TSTP Solution File: SEU284+2 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU284+2 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 15:18:04 EDT 2024
% Result : Theorem 82.59s 11.89s
% Output : CNFRefutation 82.59s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f2511)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
=> ~ proper_subset(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f5,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f6,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f7,axiom,
! [X0] :
( ( function(X0)
& empty(X0)
& relation(X0) )
=> ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(f9,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f10,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f11,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f12,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f13,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f14,axiom,
! [X0,X1] :
( relation(X1)
=> ( identity_relation(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f15,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f16,axiom,
! [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) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f17,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f18,axiom,
! [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) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
fof(f19,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
fof(f20,axiom,
! [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)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f21,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f22,axiom,
! [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) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f23,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
fof(f24,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
fof(f25,axiom,
! [X0,X1,X2,X3] :
( unordered_triple(X0,X1,X2) = X3
<=> ! [X4] :
( in(X4,X3)
<=> ~ ( X2 != X4
& X1 != X4
& X0 != X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_enumset1) ).
fof(f26,axiom,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
fof(f27,axiom,
! [X0] :
( ? [X1,X2] : ordered_pair(X1,X2) = X0
=> ! [X1] :
( pair_first(X0) = X1
<=> ! [X2,X3] :
( ordered_pair(X2,X3) = X0
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_mcart_1) ).
fof(f28,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f29,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f30,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(X2,X1)
=> in(ordered_pair(X2,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).
fof(f31,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
<=> subset(X2,cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
fof(f32,axiom,
! [X0,X1] :
( ( empty_set = X0
=> ( set_meet(X0) = X1
<=> empty_set = X1 ) )
& ( empty_set != X0
=> ( set_meet(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X3,X0)
=> in(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
fof(f33,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f34,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( fiber(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(ordered_pair(X3,X1),X0)
& X1 != X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord1) ).
fof(f35,axiom,
! [X0,X1] :
( relation(X1)
=> ( inclusion_relation(X0) = X1
<=> ( ! [X2,X3] :
( ( in(X3,X0)
& in(X2,X0) )
=> ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) ) )
& relation_field(X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord2) ).
fof(f36,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f37,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f38,axiom,
! [X0] :
( ? [X1,X2] : ordered_pair(X1,X2) = X0
=> ! [X1] :
( pair_second(X0) = X1
<=> ! [X2,X3] :
( ordered_pair(X2,X3) = X0
=> X1 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_mcart_1) ).
fof(f39,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f40,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/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
fof(f41,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f42,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f43,axiom,
! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> ! [X1] :
~ ( ! [X2] :
~ ( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
& empty_set != X1
& subset(X1,relation_field(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_wellord1) ).
fof(f44,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f45,axiom,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f46,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f47,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/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
fof(f48,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f49,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_well_founded_in(X0,X1)
<=> ! [X2] :
~ ( ! [X3] :
~ ( disjoint(fiber(X0,X3),X2)
& in(X3,X2) )
& empty_set != X2
& subset(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_wellord1) ).
fof(f50,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f51,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> empty_set = X2 ) )
& ( in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f52,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(f53,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f54,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_2) ).
fof(f55,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f56,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f57,axiom,
! [X0] :
( relation(X0)
=> ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
fof(f58,axiom,
! [X0,X1] :
( equipotent(X0,X1)
<=> ? [X2] :
( relation_rng(X2) = X1
& relation_dom(X2) = X0
& one_to_one(X2)
& function(X2)
& relation(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord2) ).
fof(f59,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f60,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f61,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f62,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> set_difference(X0,X1) = subset_complement(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f63,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f64,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( well_orders(X0,X1)
<=> ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_wellord1) ).
fof(f65,axiom,
! [X0] :
( being_limit_ordinal(X0)
<=> union(X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_ordinal1) ).
fof(f66,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f67,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X2,X3] :
~ ( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_2) ).
fof(f68,axiom,
! [X0] :
( relation(X0)
=> ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_wellord1) ).
fof(f69,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( relation_inverse(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
fof(f70,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_isomorphism(X0,X1,X2)
<=> ( ! [X3,X4] :
( in(ordered_pair(X3,X4),X0)
<=> ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& one_to_one(X2)
& relation_field(X1) = relation_rng(X2)
& relation_field(X0) = relation_dom(X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_wellord1) ).
fof(f71,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f72,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/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f73,axiom,
! [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) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f74,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) )
=> in(ordered_pair(X2,X4),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_2) ).
fof(f75,axiom,
! [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) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(f76,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f77,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> relation_inverse(X0) = function_inverse(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_funct_1) ).
fof(f78,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
fof(f88,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f91,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f94,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f96,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f100,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f103,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f104,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
fof(f107,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f108,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_1) ).
fof(f109,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(union_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(f110,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f111,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(meet_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(f112,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> element(subset_difference(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
fof(f113,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f114,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f115,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f119,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f120,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f121,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f122,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f123,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f124,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
fof(f126,axiom,
! [X0,X1] :
( ( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_relat_1) ).
fof(f127,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f128,axiom,
! [X0] : ~ empty(succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(f129,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f130,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f133,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f134,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f135,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(f137,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f138,axiom,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_funct_1) ).
fof(f139,axiom,
! [X0] :
( ordinal(X0)
=> ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(f140,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
fof(f141,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f142,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f143,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f144,axiom,
! [X0] :
( ordinal(X0)
=> ( ordinal(union(X0))
& epsilon_connected(union(X0))
& epsilon_transitive(union(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_ordinal1) ).
fof(f145,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f146,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f147,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f148,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f149,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f150,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f151,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f152,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(f153,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f154,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f155,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f156,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f157,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(f158,axiom,
! [X0,X1] : ~ proper_subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f159,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_wellord1) ).
fof(f160,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f162,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f163,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f164,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l29_wellord1) ).
fof(f165,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> in(ordered_pair(X1,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_wellord1) ).
fof(f167,axiom,
! [X0,X1] :
( relation(X1)
=> ~ ( ! [X2] :
( relation(X2)
=> ~ well_orders(X2,X0) )
& equipotent(X0,relation_field(X1))
& well_ordering(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l30_wellord2) ).
fof(f169,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
fof(f170,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> ! [X1,X2] :
( ( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_wellord1) ).
fof(f171,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f172,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& X1 != X2
& in(X2,relation_field(X0))
& in(X1,relation_field(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_wellord1) ).
fof(f175,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f176,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f178,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f179,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f180,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f181,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f182,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f183,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f184,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(f185,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f186,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f187,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f188,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f189,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f190,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f191,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(f192,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom(X2) = relation_dom_as_subset(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f193,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_rng(X2) = relation_rng_as_subset(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
fof(f194,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> union_of_subsets(X0,X1) = union(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(f195,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> meet_of_subsets(X0,X1) = set_meet(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
fof(f196,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f197,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f198,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f199,axiom,
! [X0,X1] :
( equipotent(X0,X1)
<=> are_equipotent(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r2_wellord2) ).
fof(f200,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ordinal_subset(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(f201,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f202,axiom,
! [X0,X1] : equipotent(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_wellord2) ).
fof(f203,axiom,
! [X0] :
( ! [X1,X2,X3] :
( ( singleton(X1) = X3
& in(X1,X0)
& singleton(X1) = X2
& in(X1,X0) )
=> X2 = X3 )
=> ? [X1] :
( ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( singleton(X2) = X3
& in(X2,X0)
& in(X2,X0) ) )
& function(X1)
& relation(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_funct_1__e16_22__wellord2__1) ).
fof(f204,axiom,
! [X0] :
( ? [X1] :
( in(X1,X0)
& ordinal(X1) )
=> ? [X1] :
( ! [X2] :
( ordinal(X2)
=> ( in(X2,X0)
=> ordinal_subset(X1,X2) ) )
& in(X1,X0)
& ordinal(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_ordinal1__e8_6__wellord2) ).
fof(f205,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ? [X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
& relation(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_relat_1__e6_21__wellord2) ).
fof(f206,axiom,
! [X0] :
( ! [X1,X2,X3] :
( ( singleton(X1) = X3
& in(X1,X0)
& singleton(X1) = X2
& in(X1,X0) )
=> X2 = X3 )
=> ? [X1] :
! [X2] :
( in(X2,X1)
<=> ? [X3] :
( singleton(X3) = X2
& in(X3,X0)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__1) ).
fof(f207,axiom,
! [X0,X1] :
( ! [X2,X3,X4] :
( ( ? [X7,X8] :
( singleton(X7) = X8
& in(X7,X0)
& ordered_pair(X7,X8) = X4 )
& X2 = X4
& ? [X5,X6] :
( singleton(X5) = X6
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X9,X10] :
( singleton(X9) = X10
& in(X9,X0)
& ordered_pair(X9,X10) = X3 )
& X3 = X4
& in(X4,cartesian_product2(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__2) ).
fof(f208,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ( ! [X3,X4,X5] :
( ( ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& ordered_pair(X8,X9) = X5 )
& X3 = X5
& ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& ordered_pair(X6,X7) = X4 )
& X3 = X4 )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( ? [X10,X11] :
( in(ordered_pair(apply(X2,X10),apply(X2,X11)),X1)
& ordered_pair(X10,X11) = X4 )
& X4 = X5
& in(X5,cartesian_product2(X0,X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_21__wellord2__1) ).
fof(f209,axiom,
! [X0] :
( ! [X1,X2,X3] :
( ( ordinal(X3)
& X1 = X3
& ordinal(X2)
& X1 = X2 )
=> X2 = X3 )
=> ? [X1] :
! [X2] :
( in(X2,X1)
<=> ? [X3] :
( ordinal(X2)
& X2 = X3
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).
fof(f210,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( ! [X2,X3,X4] :
( ( ? [X6] :
( in(X6,X0)
& X4 = X6
& ordinal(X6) )
& X2 = X4
& ? [X5] :
( in(X5,X0)
& X3 = X5
& ordinal(X5) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X7] :
( in(X7,X0)
& X3 = X7
& ordinal(X7) )
& X3 = X4
& in(X4,succ(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e8_6__wellord2__1) ).
fof(f211,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4,X5] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e16_22__wellord2__1) ).
fof(f212,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).
fof(f213,axiom,
! [X0] :
? [X1] :
! [X2] :
( in(X2,X1)
<=> ( ordinal(X2)
& in(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).
fof(f214,axiom,
! [X0,X1] :
( ordinal(X1)
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( in(X4,X0)
& X3 = X4
& ordinal(X4) )
& in(X3,succ(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e8_6__wellord2__1) ).
fof(f215,axiom,
! [X0] :
( ( ! [X1] :
~ ( ! [X2] : singleton(X1) != X2
& in(X1,X0) )
& ! [X1,X2,X3] :
( ( singleton(X1) = X3
& singleton(X1) = X2
& in(X1,X0) )
=> X2 = X3 ) )
=> ? [X1] :
( ! [X2] :
( in(X2,X0)
=> singleton(X2) = apply(X1,X2) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
fof(f216,conjecture,
! [X0] :
? [X1] :
( ! [X2] :
( in(X2,X0)
=> singleton(X2) = apply(X1,X2) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_1__e16_22__wellord2) ).
fof(f217,negated_conjecture,
~ ! [X0] :
? [X1] :
( ! [X2] :
( in(X2,X0)
=> singleton(X2) = apply(X1,X2) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ),
inference(negated_conjecture,[],[f216]) ).
fof(f218,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f219,axiom,
! [X0,X1] :
( equipotent(X0,X1)
=> equipotent(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r2_wellord2) ).
fof(f220,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f221,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f222,axiom,
! [X0,X1,X2,X3] :
~ ( X0 != X3
& X0 != X2
& unordered_pair(X0,X1) = unordered_pair(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f223,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/sandbox2/benchmark/theBenchmark.p',t115_relat_1) ).
fof(f224,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_relat_1) ).
fof(f225,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng_restriction(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
fof(f226,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_relat_1) ).
fof(f227,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/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f228,axiom,
! [X0,X1] :
( relation(X1)
=> relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_relat_1) ).
fof(f229,axiom,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f230,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
fof(f231,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f232,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/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(f233,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/sandbox2/benchmark/theBenchmark.p',t140_relat_1) ).
fof(f234,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/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
fof(f235,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
fof(f236,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
fof(f237,axiom,
! [X0,X1] :
( relation(X1)
=> relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
fof(f238,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset(X0,relation_dom(X1))
=> subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
fof(f239,axiom,
! [X0] :
( relation(X0)
=> relation_rng(X0) = relation_image(X0,relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
fof(f240,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( subset(X0,relation_rng(X1))
=> relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
fof(f241,axiom,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(relation_rng(X3),X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
fof(f242,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
fof(f243,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/sandbox2/benchmark/theBenchmark.p',t166_relat_1) ).
fof(f244,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
fof(f245,axiom,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(X0,X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
fof(f246,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f247,axiom,
! [X0,X1] :
( relation(X1)
=> ~ ( empty_set = relation_inverse_image(X1,X0)
& subset(X0,relation_rng(X1))
& empty_set != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_relat_1) ).
fof(f248,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( subset(X0,X1)
=> subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
fof(f249,axiom,
! [X0,X1] :
( relation(X1)
=> relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_wellord1) ).
fof(f251,axiom,
! [X0,X1] :
( relation(X1)
=> relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_wellord1) ).
fof(f252,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_field(relation_restriction(X2,X1)))
=> ( in(X0,X1)
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_wellord1) ).
fof(f253,axiom,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f254,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(f255,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f256,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f257,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f258,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f259,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset(relation_field(relation_restriction(X1,X0)),X0)
& subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_wellord1) ).
fof(f260,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/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f261,axiom,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ( proper_subset(X0,X1)
=> in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(f262,axiom,
! [X0] :
( relation(X0)
=> subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f263,axiom,
! [X0,X1,X2] :
( relation(X2)
=> subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_wellord1) ).
