plain,
! [X0: $i] : subset(set_difference(set_difference(X0,empty_set),empty_set),set_union2(X0,relation_dom(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29867,c_22396]) ).
tcf(c_34860,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_rng(sK5),empty_set),empty_set),set_union2(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_29913,c_22396]) ).
tcf(c_34862,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,set_difference(set_difference(X1,X0),X0)),set_difference(set_difference(X1,X0),X0)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_145,c_22396]) ).
tcf(c_34863,plain,
! [X0: $i] : subset(set_difference(set_difference(X0,set_difference(empty_set,X0)),set_difference(empty_set,X0)),X0),
inference(superposition,[status(thm)],[c_244,c_22396]) ).
tcf(c_34864,plain,
! [X0: $i] : subset(set_difference(set_difference(X0,set_difference(X0,X0)),set_difference(X0,X0)),X0),
inference(superposition,[status(thm)],[c_245,c_22396]) ).
tcf(c_34865,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_255,c_22396]) ).
tcf(c_34866,plain,
! [X0: $i] : subset(set_difference(set_difference(empty_set,set_difference(X0,empty_set)),set_difference(X0,empty_set)),X0),
inference(superposition,[status(thm)],[c_19599,c_22396]) ).
tcf(c_34867,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_rng(sK5),set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))),set_difference(relation_inverse_image(relation_inverse(sK5),X0),relation_rng(sK5))),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21870,c_22396]) ).
tcf(c_34868,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_dom(sK5),set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))),set_difference(relation_image(relation_inverse(sK5),X0),relation_dom(sK5))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22341,c_22396]) ).
tcf(c_34869,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_dom(sK5),set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))),set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),relation_dom(sK5))),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_31729,c_22396]) ).
tcf(c_34870,plain,
subset(set_difference(set_difference(relation_dom(sK5),set_difference(relation_rng(sK5),relation_dom(sK5))),set_difference(relation_rng(sK5),relation_dom(sK5))),relation_field(sK5)),
inference(superposition,[status(thm)],[c_27464,c_22396]) ).
tcf(c_34871,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0))) = subset_complement(set_union2(X0,X1),set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_22396,c_6703]) ).
tcf(c_34872,plain,
! [X0: $i,X1: $i] : subset_complement(set_union2(X0,X1),subset_complement(set_union2(X0,X1),set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)))) = set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_22396,c_6699]) ).
tcf(c_34873,plain,
! [X0: $i,X1: $i] :
( ( set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)) = set_union2(X0,X1) )
| ~ subset(set_union2(X0,X1),set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0))) ),
inference(superposition,[status(thm)],[c_22396,c_260]) ).
tcf(c_34874,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),set_difference(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),set_union2(X0,X1))) = set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_22396,c_123]) ).
tcf(c_34875,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),set_union2(X0,X1))
| ( set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_22396,c_468]) ).
tcf(c_34876,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),X2)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_22396,c_110]) ).
tcf(c_34877,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),set_union2(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_22396,c_138]) ).
tcf(c_34878,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),set_union2(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_22396,c_85]) ).
tcf(c_34879,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_22396,c_188]) ).
tcf(c_34880,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(set_difference(X0,set_difference(X1,X0)),set_difference(X1,X0)),X2)
| ~ disjoint(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_22396,c_190]) ).
tcf(c_34887,plain,
subset(set_difference(set_difference(relation_rng(sK5),empty_set),empty_set),set_union2(relation_rng(sK5),empty_set)),
inference(light_normalisation,[status(thm)],[c_34860,c_30747]) ).
tcf(c_34888,plain,
subset(set_difference(set_difference(relation_dom(sK5),empty_set),empty_set),relation_dom(sK5)),
inference(light_normalisation,[status(thm)],[c_34856,c_22341]) ).
tcf(c_34889,plain,
subset(set_difference(set_difference(relation_rng(sK5),empty_set),empty_set),relation_rng(sK5)),
inference(light_normalisation,[status(thm)],[c_34855,c_21870]) ).
tcf(c_34896,plain,
subset(set_difference(set_difference(relation_rng(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),set_difference(relation_dom(sK5),relation_rng(sK5))),relation_field(sK5)),
inference(light_normalisation,[status(thm)],[c_34858,c_27806]) ).
tcf(c_34899,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X1,X0))),set_difference(X1,set_difference(X1,X0))),X0),
inference(light_normalisation,[status(thm)],[c_34854,c_20834]) ).
tcf(c_35071,plain,
! [X0: $i,X1: $i] :
( ( complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0 )
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_273,c_448]) ).
tcf(c_35072,plain,
! [X0: $i] :
( empty(powerset(X0))
| ( complements_of_subsets(X0,complements_of_subsets(X0,sK22(powerset(X0)))) = sK22(powerset(X0)) ) ),
inference(superposition,[status(thm)],[c_279,c_448]) ).
tcf(c_35073,plain,
! [X0: $i] : complements_of_subsets(X0,complements_of_subsets(X0,sK23(powerset(powerset(X0))))) = sK23(powerset(powerset(X0))),
inference(superposition,[status(thm)],[c_281,c_448]) ).
tcf(c_35074,plain,
! [X0: $i,X1: $i] :
( ( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 )
| ~ empty(X1)
| ~ empty(powerset(powerset(X0))) ),
inference(superposition,[status(thm)],[c_284,c_448]) ).
tcf(c_35075,plain,
! [X0: $i,X1: $i] :
( ( complements_of_subsets(X1,complements_of_subsets(X1,subset_complement(powerset(X1),X0))) = subset_complement(powerset(X1),X0) )
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_6701,c_448]) ).
tcf(c_35076,plain,
! [X0: $i,X1: $i] :
( ( complements_of_subsets(X1,complements_of_subsets(X1,complements_of_subsets(X1,X0))) = complements_of_subsets(X1,X0) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(superposition,[status(thm)],[c_449,c_448]) ).
tcf(c_35077,plain,
! [X0: $i,X1: $i] :
( ( complements_of_subsets(X1,complements_of_subsets(X1,union_of_subsets(powerset(X1),X0))) = union_of_subsets(powerset(X1),X0) )
| ~ element(X0,powerset(powerset(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_452,c_448]) ).
tcf(c_35078,plain,
! [X0: $i,X1: $i] :
( ( complements_of_subsets(X1,complements_of_subsets(X1,meet_of_subsets(powerset(X1),X0))) = meet_of_subsets(powerset(X1),X0) )
| ~ element(X0,powerset(powerset(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_453,c_448]) ).
tcf(c_35079,plain,
! [X0: $i] : complements_of_subsets(X0,complements_of_subsets(X0,powerset(X0))) = powerset(X0),
inference(superposition,[status(thm)],[c_4010,c_448]) ).
tcf(c_35080,plain,
! [X0: $i] : complements_of_subsets(X0,complements_of_subsets(X0,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_19225,c_448]) ).
tcf(c_35081,plain,
! [X0: $i] :
( relation(powerset(powerset(X0)))
| ( complements_of_subsets(X0,complements_of_subsets(X0,sK38(powerset(powerset(X0))))) = sK38(powerset(powerset(X0))) ) ),
inference(superposition,[status(thm)],[c_19315,c_448]) ).
tcf(c_35082,plain,
! [X0: $i,X1: $i] :
( disjoint(powerset(powerset(X0)),X1)
| ( complements_of_subsets(X0,complements_of_subsets(X0,sK8(powerset(powerset(X0)),X1))) = sK8(powerset(powerset(X0)),X1) ) ),
inference(superposition,[status(thm)],[c_19396,c_448]) ).
tcf(c_35083,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,powerset(powerset(X0)))
| ( complements_of_subsets(X0,complements_of_subsets(X0,sK8(X1,powerset(powerset(X0))))) = sK8(X1,powerset(powerset(X0))) ) ),
inference(superposition,[status(thm)],[c_19408,c_448]) ).
tcf(c_35084,plain,
! [X0: $i] : complements_of_subsets(X0,complements_of_subsets(X0,set_difference(powerset(X0),relation_dom(relation_dom_restriction(sK5,powerset(X0)))))) = set_difference(powerset(X0),relation_dom(relation_dom_restriction(sK5,powerset(X0)))),
inference(superposition,[status(thm)],[c_34742,c_448]) ).
tcf(c_35087,plain,
! [X0: $i] : complements_of_subsets(X0,complements_of_subsets(X0,sK22(powerset(X0)))) = sK22(powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_35072,c_286]) ).
tcf(c_35118,plain,
! [X0: $i] :
( in(unordered_pair(powerset(empty_set),powerset(empty_set)),identity_relation(X0))
| ~ in(empty_set,X0) ),
inference(superposition,[status(thm)],[c_111,c_6679]) ).
tcf(c_35121,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,X2)),union(X1))
| ~ in(X2,X0)
| ~ in(identity_relation(X0),X1) ),
inference(superposition,[status(thm)],[c_6679,c_295]) ).
tcf(c_35122,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0))),identity_relation(X1)) = identity_relation(X1) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_6679,c_161]) ).
tcf(c_35123,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ disjoint(identity_relation(X2),X1)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),X1) ),
inference(superposition,[status(thm)],[c_6679,c_151]) ).
tcf(c_35124,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,X2)),X1)
| ~ in(X2,X0)
| ~ subset(identity_relation(X0),X1) ),
inference(superposition,[status(thm)],[c_6679,c_242]) ).
tcf(c_35125,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(identity_relation(X1)),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0))) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_6679,c_134]) ).
tcf(c_35126,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(identity_relation(X0),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X1))) ),
inference(superposition,[status(thm)],[c_6679,c_243]) ).
tcf(c_35127,plain,
! [X0: $i,X1: $i] :
( ~ empty(identity_relation(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_6679,c_471]) ).
tcf(c_35128,plain,
! [X0: $i,X1: $i] :
( element(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),identity_relation(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_6679,c_276]) ).
tcf(c_35169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,X0)
| ( set_difference(cartesian_product2(X0,X1),unordered_pair(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)))) = cartesian_product2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_195,c_72]) ).
tcf(c_35170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_351,c_72]) ).
tcf(c_35173,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X0)
| ~ in(unordered_pair(powerset(empty_set),powerset(empty_set)),cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_111,c_72]) ).
tcf(c_35174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_351,c_72]) ).
tcf(c_35175,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(empty_set,X1)
| ~ in(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_111,c_72]) ).
tcf(c_35176,plain,
! [X0: $i,X1: $i] :
( in(X0,empty_set)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),empty_set) ),
inference(superposition,[status(thm)],[c_26653,c_72]) ).
tcf(c_35177,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),empty_set) ),
inference(superposition,[status(thm)],[c_29072,c_72]) ).
tcf(c_35195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X1)
| ( set_difference(cartesian_product2(X0,X1),unordered_pair(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)))) = cartesian_product2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_195,c_73]) ).
tcf(c_35196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_351,c_73]) ).
tcf(c_35199,plain,
! [X0: $i,X1: $i] :
( in(empty_set,X1)
| ~ in(unordered_pair(powerset(empty_set),powerset(empty_set)),cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_111,c_73]) ).
tcf(c_35200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_351,c_73]) ).
tcf(c_35201,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_111,c_73]) ).
tcf(c_35202,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),empty_set) ),
inference(superposition,[status(thm)],[c_26653,c_73]) ).
tcf(c_35203,plain,
! [X0: $i,X1: $i] :
( in(X1,empty_set)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),empty_set) ),
inference(superposition,[status(thm)],[c_29072,c_73]) ).
tcf(c_35219,plain,
( function(relation_dom(sK75))
| ~ empty(sK75) ),
inference(superposition,[status(thm)],[c_432,c_24182]) ).
tcf(c_35222,plain,
( one_to_one(sK5)
| ( set_union2(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5))) = relation_field(sK5) ) ),
inference(demodulation,[status(thm)],[c_32803,c_255]) ).
tcf(c_35233,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_dom(relation_dom_restriction(sK5,X0)),set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_dom(relation_dom_restriction(sK5,X0)))),set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_dom(relation_dom_restriction(sK5,X0)))),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_22396]) ).
tcf(c_35234,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(relation_dom(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(sK5,X0))),relation_rng(relation_dom_restriction(sK5,X0))),relation_rng(relation_dom_restriction(sK5,X0))),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_22121]) ).
tcf(c_35235,plain,
! [X0: $i] : subset(set_difference(relation_dom(relation_dom_restriction(sK5,X0)),set_difference(set_difference(set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_dom(relation_dom_restriction(sK5,X0))),relation_dom(relation_dom_restriction(sK5,X0))),relation_dom(relation_dom_restriction(sK5,X0)))),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_20482]) ).
tcf(c_35236,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_dom(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(sK5,X0))),relation_rng(relation_dom_restriction(sK5,X0))),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_20247]) ).
tcf(c_35237,plain,
! [X0: $i] :
( relation(relation_field(relation_dom_restriction(sK5,X0)))
| ~ relation(relation_rng(relation_dom_restriction(sK5,X0)))
| ~ relation(relation_dom(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_27483,c_248]) ).
tcf(c_35238,plain,
! [X0: $i] : ~ proper_subset(relation_field(relation_dom_restriction(sK5,X0)),set_difference(relation_dom(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(sK5,X0)))),
inference(superposition,[status(thm)],[c_27483,c_19484]) ).
tcf(c_35239,plain,
! [X0: $i] : subset(set_difference(relation_dom(relation_dom_restriction(sK5,X0)),set_difference(set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_dom(relation_dom_restriction(sK5,X0))),relation_dom(relation_dom_restriction(sK5,X0)))),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_19741]) ).
tcf(c_35240,plain,
! [X0: $i] : ~ in(powerset(relation_field(relation_dom_restriction(sK5,X0))),relation_rng(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_20137]) ).
tcf(c_35241,plain,
! [X0: $i] : ~ in(sK54(relation_field(relation_dom_restriction(sK5,X0))),relation_rng(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_20134]) ).
tcf(c_35242,plain,
! [X0: $i] : ~ in(sK2(relation_field(relation_dom_restriction(sK5,X0))),relation_rng(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_20131]) ).
tcf(c_35243,plain,
! [X0: $i] : ~ in(powerset(relation_field(relation_dom_restriction(sK5,X0))),relation_dom(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_20101]) ).
tcf(c_35244,plain,
! [X0: $i] : ~ in(sK54(relation_field(relation_dom_restriction(sK5,X0))),relation_dom(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_20098]) ).
tcf(c_35245,plain,
! [X0: $i] : ~ in(sK2(relation_field(relation_dom_restriction(sK5,X0))),relation_dom(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_20095]) ).
tcf(c_35246,plain,
! [X0: $i] : subset(set_difference(relation_dom(relation_dom_restriction(sK5,X0)),set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_dom(relation_dom_restriction(sK5,X0)))),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_19566]) ).
tcf(c_35247,plain,
! [X0: $i] : ~ proper_subset(relation_field(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_19595]) ).
tcf(c_35248,plain,
! [X0: $i] : subset(set_difference(relation_dom(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(sK5,X0))),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_19485]) ).
tcf(c_35249,plain,
! [X0: $i] : set_difference(relation_dom(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(sK5,X0))) = set_difference(relation_field(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_153]) ).
tcf(c_35250,plain,
! [X0: $i] : ~ proper_subset(relation_field(relation_dom_restriction(sK5,X0)),relation_dom(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_19458]) ).
tcf(c_35251,plain,
! [X0: $i] :
( empty(relation_dom(relation_dom_restriction(sK5,X0)))
| ~ empty(relation_field(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_27483,c_247]) ).
tcf(c_35252,plain,
! [X0: $i] :
( empty(relation_rng(relation_dom_restriction(sK5,X0)))
| ~ empty(relation_field(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_27483,c_246]) ).
tcf(c_35253,plain,
! [X0: $i] : subset(relation_dom(relation_dom_restriction(sK5,X0)),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_209]) ).
tcf(c_35254,plain,
! [X0: $i,X1: $i] :
( subset(relation_field(relation_dom_restriction(sK5,X0)),X1)
| ~ subset(relation_rng(relation_dom_restriction(sK5,X0)),X1)
| ~ subset(relation_dom(relation_dom_restriction(sK5,X0)),X1) ),
inference(superposition,[status(thm)],[c_27483,c_219]) ).
tcf(c_35255,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_dom(relation_dom_restriction(sK5,X0))),relation_dom(relation_dom_restriction(sK5,X0))),relation_dom(relation_dom_restriction(sK5,X0))),relation_dom(relation_dom_restriction(sK5,X0))),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_22118]) ).
tcf(c_35256,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_dom(relation_dom_restriction(sK5,X0))),set_difference(relation_dom(relation_dom_restriction(sK5,X0)),set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_dom(relation_dom_restriction(sK5,X0))))),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_20651]) ).
tcf(c_35257,plain,
! [X0: $i] : subset(set_difference(relation_rng(relation_dom_restriction(sK5,X0)),set_difference(set_difference(relation_dom(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(sK5,X0))),relation_rng(relation_dom_restriction(sK5,X0)))),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_20485]) ).
tcf(c_35258,plain,
! [X0: $i] : subset(set_difference(set_difference(set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_dom(relation_dom_restriction(sK5,X0))),relation_dom(relation_dom_restriction(sK5,X0))),relation_dom(relation_dom_restriction(sK5,X0))),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_20244]) ).
tcf(c_35259,plain,
! [X0: $i] : subset(set_difference(relation_rng(relation_dom_restriction(sK5,X0)),set_difference(relation_dom(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(sK5,X0)))),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_19744]) ).
tcf(c_35260,plain,
! [X0: $i] : subset(set_difference(set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_dom(relation_dom_restriction(sK5,X0))),relation_dom(relation_dom_restriction(sK5,X0))),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_19715]) ).
tcf(c_35261,plain,
! [X0: $i] : subset(set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_dom(relation_dom_restriction(sK5,X0))),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_19593]) ).
tcf(c_35262,plain,
! [X0: $i] : subset(relation_rng(relation_dom_restriction(sK5,X0)),relation_field(relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_27483,c_19598]) ).
tcf(c_35263,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(relation_dom_restriction(sK5,X1)))
| in(X0,relation_dom(relation_dom_restriction(sK5,X1)))
| ~ in(X0,relation_field(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_27483,c_254]) ).
tcf(c_35264,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_field(relation_dom_restriction(sK5,X1)))
| ~ in(X0,relation_dom(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_27483,c_252]) ).
tcf(c_35265,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_field(relation_dom_restriction(sK5,X1)))
| ~ in(X0,relation_rng(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_27483,c_253]) ).
tcf(c_35414,plain,
! [X0: $i] :
( ( set_difference(relation_rng(sK5),relation_dom(relation_composition(relation_inverse(sK5),X0))) = subset_complement(relation_rng(sK5),relation_dom(relation_composition(relation_inverse(sK5),X0))) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_29424,c_6703]) ).
tcf(c_35415,plain,
! [X0: $i] :
( ( subset_complement(relation_rng(sK5),subset_complement(relation_rng(sK5),relation_dom(relation_composition(relation_inverse(sK5),X0)))) = relation_dom(relation_composition(relation_inverse(sK5),X0)) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_29424,c_6699]) ).
tcf(c_35416,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(relation_inverse(sK5),X0)) = relation_rng(sK5) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK5))
| ~ subset(relation_rng(sK5),relation_dom(relation_composition(relation_inverse(sK5),X0))) ),
inference(superposition,[status(thm)],[c_29424,c_260]) ).
tcf(c_35417,plain,
! [X0: $i] :
( ( set_difference(relation_dom(relation_composition(relation_inverse(sK5),X0)),set_difference(relation_dom(relation_composition(relation_inverse(sK5),X0)),relation_rng(sK5))) = relation_dom(relation_composition(relation_inverse(sK5),X0)) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_29424,c_123]) ).
tcf(c_35418,plain,
! [X0: $i] :
( proper_subset(relation_dom(relation_composition(relation_inverse(sK5),X0)),relation_rng(sK5))
| ( relation_dom(relation_composition(relation_inverse(sK5),X0)) = relation_rng(sK5) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_29424,c_468]) ).
tcf(c_35419,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_composition(relation_inverse(sK5),X1)),X0)
| ~ relation(X1)
| ~ relation(relation_inverse(sK5))
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29424,c_110]) ).
tcf(c_35420,plain,
! [X0: $i] :
( ( set_difference(relation_dom(relation_composition(relation_inverse(sK5),X0)),relation_rng(sK5)) = empty_set )
| ~ relation(X0)
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_29424,c_138]) ).
tcf(c_35421,plain,
! [X0: $i] :
( ( set_union2(relation_dom(relation_composition(relation_inverse(sK5),X0)),relation_rng(sK5)) = relation_rng(sK5) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_29424,c_85]) ).
tcf(c_35422,plain,
! [X0: $i] :
( ~ relation(X0)
| ~ relation(relation_inverse(sK5))
| ~ proper_subset(relation_rng(sK5),relation_dom(relation_composition(relation_inverse(sK5),X0))) ),
inference(superposition,[status(thm)],[c_29424,c_188]) ).
tcf(c_35423,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_dom(relation_composition(relation_inverse(sK5),X1)),X0)
| ~ relation(X1)
| ~ relation(relation_inverse(sK5))
| ~ disjoint(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_29424,c_190]) ).
tcf(c_35511,plain,
! [X0: $i] :
( ( set_difference(relation_dom(sK5),relation_rng(relation_composition(X0,relation_inverse(sK5)))) = subset_complement(relation_dom(sK5),relation_rng(relation_composition(X0,relation_inverse(sK5)))) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_29599,c_6703]) ).
tcf(c_35512,plain,
! [X0: $i] :
( ( subset_complement(relation_dom(sK5),subset_complement(relation_dom(sK5),relation_rng(relation_composition(X0,relation_inverse(sK5))))) = relation_rng(relation_composition(X0,relation_inverse(sK5))) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_29599,c_6699]) ).
tcf(c_35513,plain,
! [X0: $i] :
( ( relation_rng(relation_composition(X0,relation_inverse(sK5))) = relation_dom(sK5) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK5))
| ~ subset(relation_dom(sK5),relation_rng(relation_composition(X0,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_29599,c_260]) ).
tcf(c_35514,plain,
! [X0: $i] :
( ( set_difference(relation_rng(relation_composition(X0,relation_inverse(sK5))),set_difference(relation_rng(relation_composition(X0,relation_inverse(sK5))),relation_dom(sK5))) = relation_rng(relation_composition(X0,relation_inverse(sK5))) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_29599,c_123]) ).
tcf(c_35515,plain,
! [X0: $i] :
( proper_subset(relation_rng(relation_composition(X0,relation_inverse(sK5))),relation_dom(sK5))
| ( relation_rng(relation_composition(X0,relation_inverse(sK5))) = relation_dom(sK5) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_29599,c_468]) ).
tcf(c_35516,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_composition(X1,relation_inverse(sK5))),X0)
| ~ relation(X1)
| ~ relation(relation_inverse(sK5))
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_29599,c_110]) ).
tcf(c_35517,plain,
! [X0: $i] :
( ( set_difference(relation_rng(relation_composition(X0,relation_inverse(sK5))),relation_dom(sK5)) = empty_set )
| ~ relation(X0)
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_29599,c_138]) ).
tcf(c_35518,plain,
! [X0: $i] :
( ( set_union2(relation_rng(relation_composition(X0,relation_inverse(sK5))),relation_dom(sK5)) = relation_dom(sK5) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_29599,c_85]) ).
tcf(c_35519,plain,
! [X0: $i] :
( ~ relation(X0)
| ~ relation(relation_inverse(sK5))
| ~ proper_subset(relation_dom(sK5),relation_rng(relation_composition(X0,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_29599,c_188]) ).
tcf(c_35520,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_rng(relation_composition(X1,relation_inverse(sK5))),X0)
| ~ relation(X1)
| ~ relation(relation_inverse(sK5))
| ~ disjoint(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_29599,c_190]) ).
tcf(c_35577,plain,
! [X0: $i] : set_difference(relation_rng(sK5),set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0))) = subset_complement(relation_rng(sK5),set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22401,c_6703]) ).
tcf(c_35578,plain,
! [X0: $i] : subset_complement(relation_rng(sK5),subset_complement(relation_rng(sK5),set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0)))) = set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_22401,c_6699]) ).
tcf(c_35579,plain,
! [X0: $i] :
( ( set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0)) = relation_rng(sK5) )
| ~ subset(relation_rng(sK5),set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0))) ),
inference(superposition,[status(thm)],[c_22401,c_260]) ).
tcf(c_35580,plain,
! [X0: $i] : set_difference(set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0)),set_difference(set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0)),relation_rng(sK5))) = set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_22401,c_123]) ).
tcf(c_35581,plain,
! [X0: $i] :
( proper_subset(set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0)),relation_rng(sK5))
| ( set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0)) = relation_rng(sK5) ) ),
inference(superposition,[status(thm)],[c_22401,c_468]) ).
tcf(c_35582,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X1)),relation_inverse_image(relation_inverse(sK5),X1)),X0)
| ~ subset(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_22401,c_110]) ).
tcf(c_35583,plain,
! [X0: $i] : set_difference(set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0)),relation_rng(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_22401,c_138]) ).
tcf(c_35584,plain,
! [X0: $i] : set_union2(set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0)),relation_rng(sK5)) = relation_rng(sK5),
inference(superposition,[status(thm)],[c_22401,c_85]) ).
tcf(c_35585,plain,
! [X0: $i] : ~ proper_subset(relation_rng(sK5),set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X0)),relation_inverse_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22401,c_188]) ).
tcf(c_35586,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(set_difference(relation_rng(sK5),relation_inverse_image(relation_inverse(sK5),X1)),relation_inverse_image(relation_inverse(sK5),X1)),X0)
| ~ disjoint(relation_rng(sK5),X0) ),
inference(superposition,[status(thm)],[c_22401,c_190]) ).
tcf(c_35611,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(empty_set,cartesian_product2(X2,X1))
| ~ subset(empty_set,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_26653,c_84]) ).
tcf(c_35612,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(empty_set,cartesian_product2(X1,X2))
| ~ subset(empty_set,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_29072,c_84]) ).
tcf(c_35613,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X2,X0),empty_set)
| ~ subset(X2,empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_26653,c_84]) ).
tcf(c_35614,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X0,X2),empty_set)
| ~ subset(X2,empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_29072,c_84]) ).
tcf(c_35615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_difference(cartesian_product2(X1,X3),cartesian_product2(X0,X2)) = subset_complement(cartesian_product2(X1,X3),cartesian_product2(X0,X2)) )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_6703]) ).
tcf(c_35616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( subset_complement(cartesian_product2(X1,X3),subset_complement(cartesian_product2(X1,X3),cartesian_product2(X0,X2))) = cartesian_product2(X0,X2) )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_6699]) ).
tcf(c_35617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
| ~ subset(X3,X1)
| ~ subset(X2,X0)
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_84,c_260]) ).
tcf(c_35618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_difference(cartesian_product2(X0,X2),set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X3))) = cartesian_product2(X0,X2) )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_123]) ).
tcf(c_35619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( proper_subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ( cartesian_product2(X0,X2) = cartesian_product2(X1,X3) )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_468]) ).
tcf(c_35620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(cartesian_product2(X3,X4),X2)
| ~ subset(X4,X1)
| ~ subset(X3,X0)
| ~ subset(cartesian_product2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_84,c_110]) ).
tcf(c_35621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_difference(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) = empty_set )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_138]) ).
tcf(c_35622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) = cartesian_product2(X1,X3) )
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_35623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ subset(X3,X1)
| ~ subset(X2,X0)
| ~ proper_subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_84,c_188]) ).
tcf(c_35624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( disjoint(cartesian_product2(X3,X4),X2)
| ~ subset(X4,X1)
| ~ subset(X3,X0)
| ~ disjoint(cartesian_product2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_84,c_190]) ).
tcf(c_35718,plain,
! [X0: $i,X1: $i] : relation_dom_restriction(relation_rng_restriction(X0,sK5),X1) = relation_rng_restriction(X0,relation_dom_restriction(sK5,X1)),
inference(superposition,[status(thm)],[c_96,c_89]) ).
tcf(c_35719,plain,
! [X0: $i,X1: $i,X2: $i] : relation_dom_restriction(relation_rng_restriction(X0,identity_relation(X1)),X2) = relation_rng_restriction(X0,relation_dom_restriction(identity_relation(X1),X2)),
inference(superposition,[status(thm)],[c_422,c_89]) ).
tcf(c_35720,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X1,function_inverse(X0)),X2) = relation_rng_restriction(X1,relation_dom_restriction(function_inverse(X0),X2)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_465,c_89]) ).
tcf(c_35721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X1,relation_dom_restriction(X0,X2)),X3) = relation_rng_restriction(X1,relation_dom_restriction(relation_dom_restriction(X0,X2),X3)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_334,c_89]) ).
tcf(c_35722,plain,
! [X0: $i,X1: $i] : relation_dom_restriction(relation_rng_restriction(X0,empty_set),X1) = relation_rng_restriction(X0,relation_dom_restriction(empty_set,X1)),
inference(superposition,[status(thm)],[c_231,c_89]) ).
tcf(c_35723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X2,set_union2(X0,X1)),X3) = relation_rng_restriction(X2,relation_dom_restriction(set_union2(X0,X1),X3)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_248,c_89]) ).
tcf(c_35724,plain,
! [X0: $i,X1: $i] : relation_dom_restriction(relation_rng_restriction(X0,sK47),X1) = relation_rng_restriction(X0,relation_dom_restriction(sK47,X1)),
inference(superposition,[status(thm)],[c_329,c_89]) ).
tcf(c_35725,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X1,relation_dom(X0)),X2) = relation_rng_restriction(X1,relation_dom_restriction(relation_dom(X0),X2)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_342,c_89]) ).
tcf(c_35726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X1,relation_rng_restriction(X2,X0)),X3) = relation_rng_restriction(X1,relation_dom_restriction(relation_rng_restriction(X2,X0),X3)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_352,c_89]) ).
tcf(c_35727,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X1,relation_rng(X0)),X2) = relation_rng_restriction(X1,relation_dom_restriction(relation_rng(X0),X2)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_360,c_89]) ).
tcf(c_35728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X2,set_difference(X0,set_difference(X0,X1))),X3) = relation_rng_restriction(X2,relation_dom_restriction(set_difference(X0,set_difference(X0,X1)),X3)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_364,c_89]) ).
tcf(c_35729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X2,relation_composition(X0,X1)),X3) = relation_rng_restriction(X2,relation_dom_restriction(relation_composition(X0,X1),X3)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_408,c_89]) ).
tcf(c_35730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X2,relation_composition(X0,X1)),X3) = relation_rng_restriction(X2,relation_dom_restriction(relation_composition(X0,X1),X3)) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_407,c_89]) ).
tcf(c_35731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X2,relation_composition(X1,X0)),X3) = relation_rng_restriction(X2,relation_dom_restriction(relation_composition(X1,X0),X3)) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_403,c_89]) ).
tcf(c_35732,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X1,relation_inverse(X0)),X2) = relation_rng_restriction(X1,relation_dom_restriction(relation_inverse(X0),X2)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_434,c_89]) ).
tcf(c_35733,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X1,relation_inverse(X0)),X2) = relation_rng_restriction(X1,relation_dom_restriction(relation_inverse(X0),X2)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_433,c_89]) ).
tcf(c_35734,plain,
! [X0: $i,X1: $i] : relation_dom_restriction(relation_rng_restriction(X0,sK75),X1) = relation_rng_restriction(X0,relation_dom_restriction(sK75,X1)),
inference(superposition,[status(thm)],[c_456,c_89]) ).