fof(f264,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/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f265,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X1,X0)
=> ( ! [X3] :
~ ( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) )
<=> relation_dom_as_subset(X1,X0,X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relset_1) ).
fof(f266,axiom,
! [X0,X1] :
( relation(X1)
=> ( reflexive(X1)
=> reflexive(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_wellord1) ).
fof(f267,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/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f268,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f269,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ! [X3] :
~ ( ! [X4] : ~ in(ordered_pair(X4,X3),X2)
& in(X3,X1) )
<=> relation_rng_as_subset(X0,X1,X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relset_1) ).
fof(f270,axiom,
! [X0,X1] :
( relation(X1)
=> ( connected(X1)
=> connected(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_wellord1) ).
fof(f271,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f272,axiom,
! [X0,X1] :
( relation(X1)
=> ( transitive(X1)
=> transitive(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_wellord1) ).
fof(f273,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/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
fof(f274,axiom,
! [X0,X1] :
( relation(X1)
=> ( antisymmetric(X1)
=> antisymmetric(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_wellord1) ).
fof(f275,axiom,
! [X0,X1] :
( relation(X1)
=> ( well_orders(X1,X0)
=> ( well_ordering(relation_restriction(X1,X0))
& relation_field(relation_restriction(X1,X0)) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_wellord2) ).
fof(f276,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f277,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f278,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(f279,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f280,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f281,axiom,
! [X0] : reflexive(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_wellord2) ).
fof(f282,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f283,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/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f284,axiom,
! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( subset(X1,X0)
& ordinal(X1) ) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(f285,axiom,
! [X0,X1] :
( relation(X1)
=> ( well_founded_relation(X1)
=> well_founded_relation(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_wellord1) ).
fof(f286,axiom,
! [X0,X1] :
( ordinal(X1)
=> ~ ( ! [X2] :
( ordinal(X2)
=> ~ ( ! [X3] :
( ordinal(X3)
=> ( in(X3,X0)
=> ordinal_subset(X2,X3) ) )
& in(X2,X0) ) )
& empty_set != X0
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).
fof(f287,axiom,
! [X0,X1] :
( relation(X1)
=> ( well_ordering(X1)
=> well_ordering(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_wellord1) ).
fof(f288,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_ordinal1) ).
fof(f289,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(f290,axiom,
! [X0,X1,X2,X3] :
( ordered_pair(X2,X3) = ordered_pair(X0,X1)
=> ( X1 = X3
& X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f291,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( identity_relation(X0) = X1
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f292,axiom,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f293,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f294,axiom,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f295,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f296,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(f297,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f298,axiom,
! [X0,X1] :
( relation(X1)
=> ( ( subset(X0,relation_field(X1))
& well_ordering(X1) )
=> relation_field(relation_restriction(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_wellord1) ).
fof(f299,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f300,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f301,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(f302,axiom,
! [X0,X1,X2] :
~ ( in(X2,X0)
& in(X1,X2)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
fof(f303,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f304,axiom,
! [X0] : transitive(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_wellord2) ).
fof(f305,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/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f306,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f307,axiom,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f308,axiom,
! [X0] :
( ordinal(X0)
=> ( being_limit_ordinal(X0)
<=> ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
=> in(succ(X1),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_ordinal1) ).
fof(f309,axiom,
! [X0] :
( ordinal(X0)
=> ( ~ ( being_limit_ordinal(X0)
& ? [X1] :
( succ(X1) = X0
& ordinal(X1) ) )
& ~ ( ! [X1] :
( ordinal(X1)
=> succ(X1) != X0 )
& ~ being_limit_ordinal(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_ordinal1) ).
fof(f310,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,powerset(X0))
=> ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
fof(f311,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
fof(f312,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
fof(f313,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,set_difference(X1,X0)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
fof(f314,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(X0) = relation_dom(relation_composition(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f315,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( empty_set = complements_of_subsets(X0,X1)
& empty_set != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(f316,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f317,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_dom(X0),relation_rng(X1))
=> relation_rng(X0) = relation_rng(relation_composition(X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
fof(f318,axiom,
! [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)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
fof(f319,axiom,
! [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)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(f320,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f321,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_isomorphism(X0,X1,X2)
=> relation_isomorphism(X1,X0,function_inverse(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_wellord1) ).
fof(f322,axiom,
! [X0] : empty_set = set_difference(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
fof(f323,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f324,axiom,
! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_wellord2) ).
fof(f325,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/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f326,axiom,
! [X0] :
( empty_set != X0
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f327,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_isomorphism(X0,X1,X2)
=> ( ( well_founded_relation(X0)
=> well_founded_relation(X1) )
& ( antisymmetric(X0)
=> antisymmetric(X1) )
& ( connected(X0)
=> connected(X1) )
& ( transitive(X0)
=> transitive(X1) )
& ( reflexive(X0)
=> reflexive(X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_wellord1) ).
fof(f328,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
=> ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
=> ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
& relation_rng(X0) = relation_dom(X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f329,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,subset_complement(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f330,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( relation_isomorphism(X0,X1,X2)
& well_ordering(X0) )
=> well_ordering(X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_wellord1) ).
fof(f331,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/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f332,axiom,
! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
fof(f333,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( in(X0,relation_rng(X1))
& one_to_one(X1) )
=> ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
& apply(X1,apply(function_inverse(X1),X0)) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f334,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f335,axiom,
! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
fof(f336,axiom,
! [X0] : antisymmetric(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord2) ).
fof(f337,axiom,
( empty_set = relation_rng(empty_set)
& empty_set = relation_dom(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f338,axiom,
! [X0,X1] :
~ ( proper_subset(X1,X0)
& subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f339,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
fof(f340,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f341,axiom,
! [X0] :
( relation(X0)
=> ( ( empty_set = relation_rng(X0)
| relation_dom(X0) = empty_set )
=> empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
fof(f342,axiom,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = empty_set
<=> empty_set = relation_rng(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
fof(f343,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f344,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X2,X3) = apply(X1,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f345,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f346,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f347,axiom,
! [X0] :
( ordinal(X0)
=> well_founded_relation(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_wellord2) ).
fof(f348,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f349,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/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).
fof(f350,axiom,
! [X0] :
( relation_rng(identity_relation(X0)) = X0
& relation_dom(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f351,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
fof(f352,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/sandbox2/benchmark/theBenchmark.p',t74_relat_1) ).
fof(f353,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f354,axiom,
! [X0,X1] :
( pair_second(ordered_pair(X0,X1)) = X1
& pair_first(ordered_pair(X0,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_mcart_1) ).
fof(f355,axiom,
! [X0,X1] :
~ ( ! [X2] :
~ ( ! [X3] :
~ ( in(X3,X2)
& in(X3,X1) )
& in(X2,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
fof(f356,axiom,
! [X0] :
( ordinal(X0)
=> well_ordering(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_wellord2) ).
fof(f357,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f358,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f359,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/sandbox2/benchmark/theBenchmark.p',t86_relat_1) ).
fof(f360,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom_restriction(X1,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
fof(f361,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f362,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f363,axiom,
! [X0] :
( relation(X0)
=> ( well_orders(X0,relation_field(X0))
<=> well_ordering(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_wellord1) ).
fof(f364,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f365,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f366,axiom,
! [X0,X1] :
( relation(X1)
=> set_intersection2(relation_dom(X1),X0) = relation_dom(relation_dom_restriction(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_relat_1) ).
fof(f367,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(f368,axiom,
! [X0,X1] :
( relation(X1)
=> relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_relat_1) ).
fof(f369,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_relat_1) ).
fof(f370,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f371,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/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
fof(f372,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f373,plain,
! [X0] :
( ? [X1,X2] : ordered_pair(X1,X2) = X0
=> ! [X3] :
( pair_first(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) = X0
=> X3 = X4 ) ) ),
inference(rectify,[],[f27]) ).
fof(f374,plain,
! [X0] :
( ? [X1,X2] : ordered_pair(X1,X2) = X0
=> ! [X3] :
( pair_second(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) = X0
=> X3 = X5 ) ) ),
inference(rectify,[],[f38]) ).
fof(f375,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f153]) ).
fof(f376,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f154]) ).
fof(f377,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(rectify,[],[f158]) ).
fof(f378,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f201]) ).
fof(f379,plain,
! [X0] : equipotent(X0,X0),
inference(rectify,[],[f202]) ).
fof(f380,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( singleton(X1) = X3
& in(X1,X0)
& singleton(X1) = X2
& in(X1,X0) )
=> X2 = X3 )
=> ? [X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& function(X4)
& relation(X4) ) ),
inference(rectify,[],[f203]) ).
fof(f381,plain,
! [X0] :
( ? [X1] :
( in(X1,X0)
& ordinal(X1) )
=> ? [X2] :
( ! [X3] :
( ordinal(X3)
=> ( in(X3,X0)
=> ordinal_subset(X2,X3) ) )
& in(X2,X0)
& ordinal(X2) ) ),
inference(rectify,[],[f204]) ).
fof(f382,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( singleton(X1) = X3
& in(X1,X0)
& singleton(X1) = X2
& in(X1,X0) )
=> X2 = X3 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( singleton(X6) = X5
& in(X6,X0)
& in(X6,X0) ) ) ),
inference(rectify,[],[f206]) ).
fof(f383,plain,
! [X0,X1] :
( ! [X2,X3,X4] :
( ( ? [X5,X6] :
( singleton(X5) = X6
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& X2 = X4
& ? [X7,X8] :
( singleton(X7) = X8
& in(X7,X0)
& ordered_pair(X7,X8) = X3 )
& X2 = X3 )
=> X3 = X4 )
=> ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) ) ),
inference(rectify,[],[f207]) ).
fof(f384,plain,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ( ! [X3,X4,X5] :
( ( ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& ordered_pair(X8,X9) = X4 )
& X3 = X4 )
=> X4 = X5 )
=> ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) ) ) ) ),
inference(rectify,[],[f208]) ).
fof(f385,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( ordinal(X3)
& X1 = X3
& ordinal(X2)
& X1 = X2 )
=> X2 = X3 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( ordinal(X5)
& X5 = X6
& in(X6,X0) ) ) ),
inference(rectify,[],[f209]) ).
fof(f386,plain,
! [X0,X1] :
( ordinal(X1)
=> ( ! [X2,X3,X4] :
( ( ? [X5] :
( in(X5,X0)
& X4 = X5
& ordinal(X5) )
& X2 = X4
& ? [X6] :
( in(X6,X0)
& X3 = X6
& ordinal(X6) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( in(X10,X0)
& X8 = X10
& ordinal(X10) )
& X8 = X9
& in(X9,succ(X1)) ) ) ) ),
inference(rectify,[],[f210]) ).
fof(f387,plain,
! [X0] :
( ( ! [X1] :
~ ( ! [X2] : singleton(X1) != X2
& in(X1,X0) )
& ! [X3,X4,X5] :
( ( singleton(X3) = X5
& singleton(X3) = X4
& in(X3,X0) )
=> X4 = X5 ) )
=> ? [X6] :
( ! [X7] :
( in(X7,X0)
=> singleton(X7) = apply(X6,X7) )
& relation_dom(X6) = X0
& function(X6)
& relation(X6) ) ),
inference(rectify,[],[f215]) ).
fof(f388,plain,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X3] :
( in(X3,X1)
=> in(powerset(X3),X1) )
& ! [X4,X5] :
( ( subset(X5,X4)
& in(X4,X1) )
=> in(X5,X1) )
& in(X0,X1) ),
inference(rectify,[],[f232]) ).
fof(f389,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X3] :
~ ( in(X3,X1)
& in(X3,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f305]) ).
fof(f390,plain,
! [X0] :
( ordinal(X0)
=> ( ~ ( being_limit_ordinal(X0)
& ? [X1] :
( succ(X1) = X0
& ordinal(X1) ) )
& ~ ( ! [X2] :
( ordinal(X2)
=> succ(X2) != X0 )
& ~ being_limit_ordinal(X0) ) ) ),
inference(rectify,[],[f309]) ).
fof(f391,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f325]) ).
fof(f392,plain,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X3] :
~ ( ! [X4] :
~ ( ! [X5] :
( subset(X5,X3)
=> in(X5,X4) )
& in(X4,X1) )
& in(X3,X1) )
& ! [X6,X7] :
( ( subset(X7,X6)
& in(X6,X1) )
=> in(X7,X1) )
& in(X0,X1) ),
inference(rectify,[],[f371]) ).
fof(f393,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f76]) ).
fof(f394,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f395,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f396,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f398,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f399,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f6]) ).
fof(f400,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f401,plain,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f400]) ).
fof(f404,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f405,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f406,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f405]) ).
fof(f407,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f408,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_dom_restriction(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f409,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f410,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f409]) ).
fof(f411,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) )
| ~ relation(X2) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f412,plain,
! [X0] :
( ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f413,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f414,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f413]) ).
fof(f415,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f416,plain,
! [X0] :
( ! [X1,X2] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f417,plain,
! [X0] :
( ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f418,plain,
! [X0] :
( ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f419,plain,
! [X0,X1,X2,X3] :
( unordered_triple(X0,X1,X2) = X3
<=> ! [X4] :
( in(X4,X3)
<=> ( X2 = X4
| X1 = X4
| X0 = X4 ) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f420,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f421,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) ) ),
inference(flattening,[],[f420]) ).
fof(f422,plain,
! [X0] :
( ! [X3] :
( pair_first(X0) = X3
<=> ! [X4,X5] :
( X3 = X4
| ordered_pair(X4,X5) != X0 ) )
| ! [X1,X2] : ordered_pair(X1,X2) != X0 ),
inference(ennf_transformation,[],[f373]) ).
fof(f423,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f424,plain,
! [X0] :
( ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f425,plain,
! [X0,X1] :
( ( ( set_meet(X0) = X1
<=> empty_set = X1 )
| empty_set != X0 )
& ( ( set_meet(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) )
| empty_set = X0 ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f426,plain,
! [X0] :
( ! [X1,X2] :
( fiber(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(ordered_pair(X3,X1),X0)
& X1 != X3 ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f427,plain,
! [X0,X1] :
( ( inclusion_relation(X0) = X1
<=> ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) )
| ~ in(X3,X0)
| ~ in(X2,X0) )
& relation_field(X1) = X0 ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f428,plain,
! [X0,X1] :
( ( inclusion_relation(X0) = X1
<=> ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) )
| ~ in(X3,X0)
| ~ in(X2,X0) )
& relation_field(X1) = X0 ) )
| ~ relation(X1) ),
inference(flattening,[],[f427]) ).
fof(f429,plain,
! [X0] :
( ! [X3] :
( pair_second(X0) = X3
<=> ! [X4,X5] :
( X3 = X5
| ordered_pair(X4,X5) != X0 ) )
| ! [X1,X2] : ordered_pair(X1,X2) != X0 ),
inference(ennf_transformation,[],[f374]) ).
fof(f430,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f431,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f432,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) )
& ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f433,plain,
! [X0] :
( ( well_founded_relation(X0)
<=> ! [X1] :
( ? [X2] :
( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
| empty_set = X1
| ~ subset(X1,relation_field(X0)) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f434,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f46]) ).
fof(f435,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f436,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f437,plain,
! [X0] :
( ! [X1] :
( is_well_founded_in(X0,X1)
<=> ! [X2] :
( ? [X3] :
( disjoint(fiber(X0,X3),X2)
& in(X3,X2) )
| empty_set = X2
| ~ subset(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f438,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f439,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f438]) ).
fof(f440,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f441,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f442,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(flattening,[],[f441]) ).
fof(f443,plain,
! [X0] :
( ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f444,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f60]) ).
fof(f445,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f444]) ).
fof(f446,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f447,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f62]) ).
fof(f448,plain,
! [X0] :
( ! [X1] :
( well_orders(X0,X1)
<=> ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f449,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f66]) ).
fof(f450,plain,
! [X0] :
( ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f451,plain,
! [X0] :
( ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f452,plain,
! [X0] :
( ! [X1] :
( ( relation_inverse(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f453,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( relation_isomorphism(X0,X1,X2)
<=> ( ! [X3,X4] :
( in(ordered_pair(X3,X4),X0)
<=> ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& one_to_one(X2)
& relation_field(X1) = relation_rng(X2)
& relation_field(X0) = relation_dom(X2) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f454,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( relation_isomorphism(X0,X1,X2)
<=> ( ! [X3,X4] :
( in(ordered_pair(X3,X4),X0)
<=> ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& one_to_one(X2)
& relation_field(X1) = relation_rng(X2)
& relation_field(X0) = relation_dom(X2) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f453]) ).
fof(f455,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f72]) ).
fof(f456,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f455]) ).
fof(f457,plain,
! [X0] :
( ! [X1] :
( ! [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) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f458,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f74]) ).
fof(f459,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(flattening,[],[f458]) ).
fof(f460,plain,
! [X0,X1] :
( ! [X2] :
( ( complements_of_subsets(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) )
| ~ element(X3,powerset(X0)) ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f75]) ).
fof(f461,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f393]) ).
fof(f462,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(flattening,[],[f461]) ).
fof(f463,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f464,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f463]) ).
fof(f465,plain,
! [X0] :
( ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f466,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f91]) ).
fof(f467,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f466]) ).
fof(f468,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f96]) ).
fof(f469,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f100]) ).
fof(f470,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f103]) ).
fof(f471,plain,
! [X0,X1,X2] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f104]) ).
fof(f472,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f107]) ).
fof(f473,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f472]) ).
fof(f474,plain,
! [X0,X1,X2] :
( element(relation_rng_as_subset(X0,X1,X2),powerset(X1))
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f108]) ).
fof(f475,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f109]) ).
fof(f476,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f111]) ).
fof(f477,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f112]) ).
fof(f478,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f477]) ).
fof(f479,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f113]) ).
fof(f480,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f114]) ).
fof(f481,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f115]) ).
fof(f482,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f119]) ).
fof(f483,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f123]) ).
fof(f484,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f483]) ).
fof(f485,plain,
! [X0] :
( ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f124]) ).
fof(f486,plain,
! [X0,X1] :
( ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f126]) ).
fof(f487,plain,
! [X0,X1] :
( ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(flattening,[],[f486]) ).
fof(f488,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f127]) ).
fof(f489,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f488]) ).
fof(f490,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f129]) ).
fof(f491,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f490]) ).
fof(f492,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f135]) ).
fof(f493,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f492]) ).
fof(f494,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f137]) ).
fof(f495,plain,
! [X0] :
( ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f138]) ).
fof(f496,plain,
! [X0] :
( ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f495]) ).
fof(f497,plain,
! [X0] :
( ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f139]) ).
fof(f498,plain,
! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f140]) ).
fof(f499,plain,
! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f498]) ).
fof(f500,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f142]) ).
fof(f501,plain,
! [X0,X1] :
( ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f143]) ).
fof(f502,plain,
! [X0,X1] :
( ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f501]) ).
fof(f503,plain,
! [X0] :
( ( ordinal(union(X0))
& epsilon_connected(union(X0))
& epsilon_transitive(union(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f144]) ).
fof(f504,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f146]) ).
fof(f505,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f504]) ).
fof(f506,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f147]) ).
fof(f507,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f506]) ).
fof(f508,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f148]) ).
fof(f509,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f508]) ).
fof(f510,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f149]) ).
fof(f511,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f510]) ).
fof(f512,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f150]) ).
fof(f513,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f151]) ).
fof(f514,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f152]) ).
fof(f515,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f514]) ).
fof(f516,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f155]) ).
fof(f517,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(ennf_transformation,[],[f156]) ).
fof(f518,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f157]) ).
fof(f519,plain,
! [X0] :
( ( reflexive(X0)
<=> ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f159]) ).
fof(f521,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f162]) ).
fof(f522,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f163]) ).
fof(f523,plain,
! [X0,X1] :
( subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f164]) ).
fof(f524,plain,
! [X0] :
( ( transitive(X0)
<=> ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f165]) ).
fof(f525,plain,
! [X0] :
( ( transitive(X0)
<=> ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f524]) ).
fof(f526,plain,
! [X0,X1] :
( ? [X2] :
( well_orders(X2,X0)
& relation(X2) )
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f167]) ).
fof(f527,plain,
! [X0,X1] :
( ? [X2] :
( well_orders(X2,X0)
& relation(X2) )
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(flattening,[],[f526]) ).
fof(f528,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f169]) ).
fof(f529,plain,
! [X0] :
( ( antisymmetric(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f170]) ).
fof(f530,plain,
! [X0] :
( ( antisymmetric(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f529]) ).
fof(f531,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f171]) ).
fof(f532,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f531]) ).
fof(f533,plain,
! [X0] :
( ( connected(X0)
<=> ! [X1,X2] :
( in(ordered_pair(X2,X1),X0)
| in(ordered_pair(X1,X2),X0)
| X1 = X2
| ~ in(X2,relation_field(X0))
| ~ in(X1,relation_field(X0)) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f172]) ).
fof(f535,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f176]) ).
fof(f538,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f181]) ).
fof(f539,plain,
! [X0,X1,X2] :
( relation_dom(X2) = relation_dom_as_subset(X0,X1,X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f192]) ).
fof(f540,plain,
! [X0,X1,X2] :
( relation_rng(X2) = relation_rng_as_subset(X0,X1,X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f193]) ).
fof(f541,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f194]) ).
fof(f542,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f195]) ).
fof(f543,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f196]) ).
fof(f544,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f543]) ).
fof(f545,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f198]) ).
fof(f546,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f545]) ).
fof(f547,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f200]) ).
fof(f548,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f547]) ).
fof(f549,plain,
! [X0] :
( ? [X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& function(X4)
& relation(X4) )
| ? [X1,X2,X3] :
( X2 != X3
& singleton(X1) = X3
& in(X1,X0)
& singleton(X1) = X2
& in(X1,X0) ) ),
inference(ennf_transformation,[],[f380]) ).
fof(f550,plain,
! [X0] :
( ? [X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& function(X4)
& relation(X4) )
| ? [X1,X2,X3] :
( X2 != X3
& singleton(X1) = X3
& in(X1,X0)
& singleton(X1) = X2
& in(X1,X0) ) ),
inference(flattening,[],[f549]) ).
fof(f551,plain,
! [X0] :
( ? [X2] :
( ! [X3] :
( ordinal_subset(X2,X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(X2,X0)
& ordinal(X2) )
| ! [X1] :
( ~ in(X1,X0)
| ~ ordinal(X1) ) ),
inference(ennf_transformation,[],[f381]) ).
fof(f552,plain,
! [X0] :
( ? [X2] :
( ! [X3] :
( ordinal_subset(X2,X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(X2,X0)
& ordinal(X2) )
| ! [X1] :
( ~ in(X1,X0)
| ~ ordinal(X1) ) ),
inference(flattening,[],[f551]) ).
fof(f553,plain,
! [X0,X1,X2] :
( ? [X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
& relation(X3) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f205]) ).
fof(f554,plain,
! [X0,X1,X2] :
( ? [X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
& relation(X3) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(flattening,[],[f553]) ).
fof(f555,plain,
! [X0] :
( ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( singleton(X6) = X5
& in(X6,X0)
& in(X6,X0) ) )
| ? [X1,X2,X3] :
( X2 != X3
& singleton(X1) = X3
& in(X1,X0)
& singleton(X1) = X2
& in(X1,X0) ) ),
inference(ennf_transformation,[],[f382]) ).
fof(f556,plain,
! [X0] :
( ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( singleton(X6) = X5
& in(X6,X0)
& in(X6,X0) ) )
| ? [X1,X2,X3] :
( X2 != X3
& singleton(X1) = X3
& in(X1,X0)
& singleton(X1) = X2
& in(X1,X0) ) ),
inference(flattening,[],[f555]) ).
fof(f557,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) )
| ? [X2,X3,X4] :
( X3 != X4
& ? [X5,X6] :
( singleton(X5) = X6
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& X2 = X4
& ? [X7,X8] :
( singleton(X7) = X8
& in(X7,X0)
& ordered_pair(X7,X8) = X3 )
& X2 = X3 ) ),
inference(ennf_transformation,[],[f383]) ).
fof(f558,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) )
| ? [X2,X3,X4] :
( X3 != X4
& ? [X5,X6] :
( singleton(X5) = X6
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& X2 = X4
& ? [X7,X8] :
( singleton(X7) = X8
& in(X7,X0)
& ordered_pair(X7,X8) = X3 )
& X2 = X3 ) ),
inference(flattening,[],[f557]) ).
fof(f559,plain,
! [X0,X1,X2] :
( ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) ) )
| ? [X3,X4,X5] :
( X4 != X5
& ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& ordered_pair(X8,X9) = X4 )
& X3 = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f384]) ).
fof(f560,plain,
! [X0,X1,X2] :
( ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) ) )
| ? [X3,X4,X5] :
( X4 != X5
& ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& ordered_pair(X8,X9) = X4 )
& X3 = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(flattening,[],[f559]) ).
fof(f561,plain,
! [X0] :
( ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( ordinal(X5)
& X5 = X6
& in(X6,X0) ) )
| ? [X1,X2,X3] :
( X2 != X3
& ordinal(X3)
& X1 = X3
& ordinal(X2)
& X1 = X2 ) ),
inference(ennf_transformation,[],[f385]) ).
fof(f562,plain,
! [X0] :
( ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( ordinal(X5)
& X5 = X6
& in(X6,X0) ) )
| ? [X1,X2,X3] :
( X2 != X3
& ordinal(X3)
& X1 = X3
& ordinal(X2)
& X1 = X2 ) ),
inference(flattening,[],[f561]) ).
fof(f563,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( in(X10,X0)
& X8 = X10
& ordinal(X10) )
& X8 = X9
& in(X9,succ(X1)) ) )
| ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( in(X5,X0)
& X4 = X5
& ordinal(X5) )
& X2 = X4
& ? [X6] :
( in(X6,X0)
& X3 = X6
& ordinal(X6) )
& X2 = X3 )
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f386]) ).
fof(f564,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( in(X10,X0)
& X8 = X10
& ordinal(X10) )
& X8 = X9
& in(X9,succ(X1)) ) )
| ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( in(X5,X0)
& X4 = X5
& ordinal(X5) )
& X2 = X4
& ? [X6] :
( in(X6,X0)
& X3 = X6
& ordinal(X6) )
& X2 = X3 )
| ~ ordinal(X1) ),
inference(flattening,[],[f563]) ).
fof(f565,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X0)) ) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f212]) ).
fof(f566,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X0)) ) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(flattening,[],[f565]) ).
fof(f567,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( in(X4,X0)
& X3 = X4
& ordinal(X4) )
& in(X3,succ(X1)) ) )
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f214]) ).
fof(f568,plain,
! [X0] :
( ? [X6] :
( ! [X7] :
( singleton(X7) = apply(X6,X7)
| ~ in(X7,X0) )
& relation_dom(X6) = X0
& function(X6)
& relation(X6) )
| ? [X1] :
( ! [X2] : singleton(X1) != X2
& in(X1,X0) )
| ? [X3,X4,X5] :
( X4 != X5
& singleton(X3) = X5
& singleton(X3) = X4
& in(X3,X0) ) ),
inference(ennf_transformation,[],[f387]) ).