tcf(c_35735,plain,
! [X0: $i,X1: $i] : relation_dom_restriction(relation_rng_restriction(X0,sK79),X1) = relation_rng_restriction(X0,relation_dom_restriction(sK79,X1)),
inference(superposition,[status(thm)],[c_474,c_89]) ).
tcf(c_35736,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X1,sK23(X0)),X2) = relation_rng_restriction(X1,relation_dom_restriction(sK23(X0),X2)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20383,c_89]) ).
tcf(c_35737,plain,
! [X0: $i,X1: $i,X2: $i] : relation_dom_restriction(relation_rng_restriction(X0,relation_dom_restriction(sK5,X1)),X2) = relation_rng_restriction(X0,relation_dom_restriction(relation_dom_restriction(sK5,X1),X2)),
inference(superposition,[status(thm)],[c_25741,c_89]) ).
tcf(c_35738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : relation_dom_restriction(relation_rng_restriction(X0,relation_dom_restriction(relation_dom_restriction(sK5,X1),X2)),X3) = relation_rng_restriction(X0,relation_dom_restriction(relation_dom_restriction(relation_dom_restriction(sK5,X1),X2),X3)),
inference(superposition,[status(thm)],[c_26788,c_89]) ).
tcf(c_35739,plain,
! [X0: $i,X1: $i] : relation_rng_restriction(X0,relation_dom_restriction(empty_set,X1)) = relation_dom_restriction(empty_set,X1),
inference(light_normalisation,[status(thm)],[c_35722,c_19422]) ).
tcf(c_35822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X2,X1),union(X3))
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_93,c_295]) ).
tcf(c_35823,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(sK3(X0,X2,X1),sK3(X0,X2,X1)),X2) = X2 )
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_93,c_161]) ).
tcf(c_35824,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X2)
| ~ disjoint(X1,X3)
| ~ in(X0,relation_image(X2,X1))
| ~ in(sK3(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_93,c_151]) ).
tcf(c_35825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X2,X1),X3)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_93,c_242]) ).
tcf(c_35826,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK3(X0,X2,X1)) = sK3(X0,X2,X1) )
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_93,c_134]) ).
tcf(c_35827,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ in(X1,relation_image(X2,X0))
| ~ in(X0,sK3(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_93,c_243]) ).
tcf(c_35828,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_93,c_471]) ).
tcf(c_35829,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_93,c_276]) ).
tcf(c_35830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,relation_dom(relation_dom_restriction(X2,X3)),X1),relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_dom(relation_dom_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_93,c_214]) ).
tcf(c_35831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,relation_dom(relation_dom_restriction(X2,X3)),X1),X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_dom(relation_dom_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_93,c_213]) ).
tcf(c_35832,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,relation_rng(relation_rng_restriction(X2,X3)),X1),relation_rng(X3))
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_rng(relation_rng_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_93,c_77]) ).
tcf(c_35833,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,relation_rng(relation_rng_restriction(X2,X3)),X1),X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_rng(relation_rng_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_93,c_76]) ).
tcf(c_35834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X2))
| ~ relation(X3)
| ~ in(X1,relation_image(X3,sK2(X2)))
| ~ subset(X0,sK3(X1,sK2(X2),X3)) ),
inference(superposition,[status(thm)],[c_93,c_87]) ).
tcf(c_35835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X1)
| ~ disjoint(X2,X3)
| ~ in(X0,relation_image(X1,set_difference(X2,set_difference(X2,X3)))) ),
inference(superposition,[status(thm)],[c_93,c_166]) ).
tcf(c_35836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,set_difference(X2,set_difference(X2,X3)),X1),X3)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_difference(X2,set_difference(X2,X3)))) ),
inference(superposition,[status(thm)],[c_93,c_370]) ).
tcf(c_35837,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ in(X0,relation_image(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_93,c_234]) ).
tcf(c_35838,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK3(X0,unordered_pair(X2,X2),X1) = X2 )
| ~ relation(X1)
| ~ in(X0,relation_image(X1,unordered_pair(X2,X2))) ),
inference(superposition,[status(thm)],[c_93,c_239]) ).
tcf(c_35839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,set_union2(X2,X3),X1),X3)
| in(sK3(X0,set_union2(X2,X3),X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_union2(X2,X3))) ),
inference(superposition,[status(thm)],[c_93,c_254]) ).
tcf(c_35840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ in(X0,relation_image(X3,set_difference(X1,X2)))
| ~ in(sK3(X0,set_difference(X1,X2),X3),X2) ),
inference(superposition,[status(thm)],[c_93,c_270]) ).
tcf(c_35841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,set_difference(X2,X3),X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_difference(X2,X3))) ),
inference(superposition,[status(thm)],[c_93,c_269]) ).
tcf(c_35842,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK3(X0,powerset(X2),X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_93,c_290]) ).
tcf(c_35843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK3(X0,unordered_pair(X2,X3),X1) = X3 )
| ( sK3(X0,unordered_pair(X2,X3),X1) = X2 )
| ~ relation(X1)
| ~ in(X0,relation_image(X1,unordered_pair(X2,X3))) ),
inference(superposition,[status(thm)],[c_93,c_350]) ).
tcf(c_35844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK54(X2))
| ~ relation(X3)
| ~ in(X1,relation_image(X3,sK54(X2)))
| ~ subset(X0,sK3(X1,sK54(X2),X3)) ),
inference(superposition,[status(thm)],[c_93,c_373]) ).
tcf(c_35845,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,relation_rng(sK5),X1),relation_field(sK5))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_93,c_27657]) ).
tcf(c_35846,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,relation_dom(sK5),X1),relation_field(sK5))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_dom(sK5))) ),
inference(superposition,[status(thm)],[c_93,c_27656]) ).
tcf(c_35847,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,relation_rng(relation_rng_restriction(X2,relation_inverse(sK5))),X1),relation_dom(sK5))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_rng(relation_rng_restriction(X2,relation_inverse(sK5))))) ),
inference(superposition,[status(thm)],[c_93,c_25255]) ).
tcf(c_35848,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,relation_field(sK5),X1),relation_rng(sK5))
| in(sK3(X0,relation_field(sK5),X1),relation_dom(sK5))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_field(sK5))) ),
inference(superposition,[status(thm)],[c_93,c_27655]) ).
tcf(c_36035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,X2,X1),union(X3))
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_104,c_295]) ).
tcf(c_36036,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(sK6(X0,X2,X1),sK6(X0,X2,X1)),X2) = X2 )
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_104,c_161]) ).
tcf(c_36037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X2)
| ~ disjoint(X1,X3)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ in(sK6(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_104,c_151]) ).
tcf(c_36038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,X2,X1),X3)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_104,c_242]) ).
tcf(c_36039,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK6(X0,X2,X1)) = sK6(X0,X2,X1) )
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_104,c_134]) ).
tcf(c_36040,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ in(X1,relation_inverse_image(X2,X0))
| ~ in(X0,sK6(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_104,c_243]) ).
tcf(c_36041,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_104,c_471]) ).
tcf(c_36042,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK6(X0,X2,X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_104,c_276]) ).
tcf(c_36043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,relation_dom(relation_dom_restriction(X2,X3)),X1),relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_dom(relation_dom_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_104,c_214]) ).
tcf(c_36044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,relation_dom(relation_dom_restriction(X2,X3)),X1),X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_dom(relation_dom_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_104,c_213]) ).
tcf(c_36045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,relation_rng(relation_rng_restriction(X2,X3)),X1),relation_rng(X3))
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_rng(relation_rng_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_104,c_77]) ).
tcf(c_36046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,relation_rng(relation_rng_restriction(X2,X3)),X1),X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_rng(relation_rng_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_104,c_76]) ).
tcf(c_36047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X2))
| ~ relation(X3)
| ~ in(X1,relation_inverse_image(X3,sK2(X2)))
| ~ subset(X0,sK6(X1,sK2(X2),X3)) ),
inference(superposition,[status(thm)],[c_104,c_87]) ).
tcf(c_36048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X1)
| ~ disjoint(X2,X3)
| ~ in(X0,relation_inverse_image(X1,set_difference(X2,set_difference(X2,X3)))) ),
inference(superposition,[status(thm)],[c_104,c_166]) ).
tcf(c_36049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,set_difference(X2,set_difference(X2,X3)),X1),X3)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,set_difference(X2,set_difference(X2,X3)))) ),
inference(superposition,[status(thm)],[c_104,c_370]) ).
tcf(c_36050,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,empty_set)) ),
inference(superposition,[status(thm)],[c_104,c_234]) ).
tcf(c_36051,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(X0,unordered_pair(X2,X2),X1) = X2 )
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,unordered_pair(X2,X2))) ),
inference(superposition,[status(thm)],[c_104,c_239]) ).
tcf(c_36052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,set_union2(X2,X3),X1),X3)
| in(sK6(X0,set_union2(X2,X3),X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,set_union2(X2,X3))) ),
inference(superposition,[status(thm)],[c_104,c_254]) ).
tcf(c_36053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ in(X0,relation_inverse_image(X3,set_difference(X1,X2)))
| ~ in(sK6(X0,set_difference(X1,X2),X3),X2) ),
inference(superposition,[status(thm)],[c_104,c_270]) ).
tcf(c_36054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,set_difference(X2,X3),X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,set_difference(X2,X3))) ),
inference(superposition,[status(thm)],[c_104,c_269]) ).
tcf(c_36055,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK6(X0,powerset(X2),X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_104,c_290]) ).
tcf(c_36056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK6(X0,unordered_pair(X2,X3),X1) = X3 )
| ( sK6(X0,unordered_pair(X2,X3),X1) = X2 )
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,unordered_pair(X2,X3))) ),
inference(superposition,[status(thm)],[c_104,c_350]) ).
tcf(c_36057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK54(X2))
| ~ relation(X3)
| ~ in(X1,relation_inverse_image(X3,sK54(X2)))
| ~ subset(X0,sK6(X1,sK54(X2),X3)) ),
inference(superposition,[status(thm)],[c_104,c_373]) ).
tcf(c_36058,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,relation_rng(sK5),X1),relation_field(sK5))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_104,c_27657]) ).
tcf(c_36059,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,relation_dom(sK5),X1),relation_field(sK5))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_dom(sK5))) ),
inference(superposition,[status(thm)],[c_104,c_27656]) ).
tcf(c_36060,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,relation_rng(relation_rng_restriction(X2,relation_inverse(sK5))),X1),relation_dom(sK5))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_rng(relation_rng_restriction(X2,relation_inverse(sK5))))) ),
inference(superposition,[status(thm)],[c_104,c_25255]) ).
tcf(c_36061,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,relation_field(sK5),X1),relation_rng(sK5))
| in(sK6(X0,relation_field(sK5),X1),relation_dom(sK5))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_field(sK5))) ),
inference(superposition,[status(thm)],[c_104,c_27655]) ).
tcf(c_36198,plain,
( one_to_one(relation_dom(sK75))
| ~ empty(sK75) ),
inference(superposition,[status(thm)],[c_432,c_24183]) ).
tcf(c_36205,plain,
( relation(relation_dom(sK75))
| ~ empty(sK75) ),
inference(superposition,[status(thm)],[c_432,c_24184]) ).
tcf(c_36208,plain,
! [X0: $i] : relation_dom_restriction(relation_rng_restriction(X0,sK5),empty_set) = relation_rng_restriction(X0,empty_set),
inference(superposition,[status(thm)],[c_28288,c_35718]) ).
tcf(c_36209,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_rng(relation_dom_restriction(sK5,X2)))
| ~ relation(relation_dom_restriction(sK5,X2))
| ~ in(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2))) ),
inference(superposition,[status(thm)],[c_35718,c_77]) ).
tcf(c_36210,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ relation(relation_dom_restriction(sK5,X2))
| ~ in(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2))) ),
inference(superposition,[status(thm)],[c_35718,c_76]) ).
tcf(c_36211,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X0)),relation_rng(relation_dom_restriction(sK5,X0)))
| ~ relation(relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_35718,c_80]) ).
tcf(c_36212,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X0)),X1)
| ~ relation(relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_35718,c_78]) ).
tcf(c_36213,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom_restriction(relation_rng_restriction(X1,sK5),X0),relation_dom_restriction(sK5,X0))
| ~ relation(relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_35718,c_79]) ).
tcf(c_36214,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(relation_rng_restriction(X1,sK5),X0))
| ~ relation(relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_35718,c_352]) ).
tcf(c_36215,plain,
! [X0: $i] : relation_dom_restriction(relation_rng_restriction(X0,sK5),empty_set) = empty_set,
inference(light_normalisation,[status(thm)],[c_36208,c_19422]) ).
tcf(c_36216,plain,
! [X0: $i,X1: $i] : relation(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_36214,c_25741]) ).
tcf(c_36217,plain,
! [X0: $i,X1: $i] : subset(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_36212,c_25741]) ).
tcf(c_36218,plain,
! [X0: $i,X1: $i] : subset(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1),relation_dom_restriction(sK5,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_36213,c_25741]) ).
tcf(c_36219,plain,
! [X0: $i,X1: $i] : subset(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),relation_rng(relation_dom_restriction(sK5,X1))),
inference(forward_subsumption_resolution,[status(thm)],[c_36211,c_25741]) ).
tcf(c_36220,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36210,c_25741]) ).
tcf(c_36223,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_rng(relation_dom_restriction(sK5,X2)))
| ~ in(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36209,c_25741]) ).
tcf(c_36254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : relation_dom_restriction(relation_rng_restriction(X0,relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)),X3) = relation_rng_restriction(X0,relation_dom_restriction(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2),X3)),
inference(superposition,[status(thm)],[c_36216,c_89]) ).
tcf(c_36255,plain,
! [X0: $i,X1: $i] : set_union2(relation_dom(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))) = relation_field(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),
inference(superposition,[status(thm)],[c_36216,c_419]) ).
tcf(c_36256,plain,
! [X0: $i,X1: $i,X2: $i] : relation_composition(identity_relation(X0),relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)) = relation_dom_restriction(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2),X0),
inference(superposition,[status(thm)],[c_36216,c_223]) ).
tcf(c_36257,plain,
! [X0: $i,X1: $i] : relation_image(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1),relation_dom(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))) = relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),
inference(superposition,[status(thm)],[c_36216,c_99]) ).
tcf(c_36258,plain,
! [X0: $i,X1: $i] : relation_rng(relation_inverse(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))) = relation_dom(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),
inference(superposition,[status(thm)],[c_36216,c_137]) ).
tcf(c_36259,plain,
! [X0: $i,X1: $i] : relation_dom(relation_inverse(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))) = relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),
inference(superposition,[status(thm)],[c_36216,c_136]) ).
tcf(c_36260,plain,
! [X0: $i,X1: $i] : relation_inverse(relation_inverse(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))) = relation_dom_restriction(relation_rng_restriction(X0,sK5),X1),
inference(superposition,[status(thm)],[c_36216,c_429]) ).
tcf(c_36284,plain,
! [X0: $i,X1: $i] : set_difference(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))) = subset_complement(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),
inference(superposition,[status(thm)],[c_36217,c_6703]) ).
tcf(c_36285,plain,
! [X0: $i,X1: $i] : subset_complement(X0,subset_complement(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)))) = relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),
inference(superposition,[status(thm)],[c_36217,c_6699]) ).
tcf(c_36286,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) = X0 )
| ~ subset(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))) ),
inference(superposition,[status(thm)],[c_36217,c_260]) ).
tcf(c_36287,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),set_difference(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X0)) = relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),
inference(superposition,[status(thm)],[c_36217,c_123]) ).
tcf(c_36288,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X0)
| ( relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_36217,c_468]) ).
tcf(c_36289,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X2)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_36217,c_110]) ).
tcf(c_36290,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X0) = empty_set,
inference(superposition,[status(thm)],[c_36217,c_138]) ).
tcf(c_36291,plain,
! [X0: $i,X1: $i] : set_union2(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X0) = X0,
inference(superposition,[status(thm)],[c_36217,c_85]) ).
tcf(c_36292,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),
inference(superposition,[status(thm)],[c_36217,c_188]) ).
tcf(c_36293,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X2)),X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_36217,c_190]) ).
tcf(c_36294,plain,
! [X0: $i] : relation_rng(relation_dom_restriction(relation_rng_restriction(empty_set,sK5),X0)) = empty_set,
inference(superposition,[status(thm)],[c_36217,c_152]) ).
tcf(c_36295,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_rng(relation_dom_restriction(relation_rng_restriction(relation_inverse_image(relation_inverse(sK5),X0),sK5),X1)),relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_36217,c_22779]) ).
tcf(c_36296,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_rng(relation_dom_restriction(relation_rng_restriction(relation_image(relation_inverse(sK5),X0),sK5),X1)),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_36217,c_22780]) ).
tcf(c_36297,plain,
! [X0: $i,X1: $i] : subset(set_difference(relation_rng(relation_dom_restriction(relation_rng_restriction(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),sK5),X1)),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_36217,c_25182]) ).
tcf(c_36405,plain,
! [X0: $i] : subset(relation_dom_restriction(relation_rng_restriction(X0,sK5),empty_set),empty_set),
inference(superposition,[status(thm)],[c_28288,c_36218]) ).
tcf(c_36406,plain,
! [X0: $i,X1: $i] : set_difference(relation_dom_restriction(sK5,X0),relation_dom_restriction(relation_rng_restriction(X1,sK5),X0)) = subset_complement(relation_dom_restriction(sK5,X0),relation_dom_restriction(relation_rng_restriction(X1,sK5),X0)),
inference(superposition,[status(thm)],[c_36218,c_6703]) ).
tcf(c_36407,plain,
! [X0: $i,X1: $i] : subset_complement(relation_dom_restriction(sK5,X0),subset_complement(relation_dom_restriction(sK5,X0),relation_dom_restriction(relation_rng_restriction(X1,sK5),X0))) = relation_dom_restriction(relation_rng_restriction(X1,sK5),X0),
inference(superposition,[status(thm)],[c_36218,c_6699]) ).
tcf(c_36408,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X1,sK5),X0) = relation_dom_restriction(sK5,X0) )
| ~ subset(relation_dom_restriction(sK5,X0),relation_dom_restriction(relation_rng_restriction(X1,sK5),X0)) ),
inference(superposition,[status(thm)],[c_36218,c_260]) ).
tcf(c_36409,plain,
! [X0: $i,X1: $i] : set_difference(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1),set_difference(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1),relation_dom_restriction(sK5,X1))) = relation_dom_restriction(relation_rng_restriction(X0,sK5),X1),
inference(superposition,[status(thm)],[c_36218,c_123]) ).
tcf(c_36410,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1),relation_dom_restriction(sK5,X1))
| ( relation_dom_restriction(relation_rng_restriction(X0,sK5),X1) = relation_dom_restriction(sK5,X1) ) ),
inference(superposition,[status(thm)],[c_36218,c_468]) ).
tcf(c_36411,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom_restriction(relation_rng_restriction(X2,sK5),X0),X1)
| ~ subset(relation_dom_restriction(sK5,X0),X1) ),
inference(superposition,[status(thm)],[c_36218,c_110]) ).
tcf(c_36412,plain,
! [X0: $i,X1: $i] : set_difference(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1),relation_dom_restriction(sK5,X1)) = empty_set,
inference(superposition,[status(thm)],[c_36218,c_138]) ).
tcf(c_36413,plain,
! [X0: $i,X1: $i] : set_union2(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1),relation_dom_restriction(sK5,X1)) = relation_dom_restriction(sK5,X1),
inference(superposition,[status(thm)],[c_36218,c_85]) ).
tcf(c_36414,plain,
! [X0: $i,X1: $i] : ~ proper_subset(relation_dom_restriction(sK5,X0),relation_dom_restriction(relation_rng_restriction(X1,sK5),X0)),
inference(superposition,[status(thm)],[c_36218,c_188]) ).
tcf(c_36415,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_dom_restriction(relation_rng_restriction(X2,sK5),X0),X1)
| ~ disjoint(relation_dom_restriction(sK5,X0),X1) ),
inference(superposition,[status(thm)],[c_36218,c_190]) ).
tcf(c_36446,plain,
! [X0: $i] : subset(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),empty_set)),relation_rng(empty_set)),
inference(superposition,[status(thm)],[c_28288,c_36219]) ).
tcf(c_36447,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X0))) = subset_complement(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X0))),
inference(superposition,[status(thm)],[c_36219,c_6703]) ).
tcf(c_36448,plain,
! [X0: $i,X1: $i] : subset_complement(relation_rng(relation_dom_restriction(sK5,X0)),subset_complement(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X0)))) = relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X0)),
inference(superposition,[status(thm)],[c_36219,c_6699]) ).
tcf(c_36449,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X0)) = relation_rng(relation_dom_restriction(sK5,X0)) )
| ~ subset(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X0))) ),
inference(superposition,[status(thm)],[c_36219,c_260]) ).
tcf(c_36450,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),set_difference(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),relation_rng(relation_dom_restriction(sK5,X1)))) = relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),
inference(superposition,[status(thm)],[c_36219,c_123]) ).
tcf(c_36451,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),relation_rng(relation_dom_restriction(sK5,X1)))
| ( relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) = relation_rng(relation_dom_restriction(sK5,X1)) ) ),
inference(superposition,[status(thm)],[c_36219,c_468]) ).
tcf(c_36452,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X0)),X1)
| ~ subset(relation_rng(relation_dom_restriction(sK5,X0)),X1) ),
inference(superposition,[status(thm)],[c_36219,c_110]) ).
tcf(c_36453,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),relation_rng(relation_dom_restriction(sK5,X1))) = empty_set,
inference(superposition,[status(thm)],[c_36219,c_138]) ).
tcf(c_36454,plain,
! [X0: $i,X1: $i] : set_union2(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),relation_rng(relation_dom_restriction(sK5,X1))) = relation_rng(relation_dom_restriction(sK5,X1)),
inference(superposition,[status(thm)],[c_36219,c_85]) ).
tcf(c_36455,plain,
! [X0: $i,X1: $i] : ~ proper_subset(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X0))),
inference(superposition,[status(thm)],[c_36219,c_188]) ).
tcf(c_36456,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X0)),X1)
| ~ disjoint(relation_rng(relation_dom_restriction(sK5,X0)),X1) ),
inference(superposition,[status(thm)],[c_36219,c_190]) ).
tcf(c_36519,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2)
| in(sK1(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2),X0) ),
inference(superposition,[status(thm)],[c_6708,c_36220]) ).
tcf(c_36520,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( set_difference(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),unordered_pair(X2,X2)) = relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) ) ),
inference(superposition,[status(thm)],[c_195,c_36220]) ).
tcf(c_36521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)),X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)))) ),
inference(superposition,[status(thm)],[c_93,c_36220]) ).
tcf(c_36522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)),X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)))) ),
inference(superposition,[status(thm)],[c_104,c_36220]) ).
tcf(c_36523,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2)
| in(sK8(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2),X0) ),
inference(superposition,[status(thm)],[c_149,c_36220]) ).
tcf(c_36524,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)))
| in(sK8(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2))),X1) ),
inference(superposition,[status(thm)],[c_150,c_36220]) ).
tcf(c_36525,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X2,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),X2)
| in(sK15(X2,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),X0)
| ( relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_228,c_36220]) ).
tcf(c_36526,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2),X2)
| in(sK15(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2),X0)
| ( relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_228,c_36220]) ).
tcf(c_36527,plain,
! [X0: $i,X1: $i] :
( in(sK16(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),X0)
| ( relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_233,c_36220]) ).
tcf(c_36528,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2)
| in(sK18(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2),X0) ),
inference(superposition,[status(thm)],[c_241,c_36220]) ).
tcf(c_36529,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK27(relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)),X0),X1)
| ~ in(X0,union(relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)))) ),
inference(superposition,[status(thm)],[c_297,c_36220]) ).
tcf(c_36530,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)))
| in(sK38(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),X0) ),
inference(superposition,[status(thm)],[c_314,c_36220]) ).
tcf(c_36531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK44(relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)),X3,X0),X1)
| ~ in(X0,cartesian_product2(relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)),X3)) ),
inference(superposition,[status(thm)],[c_323,c_36220]) ).
tcf(c_36532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK45(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)),X0),X2)
| ~ in(X0,cartesian_product2(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)))) ),
inference(superposition,[status(thm)],[c_324,c_36220]) ).
tcf(c_36533,plain,
! [X0: $i,X1: $i] :
( empty(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)))
| in(sK23(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),X0) ),
inference(superposition,[status(thm)],[c_20297,c_36220]) ).
tcf(c_36641,plain,
( proper_subset(relation_rng(empty_set),relation_rng(sK5))
| ( relation_rng(relation_dom_restriction(sK5,empty_set)) = relation_rng(sK5) ) ),
inference(superposition,[status(thm)],[c_28288,c_29911]) ).
tcf(c_36643,plain,
! [X0: $i] :
( ( relation_rng(relation_dom_restriction(sK5,X0)) = relation_rng(sK5) )
| ~ empty(relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_29911,c_19555]) ).
tcf(c_36646,plain,
( proper_subset(empty_set,relation_rng(sK5))
| ( relation_rng(sK5) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_36641,c_187,c_28290]) ).
tcf(c_36651,plain,
! [X0: $i] : set_difference(relation_dom(sK5),set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0))) = subset_complement(relation_dom(sK5),set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22402,c_6703]) ).
tcf(c_36652,plain,
! [X0: $i] : subset_complement(relation_dom(sK5),subset_complement(relation_dom(sK5),set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0)))) = set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_22402,c_6699]) ).
tcf(c_36653,plain,
! [X0: $i] :
( ( set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0)) = relation_dom(sK5) )
| ~ subset(relation_dom(sK5),set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0))) ),
inference(superposition,[status(thm)],[c_22402,c_260]) ).
tcf(c_36654,plain,
! [X0: $i] : set_difference(set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0)),set_difference(set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0)),relation_dom(sK5))) = set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0)),
inference(superposition,[status(thm)],[c_22402,c_123]) ).
tcf(c_36655,plain,
! [X0: $i] :
( proper_subset(set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0)),relation_dom(sK5))
| ( set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0)) = relation_dom(sK5) ) ),
inference(superposition,[status(thm)],[c_22402,c_468]) ).
tcf(c_36656,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X1)),relation_image(relation_inverse(sK5),X1)),X0)
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_22402,c_110]) ).
tcf(c_36657,plain,
! [X0: $i] : set_difference(set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0)),relation_dom(sK5)) = empty_set,
inference(superposition,[status(thm)],[c_22402,c_138]) ).
tcf(c_36658,plain,
! [X0: $i] : set_union2(set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0)),relation_dom(sK5)) = relation_dom(sK5),
inference(superposition,[status(thm)],[c_22402,c_85]) ).
tcf(c_36659,plain,
! [X0: $i] : ~ proper_subset(relation_dom(sK5),set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X0)),relation_image(relation_inverse(sK5),X0))),
inference(superposition,[status(thm)],[c_22402,c_188]) ).
tcf(c_36660,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(set_difference(relation_dom(sK5),relation_image(relation_inverse(sK5),X1)),relation_image(relation_inverse(sK5),X1)),X0)
| ~ disjoint(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_22402,c_190]) ).
tcf(c_36687,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X2,set_difference(X2,X1)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_371,c_109]) ).
tcf(c_36689,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(set_union2(X1,X2),set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_153,c_109]) ).
tcf(c_36690,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(empty_set,empty_set))
| ~ subset(X0,empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_263,c_109]) ).
tcf(c_36691,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(X1,X1))
| ~ subset(X0,empty_set)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_264,c_109]) ).
tcf(c_36693,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X1,set_difference(X2,set_difference(X2,X1))))
| ~ subset(X0,X1)
| ~ subset(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_371,c_109]) ).
tcf(c_36694,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(relation_inverse_image(relation_inverse(sK5),X1),empty_set))
| ~ subset(X0,relation_rng(sK5))
| ~ subset(X0,relation_inverse_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_21834,c_109]) ).
tcf(c_36695,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(relation_image(relation_inverse(sK5),X1),empty_set))
| ~ subset(X0,relation_dom(sK5))
| ~ subset(X0,relation_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_22079,c_109]) ).
tcf(c_36696,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),empty_set))
| ~ subset(X0,relation_dom(sK5))
| ~ subset(X0,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_25056,c_109]) ).
tcf(c_36697,plain,
! [X0: $i] :
( subset(X0,set_difference(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))))
| ~ subset(X0,relation_field(sK5))
| ~ subset(X0,relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_27644,c_109]) ).
tcf(c_36698,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(relation_dom(relation_dom_restriction(sK5,X1)),empty_set))
| ~ subset(X0,X1)
| ~ subset(X0,relation_dom(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_29867,c_109]) ).
tcf(c_36699,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(relation_rng(relation_dom_restriction(sK5,X1)),empty_set))
| ~ subset(X0,relation_rng(sK5))
| ~ subset(X0,relation_rng(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_29913,c_109]) ).
tcf(c_36700,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X1,set_difference(X1,X2)),X0) = subset_complement(set_difference(X1,set_difference(X1,X2)),X0) )
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_109,c_6703]) ).
tcf(c_36701,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_complement(set_difference(X1,set_difference(X1,X2)),subset_complement(set_difference(X1,set_difference(X1,X2)),X0)) = X0 )
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_109,c_6699]) ).
tcf(c_36702,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = X2 )
| ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_109,c_260]) ).
tcf(c_36703,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X0,set_difference(X1,set_difference(X1,X2)))) = X0 )
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_109,c_123]) ).
tcf(c_36704,plain,
! [X0: $i,X1: $i,X2: $i] :
( proper_subset(X0,set_difference(X1,set_difference(X1,X2)))
| ( set_difference(X1,set_difference(X1,X2)) = X0 )
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_109,c_468]) ).
tcf(c_36705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,X2)
| ~ subset(X3,X1)
| ~ subset(X3,X0)
| ~ subset(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_109,c_110]) ).
tcf(c_36706,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X1,set_difference(X1,X2))) = empty_set )
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_109,c_138]) ).
tcf(c_36707,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,set_difference(X1,set_difference(X1,X2))) = set_difference(X1,set_difference(X1,X2)) )
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_109,c_85]) ).
tcf(c_36708,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X2,X1)
| ~ subset(X2,X0)
| ~ proper_subset(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_109,c_188]) ).
tcf(c_36709,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(X3,X2)
| ~ subset(X3,X1)
| ~ subset(X3,X0)
| ~ disjoint(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_109,c_190]) ).
tcf(c_36710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,set_difference(X2,set_difference(X2,X3)))
| ~ subset(unordered_pair(X0,X1),X3)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_109,c_144]) ).
tcf(c_36711,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,set_difference(X2,set_difference(X2,X3)))
| ~ subset(unordered_pair(X0,X1),X3)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_109,c_143]) ).
tcf(c_36712,plain,
! [X0: $i,X1: $i] :
( ~ subset(sK2(powerset(set_difference(X0,set_difference(X0,X1)))),X1)
| ~ subset(sK2(powerset(set_difference(X0,set_difference(X0,X1)))),X0) ),
inference(superposition,[status(thm)],[c_109,c_19634]) ).
tcf(c_36713,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(unordered_pair(powerset(set_difference(X0,set_difference(X0,X1))),X2),X1)
| ~ subset(unordered_pair(powerset(set_difference(X0,set_difference(X0,X1))),X2),X0) ),
inference(superposition,[status(thm)],[c_109,c_19635]) ).
tcf(c_36714,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(unordered_pair(X0,powerset(set_difference(X1,set_difference(X1,X2)))),X2)
| ~ subset(unordered_pair(X0,powerset(set_difference(X1,set_difference(X1,X2)))),X1) ),
inference(superposition,[status(thm)],[c_109,c_19636]) ).
tcf(c_36715,plain,
! [X0: $i,X1: $i] :
( ~ subset(sK54(powerset(set_difference(X0,set_difference(X0,X1)))),X1)
| ~ subset(sK54(powerset(set_difference(X0,set_difference(X0,X1)))),X0) ),
inference(superposition,[status(thm)],[c_109,c_19637]) ).
tcf(c_36716,plain,
! [X0: $i,X1: $i] :
( ~ subset(powerset(powerset(set_difference(X0,set_difference(X0,X1)))),X1)
| ~ subset(powerset(powerset(set_difference(X0,set_difference(X0,X1)))),X0) ),
inference(superposition,[status(thm)],[c_109,c_20010]) ).
tcf(c_36717,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,powerset(set_difference(X1,set_difference(X1,X2))))
| ~ subset(sK18(X0,powerset(set_difference(X1,set_difference(X1,X2)))),X2)
| ~ subset(sK18(X0,powerset(set_difference(X1,set_difference(X1,X2)))),X1) ),
inference(superposition,[status(thm)],[c_109,c_20077]) ).
tcf(c_36718,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(sK2(set_union2(powerset(set_difference(X0,set_difference(X0,X1))),X2)),X1)
| ~ subset(sK2(set_union2(powerset(set_difference(X0,set_difference(X0,X1))),X2)),X0) ),
inference(superposition,[status(thm)],[c_109,c_20218]) ).
tcf(c_36719,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(sK54(set_union2(powerset(set_difference(X0,set_difference(X0,X1))),X2)),X1)
| ~ subset(sK54(set_union2(powerset(set_difference(X0,set_difference(X0,X1))),X2)),X0) ),
inference(superposition,[status(thm)],[c_109,c_20229]) ).
tcf(c_36720,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(powerset(set_union2(powerset(set_difference(X0,set_difference(X0,X1))),X2)),X1)
| ~ subset(powerset(set_union2(powerset(set_difference(X0,set_difference(X0,X1))),X2)),X0) ),
inference(superposition,[status(thm)],[c_109,c_20423]) ).
tcf(c_36721,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(sK2(set_union2(X0,powerset(set_difference(X1,set_difference(X1,X2))))),X2)
| ~ subset(sK2(set_union2(X0,powerset(set_difference(X1,set_difference(X1,X2))))),X1) ),
inference(superposition,[status(thm)],[c_109,c_20434]) ).
tcf(c_36722,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(sK54(set_union2(X0,powerset(set_difference(X1,set_difference(X1,X2))))),X2)
| ~ subset(sK54(set_union2(X0,powerset(set_difference(X1,set_difference(X1,X2))))),X1) ),
inference(superposition,[status(thm)],[c_109,c_20446]) ).
tcf(c_36723,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(powerset(set_union2(X0,powerset(set_difference(X1,set_difference(X1,X2))))),X2)
| ~ subset(powerset(set_union2(X0,powerset(set_difference(X1,set_difference(X1,X2))))),X1) ),
inference(superposition,[status(thm)],[c_109,c_20458]) ).
tcf(c_36724,plain,
! [X0: $i,X1: $i] :
( subset(relation_field(sK5),set_difference(X0,set_difference(X0,X1)))
| ~ subset(relation_rng(sK5),X1)
| ~ subset(relation_rng(sK5),X0)
| ~ subset(relation_dom(sK5),set_difference(X0,set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_109,c_30534]) ).
tcf(c_36725,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK5)
| in(sK77(sK5),set_difference(X0,set_difference(X0,X1)))
| ~ subset(relation_field(sK5),X1)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_109,c_32805]) ).
tcf(c_36726,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK5)
| in(sK76(sK5),set_difference(X0,set_difference(X0,X1)))
| ~ subset(relation_field(sK5),X1)
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_109,c_32697]) ).
tcf(c_36981,plain,
! [X0: $i,X1: $i] :
( subset(X0,relation_dom(X1))
| ~ relation(X1)
| ~ relation(identity_relation(X0))
| ~ subset(identity_relation(X0),X1) ),
inference(superposition,[status(thm)],[c_203,c_120]) ).
tcf(c_36982,plain,
! [X0: $i] :
( subset(empty_set,relation_dom(X0))
| ~ relation(empty_set)
| ~ relation(X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_186,c_120]) ).
tcf(c_36983,plain,
! [X0: $i] :
( subset(relation_rng(sK5),relation_dom(X0))
| ~ relation(X0)
| ~ relation(relation_inverse(sK5))
| ~ subset(relation_inverse(sK5),X0) ),
inference(superposition,[status(thm)],[c_20946,c_120]) ).
tcf(c_36984,plain,
! [X0: $i,X1: $i] :
( subset(X0,relation_dom(X1))
| ~ relation(X1)
| ~ relation(relation_inverse(identity_relation(X0)))
| ~ subset(relation_inverse(identity_relation(X0)),X1) ),
inference(superposition,[status(thm)],[c_20961,c_120]) ).
tcf(c_36985,plain,
! [X0: $i] :
( subset(relation_rng(sK47),relation_dom(X0))
| ~ relation(X0)
| ~ relation(relation_inverse(sK47))
| ~ subset(relation_inverse(sK47),X0) ),
inference(superposition,[status(thm)],[c_20951,c_120]) ).
tcf(c_36986,plain,
! [X0: $i] :
( subset(relation_rng(sK75),relation_dom(X0))
| ~ relation(X0)
| ~ relation(relation_inverse(sK75))
| ~ subset(relation_inverse(sK75),X0) ),
inference(superposition,[status(thm)],[c_20957,c_120]) ).
tcf(c_36987,plain,
! [X0: $i] :
( subset(relation_rng(sK79),relation_dom(X0))
| ~ relation(X0)
| ~ relation(relation_inverse(sK79))
| ~ subset(relation_inverse(sK79),X0) ),
inference(superposition,[status(thm)],[c_20958,c_120]) ).
tcf(c_36988,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_dom_restriction(sK5,X0)),relation_dom(X1))
| ~ relation(X1)
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0)))
| ~ subset(relation_inverse(relation_dom_restriction(sK5,X0)),X1) ),
inference(superposition,[status(thm)],[c_25748,c_120]) ).
tcf(c_36989,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(X0),X1)
| ~ relation(X0)
| ~ relation(identity_relation(X1))
| ~ subset(X0,identity_relation(X1)) ),
inference(superposition,[status(thm)],[c_203,c_120]) ).
tcf(c_36990,plain,
! [X0: $i] :
( subset(relation_dom(X0),empty_set)
| ~ relation(empty_set)
| ~ relation(X0)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_186,c_120]) ).
tcf(c_36991,plain,
! [X0: $i] :
( subset(relation_dom(X0),relation_rng(sK5))
| ~ relation(X0)
| ~ relation(relation_inverse(sK5))
| ~ subset(X0,relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_20946,c_120]) ).
tcf(c_36992,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(X0),X1)
| ~ relation(X0)
| ~ relation(relation_inverse(identity_relation(X1)))
| ~ subset(X0,relation_inverse(identity_relation(X1))) ),
inference(superposition,[status(thm)],[c_20961,c_120]) ).
tcf(c_36993,plain,
! [X0: $i] :
( subset(relation_dom(X0),relation_rng(sK47))
| ~ relation(X0)
| ~ relation(relation_inverse(sK47))
| ~ subset(X0,relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_20951,c_120]) ).
tcf(c_36994,plain,
! [X0: $i] :
( subset(relation_dom(X0),relation_rng(sK75))
| ~ relation(X0)
| ~ relation(relation_inverse(sK75))
| ~ subset(X0,relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_20957,c_120]) ).
tcf(c_36995,plain,
! [X0: $i] :
( subset(relation_dom(X0),relation_rng(sK79))
| ~ relation(X0)
| ~ relation(relation_inverse(sK79))
| ~ subset(X0,relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_20958,c_120]) ).
tcf(c_36996,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(X0),relation_rng(relation_dom_restriction(sK5,X1)))
| ~ relation(X0)
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X1)))
| ~ subset(X0,relation_inverse(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_25748,c_120]) ).
tcf(c_36997,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom(X1),relation_dom(X0)) = subset_complement(relation_dom(X1),relation_dom(X0)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_120,c_6703]) ).
tcf(c_36998,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(relation_dom(X1),subset_complement(relation_dom(X1),relation_dom(X0))) = relation_dom(X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_120,c_6699]) ).
tcf(c_36999,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = relation_dom(X1) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X1,X0)
| ~ subset(relation_dom(X0),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_120,c_260]) ).
tcf(c_37000,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom(X0),set_difference(relation_dom(X0),relation_dom(X1))) = relation_dom(X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_120,c_123]) ).
tcf(c_37001,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_dom(X0),relation_dom(X1))
| ( relation_dom(X0) = relation_dom(X1) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_120,c_468]) ).
tcf(c_37002,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(X2),X1)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(X2,X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_120,c_110]) ).
tcf(c_37003,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom(X0),relation_dom(X1)) = empty_set )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_120,c_138]) ).
tcf(c_37004,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_dom(X0),relation_dom(X1)) = relation_dom(X1) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_120,c_85]) ).
tcf(c_37005,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ relation(X0)
| ~ subset(X1,X0)
| ~ proper_subset(relation_dom(X0),relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_120,c_188]) ).
tcf(c_37006,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_dom(X2),X1)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(X2,X0)
| ~ disjoint(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_120,c_190]) ).
tcf(c_37007,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,relation_dom(X0))) = relation_dom(X0) )
| ~ relation(X0)
| ~ relation(relation_dom_restriction(sK5,relation_dom(X0)))
| ~ subset(X0,relation_dom_restriction(sK5,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_120,c_29863]) ).
tcf(c_37008,plain,
! [X0: $i] :
( subset(relation_dom(X0),empty_set)
| ~ relation(X0)
| ~ subset(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36990,c_231]) ).
tcf(c_37016,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(X0),X1)
| ~ relation(X0)
| ~ subset(X0,identity_relation(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36989,c_422]) ).
tcf(c_37020,plain,
! [X0: $i,X1: $i] :
( subset(X0,relation_dom(X1))
| ~ relation(X1)
| ~ subset(identity_relation(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36981,c_422]) ).
tcf(c_37112,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,relation_dom(X0))) = relation_dom(X0) )
| ~ relation(X0)
| ~ subset(X0,relation_dom_restriction(sK5,relation_dom(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37007,c_25741]) ).
tcf(c_37148,plain,
! [X0: $i] :
( subset(empty_set,relation_rng(X0))
| ~ relation(empty_set)
| ~ relation(X0)
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_187,c_121]) ).
tcf(c_37149,plain,
! [X0: $i,X1: $i] :
( subset(X0,relation_rng(X1))
| ~ relation(X1)
| ~ relation(identity_relation(X0))
| ~ subset(identity_relation(X0),X1) ),
inference(superposition,[status(thm)],[c_204,c_121]) ).
tcf(c_37150,plain,
! [X0: $i] :
( subset(relation_dom(sK5),relation_rng(X0))
| ~ relation(X0)
| ~ relation(relation_inverse(sK5))
| ~ subset(relation_inverse(sK5),X0) ),
inference(superposition,[status(thm)],[c_21123,c_121]) ).
tcf(c_37151,plain,
! [X0: $i] :
( subset(relation_dom(sK47),relation_rng(X0))
| ~ relation(X0)
| ~ relation(relation_inverse(sK47))
| ~ subset(relation_inverse(sK47),X0) ),
inference(superposition,[status(thm)],[c_21128,c_121]) ).
tcf(c_37152,plain,
! [X0: $i,X1: $i] :
( subset(X0,relation_rng(X1))
| ~ relation(X1)
| ~ relation(relation_inverse(identity_relation(X0)))
| ~ subset(relation_inverse(identity_relation(X0)),X1) ),
inference(superposition,[status(thm)],[c_21138,c_121]) ).
tcf(c_37153,plain,
! [X0: $i] :
( subset(relation_dom(sK75),relation_rng(X0))
| ~ relation(X0)
| ~ relation(relation_inverse(sK75))
| ~ subset(relation_inverse(sK75),X0) ),
inference(superposition,[status(thm)],[c_21134,c_121]) ).
tcf(c_37154,plain,
! [X0: $i] :
( subset(relation_dom(sK79),relation_rng(X0))
| ~ relation(X0)
| ~ relation(relation_inverse(sK79))
| ~ subset(relation_inverse(sK79),X0) ),
inference(superposition,[status(thm)],[c_21135,c_121]) ).
tcf(c_37155,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_dom_restriction(sK5,X0)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0)))
| ~ subset(relation_inverse(relation_dom_restriction(sK5,X0)),X1) ),
inference(superposition,[status(thm)],[c_25747,c_121]) ).
tcf(c_37156,plain,
! [X0: $i] :
( subset(relation_rng(X0),empty_set)
| ~ relation(empty_set)
| ~ relation(X0)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_187,c_121]) ).
tcf(c_37157,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(X0),X1)
| ~ relation(X0)
| ~ relation(identity_relation(X1))
| ~ subset(X0,identity_relation(X1)) ),
inference(superposition,[status(thm)],[c_204,c_121]) ).
tcf(c_37158,plain,
! [X0: $i] :
( subset(relation_rng(X0),relation_dom(sK5))
| ~ relation(X0)
| ~ relation(relation_inverse(sK5))
| ~ subset(X0,relation_inverse(sK5)) ),
inference(superposition,[status(thm)],[c_21123,c_121]) ).
tcf(c_37159,plain,
! [X0: $i] :
( subset(relation_rng(X0),relation_dom(sK47))
| ~ relation(X0)
| ~ relation(relation_inverse(sK47))
| ~ subset(X0,relation_inverse(sK47)) ),
inference(superposition,[status(thm)],[c_21128,c_121]) ).
tcf(c_37160,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(X0),X1)
| ~ relation(X0)
| ~ relation(relation_inverse(identity_relation(X1)))
| ~ subset(X0,relation_inverse(identity_relation(X1))) ),
inference(superposition,[status(thm)],[c_21138,c_121]) ).
tcf(c_37161,plain,
! [X0: $i] :
( subset(relation_rng(X0),relation_dom(sK75))
| ~ relation(X0)
| ~ relation(relation_inverse(sK75))
| ~ subset(X0,relation_inverse(sK75)) ),
inference(superposition,[status(thm)],[c_21134,c_121]) ).
tcf(c_37162,plain,
! [X0: $i] :
( subset(relation_rng(X0),relation_dom(sK79))
| ~ relation(X0)
| ~ relation(relation_inverse(sK79))
| ~ subset(X0,relation_inverse(sK79)) ),
inference(superposition,[status(thm)],[c_21135,c_121]) ).
tcf(c_37163,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(X0),relation_dom(relation_dom_restriction(sK5,X1)))
| ~ relation(X0)
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X1)))
| ~ subset(X0,relation_inverse(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_25747,c_121]) ).
tcf(c_37164,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(X1),relation_rng(X0)) = subset_complement(relation_rng(X1),relation_rng(X0)) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_121,c_6703]) ).
tcf(c_37165,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(relation_rng(X1),subset_complement(relation_rng(X1),relation_rng(X0))) = relation_rng(X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_121,c_6699]) ).
tcf(c_37166,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(X0) = relation_rng(X1) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X1,X0)
| ~ subset(relation_rng(X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_121,c_260]) ).
tcf(c_37167,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(X0),set_difference(relation_rng(X0),relation_rng(X1))) = relation_rng(X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_121,c_123]) ).
tcf(c_37168,plain,
! [X0: $i,X1: $i] :
( proper_subset(relation_rng(X0),relation_rng(X1))
| ( relation_rng(X0) = relation_rng(X1) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_121,c_468]) ).
tcf(c_37169,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(X2),X1)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(X2,X0)
| ~ subset(relation_rng(X0),X1) ),
inference(superposition,[status(thm)],[c_121,c_110]) ).
tcf(c_37170,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(X0),relation_rng(X1)) = empty_set )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_121,c_138]) ).
tcf(c_37171,plain,
! [X0: $i,X1: $i] :
( ( set_union2(relation_rng(X0),relation_rng(X1)) = relation_rng(X1) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_121,c_85]) ).
tcf(c_37172,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ relation(X0)
| ~ subset(X1,X0)
| ~ proper_subset(relation_rng(X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_121,c_188]) ).
tcf(c_37173,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(X2),X1)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(X2,X0)
| ~ disjoint(relation_rng(X0),X1) ),
inference(superposition,[status(thm)],[c_121,c_190]) ).
tcf(c_37174,plain,
! [X0: $i] :
( subset(relation_field(sK5),relation_rng(X0))
| ~ relation(sK5)
| ~ relation(X0)
| ~ subset(sK5,X0)
| ~ subset(relation_dom(sK5),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_121,c_30534]) ).
tcf(c_37175,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng(X0),relation_dom(sK5)),empty_set)
| ~ relation(X0)
| ~ relation(relation_rng_restriction(X1,relation_inverse(sK5)))
| ~ subset(X0,relation_rng_restriction(X1,relation_inverse(sK5))) ),
inference(superposition,[status(thm)],[c_121,c_25182]) ).
tcf(c_37176,plain,
! [X0: $i] :
( subset(relation_rng(X0),empty_set)
| ~ relation(X0)
| ~ subset(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37156,c_231]) ).
tcf(c_37184,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(X0),X1)
| ~ relation(X0)
| ~ subset(X0,identity_relation(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37157,c_422]) ).
tcf(c_37188,plain,
! [X0: $i,X1: $i] :
( subset(X0,relation_rng(X1))
| ~ relation(X1)
| ~ subset(identity_relation(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37149,c_422]) ).
tcf(c_37250,plain,
! [X0: $i] :
( subset(relation_field(sK5),relation_rng(X0))
| ~ relation(X0)
| ~ subset(sK5,X0)
| ~ subset(relation_dom(sK5),relation_rng(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37174,c_96]) ).
tcf(c_37394,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X0,set_difference(X0,X1)))
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_263,c_122]) ).
tcf(c_37395,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X2,set_difference(X2,X0)),set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_371,c_122]) ).
tcf(c_37397,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_union2(X0,X1),set_difference(X0,X1)),set_difference(X2,set_difference(X2,X1)))
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_153,c_122]) ).
tcf(c_37398,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(empty_set,empty_set),set_difference(X0,set_difference(X0,X1)))
| ~ subset(empty_set,X0) ),
inference(superposition,[status(thm)],[c_263,c_122]) ).
tcf(c_37399,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,X0),set_difference(X1,set_difference(X1,empty_set)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_264,c_122]) ).
tcf(c_37400,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,empty_set),set_difference(X1,set_difference(X1,X0)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4095,c_122]) ).
tcf(c_37401,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X2,set_difference(X2,X0))),set_difference(X1,set_difference(X1,set_difference(X0,X2))))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_371,c_122]) ).
tcf(c_37402,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_inverse_image(relation_inverse(sK5),X0),empty_set),set_difference(X1,set_difference(X1,relation_rng(sK5))))
| ~ subset(relation_inverse_image(relation_inverse(sK5),X0),X1) ),
inference(superposition,[status(thm)],[c_21834,c_122]) ).
tcf(c_37403,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_image(relation_inverse(sK5),X0),empty_set),set_difference(X1,set_difference(X1,relation_dom(sK5))))
| ~ subset(relation_image(relation_inverse(sK5),X0),X1) ),
inference(superposition,[status(thm)],[c_22079,c_122]) ).
tcf(c_37404,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),empty_set),set_difference(X1,set_difference(X1,relation_dom(sK5))))
| ~ subset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1) ),
inference(superposition,[status(thm)],[c_25056,c_122]) ).
tcf(c_37405,plain,
! [X0: $i] :
( subset(set_difference(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),set_difference(X0,set_difference(X0,relation_rng(sK5))))
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_27644,c_122]) ).
tcf(c_37406,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_dom(relation_dom_restriction(sK5,X0)),empty_set),set_difference(X1,set_difference(X1,X0)))
| ~ subset(relation_dom(relation_dom_restriction(sK5,X0)),X1) ),
inference(superposition,[status(thm)],[c_29867,c_122]) ).
tcf(c_37407,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(relation_rng(relation_dom_restriction(sK5,X0)),empty_set),set_difference(X1,set_difference(X1,relation_rng(sK5))))
| ~ subset(relation_rng(relation_dom_restriction(sK5,X0)),X1) ),
inference(superposition,[status(thm)],[c_29913,c_122]) ).
tcf(c_37409,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,set_difference(X0,X1)),empty_set)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_263,c_122]) ).
tcf(c_37410,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,X2)),set_difference(X2,set_difference(X2,X1)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_371,c_122]) ).
tcf(c_37412,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,X2)),set_difference(set_union2(X1,X2),set_difference(X1,X2)))
| ~ subset(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_153,c_122]) ).
tcf(c_37413,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,set_difference(X0,X1)),set_difference(empty_set,empty_set))
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_263,c_122]) ).
tcf(c_37414,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,set_difference(X0,empty_set)),set_difference(X1,X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_264,c_122]) ).
tcf(c_37415,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,set_difference(X0,X1)),set_difference(X1,empty_set))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_4095,c_122]) ).
tcf(c_37416,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,set_difference(X1,X2))),set_difference(X1,set_difference(X2,set_difference(X2,X1))))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_371,c_122]) ).
tcf(c_37417,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,set_difference(X0,relation_rng(sK5))),set_difference(relation_inverse_image(relation_inverse(sK5),X1),empty_set))
| ~ subset(X0,relation_inverse_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_21834,c_122]) ).
tcf(c_37418,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,set_difference(X0,relation_dom(sK5))),set_difference(relation_image(relation_inverse(sK5),X1),empty_set))
| ~ subset(X0,relation_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_22079,c_122]) ).
tcf(c_37419,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,set_difference(X0,relation_dom(sK5))),set_difference(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),empty_set))
| ~ subset(X0,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_25056,c_122]) ).
tcf(c_37420,plain,
! [X0: $i] :
( subset(set_difference(X0,set_difference(X0,relation_rng(sK5))),set_difference(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))))
| ~ subset(X0,relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_27644,c_122]) ).
tcf(c_37421,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,set_difference(X0,X1)),set_difference(relation_dom(relation_dom_restriction(sK5,X1)),empty_set))
| ~ subset(X0,relation_dom(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_29867,c_122]) ).
tcf(c_37422,plain,
! [X0: $i,X1: $i] :
( subset(set_difference(X0,set_difference(X0,relation_rng(sK5))),set_difference(relation_rng(relation_dom_restriction(sK5,X1)),empty_set))
| ~ subset(X0,relation_rng(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_29913,c_122]) ).
tcf(c_37423,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X1,set_difference(X1,X2)),set_difference(X0,set_difference(X0,X2))) = subset_complement(set_difference(X1,set_difference(X1,X2)),set_difference(X0,set_difference(X0,X2))) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_122,c_6703]) ).
tcf(c_37424,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_complement(set_difference(X1,set_difference(X1,X2)),subset_complement(set_difference(X1,set_difference(X1,X2)),set_difference(X0,set_difference(X0,X2)))) = set_difference(X0,set_difference(X0,X2)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_122,c_6699]) ).
tcf(c_37425,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = set_difference(X2,set_difference(X2,X1)) )
| ~ subset(X2,X0)
| ~ subset(set_difference(X0,set_difference(X0,X1)),set_difference(X2,set_difference(X2,X1))) ),
inference(superposition,[status(thm)],[c_122,c_260]) ).
tcf(c_37426,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X0,set_difference(X0,X2)),set_difference(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2)))) = set_difference(X0,set_difference(X0,X2)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_122,c_123]) ).
tcf(c_37427,plain,
! [X0: $i,X1: $i,X2: $i] :
( proper_subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2)))
| ( set_difference(X0,set_difference(X0,X2)) = set_difference(X1,set_difference(X1,X2)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_122,c_468]) ).
tcf(c_37428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_difference(X3,set_difference(X3,X1)),X2)
| ~ subset(X3,X0)
| ~ subset(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_122,c_110]) ).
tcf(c_37429,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2))) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_122,c_138]) ).
tcf(c_37430,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2))) = set_difference(X1,set_difference(X1,X2)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_122,c_85]) ).
tcf(c_37431,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X2,X0)
| ~ proper_subset(set_difference(X0,set_difference(X0,X1)),set_difference(X2,set_difference(X2,X1))) ),
inference(superposition,[status(thm)],[c_122,c_188]) ).
tcf(c_37432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(set_difference(X3,set_difference(X3,X1)),X2)
| ~ subset(X3,X0)
| ~ disjoint(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_122,c_190]) ).
tcf(c_37437,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X1,X1))
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_37414,c_264,c_4095]) ).
tcf(c_37440,plain,
! [X0: $i,X1: $i] :
( subset(X0,set_difference(X1,set_difference(X1,X0)))
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_37400,c_264]) ).
tcf(c_37443,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,set_difference(X1,set_difference(X1,empty_set)))
| ~ subset(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_37399,c_4095]) ).
tcf(c_37444,plain,
! [X0: $i,X1: $i] : subset(set_difference(empty_set,empty_set),set_difference(X0,set_difference(X0,X1))),
inference(forward_subsumption_resolution,[status(thm)],[c_37398,c_124]) ).
tcf(c_37473,plain,
! [X0: $i] :
( subset(set_difference(X0,set_difference(X0,relation_rng(sK5))),relation_rng(sK5))
| ~ subset(X0,relation_field(sK5)) ),
inference(light_normalisation,[status(thm)],[c_37420,c_31087]) ).
tcf(c_37482,plain,
! [X0: $i] :
( subset(relation_rng(sK5),set_difference(X0,set_difference(X0,relation_rng(sK5))))
| ~ subset(relation_field(sK5),X0) ),
inference(light_normalisation,[status(thm)],[c_37405,c_31087]) ).
tcf(c_37534,plain,
( empty(relation_dom(sK75))
| ~ empty(sK75) ),
inference(superposition,[status(thm)],[c_432,c_24185]) ).
tcf(c_37537,plain,
relation_composition(empty_set,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_28218,c_25482]) ).
tcf(c_37538,plain,
! [X0: $i] :
( subset(relation_rng(empty_set),relation_rng(empty_set))
| ~ relation(empty_set)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25482,c_157]) ).
tcf(c_37539,plain,
! [X0: $i] :
( subset(relation_dom(empty_set),relation_dom(identity_relation(X0)))
| ~ relation(empty_set)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_25482,c_156]) ).
tcf(c_37545,plain,
! [X0: $i] :
( subset(empty_set,empty_set)
| ~ relation(empty_set)
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_37538,c_187]) ).
tcf(c_37546,plain,
! [X0: $i] :
( subset(empty_set,X0)
| ~ relation(empty_set)
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_37539,c_186,c_203]) ).
tcf(c_37548,plain,
( subset(relation_dom(empty_set),relation_dom(empty_set))
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_37537,c_156]) ).
tcf(c_37563,plain,
! [X0: $i] :
( subset(relation_field(sK5),relation_rng(X0))
| ~ relation(X0)
| ~ empty(relation_dom(sK5))
| ~ subset(sK5,X0) ),
inference(superposition,[status(thm)],[c_19515,c_37250]) ).
tcf(c_37564,plain,
( subset(relation_field(sK5),relation_rng(empty_set))
| ~ relation(empty_set)
| ~ subset(sK5,empty_set)
| ~ subset(relation_dom(sK5),empty_set) ),
inference(superposition,[status(thm)],[c_187,c_37250]) ).
tcf(c_37565,plain,
! [X0: $i] :
( subset(relation_field(sK5),relation_rng(identity_relation(X0)))
| ~ relation(identity_relation(X0))
| ~ subset(sK5,identity_relation(X0))
| ~ subset(relation_dom(sK5),X0) ),
inference(superposition,[status(thm)],[c_204,c_37250]) ).
tcf(c_37566,plain,
( subset(relation_field(sK5),relation_rng(relation_inverse(sK5)))
| ~ relation(relation_inverse(sK5))
| ~ subset(sK5,relation_inverse(sK5))
| ~ subset(relation_dom(sK5),relation_dom(sK5)) ),
inference(superposition,[status(thm)],[c_21123,c_37250]) ).
tcf(c_37567,plain,
( subset(relation_field(sK5),relation_rng(relation_inverse(sK47)))
| ~ relation(relation_inverse(sK47))
| ~ subset(sK5,relation_inverse(sK47))
| ~ subset(relation_dom(sK5),relation_dom(sK47)) ),
inference(superposition,[status(thm)],[c_21128,c_37250]) ).
tcf(c_37568,plain,
! [X0: $i] :
( subset(relation_field(sK5),relation_rng(relation_inverse(identity_relation(X0))))
| ~ relation(relation_inverse(identity_relation(X0)))
| ~ subset(relation_dom(sK5),X0)
| ~ subset(sK5,relation_inverse(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_21138,c_37250]) ).
tcf(c_37569,plain,
( subset(relation_field(sK5),relation_rng(relation_inverse(sK75)))
| ~ relation(relation_inverse(sK75))
| ~ subset(sK5,relation_inverse(sK75))
| ~ subset(relation_dom(sK5),relation_dom(sK75)) ),
inference(superposition,[status(thm)],[c_21134,c_37250]) ).
tcf(c_37570,plain,
( subset(relation_field(sK5),relation_rng(relation_inverse(sK79)))
| ~ relation(relation_inverse(sK79))
| ~ subset(sK5,relation_inverse(sK79))
| ~ subset(relation_dom(sK5),relation_dom(sK79)) ),
inference(superposition,[status(thm)],[c_21135,c_37250]) ).
tcf(c_37571,plain,
! [X0: $i] :
( subset(relation_field(sK5),relation_rng(relation_inverse(relation_dom_restriction(sK5,X0))))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0)))
| ~ subset(sK5,relation_inverse(relation_dom_restriction(sK5,X0)))
| ~ subset(relation_dom(sK5),relation_dom(relation_dom_restriction(sK5,X0))) ),
inference(superposition,[status(thm)],[c_25747,c_37250]) ).
tcf(c_37576,plain,
( subset(relation_field(sK5),empty_set)
| ~ relation(empty_set)
| ~ subset(sK5,empty_set)
| ~ subset(relation_dom(sK5),empty_set) ),
inference(light_normalisation,[status(thm)],[c_37564,c_187]) ).
tcf(c_37577,plain,
( subset(relation_field(sK5),empty_set)
| ~ subset(sK5,empty_set)
| ~ subset(relation_dom(sK5),empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37576,c_231]) ).
tcf(c_37581,plain,
! [X0: $i] :
( subset(relation_field(sK5),X0)
| ~ relation(identity_relation(X0))
| ~ subset(sK5,identity_relation(X0))
| ~ subset(relation_dom(sK5),X0) ),
inference(light_normalisation,[status(thm)],[c_37565,c_204]) ).
tcf(c_37582,plain,
! [X0: $i] :
( subset(relation_field(sK5),X0)
| ~ subset(sK5,identity_relation(X0))
| ~ subset(relation_dom(sK5),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37581,c_422]) ).
tcf(c_37586,plain,
( subset(relation_field(sK5),relation_dom(sK79))
| ~ relation(relation_inverse(sK79))
| ~ subset(sK5,relation_inverse(sK79))
| ~ subset(relation_dom(sK5),relation_dom(sK79)) ),
inference(light_normalisation,[status(thm)],[c_37570,c_21135]) ).
tcf(c_37591,plain,
( subset(relation_field(sK5),relation_dom(sK75))
| ~ relation(relation_inverse(sK75))
| ~ subset(sK5,relation_inverse(sK75))
| ~ subset(relation_dom(sK5),relation_dom(sK75)) ),
inference(light_normalisation,[status(thm)],[c_37569,c_21134]) ).