fof(f569,plain,
! [X0] :
( ? [X6] :
( ! [X7] :
( singleton(X7) = apply(X6,X7)
| ~ in(X7,X0) )
& relation_dom(X6) = X0
& function(X6)
& relation(X6) )
| ? [X1] :
( ! [X2] : singleton(X1) != X2
& in(X1,X0) )
| ? [X3,X4,X5] :
( X4 != X5
& singleton(X3) = X5
& singleton(X3) = X4
& in(X3,X0) ) ),
inference(flattening,[],[f568]) ).
fof(f570,plain,
? [X0] :
! [X1] :
( ? [X2] :
( singleton(X2) != apply(X1,X2)
& in(X2,X0) )
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f217]) ).
fof(f571,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f218]) ).
fof(f572,plain,
! [X0,X1] :
( equipotent(X1,X0)
| ~ equipotent(X0,X1) ),
inference(ennf_transformation,[],[f219]) ).
fof(f573,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f222]) ).
fof(f574,plain,
! [X0,X1,X2] :
( ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f223]) ).
fof(f575,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f224]) ).
fof(f576,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f225]) ).
fof(f577,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f226]) ).
fof(f578,plain,
! [X0,X1,X2] :
( ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f227]) ).
fof(f579,plain,
! [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f228]) ).
fof(f580,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f229]) ).
fof(f581,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(flattening,[],[f580]) ).
fof(f582,plain,
! [X0,X1,X2] :
( ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f230]) ).
fof(f583,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f231]) ).
fof(f584,plain,
! [X0] :
? [X1] :
( ! [X2] :
( in(X2,X1)
| are_equipotent(X2,X1)
| ~ subset(X2,X1) )
& ! [X3] :
( in(powerset(X3),X1)
| ~ in(X3,X1) )
& ! [X4,X5] :
( in(X5,X1)
| ~ subset(X5,X4)
| ~ in(X4,X1) )
& in(X0,X1) ),
inference(ennf_transformation,[],[f388]) ).
fof(f585,plain,
! [X0] :
? [X1] :
( ! [X2] :
( in(X2,X1)
| are_equipotent(X2,X1)
| ~ subset(X2,X1) )
& ! [X3] :
( in(powerset(X3),X1)
| ~ in(X3,X1) )
& ! [X4,X5] :
( in(X5,X1)
| ~ subset(X5,X4)
| ~ in(X4,X1) )
& in(X0,X1) ),
inference(flattening,[],[f584]) ).
fof(f586,plain,
! [X0,X1,X2] :
( relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1))
| ~ relation(X2) ),
inference(ennf_transformation,[],[f233]) ).
fof(f587,plain,
! [X0,X1,X2] :
( ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f234]) ).
fof(f588,plain,
! [X0,X1] :
( subset(relation_image(X1,X0),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f235]) ).
fof(f589,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f236]) ).
fof(f590,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f589]) ).
fof(f591,plain,
! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f237]) ).
fof(f592,plain,
! [X0,X1] :
( subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
| ~ subset(X0,relation_dom(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f238]) ).
fof(f593,plain,
! [X0,X1] :
( subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
| ~ subset(X0,relation_dom(X1))
| ~ relation(X1) ),
inference(flattening,[],[f592]) ).
fof(f594,plain,
! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f239]) ).
fof(f595,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f240]) ).
fof(f596,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f595]) ).
fof(f597,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(relation_rng(X3),X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(ennf_transformation,[],[f241]) ).
fof(f598,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(relation_rng(X3),X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(flattening,[],[f597]) ).
fof(f599,plain,
! [X0] :
( ! [X1] :
( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f242]) ).
fof(f600,plain,
! [X0,X1,X2] :
( ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f243]) ).
fof(f601,plain,
! [X0,X1] :
( subset(relation_inverse_image(X1,X0),relation_dom(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f244]) ).
fof(f602,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(X0,X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(ennf_transformation,[],[f245]) ).
fof(f603,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(X0,X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(flattening,[],[f602]) ).
fof(f604,plain,
! [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f246]) ).
fof(f605,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) ),
inference(ennf_transformation,[],[f247]) ).
fof(f606,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) ),
inference(flattening,[],[f605]) ).
fof(f607,plain,
! [X0,X1,X2] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f248]) ).
fof(f608,plain,
! [X0,X1,X2] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(flattening,[],[f607]) ).
fof(f609,plain,
! [X0,X1] :
( relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f249]) ).
fof(f610,plain,
! [X0,X1] :
( relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f251]) ).
fof(f611,plain,
! [X0,X1,X2] :
( ( in(X0,X1)
& in(X0,relation_field(X2)) )
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(ennf_transformation,[],[f252]) ).
fof(f612,plain,
! [X0,X1,X2] :
( ( in(X0,X1)
& in(X0,relation_field(X2)) )
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(flattening,[],[f611]) ).
fof(f613,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f253]) ).
fof(f614,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f613]) ).
fof(f615,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f255]) ).
fof(f616,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f256]) ).
fof(f617,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f616]) ).
fof(f618,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f258]) ).
fof(f619,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f618]) ).
fof(f620,plain,
! [X0,X1] :
( ( subset(relation_field(relation_restriction(X1,X0)),X0)
& subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f259]) ).
fof(f621,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f260]) ).
fof(f622,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f621]) ).
fof(f623,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f261]) ).
fof(f624,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f623]) ).
fof(f625,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f262]) ).
fof(f626,plain,
! [X0,X1,X2] :
( subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1))
| ~ relation(X2) ),
inference(ennf_transformation,[],[f263]) ).
fof(f627,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f264]) ).
fof(f628,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f627]) ).
fof(f629,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] : in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1) )
<=> relation_dom_as_subset(X1,X0,X2) = X1 )
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(ennf_transformation,[],[f265]) ).
fof(f630,plain,
! [X0,X1] :
( reflexive(relation_restriction(X1,X0))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f266]) ).
fof(f631,plain,
! [X0,X1] :
( reflexive(relation_restriction(X1,X0))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(flattening,[],[f630]) ).
fof(f632,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f267]) ).
fof(f633,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f632]) ).
fof(f634,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f268]) ).
fof(f635,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(flattening,[],[f634]) ).
fof(f636,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] : in(ordered_pair(X4,X3),X2)
| ~ in(X3,X1) )
<=> relation_rng_as_subset(X0,X1,X2) = X1 )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f269]) ).
fof(f637,plain,
! [X0,X1] :
( connected(relation_restriction(X1,X0))
| ~ connected(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f270]) ).
fof(f638,plain,
! [X0,X1] :
( connected(relation_restriction(X1,X0))
| ~ connected(X1)
| ~ relation(X1) ),
inference(flattening,[],[f637]) ).
fof(f639,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f271]) ).
fof(f640,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f639]) ).
fof(f641,plain,
! [X0,X1] :
( transitive(relation_restriction(X1,X0))
| ~ transitive(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f272]) ).
fof(f642,plain,
! [X0,X1] :
( transitive(relation_restriction(X1,X0))
| ~ transitive(X1)
| ~ relation(X1) ),
inference(flattening,[],[f641]) ).
fof(f643,plain,
! [X0] :
( ! [X1] :
( ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) )
| ~ subset(X0,X1)
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f273]) ).
fof(f644,plain,
! [X0] :
( ! [X1] :
( ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) )
| ~ subset(X0,X1)
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f643]) ).
fof(f645,plain,
! [X0,X1] :
( antisymmetric(relation_restriction(X1,X0))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f274]) ).
fof(f646,plain,
! [X0,X1] :
( antisymmetric(relation_restriction(X1,X0))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(flattening,[],[f645]) ).
fof(f647,plain,
! [X0,X1] :
( ( well_ordering(relation_restriction(X1,X0))
& relation_field(relation_restriction(X1,X0)) = X0 )
| ~ well_orders(X1,X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f275]) ).
fof(f648,plain,
! [X0,X1] :
( ( well_ordering(relation_restriction(X1,X0))
& relation_field(relation_restriction(X1,X0)) = X0 )
| ~ well_orders(X1,X0)
| ~ relation(X1) ),
inference(flattening,[],[f647]) ).
fof(f649,plain,
! [X0,X1,X2] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f276]) ).
fof(f650,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f277]) ).
fof(f651,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f279]) ).
fof(f652,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f651]) ).
fof(f653,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f280]) ).
fof(f654,plain,
! [X0,X1,X2] :
( ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f283]) ).
fof(f655,plain,
! [X0,X1,X2] :
( ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f654]) ).
fof(f656,plain,
! [X0] :
( ordinal(X0)
| ? [X1] :
( ( ~ subset(X1,X0)
| ~ ordinal(X1) )
& in(X1,X0) ) ),
inference(ennf_transformation,[],[f284]) ).
fof(f657,plain,
! [X0,X1] :
( well_founded_relation(relation_restriction(X1,X0))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f285]) ).
fof(f658,plain,
! [X0,X1] :
( well_founded_relation(relation_restriction(X1,X0))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(flattening,[],[f657]) ).
fof(f659,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ordinal_subset(X2,X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(X2,X0)
& ordinal(X2) )
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f286]) ).
fof(f660,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ordinal_subset(X2,X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(X2,X0)
& ordinal(X2) )
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(flattening,[],[f659]) ).
fof(f661,plain,
! [X0,X1] :
( well_ordering(relation_restriction(X1,X0))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f287]) ).
fof(f662,plain,
! [X0,X1] :
( well_ordering(relation_restriction(X1,X0))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(flattening,[],[f661]) ).
fof(f663,plain,
! [X0] :
( ! [X1] :
( ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) )
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f288]) ).
fof(f664,plain,
! [X0,X1,X2] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f289]) ).
fof(f665,plain,
! [X0,X1,X2,X3] :
( ( X1 = X3
& X0 = X2 )
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(ennf_transformation,[],[f290]) ).
fof(f666,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f291]) ).
fof(f667,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f666]) ).
fof(f668,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f292]) ).
fof(f669,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f294]) ).
fof(f670,plain,
! [X0,X1] :
( relation_field(relation_restriction(X1,X0)) = X0
| ~ subset(X0,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f298]) ).
fof(f671,plain,
! [X0,X1] :
( relation_field(relation_restriction(X1,X0)) = X0
| ~ subset(X0,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(flattening,[],[f670]) ).
fof(f672,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f302]) ).
fof(f673,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f389]) ).
fof(f674,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f306]) ).
fof(f675,plain,
! [X0] :
( ( being_limit_ordinal(X0)
<=> ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) ) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f308]) ).
fof(f676,plain,
! [X0] :
( ( being_limit_ordinal(X0)
<=> ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) ) )
| ~ ordinal(X0) ),
inference(flattening,[],[f675]) ).
fof(f677,plain,
! [X0] :
( ( ( ~ being_limit_ordinal(X0)
| ! [X1] :
( succ(X1) != X0
| ~ ordinal(X1) ) )
& ( ? [X2] :
( succ(X2) = X0
& ordinal(X2) )
| being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f390]) ).
fof(f678,plain,
! [X0,X1] :
( ! [X2] :
( ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) )
| ~ element(X2,powerset(X0)) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f310]) ).
fof(f679,plain,
! [X0] :
( ! [X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f311]) ).
fof(f680,plain,
! [X0] :
( ! [X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f312]) ).
fof(f681,plain,
! [X0,X1] :
( set_union2(X0,set_difference(X1,X0)) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f313]) ).
fof(f682,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f314]) ).
fof(f683,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f682]) ).
fof(f684,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f315]) ).
fof(f685,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f684]) ).
fof(f686,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f316]) ).
fof(f687,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f317]) ).
fof(f688,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f687]) ).
fof(f689,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f318]) ).
fof(f690,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f689]) ).
fof(f691,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f319]) ).
fof(f692,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f691]) ).
fof(f693,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_isomorphism(X1,X0,function_inverse(X2))
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f321]) ).
fof(f694,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_isomorphism(X1,X0,function_inverse(X2))
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f693]) ).
fof(f695,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f323]) ).
fof(f696,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f695]) ).
fof(f697,plain,
! [X0] :
( connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f324]) ).
fof(f698,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( ? [X3] : in(X3,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f391]) ).
fof(f699,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(ennf_transformation,[],[f326]) ).
fof(f700,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(flattening,[],[f699]) ).
fof(f701,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( well_founded_relation(X1)
| ~ well_founded_relation(X0) )
& ( antisymmetric(X1)
| ~ antisymmetric(X0) )
& ( connected(X1)
| ~ connected(X0) )
& ( transitive(X1)
| ~ transitive(X0) )
& ( reflexive(X1)
| ~ reflexive(X0) ) )
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f327]) ).
fof(f702,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( well_founded_relation(X1)
| ~ well_founded_relation(X0) )
& ( antisymmetric(X1)
| ~ antisymmetric(X0) )
& ( connected(X1)
| ~ connected(X0) )
& ( transitive(X1)
| ~ transitive(X0) )
& ( reflexive(X1)
| ~ reflexive(X0) ) )
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f701]) ).
fof(f703,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f328]) ).
fof(f704,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f703]) ).
fof(f705,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f329]) ).
fof(f706,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f705]) ).
fof(f707,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( well_ordering(X1)
| ~ relation_isomorphism(X0,X1,X2)
| ~ well_ordering(X0)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f330]) ).
fof(f708,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( well_ordering(X1)
| ~ relation_isomorphism(X0,X1,X2)
| ~ well_ordering(X0)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f707]) ).
fof(f709,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f331]) ).
fof(f710,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f709]) ).
fof(f711,plain,
! [X0] :
( empty_set = X0
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f332]) ).
fof(f712,plain,
! [X0] :
( empty_set = X0
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(flattening,[],[f711]) ).
fof(f713,plain,
! [X0,X1] :
( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
& apply(X1,apply(function_inverse(X1),X0)) = X0 )
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f333]) ).