tcf(c_37596,plain,
( subset(relation_field(sK5),relation_dom(sK47))
| ~ relation(relation_inverse(sK47))
| ~ subset(sK5,relation_inverse(sK47))
| ~ subset(relation_dom(sK5),relation_dom(sK47)) ),
inference(light_normalisation,[status(thm)],[c_37567,c_21128]) ).
tcf(c_37601,plain,
( subset(relation_field(sK5),relation_dom(sK5))
| ~ relation(relation_inverse(sK5))
| ~ subset(sK5,relation_inverse(sK5))
| ~ subset(relation_dom(sK5),relation_dom(sK5)) ),
inference(light_normalisation,[status(thm)],[c_37566,c_21123]) ).
tcf(c_37602,plain,
( subset(relation_field(sK5),relation_dom(sK5))
| ~ relation(relation_inverse(sK5))
| ~ subset(sK5,relation_inverse(sK5)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37601,c_262]) ).
tcf(c_37606,plain,
! [X0: $i] :
( subset(relation_field(sK5),X0)
| ~ relation(relation_inverse(identity_relation(X0)))
| ~ subset(relation_dom(sK5),X0)
| ~ subset(sK5,relation_inverse(identity_relation(X0))) ),
inference(light_normalisation,[status(thm)],[c_37568,c_21138]) ).
tcf(c_37611,plain,
! [X0: $i] :
( subset(relation_field(sK5),relation_dom(relation_dom_restriction(sK5,X0)))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X0)))
| ~ subset(sK5,relation_inverse(relation_dom_restriction(sK5,X0)))
| ~ subset(relation_dom(sK5),relation_dom(relation_dom_restriction(sK5,X0))) ),
inference(light_normalisation,[status(thm)],[c_37571,c_25747]) ).
tcf(c_37661,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2)
| in(sK1(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2),relation_rng(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_6708,c_36223]) ).
tcf(c_37662,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,relation_rng(relation_dom_restriction(sK5,X1)))
| ( set_difference(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),unordered_pair(X2,X2)) = relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) ) ),
inference(superposition,[status(thm)],[c_195,c_36223]) ).
tcf(c_37663,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)),X1),relation_rng(relation_dom_restriction(sK5,X3)))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)))) ),
inference(superposition,[status(thm)],[c_93,c_36223]) ).
tcf(c_37664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)),X1),relation_rng(relation_dom_restriction(sK5,X3)))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)))) ),
inference(superposition,[status(thm)],[c_104,c_36223]) ).
tcf(c_37665,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2)
| in(sK8(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2),relation_rng(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_149,c_36223]) ).
tcf(c_37666,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)))
| in(sK8(X0,relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2))),relation_rng(relation_dom_restriction(sK5,X2))) ),
inference(superposition,[status(thm)],[c_150,c_36223]) ).
tcf(c_37667,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X2,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),X2)
| in(sK15(X2,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),relation_rng(relation_dom_restriction(sK5,X1)))
| ( relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_228,c_36223]) ).
tcf(c_37668,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2),X2)
| in(sK15(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2),relation_rng(relation_dom_restriction(sK5,X1)))
| ( relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_228,c_36223]) ).
tcf(c_37669,plain,
! [X0: $i,X1: $i] :
( in(sK16(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),relation_rng(relation_dom_restriction(sK5,X1)))
| ( relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_233,c_36223]) ).
tcf(c_37670,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2)
| in(sK18(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2),relation_rng(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_241,c_36223]) ).
tcf(c_37671,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK27(relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)),X0),relation_rng(relation_dom_restriction(sK5,X2)))
| ~ in(X0,union(relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)))) ),
inference(superposition,[status(thm)],[c_297,c_36223]) ).
tcf(c_37672,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)))
| in(sK38(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),relation_rng(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_314,c_36223]) ).
tcf(c_37673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK44(relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)),X3,X0),relation_rng(relation_dom_restriction(sK5,X2)))
| ~ in(X0,cartesian_product2(relation_rng(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)),X3)) ),
inference(superposition,[status(thm)],[c_323,c_36223]) ).
tcf(c_37674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK45(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)),X0),relation_rng(relation_dom_restriction(sK5,X3)))
| ~ in(X0,cartesian_product2(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)))) ),
inference(superposition,[status(thm)],[c_324,c_36223]) ).
tcf(c_37675,plain,
! [X0: $i,X1: $i] :
( empty(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)))
| in(sK23(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),relation_rng(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_20297,c_36223]) ).
tcf(c_37799,plain,
set_difference(relation_rng(sK5),relation_rng(empty_set)) = subset_complement(relation_rng(sK5),relation_rng(empty_set)),
inference(superposition,[status(thm)],[c_28288,c_29907]) ).
tcf(c_37800,plain,
! [X0: $i] :
( subset(set_difference(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0))),relation_rng(sK5))
| ~ subset(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_29907,c_22243]) ).
tcf(c_37801,plain,
! [X0: $i] :
( element(set_difference(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0))),powerset(relation_rng(sK5)))
| ~ subset(relation_rng(relation_dom_restriction(sK5,X0)),relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_29907,c_6701]) ).
tcf(c_37802,plain,
set_difference(relation_rng(sK5),empty_set) = subset_complement(relation_rng(sK5),empty_set),
inference(light_normalisation,[status(thm)],[c_37799,c_187]) ).
tcf(c_37803,plain,
! [X0: $i] : element(set_difference(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0))),powerset(relation_rng(sK5))),
inference(forward_subsumption_resolution,[status(thm)],[c_37801,c_29626]) ).
tcf(c_37811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X2,X1),X3)
| ~ subset(X2,X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_19515,c_22558]) ).
tcf(c_37812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X4,cartesian_product2(X0,X1))
| subset(cartesian_product2(X3,X1),set_difference(X2,unordered_pair(X4,X4)))
| ~ subset(X3,X0)
| ~ subset(cartesian_product2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_58,c_22558]) ).
tcf(c_37813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X3,X1),union(X2))
| ~ subset(X3,X0)
| ~ in(cartesian_product2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_222,c_22558]) ).
tcf(c_37814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X2,X3),cartesian_product2(X1,X3))
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_81,c_22558]) ).
tcf(c_37815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X3,X1))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_22558]) ).
tcf(c_37816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(cartesian_product2(X4,X2),cartesian_product2(X1,X3))
| ~ subset(X4,X0)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_22558]) ).
tcf(c_37817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(cartesian_product2(X4,X1),set_difference(X2,set_difference(X2,X3)))
| ~ subset(X4,X0)
| ~ subset(cartesian_product2(X0,X1),X3)
| ~ subset(cartesian_product2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_109,c_22558]) ).
tcf(c_37818,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X2,X1),cartesian_product2(relation_dom(cartesian_product2(X0,X1)),relation_rng(cartesian_product2(X0,X1))))
| ~ subset(X2,X0)
| ~ relation(cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_117,c_22558]) ).
tcf(c_37819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X0,X2),set_union2(cartesian_product2(X1,X2),X3))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_209,c_22558]) ).
tcf(c_37821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X0,X2),set_union2(X3,cartesian_product2(X1,X2)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_19598,c_22558]) ).
tcf(c_37822,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X0,X2),X1)
| ~ subset(empty_set,X1)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_26653,c_22558]) ).
tcf(c_37823,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X0,empty_set),X2)
| ~ subset(empty_set,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_29072,c_22558]) ).
tcf(c_37825,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X0,X1),X2)
| ~ subset(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37822,c_124]) ).
tcf(c_37871,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(subset_complement(X0,X1),X2)
| ~ element(X1,powerset(X0))
| ~ in(sK1(subset_complement(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_6708,c_180]) ).
tcf(c_37872,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(subset_complement(X1,X0),unordered_pair(X2,X2)) = subset_complement(X1,X0) )
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_195,c_180]) ).
tcf(c_37873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ element(X2,powerset(X1))
| ~ in(X0,relation_image(X3,subset_complement(X1,X2)))
| ~ in(sK3(X0,subset_complement(X1,X2),X3),X2) ),
inference(superposition,[status(thm)],[c_93,c_180]) ).
tcf(c_37874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X3)
| ~ element(X2,powerset(X1))
| ~ in(X0,relation_inverse_image(X3,subset_complement(X1,X2)))
| ~ in(sK6(X0,subset_complement(X1,X2),X3),X2) ),
inference(superposition,[status(thm)],[c_104,c_180]) ).
tcf(c_37875,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(subset_complement(X0,X1),X2)
| ~ element(X1,powerset(X0))
| ~ in(sK8(subset_complement(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_149,c_180]) ).
tcf(c_37876,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,subset_complement(X1,X2))
| ~ element(X2,powerset(X1))
| ~ in(sK8(X0,subset_complement(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_150,c_180]) ).
tcf(c_37877,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(X0,subset_complement(X1,X2)),X0)
| ( subset_complement(X1,X2) = X0 )
| ~ element(X2,powerset(X1))
| ~ in(sK15(X0,subset_complement(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_228,c_180]) ).
tcf(c_37878,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK15(subset_complement(X0,X1),X2),X2)
| ( subset_complement(X0,X1) = X2 )
| ~ element(X1,powerset(X0))
| ~ in(sK15(subset_complement(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_228,c_180]) ).
tcf(c_37879,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X0,X1) = empty_set )
| ~ element(X1,powerset(X0))
| ~ in(sK16(subset_complement(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_233,c_180]) ).
tcf(c_37880,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(subset_complement(X0,X1),X2)
| ~ element(X1,powerset(X0))
| ~ in(sK18(subset_complement(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_241,c_180]) ).
tcf(c_37881,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ element(X1,powerset(X0))
| ~ in(X2,union(subset_complement(X0,X1)))
| ~ in(sK27(subset_complement(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_297,c_180]) ).
tcf(c_37882,plain,
! [X0: $i,X1: $i] :
( relation(subset_complement(X0,X1))
| ~ element(X1,powerset(X0))
| ~ in(sK38(subset_complement(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_314,c_180]) ).
tcf(c_37883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ element(X1,powerset(X0))
| ~ in(X3,cartesian_product2(subset_complement(X0,X1),X2))
| ~ in(sK44(subset_complement(X0,X1),X2,X3),X1) ),
inference(superposition,[status(thm)],[c_323,c_180]) ).
tcf(c_37884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ element(X2,powerset(X1))
| ~ in(X3,cartesian_product2(X0,subset_complement(X1,X2)))
| ~ in(sK45(X0,subset_complement(X1,X2),X3),X2) ),
inference(superposition,[status(thm)],[c_324,c_180]) ).
tcf(c_37885,plain,
! [X0: $i,X1: $i] :
( empty(subset_complement(X0,X1))
| ~ element(X1,powerset(X0))
| ~ in(sK23(subset_complement(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_20297,c_180]) ).
tcf(c_37886,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,empty_set)
| ~ in(X1,X0)
| ~ element(empty_set,powerset(X0)) ),
inference(superposition,[status(thm)],[c_28543,c_180]) ).
tcf(c_37887,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,empty_set)
| ~ in(X1,X0)
| ~ element(X0,powerset(X0)) ),
inference(superposition,[status(thm)],[c_28542,c_180]) ).
tcf(c_37888,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,relation_dom(relation_dom_restriction(sK5,X1)))
| ~ element(relation_dom(relation_dom_restriction(sK5,X1)),powerset(X1))
| ~ in(X0,set_difference(X1,relation_dom(relation_dom_restriction(sK5,X1)))) ),
inference(superposition,[status(thm)],[c_29861,c_180]) ).
tcf(c_37889,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,relation_rng(relation_dom_restriction(sK5,X1)))
| ~ element(relation_rng(relation_dom_restriction(sK5,X1)),powerset(relation_rng(sK5)))
| ~ in(X0,set_difference(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X1)))) ),
inference(superposition,[status(thm)],[c_29907,c_180]) ).
tcf(c_38002,plain,
! [X0: $i,X1: $i] :
( in(sK24(X0,X1),X1)
| ( powerset(X0) = X1 )
| ( set_difference(X0,sK24(X0,X1)) = subset_complement(X0,sK24(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_288,c_6703]) ).
tcf(c_38003,plain,
! [X0: $i,X1: $i] :
( in(sK24(X0,X1),X1)
| ( powerset(X0) = X1 )
| ( subset_complement(X0,subset_complement(X0,sK24(X0,X1))) = sK24(X0,X1) ) ),
inference(superposition,[status(thm)],[c_288,c_6699]) ).
tcf(c_38004,plain,
! [X0: $i,X1: $i] :
( in(sK24(X0,X1),X1)
| ( powerset(X0) = X1 )
| ( sK24(X0,X1) = X0 )
| ~ subset(X0,sK24(X0,X1)) ),
inference(superposition,[status(thm)],[c_288,c_260]) ).
tcf(c_38005,plain,
! [X0: $i,X1: $i] :
( in(sK24(X0,X1),X1)
| ( powerset(X0) = X1 )
| ( set_difference(sK24(X0,X1),set_difference(sK24(X0,X1),X0)) = sK24(X0,X1) ) ),
inference(superposition,[status(thm)],[c_288,c_123]) ).
tcf(c_38006,plain,
! [X0: $i,X1: $i] :
( proper_subset(sK24(X0,X1),X0)
| in(sK24(X0,X1),X1)
| ( powerset(X0) = X1 )
| ( sK24(X0,X1) = X0 ) ),
inference(superposition,[status(thm)],[c_288,c_468]) ).
tcf(c_38007,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X0,X2),X1)
| in(sK24(X0,X2),X2)
| ( powerset(X0) = X2 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_288,c_110]) ).
tcf(c_38008,plain,
! [X0: $i,X1: $i] :
( in(sK24(X0,X1),X1)
| ( powerset(X0) = X1 )
| ( set_difference(sK24(X0,X1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_288,c_138]) ).
tcf(c_38009,plain,
! [X0: $i,X1: $i] :
( in(sK24(X0,X1),X1)
| ( powerset(X0) = X1 )
| ( set_union2(sK24(X0,X1),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_288,c_85]) ).
tcf(c_38010,plain,
! [X0: $i,X1: $i] :
( in(sK24(X0,X1),X1)
| ( powerset(X0) = X1 )
| ~ proper_subset(X0,sK24(X0,X1)) ),
inference(superposition,[status(thm)],[c_288,c_188]) ).
tcf(c_38011,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(sK24(X0,X2),X1)
| in(sK24(X0,X2),X2)
| ( powerset(X0) = X2 )
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_288,c_190]) ).
tcf(c_38012,plain,
! [X0: $i] :
( in(sK24(empty_set,X0),X0)
| ( powerset(empty_set) = X0 )
| ( sK24(empty_set,X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_288,c_152]) ).
tcf(c_38013,plain,
! [X0: $i,X1: $i] :
( in(sK24(relation_inverse_image(relation_inverse(sK5),X0),X1),X1)
| subset(set_difference(sK24(relation_inverse_image(relation_inverse(sK5),X0),X1),relation_rng(sK5)),empty_set)
| ( powerset(relation_inverse_image(relation_inverse(sK5),X0)) = X1 ) ),
inference(superposition,[status(thm)],[c_288,c_22779]) ).
tcf(c_38014,plain,
! [X0: $i,X1: $i] :
( in(sK24(relation_image(relation_inverse(sK5),X0),X1),X1)
| subset(set_difference(sK24(relation_image(relation_inverse(sK5),X0),X1),relation_dom(sK5)),empty_set)
| ( powerset(relation_image(relation_inverse(sK5),X0)) = X1 ) ),
inference(superposition,[status(thm)],[c_288,c_22780]) ).
tcf(c_38015,plain,
! [X0: $i,X1: $i] :
( in(sK24(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1),X1)
| subset(set_difference(sK24(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1),relation_dom(sK5)),empty_set)
| ( powerset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))) = X1 ) ),
inference(superposition,[status(thm)],[c_288,c_25182]) ).
tcf(c_38016,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X2,X0),X2)
| in(sK24(X2,X0),union(X1))
| ( powerset(X2) = X0 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_288,c_295]) ).
tcf(c_38017,plain,
! [X0: $i,X1: $i] :
( subset(sK24(X0,X1),X0)
| ( powerset(X0) = X1 )
| ( set_union2(unordered_pair(sK24(X0,X1),sK24(X0,X1)),X1) = X1 ) ),
inference(superposition,[status(thm)],[c_288,c_161]) ).
tcf(c_38018,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X0,X1),X0)
| ( powerset(X0) = X1 )
| ~ disjoint(X1,X2)
| ~ in(sK24(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_288,c_151]) ).
tcf(c_38019,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X2,X0),X2)
| in(sK24(X2,X0),X1)
| ( powerset(X2) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_288,c_242]) ).
tcf(c_38020,plain,
! [X0: $i,X1: $i] :
( subset(sK24(X1,X0),X1)
| ( powerset(X1) = X0 )
| ( apply(identity_relation(X0),sK24(X1,X0)) = sK24(X1,X0) ) ),
inference(superposition,[status(thm)],[c_288,c_134]) ).
tcf(c_38021,plain,
! [X0: $i,X1: $i] :
( subset(sK24(X1,X0),X1)
| ( powerset(X1) = X0 )
| ~ in(X0,sK24(X1,X0)) ),
inference(superposition,[status(thm)],[c_288,c_243]) ).
tcf(c_38022,plain,
! [X0: $i,X1: $i] :
( subset(sK24(X1,X0),X1)
| ( powerset(X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_288,c_471]) ).
tcf(c_38023,plain,
! [X0: $i,X1: $i] :
( element(sK24(X0,X1),X1)
| subset(sK24(X0,X1),X0)
| ( powerset(X0) = X1 ) ),
inference(superposition,[status(thm)],[c_288,c_276]) ).
tcf(c_38024,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X2,relation_dom(relation_dom_restriction(X0,X1))),X2)
| in(sK24(X2,relation_dom(relation_dom_restriction(X0,X1))),relation_dom(X0))
| ( relation_dom(relation_dom_restriction(X0,X1)) = powerset(X2) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_288,c_214]) ).
tcf(c_38025,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X2,relation_dom(relation_dom_restriction(X0,X1))),X2)
| in(sK24(X2,relation_dom(relation_dom_restriction(X0,X1))),X1)
| ( relation_dom(relation_dom_restriction(X0,X1)) = powerset(X2) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_288,c_213]) ).
tcf(c_38026,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X2,relation_rng(relation_rng_restriction(X1,X0))),X2)
| in(sK24(X2,relation_rng(relation_rng_restriction(X1,X0))),relation_rng(X0))
| ( relation_rng(relation_rng_restriction(X1,X0)) = powerset(X2) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_288,c_77]) ).
tcf(c_38027,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X2,relation_rng(relation_rng_restriction(X1,X0))),X2)
| in(sK24(X2,relation_rng(relation_rng_restriction(X1,X0))),X1)
| ( relation_rng(relation_rng_restriction(X1,X0)) = powerset(X2) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_288,c_76]) ).
tcf(c_38028,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X2))
| subset(sK24(X1,sK2(X2)),X1)
| ( powerset(X1) = sK2(X2) )
| ~ subset(X0,sK24(X1,sK2(X2))) ),
inference(superposition,[status(thm)],[c_288,c_87]) ).
tcf(c_38029,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X2,set_difference(X0,set_difference(X0,X1))),X2)
| ( set_difference(X0,set_difference(X0,X1)) = powerset(X2) )
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_288,c_166]) ).
tcf(c_38030,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X2,set_difference(X0,set_difference(X0,X1))),X2)
| in(sK24(X2,set_difference(X0,set_difference(X0,X1))),X1)
| ( set_difference(X0,set_difference(X0,X1)) = powerset(X2) ) ),
inference(superposition,[status(thm)],[c_288,c_370]) ).
tcf(c_38031,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X0,subset_complement(X1,X2)),X0)
| ( subset_complement(X1,X2) = powerset(X0) )
| ~ element(X2,powerset(X1))
| ~ in(sK24(X0,subset_complement(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_288,c_180]) ).
tcf(c_38032,plain,
! [X0: $i] :
( subset(sK24(X0,empty_set),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_288,c_234]) ).
tcf(c_38033,plain,
! [X0: $i,X1: $i] :
( subset(sK24(X0,unordered_pair(X1,X1)),X0)
| ( unordered_pair(X1,X1) = powerset(X0) )
| ( sK24(X0,unordered_pair(X1,X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_288,c_239]) ).
tcf(c_38034,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X2,set_union2(X0,X1)),X2)
| in(sK24(X2,set_union2(X0,X1)),X1)
| in(sK24(X2,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = powerset(X2) ) ),
inference(superposition,[status(thm)],[c_288,c_254]) ).
tcf(c_38035,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X0,set_difference(X1,X2)),X0)
| ( set_difference(X1,X2) = powerset(X0) )
| ~ in(sK24(X0,set_difference(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_288,c_270]) ).
tcf(c_38036,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X2,set_difference(X0,X1)),X2)
| in(sK24(X2,set_difference(X0,X1)),X0)
| ( set_difference(X0,X1) = powerset(X2) ) ),
inference(superposition,[status(thm)],[c_288,c_269]) ).
tcf(c_38037,plain,
! [X0: $i,X1: $i] :
( subset(sK24(X0,powerset(X1)),X1)
| subset(sK24(X0,powerset(X1)),X0)
| ( powerset(X0) = powerset(X1) ) ),
inference(superposition,[status(thm)],[c_288,c_290]) ).
tcf(c_38038,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X0,unordered_pair(X1,X2)),X0)
| ( unordered_pair(X1,X2) = powerset(X0) )
| ( sK24(X0,unordered_pair(X1,X2)) = X2 )
| ( sK24(X0,unordered_pair(X1,X2)) = X1 ) ),
inference(superposition,[status(thm)],[c_288,c_350]) ).
tcf(c_38039,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK54(X2))
| subset(sK24(X1,sK54(X2)),X1)
| ( powerset(X1) = sK54(X2) )
| ~ subset(X0,sK24(X1,sK54(X2))) ),
inference(superposition,[status(thm)],[c_288,c_373]) ).
tcf(c_38040,plain,
! [X0: $i] :
( subset(sK24(X0,relation_rng(sK5)),X0)
| in(sK24(X0,relation_rng(sK5)),relation_field(sK5))
| ( powerset(X0) = relation_rng(sK5) ) ),
inference(superposition,[status(thm)],[c_288,c_27657]) ).
tcf(c_38041,plain,
! [X0: $i] :
( subset(sK24(X0,relation_dom(sK5)),X0)
| in(sK24(X0,relation_dom(sK5)),relation_field(sK5))
| ( powerset(X0) = relation_dom(sK5) ) ),
inference(superposition,[status(thm)],[c_288,c_27656]) ).
tcf(c_38042,plain,
! [X0: $i,X1: $i] :
( subset(sK24(X1,relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),X1)
| in(sK24(X1,relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_dom(sK5))
| ( relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))) = powerset(X1) ) ),
inference(superposition,[status(thm)],[c_288,c_25255]) ).
tcf(c_38043,plain,
! [X0: $i] :
( subset(sK24(X0,relation_field(sK5)),X0)
| in(sK24(X0,relation_field(sK5)),relation_rng(sK5))
| in(sK24(X0,relation_field(sK5)),relation_dom(sK5))
| ( powerset(X0) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_288,c_27655]) ).
tcf(c_38044,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X2,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),X2)
| in(sK24(X2,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),relation_rng(relation_dom_restriction(sK5,X1)))
| ( relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) = powerset(X2) ) ),
inference(superposition,[status(thm)],[c_288,c_36223]) ).
tcf(c_38045,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK24(X2,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),X2)
| in(sK24(X2,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),X0)
| ( relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) = powerset(X2) ) ),
inference(superposition,[status(thm)],[c_288,c_36220]) ).
tcf(c_38326,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK25(X0,X2),X2)
| in(sK26(X0,X2),union(X1))
| ( union(X0) = X2 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_294,c_295]) ).
tcf(c_38327,plain,
! [X0: $i,X1: $i] :
( in(sK25(X0,X1),X1)
| ( union(X0) = X1 )
| ( set_union2(unordered_pair(sK26(X0,X1),sK26(X0,X1)),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_294,c_161]) ).
tcf(c_38328,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK25(X0,X1),X1)
| ( union(X0) = X1 )
| ~ disjoint(X0,X2)
| ~ in(sK26(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_294,c_151]) ).
tcf(c_38329,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X0,X2),X1)
| in(sK25(X0,X2),X2)
| ( union(X0) = X2 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_294,c_242]) ).
tcf(c_38330,plain,
! [X0: $i,X1: $i] :
( in(sK25(X0,X1),X1)
| ( union(X0) = X1 )
| ( apply(identity_relation(X0),sK26(X0,X1)) = sK26(X0,X1) ) ),
inference(superposition,[status(thm)],[c_294,c_134]) ).
tcf(c_38331,plain,
! [X0: $i,X1: $i] :
( in(sK25(X0,X1),X1)
| ( union(X0) = X1 )
| ~ in(X0,sK26(X0,X1)) ),
inference(superposition,[status(thm)],[c_294,c_243]) ).
tcf(c_38332,plain,
! [X0: $i,X1: $i] :
( in(sK25(X0,X1),X1)
| ( union(X0) = X1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_294,c_471]) ).
tcf(c_38333,plain,
! [X0: $i,X1: $i] :
( element(sK26(X0,X1),X0)
| in(sK25(X0,X1),X1)
| ( union(X0) = X1 ) ),
inference(superposition,[status(thm)],[c_294,c_276]) ).
tcf(c_38334,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK25(relation_dom(relation_dom_restriction(X0,X1)),X2),X2)
| in(sK26(relation_dom(relation_dom_restriction(X0,X1)),X2),relation_dom(X0))
| ( union(relation_dom(relation_dom_restriction(X0,X1))) = X2 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_294,c_214]) ).
tcf(c_38335,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(relation_dom(relation_dom_restriction(X0,X1)),X2),X1)
| in(sK25(relation_dom(relation_dom_restriction(X0,X1)),X2),X2)
| ( union(relation_dom(relation_dom_restriction(X0,X1))) = X2 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_294,c_213]) ).
tcf(c_38336,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK25(relation_rng(relation_rng_restriction(X1,X0)),X2),X2)
| in(sK26(relation_rng(relation_rng_restriction(X1,X0)),X2),relation_rng(X0))
| ( union(relation_rng(relation_rng_restriction(X1,X0))) = X2 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_294,c_77]) ).
tcf(c_38337,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(relation_rng(relation_rng_restriction(X1,X0)),X2),X1)
| in(sK25(relation_rng(relation_rng_restriction(X1,X0)),X2),X2)
| ( union(relation_rng(relation_rng_restriction(X1,X0))) = X2 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_294,c_76]) ).
tcf(c_38338,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X1))
| in(sK25(sK2(X1),X2),X2)
| ( union(sK2(X1)) = X2 )
| ~ subset(X0,sK26(sK2(X1),X2)) ),
inference(superposition,[status(thm)],[c_294,c_87]) ).
tcf(c_38339,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK25(set_difference(X0,set_difference(X0,X1)),X2),X2)
| ( union(set_difference(X0,set_difference(X0,X1))) = X2 )
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_294,c_166]) ).
tcf(c_38340,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(set_difference(X0,set_difference(X0,X1)),X2),X1)
| in(sK25(set_difference(X0,set_difference(X0,X1)),X2),X2)
| ( union(set_difference(X0,set_difference(X0,X1))) = X2 ) ),
inference(superposition,[status(thm)],[c_294,c_370]) ).
tcf(c_38341,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK25(subset_complement(X0,X1),X2),X2)
| ( union(subset_complement(X0,X1)) = X2 )
| ~ element(X1,powerset(X0))
| ~ in(sK26(subset_complement(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_294,c_180]) ).
tcf(c_38342,plain,
! [X0: $i] :
( in(sK25(empty_set,X0),X0)
| ( union(empty_set) = X0 ) ),
inference(superposition,[status(thm)],[c_294,c_234]) ).
tcf(c_38343,plain,
! [X0: $i,X1: $i] :
( in(sK25(unordered_pair(X0,X0),X1),X1)
| ( union(unordered_pair(X0,X0)) = X1 )
| ( sK26(unordered_pair(X0,X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_294,c_239]) ).
tcf(c_38344,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(set_union2(X0,X1),X2),X1)
| in(sK26(set_union2(X0,X1),X2),X0)
| in(sK25(set_union2(X0,X1),X2),X2)
| ( union(set_union2(X0,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_294,c_254]) ).
tcf(c_38345,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK25(set_difference(X0,X1),X2),X2)
| ( union(set_difference(X0,X1)) = X2 )
| ~ in(sK26(set_difference(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_294,c_270]) ).
tcf(c_38346,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(set_difference(X0,X1),X2),X0)
| in(sK25(set_difference(X0,X1),X2),X2)
| ( union(set_difference(X0,X1)) = X2 ) ),
inference(superposition,[status(thm)],[c_294,c_269]) ).
tcf(c_38347,plain,
! [X0: $i,X1: $i] :
( subset(sK26(powerset(X0),X1),X0)
| in(sK25(powerset(X0),X1),X1)
| ( union(powerset(X0)) = X1 ) ),
inference(superposition,[status(thm)],[c_294,c_290]) ).
tcf(c_38348,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK25(unordered_pair(X0,X1),X2),X2)
| ( union(unordered_pair(X0,X1)) = X2 )
| ( sK26(unordered_pair(X0,X1),X2) = X1 )
| ( sK26(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_294,c_350]) ).
tcf(c_38349,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK54(X1))
| in(sK25(sK54(X1),X2),X2)
| ( union(sK54(X1)) = X2 )
| ~ subset(X0,sK26(sK54(X1),X2)) ),
inference(superposition,[status(thm)],[c_294,c_373]) ).
tcf(c_38350,plain,
! [X0: $i] :
( in(sK25(relation_rng(sK5),X0),X0)
| in(sK26(relation_rng(sK5),X0),relation_field(sK5))
| ( union(relation_rng(sK5)) = X0 ) ),
inference(superposition,[status(thm)],[c_294,c_27657]) ).
tcf(c_38351,plain,
! [X0: $i] :
( in(sK25(relation_dom(sK5),X0),X0)
| in(sK26(relation_dom(sK5),X0),relation_field(sK5))
| ( union(relation_dom(sK5)) = X0 ) ),
inference(superposition,[status(thm)],[c_294,c_27656]) ).
tcf(c_38352,plain,
! [X0: $i,X1: $i] :
( in(sK25(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1),X1)
| in(sK26(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1),relation_dom(sK5))
| ( union(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))) = X1 ) ),
inference(superposition,[status(thm)],[c_294,c_25255]) ).
tcf(c_38353,plain,
! [X0: $i] :
( in(sK25(relation_field(sK5),X0),X0)
| in(sK26(relation_field(sK5),X0),relation_rng(sK5))
| in(sK26(relation_field(sK5),X0),relation_dom(sK5))
| ( union(relation_field(sK5)) = X0 ) ),
inference(superposition,[status(thm)],[c_294,c_27655]) ).
tcf(c_38354,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK25(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2),X2)
| in(sK26(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2),relation_rng(relation_dom_restriction(sK5,X1)))
| ( union(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))) = X2 ) ),
inference(superposition,[status(thm)],[c_294,c_36223]) ).
tcf(c_38355,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2),X0)
| in(sK25(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2),X2)
| ( union(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))) = X2 ) ),
inference(superposition,[status(thm)],[c_294,c_36220]) ).
tcf(c_38356,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X2,X0),X2)
| in(sK25(X2,X0),union(X1))
| ( union(X2) = X0 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_294,c_295]) ).