fof(f714,plain,
! [X0,X1] :
( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
& apply(X1,apply(function_inverse(X1),X0)) = X0 )
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f713]) ).
fof(f715,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f334]) ).
fof(f716,plain,
! [X0] :
( ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f335]) ).
fof(f717,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f338]) ).
fof(f718,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f339]) ).
fof(f719,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f718]) ).
fof(f720,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f340]) ).
fof(f721,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f720]) ).
fof(f722,plain,
! [X0] :
( empty_set = X0
| ( empty_set != relation_rng(X0)
& relation_dom(X0) != empty_set )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f341]) ).
fof(f723,plain,
! [X0] :
( empty_set = X0
| ( empty_set != relation_rng(X0)
& relation_dom(X0) != empty_set )
| ~ relation(X0) ),
inference(flattening,[],[f722]) ).
fof(f724,plain,
! [X0] :
( ( relation_dom(X0) = empty_set
<=> empty_set = relation_rng(X0) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f342]) ).
fof(f725,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f344]) ).
fof(f726,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_dom_restriction(X2,X0) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f725]) ).
fof(f727,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f346]) ).
fof(f728,plain,
! [X0] :
( well_founded_relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f347]) ).
fof(f729,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f348]) ).
fof(f730,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ~ function(X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f349]) ).
fof(f731,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f730]) ).
fof(f732,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f351]) ).
fof(f733,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f732]) ).
fof(f734,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) )
| ~ relation(X3) ),
inference(ennf_transformation,[],[f352]) ).
fof(f735,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f353]) ).
fof(f736,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ in(X3,X2)
| ~ in(X3,X1) )
& in(X2,X1) )
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f355]) ).
fof(f737,plain,
! [X0] :
( well_ordering(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f356]) ).
fof(f738,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f359]) ).
fof(f739,plain,
! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f360]) ).
fof(f740,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f361]) ).
fof(f741,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f362]) ).
fof(f742,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<=> ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f741]) ).
fof(f743,plain,
! [X0] :
( ( well_orders(X0,relation_field(X0))
<=> well_ordering(X0) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f363]) ).
fof(f744,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f364]) ).
fof(f745,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f744]) ).
fof(f746,plain,
! [X0,X1,X2] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f365]) ).
fof(f747,plain,
! [X0,X1] :
( set_intersection2(relation_dom(X1),X0) = relation_dom(relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f366]) ).
fof(f748,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f367]) ).
fof(f749,plain,
! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f368]) ).
fof(f750,plain,
! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f369]) ).
fof(f751,plain,
! [X0] :
? [X1] :
( ! [X2] :
( in(X2,X1)
| are_equipotent(X2,X1)
| ~ subset(X2,X1) )
& ! [X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,X1) )
| ~ in(X3,X1) )
& ! [X6,X7] :
( in(X7,X1)
| ~ subset(X7,X6)
| ~ in(X6,X1) )
& in(X0,X1) ),
inference(ennf_transformation,[],[f392]) ).
fof(f752,plain,
! [X0] :
? [X1] :
( ! [X2] :
( in(X2,X1)
| are_equipotent(X2,X1)
| ~ subset(X2,X1) )
& ! [X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,X1) )
| ~ in(X3,X1) )
& ! [X6,X7] :
( in(X7,X1)
| ~ subset(X7,X6)
| ~ in(X6,X1) )
& in(X0,X1) ),
inference(flattening,[],[f751]) ).
fof(f753,plain,
! [X0,X1,X2] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f372]) ).
fof(f754,plain,
! [X1,X2,X0] :
( sP0(X1,X2,X0)
<=> ( ! [X3,X4] :
( in(ordered_pair(X3,X4),X0)
<=> ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& one_to_one(X2)
& relation_field(X1) = relation_rng(X2)
& relation_field(X0) = relation_dom(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f755,plain,
! [X0,X2,X1] :
( ( relation_isomorphism(X0,X1,X2)
<=> sP0(X1,X2,X0) )
| ~ sP1(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f756,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sP1(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(definition_folding,[],[f454,f755,f754]) ).
fof(f757,plain,
! [X0] :
( ? [X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& function(X4)
& relation(X4) )
| ~ sP2(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f758,plain,
! [X0] :
( sP2(X0)
| ? [X1,X2,X3] :
( X2 != X3
& singleton(X1) = X3
& in(X1,X0)
& singleton(X1) = X2
& in(X1,X0) ) ),
inference(definition_folding,[],[f550,f757]) ).
fof(f759,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& singleton(X1) = X3
& in(X1,X0)
& singleton(X1) = X2
& in(X1,X0) )
| ~ sP3(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f760,plain,
! [X0] :
( ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( singleton(X6) = X5
& in(X6,X0)
& in(X6,X0) ) )
| sP3(X0) ),
inference(definition_folding,[],[f556,f759]) ).
fof(f761,plain,
! [X0,X3] :
( ? [X7,X8] :
( singleton(X7) = X8
& in(X7,X0)
& ordered_pair(X7,X8) = X3 )
| ~ sP4(X0,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f762,plain,
! [X0] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5,X6] :
( singleton(X5) = X6
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& X2 = X4
& sP4(X0,X3)
& X2 = X3 )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f763,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) )
| sP5(X0) ),
inference(definition_folding,[],[f558,f762,f761]) ).
fof(f764,plain,
! [X1,X2] :
( ? [X3,X4,X5] :
( X4 != X5
& ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& ordered_pair(X8,X9) = X4 )
& X3 = X4 )
| ~ sP6(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f765,plain,
! [X0,X1,X2] :
( ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) ) )
| sP6(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_folding,[],[f560,f764]) ).
fof(f766,plain,
( ? [X1,X2,X3] :
( X2 != X3
& ordinal(X3)
& X1 = X3
& ordinal(X2)
& X1 = X2 )
| ~ sP7 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f767,plain,
! [X0] :
( ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( ordinal(X5)
& X5 = X6
& in(X6,X0) ) )
| sP7 ),
inference(definition_folding,[],[f562,f766]) ).
fof(f768,plain,
! [X0,X3] :
( ? [X6] :
( in(X6,X0)
& X3 = X6
& ordinal(X6) )
| ~ sP8(X0,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f769,plain,
! [X0] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( in(X5,X0)
& X4 = X5
& ordinal(X5) )
& X2 = X4
& sP8(X0,X3)
& X2 = X3 )
| ~ sP9(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f770,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( in(X10,X0)
& X8 = X10
& ordinal(X10) )
& X8 = X9
& in(X9,succ(X1)) ) )
| sP9(X0)
| ~ ordinal(X1) ),
inference(definition_folding,[],[f564,f769,f768]) ).
fof(f771,plain,
! [X0] :
( ? [X3,X4,X5] :
( X4 != X5
& singleton(X3) = X5
& singleton(X3) = X4
& in(X3,X0) )
| ~ sP10(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f772,plain,
! [X0] :
( ? [X6] :
( ! [X7] :
( singleton(X7) = apply(X6,X7)
| ~ in(X7,X0) )
& relation_dom(X6) = X0
& function(X6)
& relation(X6) )
| ? [X1] :
( ! [X2] : singleton(X1) != X2
& in(X1,X0) )
| sP10(X0) ),
inference(definition_folding,[],[f569,f771]) ).
fof(f773,plain,
! [X2,X3,X0,X1] :
( sP11(X2,X3,X0,X1)
<=> ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f774,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP11(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f704,f773]) ).
fof(f775,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),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) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f407]) ).
fof(f776,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),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) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(flattening,[],[f775]) ).
fof(f777,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),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) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(rectify,[],[f776]) ).
fof(f778,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) )
=> ( ( sK12(X0,X1) != sK13(X0,X1)
| ~ in(sK12(X0,X1),X0)
| ~ in(ordered_pair(sK12(X0,X1),sK13(X0,X1)),X1) )
& ( ( sK12(X0,X1) = sK13(X0,X1)
& in(sK12(X0,X1),X0) )
| in(ordered_pair(sK12(X0,X1),sK13(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f779,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ( ( sK12(X0,X1) != sK13(X0,X1)
| ~ in(sK12(X0,X1),X0)
| ~ in(ordered_pair(sK12(X0,X1),sK13(X0,X1)),X1) )
& ( ( sK12(X0,X1) = sK13(X0,X1)
& in(sK12(X0,X1),X0) )
| in(ordered_pair(sK12(X0,X1),sK13(X0,X1)),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) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f777,f778]) ).
fof(f780,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f781,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f780]) ).
fof(f782,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relation_dom_restriction(X0,X1) = X2
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( 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),X0)
& in(X3,X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f408]) ).
fof(f783,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relation_dom_restriction(X0,X1) = X2
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( 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),X0)
& in(X3,X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(flattening,[],[f782]) ).
fof(f784,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relation_dom_restriction(X0,X1) = X2
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| in(ordered_pair(X3,X4),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) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(rectify,[],[f783]) ).
fof(f785,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ~ in(ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),X0)
| ~ in(sK14(X0,X1,X2),X1)
| ~ in(ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),X0)
& in(sK14(X0,X1,X2),X1) )
| in(ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f786,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relation_dom_restriction(X0,X1) = X2
| ( ( ~ in(ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),X0)
| ~ in(sK14(X0,X1,X2),X1)
| ~ in(ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),X0)
& in(sK14(X0,X1,X2),X1) )
| in(ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),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) ) )
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f784,f785]) ).
fof(f787,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(X3,X2) )
& ( ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) )
& ( ? [X4] :
( apply(X0,X4) = X3
& in(X4,X1)
& in(X4,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f410]) ).
fof(f788,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(X3,X2) )
& ( ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) ) )
& ( ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f787]) ).
fof(f789,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(X3,X2) )
& ( ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( apply(X0,X4) != sK16(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(sK16(X0,X1,X2),X2) )
& ( ? [X5] :
( apply(X0,X5) = sK16(X0,X1,X2)
& in(X5,X1)
& in(X5,relation_dom(X0)) )
| in(sK16(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f790,plain,
! [X0,X1,X2] :
( ? [X5] :
( apply(X0,X5) = sK16(X0,X1,X2)
& in(X5,X1)
& in(X5,relation_dom(X0)) )
=> ( sK16(X0,X1,X2) = apply(X0,sK17(X0,X1,X2))
& in(sK17(X0,X1,X2),X1)
& in(sK17(X0,X1,X2),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f791,plain,
! [X0,X1,X6] :
( ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) )
=> ( apply(X0,sK18(X0,X1,X6)) = X6
& in(sK18(X0,X1,X6),X1)
& in(sK18(X0,X1,X6),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f792,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ( ( ! [X4] :
( apply(X0,X4) != sK16(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| ~ in(sK16(X0,X1,X2),X2) )
& ( ( sK16(X0,X1,X2) = apply(X0,sK17(X0,X1,X2))
& in(sK17(X0,X1,X2),X1)
& in(sK17(X0,X1,X2),relation_dom(X0)) )
| in(sK16(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) ) )
& ( ( apply(X0,sK18(X0,X1,X6)) = X6
& in(sK18(X0,X1,X6),X1)
& in(sK18(X0,X1,X6),relation_dom(X0)) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18])],[f788,f791,f790,f789]) ).
fof(f793,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X1) = X2
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( 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),X1)
& in(X4,X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f411]) ).
fof(f794,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X1) = X2
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( 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),X1)
& in(X4,X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) ),
inference(flattening,[],[f793]) ).
fof(f795,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X1) = X2
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) )
| in(ordered_pair(X3,X4),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) ) )
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) ),
inference(rectify,[],[f794]) ).
fof(f796,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ~ in(ordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),X1)
| ~ in(sK20(X0,X1,X2),X0)
| ~ in(ordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),X1)
& in(sK20(X0,X1,X2),X0) )
| in(ordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f797,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X1) = X2
| ( ( ~ in(ordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),X1)
| ~ in(sK20(X0,X1,X2),X0)
| ~ in(ordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),X1)
& in(sK20(X0,X1,X2),X0) )
| in(ordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),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) ) )
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f795,f796]) ).
fof(f798,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0)) )
& ( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f412]) ).
fof(f799,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( 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(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f414]) ).
fof(f800,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( 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(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f799]) ).
fof(f801,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,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) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f800]) ).
fof(f802,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X2) )
& ( ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) )
| in(X3,X2) ) )
=> ( ( ~ in(apply(X0,sK21(X0,X1,X2)),X1)
| ~ in(sK21(X0,X1,X2),relation_dom(X0))
| ~ in(sK21(X0,X1,X2),X2) )
& ( ( in(apply(X0,sK21(X0,X1,X2)),X1)
& in(sK21(X0,X1,X2),relation_dom(X0)) )
| in(sK21(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f803,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ( ( ~ in(apply(X0,sK21(X0,X1,X2)),X1)
| ~ in(sK21(X0,X1,X2),relation_dom(X0))
| ~ in(sK21(X0,X1,X2),X2) )
& ( ( in(apply(X0,sK21(X0,X1,X2)),X1)
& in(sK21(X0,X1,X2),relation_dom(X0)) )
| in(sK21(X0,X1,X2),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) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f801,f802]) ).
fof(f804,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [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) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f415]) ).
fof(f805,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) ) )
& ( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f804]) ).
fof(f806,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK22(X0,X1,X2)),X0) )
| ~ in(sK22(X0,X1,X2),X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,sK22(X0,X1,X2)),X0) )
| in(sK22(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f807,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,sK22(X0,X1,X2)),X0) )
=> ( in(sK23(X0,X1,X2),X1)
& in(ordered_pair(sK23(X0,X1,X2),sK22(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f808,plain,
! [X0,X1,X6] :
( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) )
=> ( in(sK24(X0,X1,X6),X1)
& in(ordered_pair(sK24(X0,X1,X6),X6),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f809,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK22(X0,X1,X2)),X0) )
| ~ in(sK22(X0,X1,X2),X2) )
& ( ( in(sK23(X0,X1,X2),X1)
& in(ordered_pair(sK23(X0,X1,X2),sK22(X0,X1,X2)),X0) )
| in(sK22(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) ) )
& ( ( in(sK24(X0,X1,X6),X1)
& in(ordered_pair(sK24(X0,X1,X6),X6),X0) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24])],[f805,f808,f807,f806]) ).
fof(f810,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ in(X3,X2) )
& ( ? [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) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f416]) ).
fof(f811,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X3,X5),X0) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) ) )
& ( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X6,X8),X0) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f810]) ).
fof(f812,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(X3,X5),X0) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK25(X0,X1,X2),X4),X0) )
| ~ in(sK25(X0,X1,X2),X2) )
& ( ? [X5] :
( in(X5,X1)
& in(ordered_pair(sK25(X0,X1,X2),X5),X0) )
| in(sK25(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f813,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(X5,X1)
& in(ordered_pair(sK25(X0,X1,X2),X5),X0) )
=> ( in(sK26(X0,X1,X2),X1)
& in(ordered_pair(sK25(X0,X1,X2),sK26(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f814,plain,
! [X0,X1,X6] :
( ? [X8] :
( in(X8,X1)
& in(ordered_pair(X6,X8),X0) )
=> ( in(sK27(X0,X1,X6),X1)
& in(ordered_pair(X6,sK27(X0,X1,X6)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f815,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_inverse_image(X0,X1) = X2
| ( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK25(X0,X1,X2),X4),X0) )
| ~ in(sK25(X0,X1,X2),X2) )
& ( ( in(sK26(X0,X1,X2),X1)
& in(ordered_pair(sK25(X0,X1,X2),sK26(X0,X1,X2)),X0) )
| in(sK25(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) ) )
& ( ( in(sK27(X0,X1,X6),X1)
& in(ordered_pair(X6,sK27(X0,X1,X6)),X0) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26,sK27])],[f811,f814,f813,f812]) ).
fof(f816,plain,
! [X0] :
( ( ( connected(X0)
| ~ is_connected_in(X0,relation_field(X0)) )
& ( is_connected_in(X0,relation_field(X0))
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f417]) ).
fof(f817,plain,
! [X0] :
( ( ( transitive(X0)
| ~ is_transitive_in(X0,relation_field(X0)) )
& ( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f418]) ).
fof(f818,plain,
! [X0,X1,X2,X3] :
( ( unordered_triple(X0,X1,X2) = X3
| ? [X4] :
( ( ( X2 != X4
& X1 != X4
& X0 != X4 )
| ~ in(X4,X3) )
& ( X2 = X4
| X1 = X4
| X0 = X4
| in(X4,X3) ) ) )
& ( ! [X4] :
( ( in(X4,X3)
| ( X2 != X4
& X1 != X4
& X0 != X4 ) )
& ( X2 = X4
| X1 = X4
| X0 = X4
| ~ in(X4,X3) ) )
| unordered_triple(X0,X1,X2) != X3 ) ),
inference(nnf_transformation,[],[f419]) ).
fof(f819,plain,
! [X0,X1,X2,X3] :
( ( unordered_triple(X0,X1,X2) = X3
| ? [X4] :
( ( ( X2 != X4
& X1 != X4
& X0 != X4 )
| ~ in(X4,X3) )
& ( X2 = X4
| X1 = X4
| X0 = X4
| in(X4,X3) ) ) )
& ( ! [X4] :
( ( in(X4,X3)
| ( X2 != X4
& X1 != X4
& X0 != X4 ) )
& ( X2 = X4
| X1 = X4
| X0 = X4
| ~ in(X4,X3) ) )
| unordered_triple(X0,X1,X2) != X3 ) ),
inference(flattening,[],[f818]) ).
fof(f820,plain,
! [X0,X1,X2,X3] :
( ( unordered_triple(X0,X1,X2) = X3
| ? [X4] :
( ( ( X2 != X4
& X1 != X4
& X0 != X4 )
| ~ in(X4,X3) )
& ( X2 = X4
| X1 = X4
| X0 = X4
| in(X4,X3) ) ) )
& ( ! [X5] :
( ( in(X5,X3)
| ( X2 != X5
& X1 != X5
& X0 != X5 ) )
& ( X2 = X5
| X1 = X5
| X0 = X5
| ~ in(X5,X3) ) )
| unordered_triple(X0,X1,X2) != X3 ) ),
inference(rectify,[],[f819]) ).
fof(f821,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( ( ( X2 != X4
& X1 != X4
& X0 != X4 )
| ~ in(X4,X3) )
& ( X2 = X4
| X1 = X4
| X0 = X4
| in(X4,X3) ) )
=> ( ( ( sK28(X0,X1,X2,X3) != X2
& sK28(X0,X1,X2,X3) != X1
& sK28(X0,X1,X2,X3) != X0 )
| ~ in(sK28(X0,X1,X2,X3),X3) )
& ( sK28(X0,X1,X2,X3) = X2
| sK28(X0,X1,X2,X3) = X1
| sK28(X0,X1,X2,X3) = X0
| in(sK28(X0,X1,X2,X3),X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f822,plain,
! [X0,X1,X2,X3] :
( ( unordered_triple(X0,X1,X2) = X3
| ( ( ( sK28(X0,X1,X2,X3) != X2
& sK28(X0,X1,X2,X3) != X1
& sK28(X0,X1,X2,X3) != X0 )
| ~ in(sK28(X0,X1,X2,X3),X3) )
& ( sK28(X0,X1,X2,X3) = X2
| sK28(X0,X1,X2,X3) = X1
| sK28(X0,X1,X2,X3) = X0
| in(sK28(X0,X1,X2,X3),X3) ) ) )
& ( ! [X5] :
( ( in(X5,X3)
| ( X2 != X5
& X1 != X5
& X0 != X5 ) )
& ( X2 = X5
| X1 = X5
| X0 = X5
| ~ in(X5,X3) ) )
| unordered_triple(X0,X1,X2) != X3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f820,f821]) ).
fof(f823,plain,
! [X0] :
( ( function(X0)
| ? [X1,X2,X3] :
( X2 != X3
& in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) )
| ~ function(X0) ) ),
inference(nnf_transformation,[],[f421]) ).
fof(f824,plain,
! [X0] :
( ( function(X0)
| ? [X1,X2,X3] :
( X2 != X3
& in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ function(X0) ) ),
inference(rectify,[],[f823]) ).
fof(f825,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> ( sK30(X0) != sK31(X0)
& in(ordered_pair(sK29(X0),sK31(X0)),X0)
& in(ordered_pair(sK29(X0),sK30(X0)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f826,plain,
! [X0] :
( ( function(X0)
| ( sK30(X0) != sK31(X0)
& in(ordered_pair(sK29(X0),sK31(X0)),X0)
& in(ordered_pair(sK29(X0),sK30(X0)),X0) ) )
& ( ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ function(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31])],[f824,f825]) ).
fof(f827,plain,
! [X0] :
( ! [X3] :
( ( pair_first(X0) = X3
| ? [X4,X5] :
( X3 != X4
& ordered_pair(X4,X5) = X0 ) )
& ( ! [X4,X5] :
( X3 = X4
| ordered_pair(X4,X5) != X0 )
| pair_first(X0) != X3 ) )
| ! [X1,X2] : ordered_pair(X1,X2) != X0 ),
inference(nnf_transformation,[],[f422]) ).
fof(f828,plain,
! [X0] :
( ! [X1] :
( ( pair_first(X0) = X1
| ? [X2,X3] :
( X1 != X2
& ordered_pair(X2,X3) = X0 ) )
& ( ! [X4,X5] :
( X1 = X4
| ordered_pair(X4,X5) != X0 )
| pair_first(X0) != X1 ) )
| ! [X6,X7] : ordered_pair(X6,X7) != X0 ),
inference(rectify,[],[f827]) ).
fof(f829,plain,
! [X0,X1] :
( ? [X2,X3] :
( X1 != X2
& ordered_pair(X2,X3) = X0 )
=> ( sK32(X0,X1) != X1
& ordered_pair(sK32(X0,X1),sK33(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f830,plain,
! [X0] :
( ! [X1] :
( ( pair_first(X0) = X1
| ( sK32(X0,X1) != X1
& ordered_pair(sK32(X0,X1),sK33(X0,X1)) = X0 ) )
& ( ! [X4,X5] :
( X1 = X4
| ordered_pair(X4,X5) != X0 )
| pair_first(X0) != X1 ) )
| ! [X6,X7] : ordered_pair(X6,X7) != X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33])],[f828,f829]) ).
fof(f831,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,[],[f423]) ).
fof(f832,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(rectify,[],[f831]) ).
fof(f833,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
=> ( ! [X3,X2] : ordered_pair(X2,X3) != sK34(X0)
& in(sK34(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f834,plain,
! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
=> ordered_pair(sK35(X4),sK36(X4)) = X4 ),
introduced(choice_axiom,[]) ).
fof(f835,plain,
! [X0] :
( ( relation(X0)
| ( ! [X2,X3] : ordered_pair(X2,X3) != sK34(X0)
& in(sK34(X0),X0) ) )
& ( ! [X4] :
( ordered_pair(sK35(X4),sK36(X4)) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35,sK36])],[f832,f834,f833]) ).
fof(f836,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) ) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f424]) ).
fof(f837,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) ) )
& ( ! [X3] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f836]) ).
fof(f838,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) )
=> ( ~ in(ordered_pair(sK37(X0,X1),sK37(X0,X1)),X0)
& in(sK37(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f839,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ( ~ in(ordered_pair(sK37(X0,X1),sK37(X0,X1)),X0)
& in(sK37(X0,X1),X1) ) )
& ( ! [X3] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f837,f838]) ).
fof(f840,plain,
! [X0,X1,X2] :
( ( relation_of2(X2,X0,X1)
| ~ subset(X2,cartesian_product2(X0,X1)) )
& ( subset(X2,cartesian_product2(X0,X1))
| ~ relation_of2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f841,plain,
! [X0,X1] :
( ( ( ( set_meet(X0) = X1
| empty_set != X1 )
& ( empty_set = X1
| set_meet(X0) != X1 ) )
| empty_set != X0 )
& ( ( ( set_meet(X0) = X1
| ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) ) )
& ( ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) ) )
| set_meet(X0) != X1 ) )
| empty_set = X0 ) ),
inference(nnf_transformation,[],[f425]) ).
fof(f842,plain,
! [X0,X1] :
( ( ( ( set_meet(X0) = X1
| empty_set != X1 )
& ( empty_set = X1
| set_meet(X0) != X1 ) )
| empty_set != X0 )
& ( ( ( set_meet(X0) = X1
| ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X4] :
( in(X2,X4)
| ~ in(X4,X0) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ? [X6] :
( ~ in(X5,X6)
& in(X6,X0) ) )
& ( ! [X7] :
( in(X5,X7)
| ~ in(X7,X0) )
| ~ in(X5,X1) ) )
| set_meet(X0) != X1 ) )
| empty_set = X0 ) ),
inference(rectify,[],[f841]) ).
fof(f843,plain,
! [X0,X1] :
( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X4] :
( in(X2,X4)
| ~ in(X4,X0) )
| in(X2,X1) ) )
=> ( ( ? [X3] :
( ~ in(sK38(X0,X1),X3)
& in(X3,X0) )
| ~ in(sK38(X0,X1),X1) )
& ( ! [X4] :
( in(sK38(X0,X1),X4)
| ~ in(X4,X0) )
| in(sK38(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f844,plain,
! [X0,X1] :
( ? [X3] :
( ~ in(sK38(X0,X1),X3)
& in(X3,X0) )
=> ( ~ in(sK38(X0,X1),sK39(X0,X1))
& in(sK39(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f845,plain,
! [X0,X5] :
( ? [X6] :
( ~ in(X5,X6)
& in(X6,X0) )
=> ( ~ in(X5,sK40(X0,X5))
& in(sK40(X0,X5),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f846,plain,
! [X0,X1] :
( ( ( ( set_meet(X0) = X1
| empty_set != X1 )
& ( empty_set = X1
| set_meet(X0) != X1 ) )
| empty_set != X0 )
& ( ( ( set_meet(X0) = X1
| ( ( ( ~ in(sK38(X0,X1),sK39(X0,X1))
& in(sK39(X0,X1),X0) )
| ~ in(sK38(X0,X1),X1) )
& ( ! [X4] :
( in(sK38(X0,X1),X4)
| ~ in(X4,X0) )
| in(sK38(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ( ~ in(X5,sK40(X0,X5))
& in(sK40(X0,X5),X0) ) )
& ( ! [X7] :
( in(X5,X7)
| ~ in(X7,X0) )
| ~ in(X5,X1) ) )
| set_meet(X0) != X1 ) )
| empty_set = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39,sK40])],[f842,f845,f844,f843]) ).
fof(f847,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f848,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f847]) ).
fof(f849,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK41(X0,X1) != X0
| ~ in(sK41(X0,X1),X1) )
& ( sK41(X0,X1) = X0
| in(sK41(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f850,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK41(X0,X1) != X0
| ~ in(sK41(X0,X1),X1) )
& ( sK41(X0,X1) = X0
| in(sK41(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f848,f849]) ).
fof(f851,plain,
! [X0] :
( ! [X1,X2] :
( ( fiber(X0,X1) = X2
| ? [X3] :
( ( ~ in(ordered_pair(X3,X1),X0)
| X1 = X3
| ~ in(X3,X2) )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(ordered_pair(X3,X1),X0)
| X1 = X3 )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| ~ in(X3,X2) ) )
| fiber(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f426]) ).