tcf(c_38357,plain,
! [X0: $i,X1: $i] :
( in(sK26(X0,X1),X0)
| ( union(X0) = X1 )
| ( set_union2(unordered_pair(sK25(X0,X1),sK25(X0,X1)),X1) = X1 ) ),
inference(superposition,[status(thm)],[c_294,c_161]) ).
tcf(c_38358,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X0,X1),X0)
| ( union(X0) = X1 )
| ~ disjoint(X1,X2)
| ~ in(sK25(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_294,c_151]) ).
tcf(c_38359,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X2,X0),X2)
| in(sK25(X2,X0),X1)
| ( union(X2) = X0 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_294,c_242]) ).
tcf(c_38360,plain,
! [X0: $i,X1: $i] :
( in(sK26(X1,X0),X1)
| ( union(X1) = X0 )
| ( apply(identity_relation(X0),sK25(X1,X0)) = sK25(X1,X0) ) ),
inference(superposition,[status(thm)],[c_294,c_134]) ).
tcf(c_38361,plain,
! [X0: $i,X1: $i] :
( in(sK26(X1,X0),X1)
| ( union(X1) = X0 )
| ~ in(X0,sK25(X1,X0)) ),
inference(superposition,[status(thm)],[c_294,c_243]) ).
tcf(c_38362,plain,
! [X0: $i,X1: $i] :
( in(sK26(X1,X0),X1)
| ( union(X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_294,c_471]) ).
tcf(c_38363,plain,
! [X0: $i,X1: $i] :
( element(sK25(X0,X1),X1)
| in(sK26(X0,X1),X0)
| ( union(X0) = X1 ) ),
inference(superposition,[status(thm)],[c_294,c_276]) ).
tcf(c_38364,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X2,relation_dom(relation_dom_restriction(X0,X1))),X2)
| in(sK25(X2,relation_dom(relation_dom_restriction(X0,X1))),relation_dom(X0))
| ( relation_dom(relation_dom_restriction(X0,X1)) = union(X2) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_294,c_214]) ).
tcf(c_38365,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X2,relation_dom(relation_dom_restriction(X0,X1))),X2)
| in(sK25(X2,relation_dom(relation_dom_restriction(X0,X1))),X1)
| ( relation_dom(relation_dom_restriction(X0,X1)) = union(X2) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_294,c_213]) ).
tcf(c_38366,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X2,relation_rng(relation_rng_restriction(X1,X0))),X2)
| in(sK25(X2,relation_rng(relation_rng_restriction(X1,X0))),relation_rng(X0))
| ( relation_rng(relation_rng_restriction(X1,X0)) = union(X2) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_294,c_77]) ).
tcf(c_38367,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X2,relation_rng(relation_rng_restriction(X1,X0))),X2)
| in(sK25(X2,relation_rng(relation_rng_restriction(X1,X0))),X1)
| ( relation_rng(relation_rng_restriction(X1,X0)) = union(X2) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_294,c_76]) ).
tcf(c_38368,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK2(X2))
| in(sK26(X1,sK2(X2)),X1)
| ( union(X1) = sK2(X2) )
| ~ subset(X0,sK25(X1,sK2(X2))) ),
inference(superposition,[status(thm)],[c_294,c_87]) ).
tcf(c_38369,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X2,set_difference(X0,set_difference(X0,X1))),X2)
| ( set_difference(X0,set_difference(X0,X1)) = union(X2) )
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_294,c_166]) ).
tcf(c_38370,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X2,set_difference(X0,set_difference(X0,X1))),X2)
| in(sK25(X2,set_difference(X0,set_difference(X0,X1))),X1)
| ( set_difference(X0,set_difference(X0,X1)) = union(X2) ) ),
inference(superposition,[status(thm)],[c_294,c_370]) ).
tcf(c_38371,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X0,subset_complement(X1,X2)),X0)
| ( subset_complement(X1,X2) = union(X0) )
| ~ element(X2,powerset(X1))
| ~ in(sK25(X0,subset_complement(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_294,c_180]) ).
tcf(c_38372,plain,
! [X0: $i] :
( in(sK26(X0,empty_set),X0)
| ( union(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_294,c_234]) ).
tcf(c_38373,plain,
! [X0: $i,X1: $i] :
( in(sK26(X0,unordered_pair(X1,X1)),X0)
| ( unordered_pair(X1,X1) = union(X0) )
| ( sK25(X0,unordered_pair(X1,X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_294,c_239]) ).
tcf(c_38374,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X2,set_union2(X0,X1)),X2)
| in(sK25(X2,set_union2(X0,X1)),X1)
| in(sK25(X2,set_union2(X0,X1)),X0)
| ( set_union2(X0,X1) = union(X2) ) ),
inference(superposition,[status(thm)],[c_294,c_254]) ).
tcf(c_38375,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X0,set_difference(X1,X2)),X0)
| ( set_difference(X1,X2) = union(X0) )
| ~ in(sK25(X0,set_difference(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_294,c_270]) ).
tcf(c_38376,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X2,set_difference(X0,X1)),X2)
| in(sK25(X2,set_difference(X0,X1)),X0)
| ( set_difference(X0,X1) = union(X2) ) ),
inference(superposition,[status(thm)],[c_294,c_269]) ).
tcf(c_38377,plain,
! [X0: $i,X1: $i] :
( subset(sK25(X1,powerset(X0)),X0)
| in(sK26(X1,powerset(X0)),X1)
| ( powerset(X0) = union(X1) ) ),
inference(superposition,[status(thm)],[c_294,c_290]) ).
tcf(c_38378,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X0,unordered_pair(X1,X2)),X0)
| ( unordered_pair(X1,X2) = union(X0) )
| ( sK25(X0,unordered_pair(X1,X2)) = X2 )
| ( sK25(X0,unordered_pair(X1,X2)) = X1 ) ),
inference(superposition,[status(thm)],[c_294,c_350]) ).
tcf(c_38379,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK54(X2))
| in(sK26(X1,sK54(X2)),X1)
| ( union(X1) = sK54(X2) )
| ~ subset(X0,sK25(X1,sK54(X2))) ),
inference(superposition,[status(thm)],[c_294,c_373]) ).
tcf(c_38380,plain,
! [X0: $i] :
( in(sK26(X0,relation_rng(sK5)),X0)
| in(sK25(X0,relation_rng(sK5)),relation_field(sK5))
| ( union(X0) = relation_rng(sK5) ) ),
inference(superposition,[status(thm)],[c_294,c_27657]) ).
tcf(c_38381,plain,
! [X0: $i] :
( in(sK26(X0,relation_dom(sK5)),X0)
| in(sK25(X0,relation_dom(sK5)),relation_field(sK5))
| ( union(X0) = relation_dom(sK5) ) ),
inference(superposition,[status(thm)],[c_294,c_27656]) ).
tcf(c_38382,plain,
! [X0: $i,X1: $i] :
( in(sK26(X1,relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),X1)
| in(sK25(X1,relation_rng(relation_rng_restriction(X0,relation_inverse(sK5)))),relation_dom(sK5))
| ( relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))) = union(X1) ) ),
inference(superposition,[status(thm)],[c_294,c_25255]) ).
tcf(c_38383,plain,
! [X0: $i] :
( in(sK26(X0,relation_field(sK5)),X0)
| in(sK25(X0,relation_field(sK5)),relation_rng(sK5))
| in(sK25(X0,relation_field(sK5)),relation_dom(sK5))
| ( union(X0) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_294,c_27655]) ).
tcf(c_38384,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X2,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),X2)
| in(sK25(X2,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),relation_rng(relation_dom_restriction(sK5,X1)))
| ( relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) = union(X2) ) ),
inference(superposition,[status(thm)],[c_294,c_36223]) ).
tcf(c_38385,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK26(X2,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),X2)
| in(sK25(X2,relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),X0)
| ( relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)) = union(X2) ) ),
inference(superposition,[status(thm)],[c_294,c_36220]) ).
tcf(c_38388,plain,
! [X0: $i] :
( in(sK25(empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_38342,c_21789]) ).
tcf(c_38412,plain,
! [X0: $i,X1: $i] :
( subset(sK26(powerset(X0),X1),X0)
| in(sK25(powerset(X0),X1),X1)
| ( X0 = X1 ) ),
inference(light_normalisation,[status(thm)],[c_38347,c_225]) ).
tcf(c_38764,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(X2,set_difference(X2,X1)))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_371,c_368]) ).
tcf(c_38766,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(set_union2(X1,X2),set_difference(X1,X2)))
| ~ in(X0,X2)
| ~ in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_153,c_368]) ).
tcf(c_38769,plain,
! [X0: $i,X1: $i] :
( in(X0,set_difference(X1,empty_set))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_4095,c_368]) ).
tcf(c_38770,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(X1,set_difference(X2,set_difference(X2,X1))))
| ~ in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_371,c_368]) ).
tcf(c_38771,plain,
! [X0: $i,X1: $i] :
( in(X0,set_difference(relation_inverse_image(relation_inverse(sK5),X1),empty_set))
| ~ in(X0,relation_rng(sK5))
| ~ in(X0,relation_inverse_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_21834,c_368]) ).
tcf(c_38772,plain,
! [X0: $i,X1: $i] :
( in(X0,set_difference(relation_image(relation_inverse(sK5),X1),empty_set))
| ~ in(X0,relation_dom(sK5))
| ~ in(X0,relation_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_22079,c_368]) ).
tcf(c_38773,plain,
! [X0: $i,X1: $i] :
( in(X0,set_difference(relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))),empty_set))
| ~ in(X0,relation_dom(sK5))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_25056,c_368]) ).
tcf(c_38774,plain,
! [X0: $i] :
( in(X0,set_difference(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))))
| ~ in(X0,relation_field(sK5))
| ~ in(X0,relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_27644,c_368]) ).
tcf(c_38775,plain,
! [X0: $i,X1: $i] :
( in(X0,set_difference(relation_dom(relation_dom_restriction(sK5,X1)),empty_set))
| ~ in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_29867,c_368]) ).
tcf(c_38776,plain,
! [X0: $i,X1: $i] :
( in(X0,set_difference(relation_rng(relation_dom_restriction(sK5,X1)),empty_set))
| ~ in(X0,relation_rng(sK5))
| ~ in(X0,relation_rng(relation_dom_restriction(sK5,X1))) ),
inference(superposition,[status(thm)],[c_29913,c_368]) ).
tcf(c_38777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,union(X2))
| ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368,c_295]) ).
tcf(c_38778,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(X0,X0),set_difference(X1,set_difference(X1,X2))) = set_difference(X1,set_difference(X1,X2)) )
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_368,c_161]) ).
tcf(c_38779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0)
| ~ disjoint(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368,c_151]) ).
tcf(c_38780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0)
| ~ subset(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368,c_242]) ).
tcf(c_38781,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(set_difference(X1,set_difference(X1,X2))),X0) = X0 )
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_368,c_134]) ).
tcf(c_38782,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(X2,X0)
| ~ in(set_difference(X0,set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_368,c_243]) ).
tcf(c_38783,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(X2,X0)
| ~ empty(set_difference(X0,set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_368,c_471]) ).
tcf(c_38784,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_difference(X1,set_difference(X1,X2)))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_368,c_276]) ).
tcf(c_38787,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X1,set_difference(X1,X2)))
| ~ in(sK18(X0,set_difference(X1,set_difference(X1,X2))),X2)
| ~ in(sK18(X0,set_difference(X1,set_difference(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_368,c_240]) ).
tcf(c_38788,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_368,c_270]) ).
tcf(c_38790,plain,
! [X0: $i,X1: $i] :
( ~ in(sK2(set_difference(X0,set_difference(X0,X1))),X1)
| ~ in(sK2(set_difference(X0,set_difference(X0,X1))),X0) ),
inference(superposition,[status(thm)],[c_368,c_19526]) ).
tcf(c_38791,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(unordered_pair(set_difference(X0,set_difference(X0,X1)),X2),X1)
| ~ in(unordered_pair(set_difference(X0,set_difference(X0,X1)),X2),X0) ),
inference(superposition,[status(thm)],[c_368,c_19532]) ).
tcf(c_38792,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(unordered_pair(X0,set_difference(X1,set_difference(X1,X2))),X2)
| ~ in(unordered_pair(X0,set_difference(X1,set_difference(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_368,c_19533]) ).
tcf(c_38793,plain,
! [X0: $i,X1: $i] :
( ~ in(sK54(set_difference(X0,set_difference(X0,X1))),X1)
| ~ in(sK54(set_difference(X0,set_difference(X0,X1))),X0) ),
inference(superposition,[status(thm)],[c_368,c_19534]) ).
tcf(c_38794,plain,
! [X0: $i,X1: $i] :
( ~ in(sK2(powerset(union(set_difference(X0,set_difference(X0,X1))))),X1)
| ~ in(sK2(powerset(union(set_difference(X0,set_difference(X0,X1))))),X0) ),
inference(superposition,[status(thm)],[c_368,c_19702]) ).
tcf(c_38795,plain,
! [X0: $i,X1: $i] :
( ~ in(sK54(powerset(union(set_difference(X0,set_difference(X0,X1))))),X1)
| ~ in(sK54(powerset(union(set_difference(X0,set_difference(X0,X1))))),X0) ),
inference(superposition,[status(thm)],[c_368,c_19705]) ).
tcf(c_38796,plain,
! [X0: $i,X1: $i] :
( ~ in(powerset(set_difference(X0,set_difference(X0,X1))),X1)
| ~ in(powerset(set_difference(X0,set_difference(X0,X1))),X0) ),
inference(superposition,[status(thm)],[c_368,c_19958]) ).
tcf(c_38797,plain,
! [X0: $i,X1: $i] :
( ~ in(powerset(powerset(union(set_difference(X0,set_difference(X0,X1))))),X1)
| ~ in(powerset(powerset(union(set_difference(X0,set_difference(X0,X1))))),X0) ),
inference(superposition,[status(thm)],[c_368,c_20020]) ).
tcf(c_38798,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(sK2(set_union2(set_difference(X0,set_difference(X0,X1)),X2)),X1)
| ~ in(sK2(set_union2(set_difference(X0,set_difference(X0,X1)),X2)),X0) ),
inference(superposition,[status(thm)],[c_368,c_20095]) ).
tcf(c_38799,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(sK54(set_union2(set_difference(X0,set_difference(X0,X1)),X2)),X1)
| ~ in(sK54(set_union2(set_difference(X0,set_difference(X0,X1)),X2)),X0) ),
inference(superposition,[status(thm)],[c_368,c_20098]) ).
tcf(c_38800,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(powerset(set_union2(set_difference(X0,set_difference(X0,X1)),X2)),X1)
| ~ in(powerset(set_union2(set_difference(X0,set_difference(X0,X1)),X2)),X0) ),
inference(superposition,[status(thm)],[c_368,c_20101]) ).
tcf(c_38801,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(sK2(set_union2(X0,set_difference(X1,set_difference(X1,X2)))),X2)
| ~ in(sK2(set_union2(X0,set_difference(X1,set_difference(X1,X2)))),X1) ),
inference(superposition,[status(thm)],[c_368,c_20131]) ).
tcf(c_38802,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(sK54(set_union2(X0,set_difference(X1,set_difference(X1,X2)))),X2)
| ~ in(sK54(set_union2(X0,set_difference(X1,set_difference(X1,X2)))),X1) ),
inference(superposition,[status(thm)],[c_368,c_20134]) ).
tcf(c_38803,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(powerset(set_union2(X0,set_difference(X1,set_difference(X1,X2)))),X2)
| ~ in(powerset(set_union2(X0,set_difference(X1,set_difference(X1,X2)))),X1) ),
inference(superposition,[status(thm)],[c_368,c_20137]) ).
tcf(c_38994,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(sK5,X1) = X0 )
| ~ empty(sK5)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_25735,c_470]) ).
tcf(c_38995,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_25735,c_19213]) ).
tcf(c_38996,plain,
! [X0: $i] :
( ( relation_rng(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_25735,c_19212]) ).
tcf(c_38997,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,X0)) = empty_set )
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_25735,c_19211]) ).
tcf(c_38998,plain,
! [X0: $i] :
( ( relation_dom_restriction(sK5,X0) = empty_set )
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_25735,c_229]) ).
tcf(c_38999,plain,
! [X0: $i] :
( one_to_one(relation_dom_restriction(sK5,X0))
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_25735,c_6826]) ).
tcf(c_39001,plain,
! [X0: $i] :
( function(relation_dom_restriction(sK5,X0))
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_25735,c_331]) ).
tcf(c_39020,plain,
relation(set_difference(empty_set,empty_set)),
inference(global_subsumption_just,[status(thm)],[c_27188,c_231,c_27218]) ).
tcf(c_39025,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X0,X1)),X0),
inference(superposition,[status(thm)],[c_371,c_27286]) ).
tcf(c_39027,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_union2(X0,X1),set_difference(X0,X1)),X1),
inference(superposition,[status(thm)],[c_153,c_27286]) ).
tcf(c_39028,plain,
! [X0: $i] : subset(set_difference(empty_set,empty_set),X0),
inference(superposition,[status(thm)],[c_263,c_27286]) ).
tcf(c_39029,plain,
! [X0: $i] : subset(set_difference(X0,X0),empty_set),
inference(superposition,[status(thm)],[c_264,c_27286]) ).
tcf(c_39031,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X1,set_difference(X1,X0))),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_371,c_27286]) ).
tcf(c_39032,plain,
! [X0: $i] : subset(set_difference(relation_inverse_image(relation_inverse(sK5),X0),empty_set),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_21834,c_27286]) ).
tcf(c_39033,plain,
! [X0: $i] : subset(set_difference(relation_image(relation_inverse(sK5),X0),empty_set),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_22079,c_27286]) ).
tcf(c_39034,plain,
! [X0: $i] : subset(set_difference(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),empty_set),relation_dom(sK5)),
inference(superposition,[status(thm)],[c_25056,c_27286]) ).
tcf(c_39035,plain,
subset(set_difference(relation_field(sK5),set_difference(relation_dom(sK5),relation_rng(sK5))),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_27644,c_27286]) ).
tcf(c_39036,plain,
! [X0: $i] : subset(set_difference(relation_dom(relation_dom_restriction(sK5,X0)),empty_set),X0),
inference(superposition,[status(thm)],[c_29867,c_27286]) ).
tcf(c_39037,plain,
! [X0: $i] : subset(set_difference(relation_rng(relation_dom_restriction(sK5,X0)),empty_set),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_29913,c_27286]) ).
tcf(c_39038,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X1,set_difference(X1,X0))) = subset_complement(X0,set_difference(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_27286,c_6703]) ).
tcf(c_39039,plain,
! [X0: $i,X1: $i] : subset_complement(X0,subset_complement(X0,set_difference(X1,set_difference(X1,X0)))) = set_difference(X1,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_27286,c_6699]) ).
tcf(c_39040,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,set_difference(X1,X0)) = X0 )
| ~ subset(X0,set_difference(X1,set_difference(X1,X0))) ),
inference(superposition,[status(thm)],[c_27286,c_260]) ).
tcf(c_39041,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X0,X1)),set_difference(set_difference(X0,set_difference(X0,X1)),X1)) = set_difference(X0,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_27286,c_123]) ).
tcf(c_39042,plain,
! [X0: $i,X1: $i] :
( proper_subset(set_difference(X0,set_difference(X0,X1)),X1)
| ( set_difference(X0,set_difference(X0,X1)) = X1 ) ),
inference(superposition,[status(thm)],[c_27286,c_468]) ).
tcf(c_39043,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X2,set_difference(X2,X0)),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_27286,c_110]) ).
tcf(c_39044,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,set_difference(X0,X1)),X1) = empty_set,
inference(superposition,[status(thm)],[c_27286,c_138]) ).
tcf(c_39045,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_difference(X0,X1)),X1) = X1,
inference(superposition,[status(thm)],[c_27286,c_85]) ).
tcf(c_39047,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X2,set_difference(X2,X0)),X1)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_27286,c_190]) ).
tcf(c_39049,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,set_difference(X0,relation_inverse_image(relation_inverse(sK5),X1))),relation_rng(sK5)),empty_set),
inference(superposition,[status(thm)],[c_27286,c_22779]) ).
tcf(c_39050,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,set_difference(X0,relation_image(relation_inverse(sK5),X1))),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_27286,c_22780]) ).
tcf(c_39051,plain,
! [X0: $i,X1: $i] : subset(set_difference(set_difference(X0,set_difference(X0,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5))))),relation_dom(sK5)),empty_set),
inference(superposition,[status(thm)],[c_27286,c_25182]) ).
tcf(c_39134,plain,
element(set_difference(relation_rng(sK5),relation_rng(empty_set)),powerset(relation_rng(sK5))),
inference(superposition,[status(thm)],[c_28288,c_37803]) ).
tcf(c_39135,plain,
! [X0: $i] : subset(set_difference(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0))),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_37803,c_274]) ).
tcf(c_39136,plain,
! [X0: $i] :
( empty(set_difference(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0))))
| ~ empty(powerset(relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_37803,c_285]) ).
tcf(c_39137,plain,
! [X0: $i] :
( empty(powerset(relation_rng(sK5)))
| in(set_difference(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0))),powerset(relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_37803,c_283]) ).
tcf(c_39138,plain,
element(set_difference(relation_rng(sK5),empty_set),powerset(relation_rng(sK5))),
inference(light_normalisation,[status(thm)],[c_39134,c_187]) ).
tcf(c_39139,plain,
! [X0: $i] : in(set_difference(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0))),powerset(relation_rng(sK5))),
inference(forward_subsumption_resolution,[status(thm)],[c_39137,c_286]) ).
tcf(c_39141,plain,
! [X0: $i] : subset_complement(relation_rng(sK5),set_difference(relation_rng(sK5),relation_rng(relation_dom_restriction(sK5,X0)))) = relation_rng(relation_dom_restriction(sK5,X0)),
inference(light_normalisation,[status(thm)],[c_29908,c_29907]) ).
tcf(c_39147,plain,
! [X0: $i] :
( ( relation_rng(relation_dom_restriction(sK5,X0)) = relation_rng(sK5) )
| ~ relation(sK5)
| ~ relation(relation_dom_restriction(sK5,X0))
| ~ subset(sK5,relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_121,c_29909]) ).
tcf(c_39148,plain,
( ( relation_rng(relation_dom_restriction(sK5,empty_set)) = relation_rng(sK5) )
| ~ subset(relation_rng(sK5),relation_rng(empty_set)) ),
inference(superposition,[status(thm)],[c_28288,c_29909]) ).
tcf(c_39149,plain,
( ( relation_rng(sK5) = empty_set )
| ~ subset(relation_rng(sK5),empty_set) ),
inference(light_normalisation,[status(thm)],[c_39148,c_187,c_28290]) ).
tcf(c_39152,plain,
! [X0: $i] :
( ( relation_rng(relation_dom_restriction(sK5,X0)) = relation_rng(sK5) )
| ~ subset(sK5,relation_dom_restriction(sK5,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39147,c_96,c_25741]) ).
tcf(c_39160,plain,
! [X0: $i] :
( ( relation_rng(relation_dom_restriction(sK5,X0)) = relation_rng(sK5) )
| ~ empty(sK5) ),
inference(superposition,[status(thm)],[c_19515,c_39152]) ).
tcf(c_39161,plain,
( ( relation_rng(relation_dom_restriction(sK5,empty_set)) = relation_rng(sK5) )
| ~ subset(sK5,empty_set) ),
inference(superposition,[status(thm)],[c_28288,c_39152]) ).
tcf(c_39164,plain,
( ( relation_rng(sK5) = empty_set )
| ~ subset(sK5,empty_set) ),
inference(light_normalisation,[status(thm)],[c_39161,c_28290]) ).
tcf(c_39178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X0,X2),X3)
| ~ subset(X2,X1)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_19515,c_22559]) ).
tcf(c_39179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X4,cartesian_product2(X0,X1))
| subset(cartesian_product2(X0,X3),set_difference(X2,unordered_pair(X4,X4)))
| ~ subset(X3,X1)
| ~ subset(cartesian_product2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_58,c_22559]) ).
tcf(c_39180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X0,X3),union(X2))
| ~ subset(X3,X1)
| ~ in(cartesian_product2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_222,c_22559]) ).
tcf(c_39182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X3,X2),cartesian_product2(X3,X1))
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_82,c_22559]) ).
tcf(c_39183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(cartesian_product2(X0,X4),cartesian_product2(X1,X3))
| ~ subset(X4,X2)
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_22559]) ).
tcf(c_39184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(cartesian_product2(X0,X4),set_difference(X2,set_difference(X2,X3)))
| ~ subset(X4,X1)
| ~ subset(cartesian_product2(X0,X1),X3)
| ~ subset(cartesian_product2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_109,c_22559]) ).
tcf(c_39185,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X0,X2),cartesian_product2(relation_dom(cartesian_product2(X0,X1)),relation_rng(cartesian_product2(X0,X1))))
| ~ subset(X2,X1)
| ~ relation(cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_117,c_22559]) ).
tcf(c_39186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X2,X0),set_union2(cartesian_product2(X2,X1),X3))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_209,c_22559]) ).
tcf(c_39188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X2,X0),set_union2(X3,cartesian_product2(X2,X1)))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_19598,c_22559]) ).
tcf(c_39189,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(empty_set,X0),X2)
| ~ subset(empty_set,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_26653,c_22559]) ).
tcf(c_39190,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X2,X0),X1)
| ~ subset(empty_set,X1)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_29072,c_22559]) ).
tcf(c_39191,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X1,X0),X2)
| ~ subset(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39190,c_124]) ).
tcf(c_39236,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK58(X1,X2,X0),union(X3))
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_381,c_295]) ).
tcf(c_39237,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(sK58(X1,X2,X0),sK58(X1,X2,X0)),X2) = X2 )
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_381,c_161]) ).
tcf(c_39238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X0)
| ~ disjoint(X1,X3)
| ~ in(X2,relation_image(X0,X1))
| ~ in(sK58(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_381,c_151]) ).
tcf(c_39239,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK58(X1,X2,X0),X3)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_381,c_242]) ).
tcf(c_39240,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK58(X1,X2,X0)) = sK58(X1,X2,X0) )
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_381,c_134]) ).
tcf(c_39241,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X1)
| ~ in(X2,relation_image(X1,X0))
| ~ in(X0,sK58(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_381,c_243]) ).
tcf(c_39243,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK58(X1,X2,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_381,c_276]) ).
tcf(c_39244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK58(X1,relation_dom(relation_dom_restriction(X2,X3)),X0),relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_dom(relation_dom_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_381,c_214]) ).
tcf(c_39245,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK58(X1,relation_dom(relation_dom_restriction(X2,X3)),X0),X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_dom(relation_dom_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_381,c_213]) ).
tcf(c_39246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK58(X1,relation_rng(relation_rng_restriction(X2,X3)),X0),relation_rng(X3))
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_rng(relation_rng_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_381,c_77]) ).
tcf(c_39247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK58(X1,relation_rng(relation_rng_restriction(X2,X3)),X0),X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_rng(relation_rng_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_381,c_76]) ).
tcf(c_39248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X2))
| ~ relation(X1)
| ~ in(X3,relation_image(X1,sK2(X2)))
| ~ subset(X0,sK58(X1,sK2(X2),X3)) ),
inference(superposition,[status(thm)],[c_381,c_87]) ).
tcf(c_39250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK58(X1,set_difference(X2,set_difference(X2,X3)),X0),X3)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_difference(X2,set_difference(X2,X3)))) ),
inference(superposition,[status(thm)],[c_381,c_370]) ).
tcf(c_39251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X0)
| ~ element(X2,powerset(X1))
| ~ in(X3,relation_image(X0,subset_complement(X1,X2)))
| ~ in(sK58(X0,subset_complement(X1,X2),X3),X2) ),
inference(superposition,[status(thm)],[c_381,c_180]) ).
tcf(c_39253,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK58(X1,unordered_pair(X2,X2),X0) = X2 )
| ~ relation(X1)
| ~ in(X0,relation_image(X1,unordered_pair(X2,X2))) ),
inference(superposition,[status(thm)],[c_381,c_239]) ).
tcf(c_39254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK58(X1,set_union2(X2,X3),X0),X3)
| in(sK58(X1,set_union2(X2,X3),X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_union2(X2,X3))) ),
inference(superposition,[status(thm)],[c_381,c_254]) ).
tcf(c_39255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X0)
| ~ in(X3,relation_image(X0,set_difference(X1,X2)))
| ~ in(sK58(X0,set_difference(X1,X2),X3),X2) ),
inference(superposition,[status(thm)],[c_381,c_270]) ).
tcf(c_39256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK58(X1,set_difference(X2,X3),X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,set_difference(X2,X3))) ),
inference(superposition,[status(thm)],[c_381,c_269]) ).
tcf(c_39257,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK58(X1,powerset(X2),X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_381,c_290]) ).
tcf(c_39258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK58(X1,unordered_pair(X2,X3),X0) = X3 )
| ( sK58(X1,unordered_pair(X2,X3),X0) = X2 )
| ~ relation(X1)
| ~ in(X0,relation_image(X1,unordered_pair(X2,X3))) ),
inference(superposition,[status(thm)],[c_381,c_350]) ).
tcf(c_39259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK54(X2))
| ~ relation(X1)
| ~ in(X3,relation_image(X1,sK54(X2)))
| ~ subset(X0,sK58(X1,sK54(X2),X3)) ),
inference(superposition,[status(thm)],[c_381,c_373]) ).
tcf(c_39260,plain,
! [X0: $i,X1: $i] :
( in(sK58(X1,relation_rng(sK5),X0),relation_field(sK5))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_381,c_27657]) ).
tcf(c_39261,plain,
! [X0: $i,X1: $i] :
( in(sK58(X1,relation_dom(sK5),X0),relation_field(sK5))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_dom(sK5))) ),
inference(superposition,[status(thm)],[c_381,c_27656]) ).
tcf(c_39262,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK58(X1,relation_rng(relation_rng_restriction(X2,relation_inverse(sK5))),X0),relation_dom(sK5))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_rng(relation_rng_restriction(X2,relation_inverse(sK5))))) ),
inference(superposition,[status(thm)],[c_381,c_25255]) ).
tcf(c_39263,plain,
! [X0: $i,X1: $i] :
( in(sK58(X1,relation_field(sK5),X0),relation_rng(sK5))
| in(sK58(X1,relation_field(sK5),X0),relation_dom(sK5))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_field(sK5))) ),
inference(superposition,[status(thm)],[c_381,c_27655]) ).
tcf(c_39264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK58(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)),X0),relation_rng(relation_dom_restriction(sK5,X3)))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)))) ),
inference(superposition,[status(thm)],[c_381,c_36223]) ).
tcf(c_39265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK58(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)),X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)))) ),
inference(superposition,[status(thm)],[c_381,c_36220]) ).
tcf(c_39490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK64(X1,X2,X0),union(X3))
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_395,c_295]) ).
tcf(c_39491,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(sK64(X1,X2,X0),sK64(X1,X2,X0)),X2) = X2 )
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_395,c_161]) ).
tcf(c_39492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X0)
| ~ disjoint(X1,X3)
| ~ in(X2,relation_inverse_image(X0,X1))
| ~ in(sK64(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_395,c_151]) ).
tcf(c_39493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK64(X1,X2,X0),X3)
| ~ relation(X1)
| ~ subset(X2,X3)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_395,c_242]) ).
tcf(c_39494,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(X2),sK64(X1,X2,X0)) = sK64(X1,X2,X0) )
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_395,c_134]) ).