fof(f852,plain,
! [X0] :
( ! [X1,X2] :
( ( fiber(X0,X1) = X2
| ? [X3] :
( ( ~ in(ordered_pair(X3,X1),X0)
| X1 = X3
| ~ in(X3,X2) )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(ordered_pair(X3,X1),X0)
| X1 = X3 )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| ~ in(X3,X2) ) )
| fiber(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(flattening,[],[f851]) ).
fof(f853,plain,
! [X0] :
( ! [X1,X2] :
( ( fiber(X0,X1) = X2
| ? [X3] :
( ( ~ in(ordered_pair(X3,X1),X0)
| X1 = X3
| ~ in(X3,X2) )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(ordered_pair(X4,X1),X0)
| X1 = X4 )
& ( ( in(ordered_pair(X4,X1),X0)
& X1 != X4 )
| ~ in(X4,X2) ) )
| fiber(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f852]) ).
fof(f854,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(ordered_pair(X3,X1),X0)
| X1 = X3
| ~ in(X3,X2) )
& ( ( in(ordered_pair(X3,X1),X0)
& X1 != X3 )
| in(X3,X2) ) )
=> ( ( ~ in(ordered_pair(sK42(X0,X1,X2),X1),X0)
| sK42(X0,X1,X2) = X1
| ~ in(sK42(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK42(X0,X1,X2),X1),X0)
& sK42(X0,X1,X2) != X1 )
| in(sK42(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f855,plain,
! [X0] :
( ! [X1,X2] :
( ( fiber(X0,X1) = X2
| ( ( ~ in(ordered_pair(sK42(X0,X1,X2),X1),X0)
| sK42(X0,X1,X2) = X1
| ~ in(sK42(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK42(X0,X1,X2),X1),X0)
& sK42(X0,X1,X2) != X1 )
| in(sK42(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(ordered_pair(X4,X1),X0)
| X1 = X4 )
& ( ( in(ordered_pair(X4,X1),X0)
& X1 != X4 )
| ~ in(X4,X2) ) )
| fiber(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f853,f854]) ).
fof(f856,plain,
! [X0,X1] :
( ( ( inclusion_relation(X0) = X1
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X3,X0)
& in(X2,X0) )
| relation_field(X1) != X0 )
& ( ( ! [X2,X3] :
( ( ( in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) )
& ( subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ in(X3,X0)
| ~ in(X2,X0) )
& relation_field(X1) = X0 )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f428]) ).
fof(f857,plain,
! [X0,X1] :
( ( ( inclusion_relation(X0) = X1
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X3,X0)
& in(X2,X0) )
| relation_field(X1) != X0 )
& ( ( ! [X2,X3] :
( ( ( in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) )
& ( subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ in(X3,X0)
| ~ in(X2,X0) )
& relation_field(X1) = X0 )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(flattening,[],[f856]) ).
fof(f858,plain,
! [X0,X1] :
( ( ( inclusion_relation(X0) = X1
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X3,X0)
& in(X2,X0) )
| relation_field(X1) != X0 )
& ( ( ! [X4,X5] :
( ( ( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5) )
& ( subset(X4,X5)
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ in(X5,X0)
| ~ in(X4,X0) )
& relation_field(X1) = X0 )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(rectify,[],[f857]) ).
fof(f859,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X3,X0)
& in(X2,X0) )
=> ( ( ~ subset(sK43(X0,X1),sK44(X0,X1))
| ~ in(ordered_pair(sK43(X0,X1),sK44(X0,X1)),X1) )
& ( subset(sK43(X0,X1),sK44(X0,X1))
| in(ordered_pair(sK43(X0,X1),sK44(X0,X1)),X1) )
& in(sK44(X0,X1),X0)
& in(sK43(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f860,plain,
! [X0,X1] :
( ( ( inclusion_relation(X0) = X1
| ( ( ~ subset(sK43(X0,X1),sK44(X0,X1))
| ~ in(ordered_pair(sK43(X0,X1),sK44(X0,X1)),X1) )
& ( subset(sK43(X0,X1),sK44(X0,X1))
| in(ordered_pair(sK43(X0,X1),sK44(X0,X1)),X1) )
& in(sK44(X0,X1),X0)
& in(sK43(X0,X1),X0) )
| relation_field(X1) != X0 )
& ( ( ! [X4,X5] :
( ( ( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5) )
& ( subset(X4,X5)
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ in(X5,X0)
| ~ in(X4,X0) )
& relation_field(X1) = X0 )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44])],[f858,f859]) ).
fof(f861,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f862,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f861]) ).
fof(f863,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK45(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f864,plain,
! [X0] :
( ( empty_set = X0
| in(sK45(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f862,f863]) ).
fof(f865,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f866,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f865]) ).
fof(f867,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK46(X0,X1),X0)
| ~ in(sK46(X0,X1),X1) )
& ( subset(sK46(X0,X1),X0)
| in(sK46(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f868,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ( ( ~ subset(sK46(X0,X1),X0)
| ~ in(sK46(X0,X1),X1) )
& ( subset(sK46(X0,X1),X0)
| in(sK46(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f866,f867]) ).
fof(f869,plain,
! [X0] :
( ! [X3] :
( ( pair_second(X0) = X3
| ? [X4,X5] :
( X3 != X5
& ordered_pair(X4,X5) = X0 ) )
& ( ! [X4,X5] :
( X3 = X5
| ordered_pair(X4,X5) != X0 )
| pair_second(X0) != X3 ) )
| ! [X1,X2] : ordered_pair(X1,X2) != X0 ),
inference(nnf_transformation,[],[f429]) ).
fof(f870,plain,
! [X0] :
( ! [X1] :
( ( pair_second(X0) = X1
| ? [X2,X3] :
( X1 != X3
& ordered_pair(X2,X3) = X0 ) )
& ( ! [X4,X5] :
( X1 = X5
| ordered_pair(X4,X5) != X0 )
| pair_second(X0) != X1 ) )
| ! [X6,X7] : ordered_pair(X6,X7) != X0 ),
inference(rectify,[],[f869]) ).
fof(f871,plain,
! [X0,X1] :
( ? [X2,X3] :
( X1 != X3
& ordered_pair(X2,X3) = X0 )
=> ( sK48(X0,X1) != X1
& ordered_pair(sK47(X0,X1),sK48(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f872,plain,
! [X0] :
( ! [X1] :
( ( pair_second(X0) = X1
| ( sK48(X0,X1) != X1
& ordered_pair(sK47(X0,X1),sK48(X0,X1)) = X0 ) )
& ( ! [X4,X5] :
( X1 = X5
| ordered_pair(X4,X5) != X0 )
| pair_second(X0) != X1 ) )
| ! [X6,X7] : ordered_pair(X6,X7) != X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48])],[f870,f871]) ).
fof(f873,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f430]) ).
fof(f874,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f873]) ).
fof(f875,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK49(X0),X0)
& in(sK49(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f876,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK49(X0),X0)
& in(sK49(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49])],[f874,f875]) ).
fof(f877,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( 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),X1)
| ~ in(ordered_pair(X2,X3),X0) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f431]) ).
fof(f878,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) ) )
& ( ! [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) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f877]) ).
fof(f879,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) )
=> ( ( ~ in(ordered_pair(sK50(X0,X1),sK51(X0,X1)),X1)
| ~ in(ordered_pair(sK50(X0,X1),sK51(X0,X1)),X0) )
& ( in(ordered_pair(sK50(X0,X1),sK51(X0,X1)),X1)
| in(ordered_pair(sK50(X0,X1),sK51(X0,X1)),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f880,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ( ( ~ in(ordered_pair(sK50(X0,X1),sK51(X0,X1)),X1)
| ~ in(ordered_pair(sK50(X0,X1),sK51(X0,X1)),X0) )
& ( in(ordered_pair(sK50(X0,X1),sK51(X0,X1)),X1)
| in(ordered_pair(sK50(X0,X1),sK51(X0,X1)),X0) ) ) )
& ( ! [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) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51])],[f878,f879]) ).
fof(f881,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) )
& ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) ) ),
inference(nnf_transformation,[],[f432]) ).
fof(f882,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f883,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f882]) ).
fof(f884,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f883]) ).
fof(f885,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) )
=> ( ( ( sK52(X0,X1,X2) != X1
& sK52(X0,X1,X2) != X0 )
| ~ in(sK52(X0,X1,X2),X2) )
& ( sK52(X0,X1,X2) = X1
| sK52(X0,X1,X2) = X0
| in(sK52(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f886,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ( ( ( sK52(X0,X1,X2) != X1
& sK52(X0,X1,X2) != X0 )
| ~ in(sK52(X0,X1,X2),X2) )
& ( sK52(X0,X1,X2) = X1
| sK52(X0,X1,X2) = X0
| in(sK52(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f884,f885]) ).
fof(f887,plain,
! [X0] :
( ( ( well_founded_relation(X0)
| ? [X1] :
( ! [X2] :
( ~ disjoint(fiber(X0,X2),X1)
| ~ in(X2,X1) )
& empty_set != X1
& subset(X1,relation_field(X0)) ) )
& ( ! [X1] :
( ? [X2] :
( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
| empty_set = X1
| ~ subset(X1,relation_field(X0)) )
| ~ well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f433]) ).
fof(f888,plain,
! [X0] :
( ( ( well_founded_relation(X0)
| ? [X1] :
( ! [X2] :
( ~ disjoint(fiber(X0,X2),X1)
| ~ in(X2,X1) )
& empty_set != X1
& subset(X1,relation_field(X0)) ) )
& ( ! [X3] :
( ? [X4] :
( disjoint(fiber(X0,X4),X3)
& in(X4,X3) )
| empty_set = X3
| ~ subset(X3,relation_field(X0)) )
| ~ well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f887]) ).
fof(f889,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ~ disjoint(fiber(X0,X2),X1)
| ~ in(X2,X1) )
& empty_set != X1
& subset(X1,relation_field(X0)) )
=> ( ! [X2] :
( ~ disjoint(fiber(X0,X2),sK53(X0))
| ~ in(X2,sK53(X0)) )
& empty_set != sK53(X0)
& subset(sK53(X0),relation_field(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f890,plain,
! [X0,X3] :
( ? [X4] :
( disjoint(fiber(X0,X4),X3)
& in(X4,X3) )
=> ( disjoint(fiber(X0,sK54(X0,X3)),X3)
& in(sK54(X0,X3),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f891,plain,
! [X0] :
( ( ( well_founded_relation(X0)
| ( ! [X2] :
( ~ disjoint(fiber(X0,X2),sK53(X0))
| ~ in(X2,sK53(X0)) )
& empty_set != sK53(X0)
& subset(sK53(X0),relation_field(X0)) ) )
& ( ! [X3] :
( ( disjoint(fiber(X0,sK54(X0,X3)),X3)
& in(sK54(X0,X3),X3) )
| empty_set = X3
| ~ subset(X3,relation_field(X0)) )
| ~ well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54])],[f888,f890,f889]) ).
fof(f892,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f893,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f892]) ).
fof(f894,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f893]) ).
fof(f895,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK55(X0,X1,X2),X1)
& ~ in(sK55(X0,X1,X2),X0) )
| ~ in(sK55(X0,X1,X2),X2) )
& ( in(sK55(X0,X1,X2),X1)
| in(sK55(X0,X1,X2),X0)
| in(sK55(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f896,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ( ( ( ~ in(sK55(X0,X1,X2),X1)
& ~ in(sK55(X0,X1,X2),X0) )
| ~ in(sK55(X0,X1,X2),X2) )
& ( in(sK55(X0,X1,X2),X1)
| in(sK55(X0,X1,X2),X0)
| in(sK55(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55])],[f894,f895]) ).
fof(f897,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| ~ in(X3,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f898,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) ) )
& ( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(rectify,[],[f897]) ).
fof(f899,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) )
| in(X3,X2) ) )
=> ( ( ! [X5,X4] :
( ordered_pair(X4,X5) != sK56(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(sK56(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK56(X0,X1,X2)
& in(X7,X1)
& in(X6,X0) )
| in(sK56(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f900,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK56(X0,X1,X2)
& in(X7,X1)
& in(X6,X0) )
=> ( sK56(X0,X1,X2) = ordered_pair(sK57(X0,X1,X2),sK58(X0,X1,X2))
& in(sK58(X0,X1,X2),X1)
& in(sK57(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f901,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) )
=> ( ordered_pair(sK59(X0,X1,X8),sK60(X0,X1,X8)) = X8
& in(sK60(X0,X1,X8),X1)
& in(sK59(X0,X1,X8),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f902,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK56(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(sK56(X0,X1,X2),X2) )
& ( ( sK56(X0,X1,X2) = ordered_pair(sK57(X0,X1,X2),sK58(X0,X1,X2))
& in(sK58(X0,X1,X2),X1)
& in(sK57(X0,X1,X2),X0) )
| in(sK56(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) ) )
& ( ( ordered_pair(sK59(X0,X1,X8),sK60(X0,X1,X8)) = X8
& in(sK60(X0,X1,X8),X1)
& in(sK59(X0,X1,X8),X0) )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57,sK58,sK59,sK60])],[f898,f901,f900,f899]) ).
fof(f903,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) )
| ~ epsilon_connected(X0) ) ),
inference(nnf_transformation,[],[f434]) ).
fof(f904,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ epsilon_connected(X0) ) ),
inference(rectify,[],[f903]) ).
fof(f905,plain,
! [X0] :
( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
=> ( ~ in(sK62(X0),sK61(X0))
& sK61(X0) != sK62(X0)
& ~ in(sK61(X0),sK62(X0))
& in(sK62(X0),X0)
& in(sK61(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f906,plain,
! [X0] :
( ( epsilon_connected(X0)
| ( ~ in(sK62(X0),sK61(X0))
& sK61(X0) != sK62(X0)
& ~ in(sK61(X0),sK62(X0))
& in(sK62(X0),X0)
& in(sK61(X0),X0) ) )
& ( ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ epsilon_connected(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61,sK62])],[f904,f905]) ).