tcf(c_39495,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X0))
| ~ in(X0,sK64(X1,X0,X2)) ),
inference(superposition,[status(thm)],[c_395,c_243]) ).
tcf(c_39497,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK64(X1,X2,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_395,c_276]) ).
tcf(c_39498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK64(X1,relation_dom(relation_dom_restriction(X2,X3)),X0),relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_dom(relation_dom_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_395,c_214]) ).
tcf(c_39499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK64(X1,relation_dom(relation_dom_restriction(X2,X3)),X0),X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_dom(relation_dom_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_395,c_213]) ).
tcf(c_39500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK64(X1,relation_rng(relation_rng_restriction(X2,X3)),X0),relation_rng(X3))
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_rng(relation_rng_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_395,c_77]) ).
tcf(c_39501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK64(X1,relation_rng(relation_rng_restriction(X2,X3)),X0),X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_rng(relation_rng_restriction(X2,X3)))) ),
inference(superposition,[status(thm)],[c_395,c_76]) ).
tcf(c_39502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK2(X2))
| ~ relation(X1)
| ~ in(X3,relation_inverse_image(X1,sK2(X2)))
| ~ subset(X0,sK64(X1,sK2(X2),X3)) ),
inference(superposition,[status(thm)],[c_395,c_87]) ).
tcf(c_39504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK64(X1,set_difference(X2,set_difference(X2,X3)),X0),X3)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,set_difference(X2,set_difference(X2,X3)))) ),
inference(superposition,[status(thm)],[c_395,c_370]) ).
tcf(c_39505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X0)
| ~ element(X2,powerset(X1))
| ~ in(X3,relation_inverse_image(X0,subset_complement(X1,X2)))
| ~ in(sK64(X0,subset_complement(X1,X2),X3),X2) ),
inference(superposition,[status(thm)],[c_395,c_180]) ).
tcf(c_39507,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK64(X1,unordered_pair(X2,X2),X0) = X2 )
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,unordered_pair(X2,X2))) ),
inference(superposition,[status(thm)],[c_395,c_239]) ).
tcf(c_39508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK64(X1,set_union2(X2,X3),X0),X3)
| in(sK64(X1,set_union2(X2,X3),X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,set_union2(X2,X3))) ),
inference(superposition,[status(thm)],[c_395,c_254]) ).
tcf(c_39509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X0)
| ~ in(X3,relation_inverse_image(X0,set_difference(X1,X2)))
| ~ in(sK64(X0,set_difference(X1,X2),X3),X2) ),
inference(superposition,[status(thm)],[c_395,c_270]) ).
tcf(c_39510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK64(X1,set_difference(X2,X3),X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,set_difference(X2,X3))) ),
inference(superposition,[status(thm)],[c_395,c_269]) ).
tcf(c_39511,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK64(X1,powerset(X2),X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,powerset(X2))) ),
inference(superposition,[status(thm)],[c_395,c_290]) ).
tcf(c_39512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK64(X1,unordered_pair(X2,X3),X0) = X3 )
| ( sK64(X1,unordered_pair(X2,X3),X0) = X2 )
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,unordered_pair(X2,X3))) ),
inference(superposition,[status(thm)],[c_395,c_350]) ).
tcf(c_39513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,sK54(X2))
| ~ relation(X1)
| ~ in(X3,relation_inverse_image(X1,sK54(X2)))
| ~ subset(X0,sK64(X1,sK54(X2),X3)) ),
inference(superposition,[status(thm)],[c_395,c_373]) ).
tcf(c_39514,plain,
! [X0: $i,X1: $i] :
( in(sK64(X1,relation_rng(sK5),X0),relation_field(sK5))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_395,c_27657]) ).
tcf(c_39515,plain,
! [X0: $i,X1: $i] :
( in(sK64(X1,relation_dom(sK5),X0),relation_field(sK5))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_dom(sK5))) ),
inference(superposition,[status(thm)],[c_395,c_27656]) ).
tcf(c_39516,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK64(X1,relation_rng(relation_rng_restriction(X2,relation_inverse(sK5))),X0),relation_dom(sK5))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_rng(relation_rng_restriction(X2,relation_inverse(sK5))))) ),
inference(superposition,[status(thm)],[c_395,c_25255]) ).
tcf(c_39517,plain,
! [X0: $i,X1: $i] :
( in(sK64(X1,relation_field(sK5),X0),relation_rng(sK5))
| in(sK64(X1,relation_field(sK5),X0),relation_dom(sK5))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_field(sK5))) ),
inference(superposition,[status(thm)],[c_395,c_27655]) ).
tcf(c_39518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK64(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)),X0),relation_rng(relation_dom_restriction(sK5,X3)))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)))) ),
inference(superposition,[status(thm)],[c_395,c_36223]) ).
tcf(c_39519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK64(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)),X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,relation_rng(relation_dom_restriction(relation_rng_restriction(X2,sK5),X3)))) ),
inference(superposition,[status(thm)],[c_395,c_36220]) ).
tcf(c_39711,plain,
! [X0: $i] :
( ( relation_inverse(function_inverse(X0)) = function_inverse(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0)) ),
inference(superposition,[status(thm)],[c_189,c_435]) ).
tcf(c_39712,plain,
( ( relation_inverse(sK75) = function_inverse(sK75) )
| ~ function(sK75)
| ~ relation(sK75) ),
inference(superposition,[status(thm)],[c_458,c_435]) ).
tcf(c_39713,plain,
( ( relation_inverse(empty_set) = function_inverse(empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_19096,c_435]) ).
tcf(c_39714,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(X0)) = function_inverse(relation_dom(X0)) )
| ~ empty(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_19129,c_435]) ).
tcf(c_39715,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(X0)) = function_inverse(relation_rng(X0)) )
| ~ empty(X0)
| ~ function(relation_rng(X0))
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_19154,c_435]) ).
tcf(c_39716,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(X0)) = function_inverse(relation_inverse(X0)) )
| ~ empty(X0)
| ~ function(relation_inverse(X0))
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_19173,c_435]) ).
tcf(c_39717,plain,
! [X0: $i] :
( ( relation_inverse(sK23(X0)) = function_inverse(sK23(X0)) )
| ~ empty(X0)
| ~ function(sK23(X0))
| ~ relation(sK23(X0)) ),
inference(superposition,[status(thm)],[c_20382,c_435]) ).
tcf(c_39718,plain,
! [X0: $i] :
( ( relation_inverse(identity_relation(X0)) = function_inverse(identity_relation(X0)) )
| ~ empty(X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20572,c_435]) ).
tcf(c_39719,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( set_union2(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5))) = relation_field(sK5) )
| ~ function(sK5)
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_35222,c_435]) ).
tcf(c_39720,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( set_union2(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5))) = relation_field(sK5) )
| ~ function(sK5)
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_34829,c_435]) ).
tcf(c_39721,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( apply(identity_relation(relation_field(sK5)),sK77(sK5)) = sK77(sK5) )
| ~ function(sK5)
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_32806,c_435]) ).
tcf(c_39722,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( apply(identity_relation(relation_field(sK5)),sK76(sK5)) = sK76(sK5) )
| ~ function(sK5)
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_32698,c_435]) ).
tcf(c_39723,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom_restriction(sK5,X0)) = function_inverse(relation_dom_restriction(sK5,X0)) )
| ~ empty(identity_relation(X0))
| ~ function(relation_dom_restriction(sK5,X0))
| ~ relation(relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_25779,c_435]) ).
tcf(c_39724,plain,
( ( function_inverse(empty_set) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_39713,c_19912]) ).
tcf(c_39725,plain,
function_inverse(empty_set) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_39724,c_19076,c_231]) ).
tcf(c_39726,plain,
relation_inverse(sK75) = function_inverse(sK75),
inference(forward_subsumption_resolution,[status(thm)],[c_39712,c_457,c_456]) ).
tcf(c_39727,plain,
! [X0: $i] :
( ( relation_inverse(identity_relation(X0)) = function_inverse(identity_relation(X0)) )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39718,c_421,c_422]) ).
tcf(c_39746,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( apply(identity_relation(relation_field(sK5)),sK76(sK5)) = sK76(sK5) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39722,c_97,c_96]) ).
tcf(c_39749,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( apply(identity_relation(relation_field(sK5)),sK77(sK5)) = sK77(sK5) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39721,c_97,c_96]) ).
tcf(c_39752,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom_restriction(sK5,X0)) = function_inverse(relation_dom_restriction(sK5,X0)) )
| ~ empty(identity_relation(X0))
| ~ function(relation_dom_restriction(sK5,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39723,c_25741]) ).
tcf(c_39756,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( set_union2(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5))) = relation_field(sK5) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39720,c_97,c_96]) ).
tcf(c_39759,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( set_union2(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5))) = relation_field(sK5) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39719,c_97,c_96]) ).
tcf(c_39768,plain,
( empty(relation_dom(sK75))
| ~ empty(function_inverse(sK75)) ),
inference(demodulation,[status(thm)],[c_24185,c_39726]) ).
tcf(c_39769,plain,
( relation(relation_dom(sK75))
| ~ empty(function_inverse(sK75)) ),
inference(demodulation,[status(thm)],[c_24184,c_39726]) ).
tcf(c_39770,plain,
( one_to_one(relation_dom(sK75))
| ~ empty(function_inverse(sK75)) ),
inference(demodulation,[status(thm)],[c_24183,c_39726]) ).
tcf(c_39771,plain,
( function(relation_dom(sK75))
| ~ empty(function_inverse(sK75)) ),
inference(demodulation,[status(thm)],[c_24182,c_39726]) ).
tcf(c_39772,plain,
( empty(relation_rng(sK75))
| ~ empty(function_inverse(sK75)) ),
inference(demodulation,[status(thm)],[c_22275,c_39726]) ).
tcf(c_39773,plain,
( relation(relation_rng(sK75))
| ~ empty(function_inverse(sK75)) ),
inference(demodulation,[status(thm)],[c_22274,c_39726]) ).
tcf(c_39774,plain,
( one_to_one(relation_rng(sK75))
| ~ empty(function_inverse(sK75)) ),
inference(demodulation,[status(thm)],[c_22273,c_39726]) ).
tcf(c_39775,plain,
( function(relation_rng(sK75))
| ~ empty(function_inverse(sK75)) ),
inference(demodulation,[status(thm)],[c_22272,c_39726]) ).
tcf(c_39776,plain,
relation_rng(function_inverse(sK75)) = relation_dom(sK75),
inference(demodulation,[status(thm)],[c_21134,c_39726]) ).
tcf(c_39777,plain,
relation_dom(function_inverse(sK75)) = relation_rng(sK75),
inference(demodulation,[status(thm)],[c_20957,c_39726]) ).
tcf(c_39778,plain,
( empty(sK75)
| ~ empty(function_inverse(sK75)) ),
inference(demodulation,[status(thm)],[c_20612,c_39726]) ).
tcf(c_39779,plain,
relation_inverse(function_inverse(sK75)) = sK75,
inference(demodulation,[status(thm)],[c_20538,c_39726]) ).
tcf(c_39817,plain,
( function(function_inverse(sK75))
| ~ one_to_one(sK75)
| ~ function(sK75)
| ~ relation(sK75) ),
inference(superposition,[status(thm)],[c_39726,c_431]) ).
tcf(c_39819,plain,
( one_to_one(function_inverse(sK75))
| ~ empty(sK75) ),
inference(superposition,[status(thm)],[c_39726,c_19173]) ).
tcf(c_39820,plain,
( relation(function_inverse(sK75))
| ~ relation(sK75) ),
inference(superposition,[status(thm)],[c_39726,c_434]) ).
tcf(c_39822,plain,
( empty(function_inverse(sK75))
| ~ empty(sK75) ),
inference(superposition,[status(thm)],[c_39726,c_432]) ).
tcf(c_39827,plain,
relation(function_inverse(sK75)),
inference(forward_subsumption_resolution,[status(thm)],[c_39820,c_456]) ).
tcf(c_39832,plain,
function(function_inverse(sK75)),
inference(forward_subsumption_resolution,[status(thm)],[c_39817,c_458,c_457,c_456]) ).
tcf(c_39840,plain,
! [X0: $i,X1: $i] : relation_dom_restriction(relation_rng_restriction(X0,function_inverse(sK75)),X1) = relation_rng_restriction(X0,relation_dom_restriction(function_inverse(sK75),X1)),
inference(superposition,[status(thm)],[c_39827,c_89]) ).
tcf(c_39841,plain,
set_union2(relation_dom(function_inverse(sK75)),relation_rng(function_inverse(sK75))) = relation_field(function_inverse(sK75)),
inference(superposition,[status(thm)],[c_39827,c_419]) ).
tcf(c_39842,plain,
! [X0: $i] : relation_composition(identity_relation(X0),function_inverse(sK75)) = relation_dom_restriction(function_inverse(sK75),X0),
inference(superposition,[status(thm)],[c_39827,c_223]) ).
tcf(c_39843,plain,
relation_image(function_inverse(sK75),relation_dom(function_inverse(sK75))) = relation_rng(function_inverse(sK75)),
inference(superposition,[status(thm)],[c_39827,c_99]) ).
tcf(c_39844,plain,
relation_rng(relation_inverse(function_inverse(sK75))) = relation_dom(function_inverse(sK75)),
inference(superposition,[status(thm)],[c_39827,c_137]) ).
tcf(c_39845,plain,
relation_dom(relation_inverse(function_inverse(sK75))) = relation_rng(function_inverse(sK75)),
inference(superposition,[status(thm)],[c_39827,c_136]) ).
tcf(c_39846,plain,
relation_inverse(relation_inverse(function_inverse(sK75))) = function_inverse(sK75),
inference(superposition,[status(thm)],[c_39827,c_429]) ).
tcf(c_39850,plain,
relation_image(function_inverse(sK75),relation_rng(sK75)) = relation_dom(sK75),
inference(light_normalisation,[status(thm)],[c_39843,c_39776,c_39777]) ).
tcf(c_39851,plain,
set_union2(relation_rng(sK75),relation_dom(sK75)) = relation_field(function_inverse(sK75)),
inference(light_normalisation,[status(thm)],[c_39841,c_39776,c_39777]) ).
tcf(c_39952,plain,
( subset(set_difference(set_difference(relation_field(sK5),set_difference(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5))),set_difference(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_22396]) ).
tcf(c_39953,plain,
( subset(set_difference(set_difference(set_difference(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5))),unordered_pair(sK76(sK5),sK76(sK5))),unordered_pair(sK76(sK5),sK76(sK5))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_22121]) ).
tcf(c_39954,plain,
( subset(set_difference(relation_field(sK5),set_difference(set_difference(set_difference(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5)),relation_field(sK5)),relation_field(sK5))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_20482]) ).
tcf(c_39955,plain,
( subset(set_difference(set_difference(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5))),unordered_pair(sK76(sK5),sK76(sK5))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_20247]) ).
tcf(c_39957,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ proper_subset(relation_field(sK5),set_difference(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5)))) ),
inference(superposition,[status(thm)],[c_39756,c_19484]) ).
tcf(c_39958,plain,
( subset(set_difference(relation_field(sK5),set_difference(set_difference(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5)),relation_field(sK5))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_19741]) ).
tcf(c_39959,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(powerset(relation_field(sK5)),unordered_pair(sK76(sK5),sK76(sK5))) ),
inference(superposition,[status(thm)],[c_39756,c_20137]) ).
tcf(c_39960,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(sK54(relation_field(sK5)),unordered_pair(sK76(sK5),sK76(sK5))) ),
inference(superposition,[status(thm)],[c_39756,c_20134]) ).
tcf(c_39961,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(sK2(relation_field(sK5)),unordered_pair(sK76(sK5),sK76(sK5))) ),
inference(superposition,[status(thm)],[c_39756,c_20131]) ).
tcf(c_39962,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(powerset(relation_field(sK5)),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_39756,c_20101]) ).
tcf(c_39963,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(sK54(relation_field(sK5)),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_39756,c_20098]) ).
tcf(c_39964,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(sK2(relation_field(sK5)),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_39756,c_20095]) ).
tcf(c_39965,plain,
( subset(set_difference(relation_field(sK5),set_difference(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_19566]) ).
tcf(c_39966,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ proper_subset(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5))) ),
inference(superposition,[status(thm)],[c_39756,c_19595]) ).
tcf(c_39967,plain,
( subset(set_difference(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_19485]) ).
tcf(c_39968,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ proper_subset(relation_field(sK5),relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_39756,c_19458]) ).
tcf(c_39971,plain,
( subset(relation_field(sK5),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_209]) ).
tcf(c_39973,plain,
( subset(set_difference(set_difference(set_difference(set_difference(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5)),relation_field(sK5)),relation_field(sK5)),relation_field(sK5)),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_22118]) ).
tcf(c_39974,plain,
( subset(set_difference(set_difference(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5)),set_difference(relation_field(sK5),set_difference(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5)))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_20651]) ).
tcf(c_39975,plain,
( subset(set_difference(unordered_pair(sK76(sK5),sK76(sK5)),set_difference(set_difference(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5))),unordered_pair(sK76(sK5),sK76(sK5)))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_20485]) ).
tcf(c_39976,plain,
( subset(set_difference(set_difference(set_difference(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5)),relation_field(sK5)),relation_field(sK5)),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_20244]) ).
tcf(c_39977,plain,
( subset(set_difference(unordered_pair(sK76(sK5),sK76(sK5)),set_difference(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5)))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_19744]) ).
tcf(c_39978,plain,
( subset(set_difference(set_difference(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5)),relation_field(sK5)),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_19715]) ).
tcf(c_39979,plain,
( subset(set_difference(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5)),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_19593]) ).
tcf(c_39980,plain,
( subset(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_19598]) ).
tcf(c_39983,plain,
! [X0: $i] :
( in(X0,relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(X0,unordered_pair(sK76(sK5),sK76(sK5))) ),
inference(superposition,[status(thm)],[c_39756,c_253]) ).
tcf(c_39986,plain,
( element(sK76(sK5),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_20190]) ).
tcf(c_39987,plain,
( in(sK76(sK5),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39756,c_19994]) ).
tcf(c_39988,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_39756,c_20165]) ).
tcf(c_40033,plain,
( subset(set_difference(set_difference(relation_field(sK5),set_difference(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5))),set_difference(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_22396]) ).
tcf(c_40034,plain,
( subset(set_difference(set_difference(set_difference(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5))),unordered_pair(sK77(sK5),sK77(sK5))),unordered_pair(sK77(sK5),sK77(sK5))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_22121]) ).
tcf(c_40035,plain,
( subset(set_difference(relation_field(sK5),set_difference(set_difference(set_difference(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5)),relation_field(sK5)),relation_field(sK5))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_20482]) ).
tcf(c_40036,plain,
( subset(set_difference(set_difference(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5))),unordered_pair(sK77(sK5),sK77(sK5))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_20247]) ).
tcf(c_40038,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ proper_subset(relation_field(sK5),set_difference(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5)))) ),
inference(superposition,[status(thm)],[c_39759,c_19484]) ).
tcf(c_40039,plain,
( subset(set_difference(relation_field(sK5),set_difference(set_difference(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5)),relation_field(sK5))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_19741]) ).
tcf(c_40040,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(powerset(relation_field(sK5)),unordered_pair(sK77(sK5),sK77(sK5))) ),
inference(superposition,[status(thm)],[c_39759,c_20137]) ).
tcf(c_40041,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(sK54(relation_field(sK5)),unordered_pair(sK77(sK5),sK77(sK5))) ),
inference(superposition,[status(thm)],[c_39759,c_20134]) ).
tcf(c_40042,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(sK2(relation_field(sK5)),unordered_pair(sK77(sK5),sK77(sK5))) ),
inference(superposition,[status(thm)],[c_39759,c_20131]) ).
tcf(c_40046,plain,
( subset(set_difference(relation_field(sK5),set_difference(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_19566]) ).
tcf(c_40047,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ proper_subset(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5))) ),
inference(superposition,[status(thm)],[c_39759,c_19595]) ).
tcf(c_40048,plain,
( subset(set_difference(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_19485]) ).
tcf(c_40054,plain,
( subset(set_difference(set_difference(set_difference(set_difference(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5)),relation_field(sK5)),relation_field(sK5)),relation_field(sK5)),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_22118]) ).
tcf(c_40055,plain,
( subset(set_difference(set_difference(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5)),set_difference(relation_field(sK5),set_difference(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5)))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_20651]) ).
tcf(c_40056,plain,
( subset(set_difference(unordered_pair(sK77(sK5),sK77(sK5)),set_difference(set_difference(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5))),unordered_pair(sK77(sK5),sK77(sK5)))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_20485]) ).
tcf(c_40057,plain,
( subset(set_difference(set_difference(set_difference(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5)),relation_field(sK5)),relation_field(sK5)),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_20244]) ).
tcf(c_40058,plain,
( subset(set_difference(unordered_pair(sK77(sK5),sK77(sK5)),set_difference(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5)))),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_19744]) ).
tcf(c_40059,plain,
( subset(set_difference(set_difference(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5)),relation_field(sK5)),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_19715]) ).
tcf(c_40060,plain,
( subset(set_difference(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5)),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_19593]) ).
tcf(c_40061,plain,
( subset(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_19598]) ).
tcf(c_40064,plain,
! [X0: $i] :
( in(X0,relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(X0,unordered_pair(sK77(sK5),sK77(sK5))) ),
inference(superposition,[status(thm)],[c_39759,c_253]) ).
tcf(c_40067,plain,
( element(sK77(sK5),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_20190]) ).
tcf(c_40068,plain,
( in(sK77(sK5),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39759,c_19994]) ).
tcf(c_40187,plain,
! [X0: $i] :
( in(sK76(sK5),union(X0))
| ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_39987,c_295]) ).
tcf(c_40188,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( set_union2(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5)) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_39987,c_161]) ).
tcf(c_40189,plain,
! [X0: $i] :
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ disjoint(relation_field(sK5),X0)
| ~ in(sK76(sK5),X0) ),
inference(superposition,[status(thm)],[c_39987,c_151]) ).
tcf(c_40190,plain,
! [X0: $i] :
( in(sK76(sK5),X0)
| ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_39987,c_242]) ).
tcf(c_40192,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(relation_field(sK5),sK76(sK5)) ),
inference(superposition,[status(thm)],[c_39987,c_243]) ).
tcf(c_40195,plain,
( in(sK76(sK5),relation_rng(sK5))
| in(sK76(sK5),relation_dom(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_39987,c_27655]) ).
tcf(c_40231,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,X1)
| ~ subset(relation_inverse_image(relation_inverse(sK5),X0),X1) ),
inference(superposition,[status(thm)],[c_21834,c_22564]) ).
tcf(c_40232,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,X1)
| ~ subset(relation_image(relation_inverse(sK5),X0),X1) ),
inference(superposition,[status(thm)],[c_22079,c_22564]) ).
tcf(c_40233,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,X1)
| ~ subset(relation_rng(relation_rng_restriction(X0,relation_inverse(sK5))),X1) ),
inference(superposition,[status(thm)],[c_25056,c_22564]) ).
tcf(c_40235,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,X1)
| ~ subset(relation_dom(relation_dom_restriction(sK5,X0)),X1) ),
inference(superposition,[status(thm)],[c_29867,c_22564]) ).
tcf(c_40236,plain,
! [X0: $i,X1: $i] :
( subset(empty_set,X1)
| ~ subset(relation_rng(relation_dom_restriction(sK5,X0)),X1) ),
inference(superposition,[status(thm)],[c_29913,c_22564]) ).
tcf(c_40237,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X1,set_difference(X0,X2)) = subset_complement(X1,set_difference(X0,X2)) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_22564,c_6703]) ).
tcf(c_40238,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_complement(X1,subset_complement(X1,set_difference(X0,X2))) = set_difference(X0,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_22564,c_6699]) ).
tcf(c_40239,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X1,X2) = X0 )
| ~ subset(X1,X0)
| ~ subset(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_22564,c_260]) ).
tcf(c_40240,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X0,X2),set_difference(set_difference(X0,X2),X1)) = set_difference(X0,X2) )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_22564,c_123]) ).
tcf(c_40241,plain,
! [X0: $i,X1: $i,X2: $i] :
( proper_subset(set_difference(X0,X2),X1)
| ( set_difference(X0,X2) = X1 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_22564,c_468]) ).
tcf(c_40242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(set_difference(X0,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_22564,c_110]) ).
tcf(c_40243,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(set_difference(X0,X2),X1) = empty_set )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_22564,c_138]) ).
tcf(c_40244,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(set_difference(X0,X2),X1) = X1 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_22564,c_85]) ).
tcf(c_40245,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X1,X0)
| ~ proper_subset(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_22564,c_188]) ).
tcf(c_40246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(set_difference(X2,X3),X1)
| ~ subset(X2,X0)
| ~ disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_22564,c_190]) ).
tcf(c_40247,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = empty_set )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_22564,c_152]) ).
tcf(c_40248,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(X0,X2),relation_rng(sK5)),empty_set)
| ~ subset(X0,relation_inverse_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_22564,c_22779]) ).
tcf(c_40249,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(X0,X2),relation_dom(sK5)),empty_set)
| ~ subset(X0,relation_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_22564,c_22780]) ).
tcf(c_40250,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(set_difference(X0,X2),relation_dom(sK5)),empty_set)
| ~ subset(X0,relation_rng(relation_rng_restriction(X1,relation_inverse(sK5)))) ),
inference(superposition,[status(thm)],[c_22564,c_25182]) ).
tcf(c_40251,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom_restriction(sK5,set_difference(X0,X1))) = set_difference(X0,X1) )
| ~ subset(X0,relation_dom(relation_dom_restriction(sK5,set_difference(X0,X1)))) ),
inference(superposition,[status(thm)],[c_22564,c_29863]) ).
tcf(c_40349,plain,
! [X0: $i,X1: $i] :
( sP0(empty_set,X0,X1,empty_set)
| ~ one_to_one(empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_39725,c_769]) ).
tcf(c_40350,plain,
! [X0: $i,X1: $i] : sP0(empty_set,X0,X1,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_40349,c_19096,c_19076,c_231]) ).
tcf(c_40356,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( set_difference(identity_relation(X0),unordered_pair(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_195,c_6907]) ).
tcf(c_40358,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),identity_relation(X2)) ),
inference(superposition,[status(thm)],[c_351,c_6907]) ).
tcf(c_40362,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),identity_relation(X2)) ),
inference(superposition,[status(thm)],[c_351,c_6907]) ).
tcf(c_40363,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ~ in(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),identity_relation(X1)) ),
inference(superposition,[status(thm)],[c_111,c_6907]) ).
tcf(c_40364,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),empty_set) ),
inference(superposition,[status(thm)],[c_28218,c_6907]) ).
tcf(c_40396,plain,
! [X0: $i] : set_difference(relation_rng(sK5),set_difference(relation_rng(sK5),X0)) = relation_rng(relation_rng_restriction(X0,sK5)),
inference(superposition,[status(thm)],[c_96,c_83]) ).
tcf(c_40397,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(identity_relation(X0)),set_difference(relation_rng(identity_relation(X0)),X1)) = relation_rng(relation_rng_restriction(X1,identity_relation(X0))),
inference(superposition,[status(thm)],[c_422,c_83]) ).
tcf(c_40398,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(function_inverse(X0)),set_difference(relation_rng(function_inverse(X0)),X1)) = relation_rng(relation_rng_restriction(X1,function_inverse(X0))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_465,c_83]) ).
tcf(c_40399,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng(relation_dom_restriction(X0,X1)),set_difference(relation_rng(relation_dom_restriction(X0,X1)),X2)) = relation_rng(relation_rng_restriction(X2,relation_dom_restriction(X0,X1))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_334,c_83]) ).
tcf(c_40400,plain,
! [X0: $i] : set_difference(relation_rng(empty_set),set_difference(relation_rng(empty_set),X0)) = relation_rng(relation_rng_restriction(X0,empty_set)),
inference(superposition,[status(thm)],[c_231,c_83]) ).
tcf(c_40401,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng(set_union2(X0,X1)),set_difference(relation_rng(set_union2(X0,X1)),X2)) = relation_rng(relation_rng_restriction(X2,set_union2(X0,X1))) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_248,c_83]) ).
tcf(c_40402,plain,
! [X0: $i] : set_difference(relation_rng(sK47),set_difference(relation_rng(sK47),X0)) = relation_rng(relation_rng_restriction(X0,sK47)),
inference(superposition,[status(thm)],[c_329,c_83]) ).
tcf(c_40403,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_dom(X0)),set_difference(relation_rng(relation_dom(X0)),X1)) = relation_rng(relation_rng_restriction(X1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_342,c_83]) ).
tcf(c_40404,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,X0)),set_difference(relation_rng(relation_rng_restriction(X1,X0)),X2)) = relation_rng(relation_rng_restriction(X2,relation_rng_restriction(X1,X0))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_352,c_83]) ).
tcf(c_40405,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_rng(X0)),set_difference(relation_rng(relation_rng(X0)),X1)) = relation_rng(relation_rng_restriction(X1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_360,c_83]) ).
tcf(c_40406,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng(set_difference(X0,set_difference(X0,X1))),set_difference(relation_rng(set_difference(X0,set_difference(X0,X1))),X2)) = relation_rng(relation_rng_restriction(X2,set_difference(X0,set_difference(X0,X1)))) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_364,c_83]) ).
tcf(c_40407,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng(relation_composition(X0,X1)),set_difference(relation_rng(relation_composition(X0,X1)),X2)) = relation_rng(relation_rng_restriction(X2,relation_composition(X0,X1))) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_408,c_83]) ).
tcf(c_40408,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng(relation_composition(X0,X1)),set_difference(relation_rng(relation_composition(X0,X1)),X2)) = relation_rng(relation_rng_restriction(X2,relation_composition(X0,X1))) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_407,c_83]) ).
tcf(c_40409,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng(relation_composition(X1,X0)),set_difference(relation_rng(relation_composition(X1,X0)),X2)) = relation_rng(relation_rng_restriction(X2,relation_composition(X1,X0))) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_403,c_83]) ).
tcf(c_40410,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_inverse(X0)),set_difference(relation_rng(relation_inverse(X0)),X1)) = relation_rng(relation_rng_restriction(X1,relation_inverse(X0))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_434,c_83]) ).
tcf(c_40411,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_inverse(X0)),set_difference(relation_rng(relation_inverse(X0)),X1)) = relation_rng(relation_rng_restriction(X1,relation_inverse(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_433,c_83]) ).
tcf(c_40412,plain,
! [X0: $i] : set_difference(relation_rng(sK75),set_difference(relation_rng(sK75),X0)) = relation_rng(relation_rng_restriction(X0,sK75)),
inference(superposition,[status(thm)],[c_456,c_83]) ).
tcf(c_40413,plain,
! [X0: $i] : set_difference(relation_rng(sK79),set_difference(relation_rng(sK79),X0)) = relation_rng(relation_rng_restriction(X0,sK79)),
inference(superposition,[status(thm)],[c_474,c_83]) ).
tcf(c_40414,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(sK23(X0)),set_difference(relation_rng(sK23(X0)),X1)) = relation_rng(relation_rng_restriction(X1,sK23(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_20383,c_83]) ).
tcf(c_40415,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_dom_restriction(sK5,X0)),set_difference(relation_rng(relation_dom_restriction(sK5,X0)),X1)) = relation_rng(relation_rng_restriction(X1,relation_dom_restriction(sK5,X0))),
inference(superposition,[status(thm)],[c_25741,c_83]) ).
tcf(c_40416,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),set_difference(relation_rng(relation_dom_restriction(relation_dom_restriction(sK5,X0),X1)),X2)) = relation_rng(relation_rng_restriction(X2,relation_dom_restriction(relation_dom_restriction(sK5,X0),X1))),
inference(superposition,[status(thm)],[c_26788,c_83]) ).
tcf(c_40417,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),set_difference(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,sK5),X1)),X2)) = relation_rng(relation_rng_restriction(X2,relation_dom_restriction(relation_rng_restriction(X0,sK5),X1))),
inference(superposition,[status(thm)],[c_36216,c_83]) ).
tcf(c_40418,plain,
! [X0: $i] : set_difference(relation_rng(function_inverse(sK75)),set_difference(relation_rng(function_inverse(sK75)),X0)) = relation_rng(relation_rng_restriction(X0,function_inverse(sK75))),
inference(superposition,[status(thm)],[c_39827,c_83]) ).
tcf(c_40420,plain,
! [X0: $i] : set_difference(relation_dom(sK75),set_difference(relation_dom(sK75),X0)) = relation_rng(relation_rng_restriction(X0,function_inverse(sK75))),
inference(light_normalisation,[status(thm)],[c_40418,c_39776]) ).
tcf(c_40421,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,X1)) = relation_rng(relation_rng_restriction(X1,identity_relation(X0))),
inference(light_normalisation,[status(thm)],[c_40397,c_204]) ).
tcf(c_40454,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng_restriction(X1,identity_relation(relation_rng(X0)))) = relation_rng(relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_83,c_40421]) ).
tcf(c_40534,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,identity_relation(X1)),X1)
| ~ relation(identity_relation(X1))
| ~ in(X0,relation_image(identity_relation(X1),X2)) ),
inference(superposition,[status(thm)],[c_203,c_91]) ).
tcf(c_40535,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,empty_set),empty_set)
| ~ relation(empty_set)
| ~ in(X0,relation_image(empty_set,X1)) ),
inference(superposition,[status(thm)],[c_186,c_91]) ).
tcf(c_40536,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,relation_inverse(sK5)),relation_rng(sK5))
| ~ relation(relation_inverse(sK5))
| ~ in(X0,relation_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_20946,c_91]) ).
tcf(c_40537,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,relation_inverse(identity_relation(X1))),X1)
| ~ relation(relation_inverse(identity_relation(X1)))
| ~ in(X0,relation_image(relation_inverse(identity_relation(X1)),X2)) ),
inference(superposition,[status(thm)],[c_20961,c_91]) ).
tcf(c_40538,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,relation_inverse(sK47)),relation_rng(sK47))
| ~ relation(relation_inverse(sK47))
| ~ in(X0,relation_image(relation_inverse(sK47),X1)) ),
inference(superposition,[status(thm)],[c_20951,c_91]) ).
tcf(c_40539,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,relation_inverse(sK79)),relation_rng(sK79))
| ~ relation(relation_inverse(sK79))
| ~ in(X0,relation_image(relation_inverse(sK79),X1)) ),
inference(superposition,[status(thm)],[c_20958,c_91]) ).
tcf(c_40540,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,relation_inverse(relation_dom_restriction(sK5,X1))),relation_rng(relation_dom_restriction(sK5,X1)))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X1)))
| ~ in(X0,relation_image(relation_inverse(relation_dom_restriction(sK5,X1)),X2)) ),
inference(superposition,[status(thm)],[c_25748,c_91]) ).
tcf(c_40541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X2,X1),union(X3))
| ~ relation(X1)
| ~ in(relation_dom(X1),X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_91,c_295]) ).
tcf(c_40542,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(sK3(X0,X2,X1),sK3(X0,X2,X1)),relation_dom(X1)) = relation_dom(X1) )
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_91,c_161]) ).
tcf(c_40543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X2)
| ~ disjoint(relation_dom(X2),X3)
| ~ in(X0,relation_image(X2,X1))
| ~ in(sK3(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_91,c_151]) ).
tcf(c_40544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X2,X1),X3)
| ~ relation(X1)
| ~ subset(relation_dom(X1),X3)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_91,c_242]) ).
tcf(c_40545,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(relation_dom(X1)),sK3(X0,X2,X1)) = sK3(X0,X2,X1) )
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_91,c_134]) ).
tcf(c_40546,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X0)
| ~ in(X1,relation_image(X0,X2))
| ~ in(relation_dom(X0),sK3(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_91,c_243]) ).
tcf(c_40547,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_91,c_471]) ).
tcf(c_40548,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK3(X0,X2,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_91,c_276]) ).
tcf(c_40549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X3,relation_dom_restriction(X1,X2)),relation_dom(X1))
| ~ relation(X1)
| ~ relation(relation_dom_restriction(X1,X2))
| ~ in(X0,relation_image(relation_dom_restriction(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_91,c_214]) ).
tcf(c_40550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3(X0,X3,relation_dom_restriction(X1,X2)),X2)
| ~ relation(X1)
| ~ relation(relation_dom_restriction(X1,X2))
| ~ in(X0,relation_image(relation_dom_restriction(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_91,c_213]) ).
tcf(c_40551,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,sK5),relation_field(sK5))
| ~ relation(sK5)
| ~ in(X0,relation_image(sK5,X1)) ),
inference(superposition,[status(thm)],[c_91,c_27656]) ).
tcf(c_40555,plain,
! [X0: $i,X1: $i] : ~ in(X0,relation_image(empty_set,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_40535,c_234,c_231]) ).
tcf(c_40556,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,sK5),relation_field(sK5))
| ~ in(X0,relation_image(sK5,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40551,c_96]) ).
tcf(c_40565,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X2,identity_relation(X1)),X1)
| ~ in(X0,relation_image(identity_relation(X1),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40534,c_422]) ).
tcf(c_40660,plain,
! [X0: $i] : relation_rng(relation_rng_restriction(X0,identity_relation(relation_rng(sK5)))) = relation_rng(relation_rng_restriction(X0,sK5)),
inference(demodulation,[status(thm)],[c_40396,c_40421]) ).
tcf(c_40661,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(identity_relation(relation_rng(sK5))))
| ~ relation(identity_relation(relation_rng(sK5)))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,sK5))) ),
inference(superposition,[status(thm)],[c_40660,c_77]) ).
tcf(c_40662,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ relation(identity_relation(relation_rng(sK5)))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,sK5))) ),
inference(superposition,[status(thm)],[c_40660,c_76]) ).
tcf(c_40663,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(X0),relation_rng(relation_rng_restriction(X1,sK5)))
| ~ relation(X0)
| ~ relation(relation_rng_restriction(X1,identity_relation(relation_rng(sK5))))
| ~ subset(X0,relation_rng_restriction(X1,identity_relation(relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_40660,c_121]) ).
tcf(c_40664,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_composition(X1,relation_rng_restriction(X0,identity_relation(relation_rng(sK5))))),relation_rng(relation_rng_restriction(X0,sK5)))
| ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,identity_relation(relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_40660,c_157]) ).
tcf(c_40665,plain,
! [X0: $i] :
( subset(relation_rng(relation_rng_restriction(X0,sK5)),relation_rng(identity_relation(relation_rng(sK5))))
| ~ relation(identity_relation(relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_40660,c_80]) ).
tcf(c_40666,plain,
! [X0: $i] :
( subset(relation_rng(relation_rng_restriction(X0,sK5)),X0)
| ~ relation(identity_relation(relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_40660,c_78]) ).
tcf(c_40667,plain,
! [X0: $i] :
( subset(relation_field(sK5),relation_rng(relation_rng_restriction(X0,identity_relation(relation_rng(sK5)))))
| ~ relation(relation_rng_restriction(X0,identity_relation(relation_rng(sK5))))
| ~ subset(sK5,relation_rng_restriction(X0,identity_relation(relation_rng(sK5))))
| ~ subset(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,sK5))) ),
inference(superposition,[status(thm)],[c_40660,c_37250]) ).
tcf(c_40668,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X0,sK5)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,identity_relation(relation_rng(sK5))))
| ~ subset(relation_rng_restriction(X0,identity_relation(relation_rng(sK5))),X1) ),
inference(superposition,[status(thm)],[c_40660,c_121]) ).
tcf(c_40669,plain,
! [X0: $i] :
( ( relation_dom(relation_rng_restriction(X0,identity_relation(relation_rng(sK5)))) = empty_set )
| ~ relation(relation_rng_restriction(X0,identity_relation(relation_rng(sK5))))
| ( relation_rng(relation_rng_restriction(X0,sK5)) != empty_set ) ),
inference(superposition,[status(thm)],[c_40660,c_193]) ).
tcf(c_40670,plain,
! [X0: $i] :
( ( relation_rng_restriction(X0,identity_relation(relation_rng(sK5))) = empty_set )
| ~ relation(relation_rng_restriction(X0,identity_relation(relation_rng(sK5))))
| ( relation_rng(relation_rng_restriction(X0,sK5)) != empty_set ) ),
inference(superposition,[status(thm)],[c_40660,c_192]) ).
tcf(c_40671,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_dom_restriction(relation_rng_restriction(X0,identity_relation(relation_rng(sK5))),X1)),relation_rng(relation_rng_restriction(X0,sK5)))
| ~ relation(relation_rng_restriction(X0,identity_relation(relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_40660,c_224]) ).
tcf(c_40672,plain,
! [X0: $i] :
( subset(relation_rng_restriction(X0,identity_relation(relation_rng(sK5))),cartesian_product2(relation_dom(relation_rng_restriction(X0,identity_relation(relation_rng(sK5)))),relation_rng(relation_rng_restriction(X0,sK5))))
| ~ relation(relation_rng_restriction(X0,identity_relation(relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_40660,c_117]) ).
tcf(c_40673,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X1,relation_rng_restriction(X0,identity_relation(relation_rng(sK5))))),relation_rng(relation_rng_restriction(X0,sK5)))
| ~ relation(relation_rng_restriction(X0,identity_relation(relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_40660,c_80]) ).
tcf(c_40674,plain,
! [X0: $i] :
( empty(relation_rng_restriction(X0,identity_relation(relation_rng(sK5))))
| ~ empty(relation_rng(relation_rng_restriction(X0,sK5)))
| ~ relation(relation_rng_restriction(X0,identity_relation(relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_40660,c_361]) ).
tcf(c_40675,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(relation_rng_restriction(X0,identity_relation(relation_rng(sK5))),X1),relation_rng(relation_rng_restriction(X0,sK5)))
| ~ relation(relation_rng_restriction(X0,identity_relation(relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_40660,c_94]) ).
tcf(c_40676,plain,
! [X0: $i] :
( function(relation_rng(relation_rng_restriction(X0,sK5)))
| ~ empty(relation_rng_restriction(X0,identity_relation(relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_40660,c_19156]) ).
tcf(c_40677,plain,
! [X0: $i] :
( one_to_one(relation_rng(relation_rng_restriction(X0,sK5)))
| ~ empty(relation_rng_restriction(X0,identity_relation(relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_40660,c_19154]) ).
tcf(c_40678,plain,
! [X0: $i] :
( relation(relation_rng(relation_rng_restriction(X0,sK5)))
| ~ empty(relation_rng_restriction(X0,identity_relation(relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_40660,c_360]) ).
tcf(c_40679,plain,
! [X0: $i] :
( empty(relation_rng(relation_rng_restriction(X0,sK5)))
| ~ empty(relation_rng_restriction(X0,identity_relation(relation_rng(sK5)))) ),
inference(superposition,[status(thm)],[c_40660,c_359]) ).
tcf(c_40680,plain,
! [X0: $i] : subset(relation_rng(relation_rng_restriction(X0,sK5)),relation_rng(sK5)),
inference(superposition,[status(thm)],[c_40660,c_20703]) ).
tcf(c_40681,plain,
! [X0: $i] : subset(relation_rng(relation_rng_restriction(X0,sK5)),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_40666,c_422]) ).
tcf(c_40690,plain,
! [X0: $i] : subset(relation_rng(relation_rng_restriction(X0,sK5)),relation_rng(identity_relation(relation_rng(sK5)))),
inference(forward_subsumption_resolution,[status(thm)],[c_40665,c_422]) ).
tcf(c_40691,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,sK5))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40662,c_422]) ).
tcf(c_40694,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(identity_relation(relation_rng(sK5))))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,sK5))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40661,c_422]) ).
tcf(c_40725,plain,
! [X0: $i] :
( subset(relation_field(sK5),relation_rng(relation_rng_restriction(X0,sK5)))
| ~ relation(relation_rng_restriction(X0,identity_relation(relation_rng(sK5))))
| ~ subset(sK5,relation_rng_restriction(X0,identity_relation(relation_rng(sK5))))
| ~ subset(relation_dom(sK5),relation_rng(relation_rng_restriction(X0,sK5))) ),
inference(light_normalisation,[status(thm)],[c_40667,c_40660]) ).
tcf(c_40872,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,sK5),union(X2))
| ~ in(relation_field(sK5),X2)
| ~ in(X0,relation_image(sK5,X1)) ),
inference(superposition,[status(thm)],[c_40556,c_295]) ).
tcf(c_40873,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(sK3(X0,X1,sK5),sK3(X0,X1,sK5)),relation_field(sK5)) = relation_field(sK5) )
| ~ in(X0,relation_image(sK5,X1)) ),
inference(superposition,[status(thm)],[c_40556,c_161]) ).
tcf(c_40874,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(relation_field(sK5),X2)
| ~ in(X0,relation_image(sK5,X1))
| ~ in(sK3(X0,X1,sK5),X2) ),
inference(superposition,[status(thm)],[c_40556,c_151]) ).
tcf(c_40875,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,sK5),X2)
| ~ subset(relation_field(sK5),X2)
| ~ in(X0,relation_image(sK5,X1)) ),
inference(superposition,[status(thm)],[c_40556,c_242]) ).
tcf(c_40876,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(relation_field(sK5)),sK3(X0,X1,sK5)) = sK3(X0,X1,sK5) )
| ~ in(X0,relation_image(sK5,X1)) ),
inference(superposition,[status(thm)],[c_40556,c_134]) ).
tcf(c_40877,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,relation_image(sK5,X1))
| ~ in(relation_field(sK5),sK3(X0,X1,sK5)) ),
inference(superposition,[status(thm)],[c_40556,c_243]) ).
tcf(c_40878,plain,
! [X0: $i,X1: $i] :
( ~ empty(relation_field(sK5))
| ~ in(X0,relation_image(sK5,X1)) ),
inference(superposition,[status(thm)],[c_40556,c_471]) ).
tcf(c_40879,plain,
! [X0: $i,X1: $i] :
( element(sK3(X0,X1,sK5),relation_field(sK5))
| ~ in(X0,relation_image(sK5,X1)) ),
inference(superposition,[status(thm)],[c_40556,c_276]) ).
tcf(c_40880,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,sK5),relation_rng(sK5))
| in(sK3(X0,X1,sK5),relation_dom(sK5))
| ~ in(X0,relation_image(sK5,X1)) ),
inference(superposition,[status(thm)],[c_40556,c_27655]) ).
tcf(c_40930,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_image(sK5,X0),unordered_pair(X1,X1)) = relation_image(sK5,X0) )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_195,c_40878]) ).
tcf(c_40933,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_image(sK5,X0),X1)
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_149,c_40878]) ).
tcf(c_40934,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,relation_image(sK5,X1))
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_150,c_40878]) ).
tcf(c_40935,plain,
! [X0: $i,X1: $i] :
( in(sK15(X1,relation_image(sK5,X0)),X1)
| ( relation_image(sK5,X0) = X1 )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_228,c_40878]) ).
tcf(c_40936,plain,
! [X0: $i,X1: $i] :
( in(sK15(relation_image(sK5,X0),X1),X1)
| ( relation_image(sK5,X0) = X1 )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_228,c_40878]) ).
tcf(c_40937,plain,
! [X0: $i] :
( ( relation_image(sK5,X0) = empty_set )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_233,c_40878]) ).
tcf(c_40938,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(sK5,X0),X1)
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_241,c_40878]) ).
tcf(c_40939,plain,
! [X0: $i,X1: $i] :
( subset(sK24(X1,relation_image(sK5,X0)),X1)
| ( relation_image(sK5,X0) = powerset(X1) )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_288,c_40878]) ).
tcf(c_40940,plain,
! [X0: $i,X1: $i] :
( in(sK26(X1,relation_image(sK5,X0)),X1)
| ( relation_image(sK5,X0) = union(X1) )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_294,c_40878]) ).
tcf(c_40941,plain,
! [X0: $i,X1: $i] :
( in(sK25(relation_image(sK5,X0),X1),X1)
| ( union(relation_image(sK5,X0)) = X1 )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_294,c_40878]) ).
tcf(c_40942,plain,
! [X0: $i,X1: $i] :
( ~ empty(relation_field(sK5))
| ~ in(X0,union(relation_image(sK5,X1))) ),
inference(superposition,[status(thm)],[c_297,c_40878]) ).
tcf(c_40943,plain,
! [X0: $i] :
( relation(relation_image(sK5,X0))
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_314,c_40878]) ).
tcf(c_40944,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(relation_field(sK5))
| ~ in(X0,cartesian_product2(relation_image(sK5,X1),X2)) ),
inference(superposition,[status(thm)],[c_323,c_40878]) ).
tcf(c_40945,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(relation_field(sK5))
| ~ in(X0,cartesian_product2(X1,relation_image(sK5,X2))) ),
inference(superposition,[status(thm)],[c_324,c_40878]) ).
tcf(c_40946,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X1)
| ~ empty(relation_field(sK5))
| ~ in(X0,relation_image(X1,relation_image(sK5,X2))) ),
inference(superposition,[status(thm)],[c_381,c_40878]) ).
tcf(c_40947,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X1)
| ~ empty(relation_field(sK5))
| ~ in(X0,relation_inverse_image(X1,relation_image(sK5,X2))) ),
inference(superposition,[status(thm)],[c_395,c_40878]) ).
tcf(c_40948,plain,
! [X0: $i] :
( empty(relation_image(sK5,X0))
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_20297,c_40878]) ).
tcf(c_40949,plain,
! [X0: $i] :
( ~ empty(relation_field(sK5))
| ~ in(X0,relation_rng(sK5)) ),
inference(superposition,[status(thm)],[c_22463,c_40878]) ).
tcf(c_41046,plain,
! [X0: $i] :
( ( set_difference(relation_rng(sK5),unordered_pair(X0,X0)) = relation_rng(sK5) )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_195,c_40949]) ).
tcf(c_41049,plain,
! [X0: $i] :
( disjoint(relation_rng(sK5),X0)
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_149,c_40949]) ).
tcf(c_41050,plain,
! [X0: $i] :
( disjoint(X0,relation_rng(sK5))
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_150,c_40949]) ).
tcf(c_41051,plain,
! [X0: $i] :
( in(sK15(X0,relation_rng(sK5)),X0)
| ( relation_rng(sK5) = X0 )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_228,c_40949]) ).
tcf(c_41052,plain,
! [X0: $i] :
( in(sK15(relation_rng(sK5),X0),X0)
| ( relation_rng(sK5) = X0 )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_228,c_40949]) ).
tcf(c_41053,plain,
( ( relation_rng(sK5) = empty_set )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_233,c_40949]) ).
tcf(c_41054,plain,
! [X0: $i] :
( subset(relation_rng(sK5),X0)
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_241,c_40949]) ).
tcf(c_41055,plain,
! [X0: $i] :
( subset(sK24(X0,relation_rng(sK5)),X0)
| ( powerset(X0) = relation_rng(sK5) )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_288,c_40949]) ).
tcf(c_41056,plain,
! [X0: $i] :
( in(sK26(X0,relation_rng(sK5)),X0)
| ( union(X0) = relation_rng(sK5) )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_294,c_40949]) ).
tcf(c_41057,plain,
! [X0: $i] :
( in(sK25(relation_rng(sK5),X0),X0)
| ( union(relation_rng(sK5)) = X0 )
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_294,c_40949]) ).
tcf(c_41058,plain,
! [X0: $i] :
( ~ empty(relation_field(sK5))
| ~ in(X0,union(relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_297,c_40949]) ).
tcf(c_41059,plain,
( relation(relation_rng(sK5))
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_314,c_40949]) ).
tcf(c_41060,plain,
! [X0: $i,X1: $i] :
( ~ empty(relation_field(sK5))
| ~ in(X0,cartesian_product2(relation_rng(sK5),X1)) ),
inference(superposition,[status(thm)],[c_323,c_40949]) ).
tcf(c_41061,plain,
! [X0: $i,X1: $i] :
( ~ empty(relation_field(sK5))
| ~ in(X0,cartesian_product2(X1,relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_324,c_40949]) ).
tcf(c_41062,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ empty(relation_field(sK5))
| ~ in(X0,relation_image(X1,relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_381,c_40949]) ).
tcf(c_41063,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ empty(relation_field(sK5))
| ~ in(X0,relation_inverse_image(X1,relation_rng(sK5))) ),
inference(superposition,[status(thm)],[c_395,c_40949]) ).
tcf(c_41065,plain,
( one_to_one(sK5)
| in(sK76(sK5),relation_dom(sK5))
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_32702,c_40949]) ).
tcf(c_41066,plain,
( one_to_one(sK5)
| in(sK77(sK5),relation_dom(sK5))
| ~ empty(relation_field(sK5)) ),
inference(superposition,[status(thm)],[c_32810,c_40949]) ).
tcf(c_41176,plain,
! [X0: $i] :
( in(sK77(sK5),union(X0))
| ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_40068,c_295]) ).
tcf(c_41177,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( set_union2(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5)) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_40068,c_161]) ).
tcf(c_41178,plain,
! [X0: $i] :
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ disjoint(relation_field(sK5),X0)
| ~ in(sK77(sK5),X0) ),
inference(superposition,[status(thm)],[c_40068,c_151]) ).
tcf(c_41179,plain,
! [X0: $i] :
( in(sK77(sK5),X0)
| ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_40068,c_242]) ).
tcf(c_41181,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(relation_field(sK5),sK77(sK5)) ),
inference(superposition,[status(thm)],[c_40068,c_243]) ).
tcf(c_41184,plain,
( in(sK77(sK5),relation_rng(sK5))
| in(sK77(sK5),relation_dom(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) ) ),
inference(superposition,[status(thm)],[c_40068,c_27655]) ).
tcf(c_41271,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( set_difference(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5))) = subset_complement(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5))) ) ),
inference(superposition,[status(thm)],[c_39980,c_6703]) ).
tcf(c_41272,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( subset_complement(relation_field(sK5),subset_complement(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5)))) = unordered_pair(sK76(sK5),sK76(sK5)) ) ),
inference(superposition,[status(thm)],[c_39980,c_6699]) ).
tcf(c_41273,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( unordered_pair(sK76(sK5),sK76(sK5)) = relation_field(sK5) )
| ~ subset(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5))) ),
inference(superposition,[status(thm)],[c_39980,c_260]) ).
tcf(c_41274,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( set_difference(unordered_pair(sK76(sK5),sK76(sK5)),set_difference(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5))) = unordered_pair(sK76(sK5),sK76(sK5)) ) ),
inference(superposition,[status(thm)],[c_39980,c_123]) ).
tcf(c_41275,plain,
( proper_subset(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) )
| ( unordered_pair(sK76(sK5),sK76(sK5)) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_39980,c_468]) ).
tcf(c_41276,plain,
! [X0: $i] :
( subset(unordered_pair(sK76(sK5),sK76(sK5)),X0)
| ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_39980,c_110]) ).
tcf(c_41277,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( set_difference(unordered_pair(sK76(sK5),sK76(sK5)),relation_field(sK5)) = empty_set ) ),
inference(superposition,[status(thm)],[c_39980,c_138]) ).
tcf(c_41280,plain,
! [X0: $i] :
( disjoint(unordered_pair(sK76(sK5),sK76(sK5)),X0)
| ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ disjoint(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_39980,c_190]) ).
tcf(c_41309,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( set_difference(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5))) = subset_complement(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5))) ) ),
inference(superposition,[status(thm)],[c_40061,c_6703]) ).
tcf(c_41310,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( subset_complement(relation_field(sK5),subset_complement(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5)))) = unordered_pair(sK77(sK5),sK77(sK5)) ) ),
inference(superposition,[status(thm)],[c_40061,c_6699]) ).
tcf(c_41311,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( unordered_pair(sK77(sK5),sK77(sK5)) = relation_field(sK5) )
| ~ subset(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5))) ),
inference(superposition,[status(thm)],[c_40061,c_260]) ).
tcf(c_41312,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( set_difference(unordered_pair(sK77(sK5),sK77(sK5)),set_difference(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5))) = unordered_pair(sK77(sK5),sK77(sK5)) ) ),
inference(superposition,[status(thm)],[c_40061,c_123]) ).
tcf(c_41313,plain,
( proper_subset(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5))
| ( relation_inverse(sK5) = function_inverse(sK5) )
| ( unordered_pair(sK77(sK5),sK77(sK5)) = relation_field(sK5) ) ),
inference(superposition,[status(thm)],[c_40061,c_468]) ).
tcf(c_41314,plain,
! [X0: $i] :
( subset(unordered_pair(sK77(sK5),sK77(sK5)),X0)
| ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ subset(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_40061,c_110]) ).
tcf(c_41315,plain,
( ( relation_inverse(sK5) = function_inverse(sK5) )
| ( set_difference(unordered_pair(sK77(sK5),sK77(sK5)),relation_field(sK5)) = empty_set ) ),
inference(superposition,[status(thm)],[c_40061,c_138]) ).
tcf(c_41318,plain,
! [X0: $i] :
( disjoint(unordered_pair(sK77(sK5),sK77(sK5)),X0)
| ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ disjoint(relation_field(sK5),X0) ),
inference(superposition,[status(thm)],[c_40061,c_190]) ).
tcf(c_41347,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_19515,c_22565]) ).
tcf(c_41348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,set_union2(X0,X1))
| subset(X0,set_difference(X2,unordered_pair(X3,X3)))
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_58,c_22565]) ).
tcf(c_41349,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,union(X2))
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_222,c_22565]) ).
tcf(c_41350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,set_difference(X2,set_difference(X2,X3)))
| ~ subset(set_union2(X0,X1),X3)
| ~ subset(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_109,c_22565]) ).
tcf(c_41351,plain,
! [X0: $i,X1: $i] :
( subset(X0,cartesian_product2(relation_dom(set_union2(X0,X1)),relation_rng(set_union2(X0,X1))))
| ~ relation(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_117,c_22565]) ).
tcf(c_41352,plain,
! [X0: $i,X1: $i,X2: $i] : subset(X0,set_union2(set_union2(X0,X1),X2)),
inference(superposition,[status(thm)],[c_209,c_22565]) ).
tcf(c_41355,plain,
! [X0: $i,X1: $i,X2: $i] : subset(X0,set_union2(X1,set_union2(X0,X2))),
inference(superposition,[status(thm)],[c_19598,c_22565]) ).
tcf(c_41366,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_dom_restriction(sK5,X0)),X1)
| ~ subset(relation_field(relation_dom_restriction(sK5,X0)),X1) ),
inference(superposition,[status(thm)],[c_27483,c_22565]) ).
tcf(c_41395,plain,
! [X0: $i] :
( ( relation_rng(relation_composition(X0,sK5)) = relation_image(sK5,relation_rng(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_96,c_100]) ).
tcf(c_41396,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X0,identity_relation(X1))) = relation_image(identity_relation(X1),relation_rng(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_422,c_100]) ).
tcf(c_41397,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X1,function_inverse(X0))) = relation_image(function_inverse(X0),relation_rng(X1)) )
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_465,c_100]) ).
tcf(c_41398,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(relation_composition(X1,relation_dom_restriction(X0,X2))) = relation_image(relation_dom_restriction(X0,X2),relation_rng(X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_334,c_100]) ).
tcf(c_41399,plain,
! [X0: $i] :
( ( relation_rng(relation_composition(X0,empty_set)) = relation_image(empty_set,relation_rng(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_231,c_100]) ).
tcf(c_41400,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(relation_composition(X2,set_union2(X0,X1))) = relation_image(set_union2(X0,X1),relation_rng(X2)) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_248,c_100]) ).
tcf(c_41401,plain,
! [X0: $i] :
( ( relation_rng(relation_composition(X0,sK47)) = relation_image(sK47,relation_rng(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_329,c_100]) ).
tcf(c_41402,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X0,relation_dom(X1))) = relation_image(relation_dom(X1),relation_rng(X0)) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_342,c_100]) ).
tcf(c_41403,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(relation_composition(X1,relation_rng_restriction(X2,X0))) = relation_image(relation_rng_restriction(X2,X0),relation_rng(X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_352,c_100]) ).
tcf(c_41404,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X0,relation_rng(X1))) = relation_image(relation_rng(X1),relation_rng(X0)) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_360,c_100]) ).
tcf(c_41405,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(relation_composition(X2,set_difference(X0,set_difference(X0,X1)))) = relation_image(set_difference(X0,set_difference(X0,X1)),relation_rng(X2)) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_364,c_100]) ).
tcf(c_41406,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(relation_composition(X2,relation_composition(X0,X1))) = relation_image(relation_composition(X0,X1),relation_rng(X2)) )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_408,c_100]) ).
tcf(c_41407,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(relation_composition(X1,relation_composition(X0,X2))) = relation_image(relation_composition(X0,X2),relation_rng(X1)) )
| ~ empty(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_407,c_100]) ).
tcf(c_41408,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(relation_composition(X1,relation_composition(X2,X0))) = relation_image(relation_composition(X2,X0),relation_rng(X1)) )
| ~ empty(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_403,c_100]) ).
tcf(c_41409,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X1,relation_inverse(X0))) = relation_image(relation_inverse(X0),relation_rng(X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_434,c_100]) ).
tcf(c_41410,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X0,relation_inverse(X1))) = relation_image(relation_inverse(X1),relation_rng(X0)) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_433,c_100]) ).
tcf(c_41411,plain,
! [X0: $i] :
( ( relation_rng(relation_composition(X0,sK75)) = relation_image(sK75,relation_rng(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_456,c_100]) ).
tcf(c_41412,plain,
! [X0: $i] :
( ( relation_rng(relation_composition(X0,sK79)) = relation_image(sK79,relation_rng(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_474,c_100]) ).
tcf(c_41413,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X0,sK23(X1))) = relation_image(sK23(X1),relation_rng(X0)) )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_20383,c_100]) ).
tcf(c_41414,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X0,relation_dom_restriction(sK5,X1))) = relation_image(relation_dom_restriction(sK5,X1),relation_rng(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_25741,c_100]) ).
tcf(c_41415,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(relation_composition(X0,relation_dom_restriction(relation_dom_restriction(sK5,X1),X2))) = relation_image(relation_dom_restriction(relation_dom_restriction(sK5,X1),X2),relation_rng(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_26788,c_100]) ).
tcf(c_41416,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(relation_composition(X0,relation_dom_restriction(relation_rng_restriction(X1,sK5),X2))) = relation_image(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2),relation_rng(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_36216,c_100]) ).
tcf(c_41417,plain,
! [X0: $i] :
( ( relation_rng(relation_composition(X0,function_inverse(sK75))) = relation_image(function_inverse(sK75),relation_rng(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_39827,c_100]) ).
tcf(c_41548,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1,empty_set),empty_set)
| ~ relation(empty_set)
| ~ in(X0,relation_inverse_image(empty_set,X1)) ),
inference(superposition,[status(thm)],[c_187,c_102]) ).
tcf(c_41549,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,X2,identity_relation(X1)),X1)
| ~ relation(identity_relation(X1))
| ~ in(X0,relation_inverse_image(identity_relation(X1),X2)) ),
inference(superposition,[status(thm)],[c_204,c_102]) ).
tcf(c_41550,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1,relation_inverse(sK5)),relation_dom(sK5))
| ~ relation(relation_inverse(sK5))
| ~ in(X0,relation_inverse_image(relation_inverse(sK5),X1)) ),
inference(superposition,[status(thm)],[c_21123,c_102]) ).
tcf(c_41551,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1,relation_inverse(sK47)),relation_dom(sK47))
| ~ relation(relation_inverse(sK47))
| ~ in(X0,relation_inverse_image(relation_inverse(sK47),X1)) ),
inference(superposition,[status(thm)],[c_21128,c_102]) ).
tcf(c_41552,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,X2,relation_inverse(identity_relation(X1))),X1)
| ~ relation(relation_inverse(identity_relation(X1)))
| ~ in(X0,relation_inverse_image(relation_inverse(identity_relation(X1)),X2)) ),
inference(superposition,[status(thm)],[c_21138,c_102]) ).
tcf(c_41553,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1,relation_inverse(sK79)),relation_dom(sK79))
| ~ relation(relation_inverse(sK79))
| ~ in(X0,relation_inverse_image(relation_inverse(sK79),X1)) ),
inference(superposition,[status(thm)],[c_21135,c_102]) ).
tcf(c_41554,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,X2,relation_inverse(relation_dom_restriction(sK5,X1))),relation_dom(relation_dom_restriction(sK5,X1)))
| ~ relation(relation_inverse(relation_dom_restriction(sK5,X1)))
| ~ in(X0,relation_inverse_image(relation_inverse(relation_dom_restriction(sK5,X1)),X2)) ),
inference(superposition,[status(thm)],[c_25747,c_102]) ).
tcf(c_41555,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,X2,relation_rng_restriction(X1,identity_relation(relation_rng(sK5)))),relation_rng(relation_rng_restriction(X1,sK5)))
| ~ relation(relation_rng_restriction(X1,identity_relation(relation_rng(sK5))))
| ~ in(X0,relation_inverse_image(relation_rng_restriction(X1,identity_relation(relation_rng(sK5))),X2)) ),
inference(superposition,[status(thm)],[c_40660,c_102]) ).
tcf(c_41556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,X2,X1),union(X3))
| ~ relation(X1)
| ~ in(relation_rng(X1),X3)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_102,c_295]) ).
tcf(c_41557,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(unordered_pair(sK6(X0,X2,X1),sK6(X0,X2,X1)),relation_rng(X1)) = relation_rng(X1) )
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_102,c_161]) ).
tcf(c_41558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ relation(X2)
| ~ disjoint(relation_rng(X2),X3)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ in(sK6(X0,X1,X2),X3) ),
inference(superposition,[status(thm)],[c_102,c_151]) ).
tcf(c_41559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,X2,X1),X3)
| ~ relation(X1)
| ~ subset(relation_rng(X1),X3)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_102,c_242]) ).
tcf(c_41560,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(identity_relation(relation_rng(X1)),sK6(X0,X2,X1)) = sK6(X0,X2,X1) )
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_102,c_134]) ).
tcf(c_41561,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X0)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ in(relation_rng(X0),sK6(X1,X2,X0)) ),
inference(superposition,[status(thm)],[c_102,c_243]) ).
tcf(c_41562,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X1)
| ~ empty(relation_rng(X1))
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_102,c_471]) ).
tcf(c_41563,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK6(X0,X2,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_102,c_276]) ).
tcf(c_41564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,X3,relation_rng_restriction(X1,X2)),relation_rng(X2))
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ in(X0,relation_inverse_image(relation_rng_restriction(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_102,c_77]) ).
tcf(c_41565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,X3,relation_rng_restriction(X1,X2)),X1)
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ in(X0,relation_inverse_image(relation_rng_restriction(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_102,c_76]) ).
tcf(c_41566,plain,
! [X0: $i,X1: $i] :
( ~ relation(sK5)
| ~ empty(relation_field(sK5))
| ~ in(X0,relation_inverse_image(sK5,X1)) ),
inference(superposition,[status(thm)],[c_102,c_40949]) ).
tcf(c_41567,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1,sK5),relation_field(sK5))
| ~ relation(sK5)
| ~ in(X0,relation_inverse_image(sK5,X1)) ),
inference(superposition,[status(thm)],[c_102,c_27657]) ).
tcf(c_41568,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,X2,relation_rng_restriction(X1,relation_inverse(sK5))),relation_dom(sK5))
| ~ relation(relation_rng_restriction(X1,relation_inverse(sK5)))
| ~ in(X0,relation_inverse_image(relation_rng_restriction(X1,relation_inverse(sK5)),X2)) ),
inference(superposition,[status(thm)],[c_102,c_25255]) ).
tcf(c_41569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,X3,relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)),relation_rng(relation_dom_restriction(sK5,X2)))
| ~ relation(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2))
| ~ in(X0,relation_inverse_image(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2),X3)) ),
inference(superposition,[status(thm)],[c_102,c_36223]) ).
tcf(c_41570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,X3,relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)),X1)
| ~ relation(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2))
| ~ in(X0,relation_inverse_image(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2),X3)) ),
inference(superposition,[status(thm)],[c_102,c_36220]) ).
tcf(c_41571,plain,
! [X0: $i,X1: $i] :
( ~ empty(relation_field(sK5))
| ~ in(X0,relation_inverse_image(sK5,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41566,c_96]) ).
tcf(c_41577,plain,
! [X0: $i,X1: $i] : ~ in(X0,relation_inverse_image(empty_set,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_41548,c_234,c_231]) ).
tcf(c_41578,plain,
! [X0: $i,X1: $i] :
( in(sK6(X0,X1,sK5),relation_field(sK5))
| ~ in(X0,relation_inverse_image(sK5,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41567,c_96]) ).
tcf(c_41587,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK6(X0,X2,identity_relation(X1)),X1)
| ~ in(X0,relation_inverse_image(identity_relation(X1),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41549,c_422]) ).
tcf(c_41631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,X3,relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)),X1)
| ~ in(X0,relation_inverse_image(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2),X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41570,c_36216]) ).
tcf(c_41637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK6(X0,X3,relation_dom_restriction(relation_rng_restriction(X1,sK5),X2)),relation_rng(relation_dom_restriction(sK5,X2)))
| ~ in(X0,relation_inverse_image(relation_dom_restriction(relation_rng_restriction(X1,sK5),X2),X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41569,c_36216]) ).
tcf(c_41721,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X0) = empty_set )
| ( unordered_pair(X0,X0) = unordered_pair(X1,X1) )
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_140,c_148]) ).
tcf(c_41722,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( unordered_pair(X1,X1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_19515,c_148]) ).
tcf(c_41723,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng_restriction(unordered_pair(X1,X1),X0)) = empty_set )
| ( relation_rng(relation_rng_restriction(unordered_pair(X1,X1),X0)) = unordered_pair(X1,X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_78,c_148]) ).
tcf(c_41724,plain,
! [X0: $i,X1: $i] :
( ( relation_rng_restriction(X1,unordered_pair(X0,X0)) = empty_set )
| ( relation_rng_restriction(X1,unordered_pair(X0,X0)) = unordered_pair(X0,X0) )
| ~ relation(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_79,c_148]) ).
tcf(c_41726,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X0,X0),X1) = empty_set )
| ( set_difference(unordered_pair(X0,X0),X1) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_135,c_148]) ).
tcf(c_41727,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X0,X2) = empty_set )
| ( unordered_pair(X0,X2) = unordered_pair(X1,X1) )
| ~ in(X2,unordered_pair(X1,X1))
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_142,c_148]) ).
tcf(c_41728,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(unordered_pair(X0,X0),X1) = empty_set )
| ( relation_dom_restriction(unordered_pair(X0,X0),X1) = unordered_pair(X0,X0) )
| ~ relation(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_215,c_148]) ).
tcf(c_41729,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X2) = empty_set )
| ( unordered_pair(X1,X1) = set_union2(X0,X2) )
| ~ subset(X2,unordered_pair(X1,X1))
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_219,c_148]) ).
tcf(c_41731,plain,
! [X0: $i,X1: $i] :
( in(sK24(unordered_pair(X0,X0),X1),X1)
| ( powerset(unordered_pair(X0,X0)) = X1 )
| ( sK24(unordered_pair(X0,X0),X1) = empty_set )
| ( sK24(unordered_pair(X0,X0),X1) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_288,c_148]) ).
tcf(c_41732,plain,
! [X0: $i] :
( empty(unordered_pair(X0,X0))
| ( sK22(unordered_pair(X0,X0)) = empty_set )
| ( sK22(unordered_pair(X0,X0)) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_19616,c_148]) ).
tcf(c_41733,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(unordered_pair(X1,X1),X0) = empty_set )
| ( subset_complement(unordered_pair(X1,X1),X0) = unordered_pair(X1,X1) )
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_22243,c_148]) ).
tcf(c_41734,plain,
! [X0: $i] :
( ( sK23(powerset(unordered_pair(X0,X0))) = empty_set )
| ( sK23(powerset(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_19617,c_148]) ).
tcf(c_41735,plain,
! [X0: $i,X1: $i] :
( subset(powerset(unordered_pair(X0,X0)),X1)
| ( sK18(powerset(unordered_pair(X0,X0)),X1) = empty_set )
| ( sK18(powerset(unordered_pair(X0,X0)),X1) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_19652,c_148]) ).
tcf(c_41736,plain,
! [X0: $i,X1: $i] :
( ( relation_image(identity_relation(unordered_pair(X0,X0)),X1) = empty_set )
| ( relation_image(identity_relation(unordered_pair(X0,X0)),X1) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_19833,c_148]) ).
tcf(c_41737,plain,
! [X0: $i,X1: $i] :
( subset(powerset(unordered_pair(X0,X0)),X1)
| ( sK1(powerset(unordered_pair(X0,X0)),X1) = empty_set )
| ( sK1(powerset(unordered_pair(X0,X0)),X1) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_19866,c_148]) ).
tcf(c_41738,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(identity_relation(unordered_pair(X0,X0)),X1) = empty_set )
| ( relation_inverse_image(identity_relation(unordered_pair(X0,X0)),X1) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_19947,c_148]) ).
tcf(c_41739,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng_restriction(X0,identity_relation(unordered_pair(X1,X1)))) = empty_set )
| ( relation_rng(relation_rng_restriction(X0,identity_relation(unordered_pair(X1,X1)))) = unordered_pair(X1,X1) ) ),
inference(superposition,[status(thm)],[c_20703,c_148]) ).
tcf(c_41740,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom_restriction(identity_relation(unordered_pair(X0,X0)),X1)) = empty_set )
| ( relation_rng(relation_dom_restriction(identity_relation(unordered_pair(X0,X0)),X1)) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_21501,c_148]) ).
tcf(c_41741,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,X2) = empty_set )
| ( unordered_pair(X1,X1) = set_difference(X0,X2) )
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_22564,c_148]) ).
tcf(c_41742,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(relation_inverse(sK5),X1) = empty_set )
| ( relation_inverse_image(relation_inverse(sK5),X1) = unordered_pair(X0,X0) )
| ~ subset(relation_rng(sK5),unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_22586,c_148]) ).
tcf(c_41743,plain,
! [X0: $i,X1: $i] :
( ( relation_image(relation_inverse(sK5),X1) = empty_set )
| ( relation_image(relation_inverse(sK5),X1) = unordered_pair(X0,X0) )
| ~ subset(relation_dom(sK5),unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_22588,c_148]) ).
tcf(c_41744,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,unordered_pair(X1,X1))) = empty_set )
| ( set_difference(X0,set_difference(X0,unordered_pair(X1,X1))) = unordered_pair(X1,X1) ) ),
inference(superposition,[status(thm)],[c_27286,c_148]) ).
tcf(c_41745,plain,
! [X0: $i] :
( ( relation_dom(relation_dom_restriction(sK5,unordered_pair(X0,X0))) = empty_set )
| ( relation_dom(relation_dom_restriction(sK5,unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_29463,c_148]) ).
tcf(c_41746,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom_restriction(sK5,X0)) = empty_set )
| ( relation_dom(relation_dom_restriction(sK5,X0)) = unordered_pair(X1,X1) )
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_29866,c_148]) ).
tcf(c_41747,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom_restriction(sK5,X1)) = empty_set )
| ( relation_rng(relation_dom_restriction(sK5,X1)) = unordered_pair(X0,X0) )
| ~ subset(relation_rng(sK5),unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_29912,c_148]) ).
tcf(c_41748,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),unordered_pair(X1,X1))) = empty_set )
| ( relation_dom(relation_dom_restriction(relation_dom_restriction(sK5,X0),unordered_pair(X1,X1))) = unordered_pair(X1,X1) ) ),
inference(superposition,[status(thm)],[c_30033,c_148]) ).
tcf(c_41749,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom_restriction(relation_rng_restriction(unordered_pair(X0,X0),sK5),X1)) = empty_set )
| ( relation_rng(relation_dom_restriction(relation_rng_restriction(unordered_pair(X0,X0),sK5),X1)) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_36217,c_148]) ).
tcf(c_41750,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( unordered_pair(empty_set,empty_set) = X0 )
| ~ subset(X0,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_111,c_148]) ).
tcf(c_41754,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( powerset(empty_set) = X0 )
| ~ subset(X0,powerset(empty_set)) ),
inference(light_normalisation,[status(thm)],[c_41750,c_111]) ).
tcf(c_41771,plain,
! [X0: $i] :
( ( sK22(unordered_pair(X0,X0)) = empty_set )
| ( sK22(unordered_pair(X0,X0)) = unordered_pair(X0,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41732,c_344]) ).
tcf(c_41774,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X0) = unordered_pair(X1,X1) )
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41721,c_49]) ).
tcf(c_41943,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(function_inverse(X0))) = relation_rng(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0)) ),
inference(superposition,[status(thm)],[c_189,c_181]) ).
tcf(c_41945,plain,
( ( relation_dom(function_inverse(empty_set)) = relation_rng(empty_set) )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_19096,c_181]) ).
tcf(c_41946,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(relation_dom(X0))) = relation_rng(relation_dom(X0)) )
| ~ empty(X0)
| ~ function(relation_dom(X0))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_19129,c_181]) ).
tcf(c_41947,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(relation_rng(X0))) = relation_rng(relation_rng(X0)) )
| ~ empty(X0)
| ~ function(relation_rng(X0))
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_19154,c_181]) ).
tcf(c_41948,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(relation_inverse(X0))) = relation_rng(relation_inverse(X0)) )
| ~ empty(X0)
| ~ function(relation_inverse(X0))
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_19173,c_181]) ).
tcf(c_41949,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(sK23(X0))) = relation_rng(sK23(X0)) )
| ~ empty(X0)
| ~ function(sK23(X0))
| ~ relation(sK23(X0)) ),
inference(superposition,[status(thm)],[c_20382,c_181]) ).
tcf(c_41950,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(identity_relation(X0))) = relation_rng(identity_relation(X0)) )
| ~ empty(X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_20572,c_181]) ).
tcf(c_41951,plain,
( ( relation_dom(function_inverse(sK5)) = relation_rng(sK5) )
| ( set_union2(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5))) = relation_field(sK5) )
| ~ function(sK5)
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_35222,c_181]) ).
tcf(c_41952,plain,
( ( relation_dom(function_inverse(sK5)) = relation_rng(sK5) )
| ( set_union2(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5))) = relation_field(sK5) )
| ~ function(sK5)
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_34829,c_181]) ).
tcf(c_41953,plain,
( ( relation_dom(function_inverse(sK5)) = relation_rng(sK5) )
| ( apply(identity_relation(relation_field(sK5)),sK77(sK5)) = sK77(sK5) )
| ~ function(sK5)
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_32806,c_181]) ).
tcf(c_41954,plain,
( ( relation_dom(function_inverse(sK5)) = relation_rng(sK5) )
| ( apply(identity_relation(relation_field(sK5)),sK76(sK5)) = sK76(sK5) )
| ~ function(sK5)
| ~ relation(sK5) ),
inference(superposition,[status(thm)],[c_32698,c_181]) ).
tcf(c_41955,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(relation_dom_restriction(sK5,X0))) = relation_rng(relation_dom_restriction(sK5,X0)) )
| ~ empty(identity_relation(X0))
| ~ function(relation_dom_restriction(sK5,X0))
| ~ relation(relation_dom_restriction(sK5,X0)) ),
inference(superposition,[status(thm)],[c_25779,c_181]) ).
tcf(c_41957,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(identity_relation(X0))) = X0 )
| ~ empty(X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_41950,c_204]) ).
tcf(c_41958,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(identity_relation(X0))) = X0 )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41957,c_421,c_422]) ).
tcf(c_41977,plain,
( ( relation_dom(function_inverse(sK5)) = relation_rng(sK5) )
| ( apply(identity_relation(relation_field(sK5)),sK76(sK5)) = sK76(sK5) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41954,c_97,c_96]) ).
tcf(c_41980,plain,
( ( relation_dom(function_inverse(sK5)) = relation_rng(sK5) )
| ( apply(identity_relation(relation_field(sK5)),sK77(sK5)) = sK77(sK5) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41953,c_97,c_96]) ).
tcf(c_41983,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(relation_dom_restriction(sK5,X0))) = relation_rng(relation_dom_restriction(sK5,X0)) )
| ~ empty(identity_relation(X0))
| ~ function(relation_dom_restriction(sK5,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41955,c_25741]) ).
tcf(c_41987,plain,
( ( relation_dom(function_inverse(sK5)) = relation_rng(sK5) )
| ( set_union2(relation_field(sK5),unordered_pair(sK76(sK5),sK76(sK5))) = relation_field(sK5) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41952,c_97,c_96]) ).
tcf(c_41990,plain,
( ( relation_dom(function_inverse(sK5)) = relation_rng(sK5) )
| ( set_union2(relation_field(sK5),unordered_pair(sK77(sK5),sK77(sK5))) = relation_field(sK5) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41951,c_97,c_96]) ).
fof(f468,definition,
! [X0,X2,X3,X1] :
( sP0(X0,X2,X3,X1)
<=> ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f469,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = function_inverse(X0)
<=> ( ! [X2,X3] :
( sP0(X0,X2,X3,X1)
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ),
inference(definition_folding,[],[f338,f468]) ).
fof(f506,plain,
! [X0,X2,X3,X1] :
( ( ~ sP0(X0,X2,X3,X1)
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0))
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
| sP0(X0,X2,X3,X1) ) ),
inference(nnf_transformation,[],[f468]) ).
fof(f507,plain,
! [X0,X2,X3,X1] :
( ( ~ sP0(X0,X2,X3,X1)
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0))
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
| sP0(X0,X2,X3,X1) ) ),
inference(flattening,[],[f506]) ).
fof(f508,plain,
! [X0,X1,X2,X3] :
( ( ~ sP0(X0,X1,X2,X3)
| apply(X0,X2) != X1
| ~ in(X2,relation_dom(X0))
| ( apply(X3,X1) = X2
& in(X1,relation_rng(X0)) ) )
& ( ( apply(X0,X2) = X1
& in(X2,relation_dom(X0))
& ( apply(X3,X1) != X2
| ~ in(X1,relation_rng(X0)) ) )
| sP0(X0,X1,X2,X3) ) ),
inference(rectify,[],[f507]) ).
fof(f753,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| apply(X0,X2) != X1
| ~ in(X2,relation_dom(X0))
| apply(X3,X1) = X2 ),
inference(cnf_transformation,[],[f508]) ).
fof(f754,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| apply(X0,X2) != X1
| ~ in(X2,relation_dom(X0))
| in(X1,relation_rng(X0)) ),
inference(cnf_transformation,[],[f508]) ).
fof(f755,plain,
! [X2,X3,X0,X1] :
( apply(X0,X2) = X1
| sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f508]) ).
fof(f756,plain,
! [X2,X3,X0,X1] :
( in(X2,relation_dom(X0))
| sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f508]) ).
fof(f757,plain,
! [X2,X3,X0,X1] :
( apply(X3,X1) != X2
| ~ in(X1,relation_rng(X0))
| sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f508]) ).
fof(f1211,plain,
! [X3,X0,X1] :
( ~ in(X1,relation_rng(X0))
| sP0(X0,X1,apply(X3,X1),X3) ),
inference(equality_resolution,[],[f757]) ).
fof(f1212,plain,
! [X2,X3,X0] :
( ~ sP0(X0,apply(X0,X2),X2,X3)
| ~ in(X2,relation_dom(X0))
| in(apply(X0,X2),relation_rng(X0)) ),
inference(equality_resolution,[],[f754]) ).
fof(f1213,plain,
! [X2,X3,X0] :
( ~ sP0(X0,apply(X0,X2),X2,X3)
| ~ in(X2,relation_dom(X0))
| apply(X3,apply(X0,X2)) = X2 ),
inference(equality_resolution,[],[f753]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X1,X0,apply(X2,X0),X2)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f1211]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,relation_dom(X0))
| sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f756]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(X0,X2,X1,X3)
| ( apply(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f755]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,X1),relation_rng(X0))
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,apply(X0,X1),X1,X2) ),
inference(cnf_transformation,[],[f1212]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,apply(X0,X1)) = X1 )
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,apply(X0,X1),X1,X2) ),
inference(cnf_transformation,[],[f1213]) ).
tcf(c_39934,plain,
! [X0: $i] :
( sP0(X0,sK76(sK5),sK76(sK5),identity_relation(relation_field(sK5)))
| ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(sK76(sK5),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_39746,c_168]) ).
tcf(c_39943,plain,
! [X0: $i] :
( sP0(X0,sK77(sK5),sK77(sK5),identity_relation(relation_field(sK5)))
| ( relation_inverse(sK5) = function_inverse(sK5) )
| ~ in(sK77(sK5),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_39749,c_168]) ).
tcf(c_42072,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_41990,c_41987,c_41983,c_41980,c_41977,c_41958,c_41957,c_41955,c_41954,c_41953,c_41952,c_41951,c_41950,c_41949,c_41948,c_41947,c_41946,c_41945,c_41943,c_41774,c_41771,c_41754,c_41750,c_41749,c_41748,c_41747,c_41746,c_41745,c_41744,c_41743,c_41742,c_41741,c_41740,c_41739,c_41738,c_41737,c_41736,c_41735,c_41734,c_41733,c_41732,c_41731,c_41729,c_41728,c_41727,c_41726,c_41724,c_41723,c_41722,c_41721,c_41637,c_41631,c_41587,c_41578,c_41577,c_41571,c_41570,c_41569,c_41568,c_41567,c_41566,c_41565,c_41564,c_41563,c_41562,c_41561,c_41560,c_41559,c_41558,c_41557,c_41556,c_41555,c_41554,c_41553,c_41552,c_41551,c_41550,c_41549,c_41548,c_41417,c_41416,c_41415,c_41414,c_41413,c_41412,c_41411,c_41410,c_41409,c_41408,c_41407,c_41406,c_41405,c_41404,c_41403,c_41402,c_41401,c_41400,c_41399,c_41398,c_41397,c_41396,c_41395,c_41366,c_41355,c_41352,c_41351,c_41350,c_41349,c_41348,c_41347,c_41318,c_41315,c_41314,c_41313,c_41312,c_41311,c_41310,c_41309,c_41280,c_41277,c_41276,c_41275,c_41274,c_41273,c_41272,c_41271,c_41184,c_41181,c_41179,c_41178,c_41177,c_41176,c_41066,c_41065,c_41061,c_41060,c_41059,c_41058,c_41057,c_41056,c_41055,c_41053,c_41052,c_41051,c_41050,c_41049,c_41063,c_41062,c_41046,c_41054,c_40949,c_40948,c_40945,c_40944,c_40943,c_40942,c_40941,c_40940,c_40939,c_40937,c_40936,c_40935,c_40934,c_40933,c_40947,c_40946,c_40930,c_40938,c_40880,c_40879,c_40878,c_40877,c_40876,c_40875,c_40874,c_40873,c_40872,c_40725,c_40694,c_40691,c_40690,c_40681,c_40680,c_40679,c_40678,c_40677,c_40676,c_40675,c_40674,c_40673,c_40672,c_40671,c_40670,c_40669,c_40668,c_40667,c_40666,c_40665,c_40664,c_40663,c_40662,c_40661,c_40660,c_40565,c_40556,c_40555,c_40551,c_40550,c_40549,c_40548,c_40547,c_40546,c_40545,c_40544,c_40543,c_40542,c_40541,c_40540,c_40539,c_40538,c_40537,c_40536,c_40535,c_40534,c_40454,c_40421,c_40420,c_40418,c_40417,c_40416,c_40415,c_40414,c_40413,c_40412,c_40411,c_40410,c_40409,c_40408,c_40407,c_40406,c_40405,c_40404,c_40403,c_40402,c_40401,c_40400,c_40399,c_40398,c_40397,c_40396,c_40364,c_40363,c_40362,c_40358,c_40356,c_40350,c_40349,c_40251,c_40250,c_40249,c_40248,c_40247,c_40246,c_40245,c_40244,c_40243,c_40242,c_40241,c_40240,c_40239,c_40238,c_40237,c_40236,c_40235,c_40233,c_40232,c_40231,c_40195,c_40192,c_40190,c_40189,c_40188,c_40187,c_40068,c_40067,c_40064,c_40061,c_40060,c_40059,c_40058,c_40057,c_40056,c_40055,c_40054,c_40048,c_40047,c_40046,c_40042,c_40041,c_40040,c_40039,c_40038,c_40036,c_40035,c_40034,c_40033,c_39988,c_39987,c_39986,c_39983,c_39980,c_39979,c_39978,c_39977,c_39976,c_39975,c_39974,c_39973,c_39971,c_39968,c_39967,c_39966,c_39965,c_39964,c_39963,c_39962,c_39961,c_39960,c_39959,c_39958,c_39957,c_39955,c_39954,c_39953,c_39952,c_39943,c_39934,c_39851,c_39850,c_39846,c_39845,c_39844,c_39843,c_39842,c_39841,c_39840,c_39832,c_39827,c_39822,c_39820,c_39819,c_39817,c_39779,c_39778,c_39777,c_39776,c_39775,c_39774,c_39773,c_39772,c_39771,c_39770,c_39769,c_39768,c_39759,c_39756,c_39752,c_39749,c_39746,c_39727,c_39726,c_39725,c_39724,c_39723,c_39722,c_39721,c_39720,c_39719,c_39718,c_39717,c_39716,c_39715,c_39714,c_39713,c_39712,c_39711,c_39519,c_39518,c_39517,c_39516,c_39515,c_39514,c_39513,c_39512,c_39511,c_39510,c_39509,c_39508,c_39507,c_39505,c_39504,c_39502,c_39501,c_39500,c_39499,c_39498,c_39497,c_39495,c_39494,c_39493,c_39492,c_39491,c_39490,c_39265,c_39264,c_39263,c_39262,c_39261,c_39260,c_39259,c_39258,c_39257,c_39256,c_39255,c_39254,c_39253,c_39251,c_39250,c_39248,c_39247,c_39246,c_39245,c_39244,c_39243,c_39241,c_39240,c_39239,c_39238,c_39237,c_39236,c_39191,c_39190,c_39189,c_39188,c_39186,c_39185,c_39184,c_39183,c_39182,c_39180,c_39179,c_39178,c_39164,c_39161,c_39160,c_39152,c_39149,c_39148,c_39147,c_39141,c_39139,c_39138,c_39137,c_39136,c_39135,c_39134,c_39051,c_39050,c_39049,c_39047,c_39045,c_39044,c_39043,c_39042,c_39041,c_39040,c_39039,c_39038,c_39037,c_39036,c_39035,c_39034,c_39033,c_39032,c_39029,c_39028,c_39027,c_39031,c_39020,c_39001,c_38999,c_38998,c_38997,c_38996,c_38995,c_38994,c_38803,c_38802,c_38801,c_38800,c_38799,c_38798,c_38797,c_38796,c_38795,c_38794,c_38793,c_38792,c_38791,c_38790,c_38788,c_38787,c_38784,c_38783,c_38782,c_38781,c_38780,c_38779,c_38778,c_38777,c_38776,c_38775,c_38774,c_38773,c_38772,c_38771,c_38769,c_38766,c_38770,c_38764,c_38412,c_38388,c_38385,c_38384,c_38383,c_38382,c_38381,c_38380,c_38379,c_38378,c_38377,c_38376,c_38375,c_38374,c_38373,c_38372,c_38371,c_38370,c_38369,c_38368,c_38367,c_38366,c_38365,c_38364,c_38363,c_38362,c_38361,c_38360,c_38359,c_38358,c_38357,c_38356,c_38355,c_38354,c_38353,c_38352,c_38351,c_38350,c_38349,c_38348,c_38347,c_38346,c_38345,c_38344,c_38343,c_38342,c_38341,c_38340,c_38339,c_38338,c_38337,c_38336,c_38335,c_38334,c_38333,c_38332,c_38331,c_38330,c_38329,c_38328,c_38327,c_38326,c_38045,c_38044,c_38043,c_38042,c_38041,c_38040,c_38039,c_38038,c_38037,c_38036,c_38035,c_38034,c_38033,c_38032,c_38031,c_38030,c_38029,c_38028,c_38027,c_38026,c_38025,c_38024,c_38023,c_38022,c_38021,c_38020,c_38019,c_38018,c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c_301,c_305,c_111,c_110,c_109,c_39025,c_107,c_106,c_105,c_104,c_102,c_100,c_99,c_98,c_97,c_96,c_95,c_94,c_93,c_91,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_322,c_222,c_148,c_58,c_139,c_138,c_140,c_52,c_51,c_161,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU226+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 13:14:55 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 22.75/4.25 % SZS status Started for theBenchmark.p
% 22.75/4.25 % SZS status Theorem for theBenchmark.p
% 22.75/4.25
% 22.75/4.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.75/4.25
% 22.75/4.25 % ------ iProver source info
% 22.75/4.25
% 22.75/4.25 % git: date: 2026-07-19 20:42:38 +0200
% 22.75/4.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.75/4.25 % git: non_committed_changes: false
% 22.75/4.25
% 22.75/4.25 % ------ Parsing...
% 22.75/4.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.75/4.25
% 22.75/4.25 % ------ Preprocessing... sup_sim: 42 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 %
% 22.75/4.25
% 22.75/4.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 22.75/4.25
% 22.75/4.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 22.75/4.25 % ------ Proving...
% 22.75/4.25 % ------ Problem Properties
% 22.75/4.25
% 22.75/4.25 %
% 22.75/4.25 % clauses 377
% 22.75/4.25 % conjectures 3
% 22.75/4.25 % EPR 45
% 22.75/4.25 % Horn 305
% 22.75/4.25 % unary 55
% 22.75/4.25 % binary 113
% 22.75/4.25 % lits 1090
% 22.75/4.25 % lits eq 200
% 22.75/4.25 % fd_pure 0
% 22.75/4.25 % fd_pseudo 0
% 22.75/4.25 % fd_cond 11
% 22.75/4.25 % fd_pseudo_cond 80
% 22.75/4.25 % AC symbols 0
% 22.75/4.25
% 22.75/4.25 % ------ Schedule dynamic 5 is on
% 22.75/4.25
% 22.75/4.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 22.75/4.25
% 22.75/4.25
% 22.75/4.25 % ------
% 22.75/4.25 % Current options:
% 22.75/4.25 % ------
% 22.75/4.25
% 22.75/4.25
% 22.75/4.25 %
% 22.75/4.25
% 22.75/4.25 % ------ Proving...
% 22.75/4.25 %
% 22.75/4.25
% 22.75/4.25 % SZS status Theorem for theBenchmark.p
% 22.75/4.25
% 22.75/4.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.39/4.39
% 26.39/4.39
%------------------------------------------------------------------------------