fof(f907,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X3),X0) ) )
& ( ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
| ~ subset(X0,X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f435]) ).
fof(f908,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X3),X0) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ subset(X0,X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f907]) ).
fof(f909,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X3),X0) )
=> ( ~ in(ordered_pair(sK63(X0,X1),sK64(X0,X1)),X1)
& in(ordered_pair(sK63(X0,X1),sK64(X0,X1)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f910,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ in(ordered_pair(sK63(X0,X1),sK64(X0,X1)),X1)
& in(ordered_pair(sK63(X0,X1),sK64(X0,X1)),X0) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ subset(X0,X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64])],[f908,f909]) ).
fof(f911,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f436]) ).
fof(f912,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f911]) ).
fof(f913,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK65(X0,X1),X1)
& in(sK65(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f914,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK65(X0,X1),X1)
& in(sK65(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f912,f913]) ).
fof(f915,plain,
! [X0] :
( ! [X1] :
( ( is_well_founded_in(X0,X1)
| ? [X2] :
( ! [X3] :
( ~ disjoint(fiber(X0,X3),X2)
| ~ in(X3,X2) )
& empty_set != X2
& subset(X2,X1) ) )
& ( ! [X2] :
( ? [X3] :
( disjoint(fiber(X0,X3),X2)
& in(X3,X2) )
| empty_set = X2
| ~ subset(X2,X1) )
| ~ is_well_founded_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f437]) ).
fof(f916,plain,
! [X0] :
( ! [X1] :
( ( is_well_founded_in(X0,X1)
| ? [X2] :
( ! [X3] :
( ~ disjoint(fiber(X0,X3),X2)
| ~ in(X3,X2) )
& empty_set != X2
& subset(X2,X1) ) )
& ( ! [X4] :
( ? [X5] :
( disjoint(fiber(X0,X5),X4)
& in(X5,X4) )
| empty_set = X4
| ~ subset(X4,X1) )
| ~ is_well_founded_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f915]) ).
fof(f917,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ disjoint(fiber(X0,X3),X2)
| ~ in(X3,X2) )
& empty_set != X2
& subset(X2,X1) )
=> ( ! [X3] :
( ~ disjoint(fiber(X0,X3),sK66(X0,X1))
| ~ in(X3,sK66(X0,X1)) )
& empty_set != sK66(X0,X1)
& subset(sK66(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f918,plain,
! [X0,X4] :
( ? [X5] :
( disjoint(fiber(X0,X5),X4)
& in(X5,X4) )
=> ( disjoint(fiber(X0,sK67(X0,X4)),X4)
& in(sK67(X0,X4),X4) ) ),
introduced(choice_axiom,[]) ).
fof(f919,plain,
! [X0] :
( ! [X1] :
( ( is_well_founded_in(X0,X1)
| ( ! [X3] :
( ~ disjoint(fiber(X0,X3),sK66(X0,X1))
| ~ in(X3,sK66(X0,X1)) )
& empty_set != sK66(X0,X1)
& subset(sK66(X0,X1),X1) ) )
& ( ! [X4] :
( ( disjoint(fiber(X0,sK67(X0,X4)),X4)
& in(sK67(X0,X4),X4) )
| empty_set = X4
| ~ subset(X4,X1) )
| ~ is_well_founded_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66,sK67])],[f916,f918,f917]) ).
fof(f920,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f921,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f920]) ).
fof(f922,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f921]) ).
fof(f923,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( ~ in(sK68(X0,X1,X2),X1)
| ~ in(sK68(X0,X1,X2),X0)
| ~ in(sK68(X0,X1,X2),X2) )
& ( ( in(sK68(X0,X1,X2),X1)
& in(sK68(X0,X1,X2),X0) )
| in(sK68(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f924,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ( ( ~ in(sK68(X0,X1,X2),X1)
| ~ in(sK68(X0,X1,X2),X0)
| ~ in(sK68(X0,X1,X2),X2) )
& ( ( in(sK68(X0,X1,X2),X1)
& in(sK68(X0,X1,X2),X0) )
| in(sK68(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68])],[f922,f923]) ).
fof(f925,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( apply(X0,X1) = X2
| empty_set != X2 )
& ( empty_set = X2
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) )
& ( ( ( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f439]) ).
fof(f926,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) )
& ( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f927,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) )
& ( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ) ),
inference(flattening,[],[f926]) ).
fof(f928,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f440]) ).
fof(f929,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f928]) ).
fof(f930,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(sK69(X0,X1),X3),X0)
| ~ in(sK69(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK69(X0,X1),X4),X0)
| in(sK69(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f931,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK69(X0,X1),X4),X0)
=> in(ordered_pair(sK69(X0,X1),sK70(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f932,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK71(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f933,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK69(X0,X1),X3),X0)
| ~ in(sK69(X0,X1),X1) )
& ( in(ordered_pair(sK69(X0,X1),sK70(X0,X1)),X0)
| in(sK69(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK71(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70,sK71])],[f929,f932,f931,f930]) ).
fof(f934,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ? [X2,X3] :
( X2 != X3
& in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f442]) ).
fof(f935,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ? [X2,X3] :
( X2 != X3
& in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f934]) ).
fof(f936,plain,
! [X0,X1] :
( ? [X2,X3] :
( X2 != X3
& in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) )
=> ( sK72(X0,X1) != sK73(X0,X1)
& in(ordered_pair(sK73(X0,X1),sK72(X0,X1)),X0)
& in(ordered_pair(sK72(X0,X1),sK73(X0,X1)),X0)
& in(sK73(X0,X1),X1)
& in(sK72(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f937,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ( sK72(X0,X1) != sK73(X0,X1)
& in(ordered_pair(sK73(X0,X1),sK72(X0,X1)),X0)
& in(ordered_pair(sK72(X0,X1),sK73(X0,X1)),X0)
& in(sK73(X0,X1),X1)
& in(sK72(X0,X1),X1) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72,sK73])],[f935,f936]) ).
fof(f938,plain,
! [X0,X1] :
( ( union(X0) = X1
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ in(X2,X1) ) )
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f939,plain,
! [X0,X1] :
( ( union(X0) = X1
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(rectify,[],[f938]) ).
fof(f940,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK74(X0,X1),X3) )
| ~ in(sK74(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK74(X0,X1),X4) )
| in(sK74(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f941,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK74(X0,X1),X4) )
=> ( in(sK75(X0,X1),X0)
& in(sK74(X0,X1),sK75(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f942,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK76(X0,X5),X0)
& in(X5,sK76(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f943,plain,
! [X0,X1] :
( ( union(X0) = X1
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK74(X0,X1),X3) )
| ~ in(sK74(X0,X1),X1) )
& ( ( in(sK75(X0,X1),X0)
& in(sK74(X0,X1),sK75(X0,X1)) )
| in(sK74(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK76(X0,X5),X0)
& in(X5,sK76(X0,X5)) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74,sK75,sK76])],[f939,f942,f941,f940]) ).
fof(f944,plain,
! [X0] :
( ( ( well_ordering(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0) )
& ( ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) )
| ~ well_ordering(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f443]) ).
fof(f945,plain,
! [X0] :
( ( ( well_ordering(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0) )
& ( ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) )
| ~ well_ordering(X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f944]) ).
fof(f946,plain,
! [X0,X1] :
( ( equipotent(X0,X1)
| ! [X2] :
( relation_rng(X2) != X1
| relation_dom(X2) != X0
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2) ) )
& ( ? [X2] :
( relation_rng(X2) = X1
& relation_dom(X2) = X0
& one_to_one(X2)
& function(X2)
& relation(X2) )
| ~ equipotent(X0,X1) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f947,plain,
! [X0,X1] :
( ( equipotent(X0,X1)
| ! [X2] :
( relation_rng(X2) != X1
| relation_dom(X2) != X0
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2) ) )
& ( ? [X3] :
( relation_rng(X3) = X1
& relation_dom(X3) = X0
& one_to_one(X3)
& function(X3)
& relation(X3) )
| ~ equipotent(X0,X1) ) ),
inference(rectify,[],[f946]) ).
fof(f948,plain,
! [X0,X1] :
( ? [X3] :
( relation_rng(X3) = X1
& relation_dom(X3) = X0
& one_to_one(X3)
& function(X3)
& relation(X3) )
=> ( relation_rng(sK77(X0,X1)) = X1
& relation_dom(sK77(X0,X1)) = X0
& one_to_one(sK77(X0,X1))
& function(sK77(X0,X1))
& relation(sK77(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f949,plain,
! [X0,X1] :
( ( equipotent(X0,X1)
| ! [X2] :
( relation_rng(X2) != X1
| relation_dom(X2) != X0
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2) ) )
& ( ( relation_rng(sK77(X0,X1)) = X1
& relation_dom(sK77(X0,X1)) = X0
& one_to_one(sK77(X0,X1))
& function(sK77(X0,X1))
& relation(sK77(X0,X1)) )
| ~ equipotent(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK77])],[f947,f948]) ).
fof(f950,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f951,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f950]) ).
fof(f952,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f951]) ).
fof(f953,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( in(sK78(X0,X1,X2),X1)
| ~ in(sK78(X0,X1,X2),X0)
| ~ in(sK78(X0,X1,X2),X2) )
& ( ( ~ in(sK78(X0,X1,X2),X1)
& in(sK78(X0,X1,X2),X0) )
| in(sK78(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f954,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ( ( in(sK78(X0,X1,X2),X1)
| ~ in(sK78(X0,X1,X2),X0)
| ~ in(sK78(X0,X1,X2),X2) )
& ( ( ~ in(sK78(X0,X1,X2),X1)
& in(sK78(X0,X1,X2),X0) )
| in(sK78(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK78])],[f952,f953]) ).
fof(f955,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f445]) ).
fof(f956,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f955]) ).
fof(f957,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| ~ in(X2,X1) )
& ( ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( apply(X0,X3) != sK79(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK79(X0,X1),X1) )
& ( ? [X4] :
( apply(X0,X4) = sK79(X0,X1)
& in(X4,relation_dom(X0)) )
| in(sK79(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f958,plain,
! [X0,X1] :
( ? [X4] :
( apply(X0,X4) = sK79(X0,X1)
& in(X4,relation_dom(X0)) )
=> ( sK79(X0,X1) = apply(X0,sK80(X0,X1))
& in(sK80(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f959,plain,
! [X0,X5] :
( ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) )
=> ( apply(X0,sK81(X0,X5)) = X5
& in(sK81(X0,X5),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f960,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] :
( apply(X0,X3) != sK79(X0,X1)
| ~ in(X3,relation_dom(X0)) )
| ~ in(sK79(X0,X1),X1) )
& ( ( sK79(X0,X1) = apply(X0,sK80(X0,X1))
& in(sK80(X0,X1),relation_dom(X0)) )
| in(sK79(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) ) )
& ( ( apply(X0,sK81(X0,X5)) = X5
& in(sK81(X0,X5),relation_dom(X0)) )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80,sK81])],[f956,f959,f958,f957]) ).
fof(f961,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f446]) ).
fof(f962,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f961]) ).
fof(f963,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(X3,sK82(X0,X1)),X0)
| ~ in(sK82(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK82(X0,X1)),X0)
| in(sK82(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f964,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK82(X0,X1)),X0)
=> in(ordered_pair(sK83(X0,X1),sK82(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f965,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK84(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f966,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK82(X0,X1)),X0)
| ~ in(sK82(X0,X1),X1) )
& ( in(ordered_pair(sK83(X0,X1),sK82(X0,X1)),X0)
| in(sK82(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK84(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK82,sK83,sK84])],[f962,f965,f964,f963]) ).
fof(f967,plain,
! [X0] :
( ! [X1] :
( ( well_orders(X0,X1)
| ~ is_well_founded_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_reflexive_in(X0,X1) )
& ( ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) )
| ~ well_orders(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f448]) ).
fof(f968,plain,
! [X0] :
( ! [X1] :
( ( well_orders(X0,X1)
| ~ is_well_founded_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_reflexive_in(X0,X1) )
& ( ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) )
| ~ well_orders(X0,X1) ) )
| ~ relation(X0) ),
inference(flattening,[],[f967]) ).
fof(f969,plain,
! [X0] :
( ( being_limit_ordinal(X0)
| union(X0) != X0 )
& ( union(X0) = X0
| ~ being_limit_ordinal(X0) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f970,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X2,X3] :
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1) )
| ~ is_connected_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f450]) ).
fof(f971,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) )
| ~ is_connected_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f970]) ).
fof(f972,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) )
=> ( ~ in(ordered_pair(sK86(X0,X1),sK85(X0,X1)),X0)
& ~ in(ordered_pair(sK85(X0,X1),sK86(X0,X1)),X0)
& sK85(X0,X1) != sK86(X0,X1)
& in(sK86(X0,X1),X1)
& in(sK85(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f973,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ( ~ in(ordered_pair(sK86(X0,X1),sK85(X0,X1)),X0)
& ~ in(ordered_pair(sK85(X0,X1),sK86(X0,X1)),X0)
& sK85(X0,X1) != sK86(X0,X1)
& in(sK86(X0,X1),X1)
& in(sK85(X0,X1),X1) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) )
| ~ is_connected_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85,sK86])],[f971,f972]) ).
fof(f974,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( 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(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f452]) ).
fof(f975,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),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) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f974]) ).
fof(f976,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) )
=> ( ( ~ in(ordered_pair(sK88(X0,X1),sK87(X0,X1)),X0)
| ~ in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X1) )
& ( in(ordered_pair(sK88(X0,X1),sK87(X0,X1)),X0)
| in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f977,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ( ( ~ in(ordered_pair(sK88(X0,X1),sK87(X0,X1)),X0)
| ~ in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X1) )
& ( in(ordered_pair(sK88(X0,X1),sK87(X0,X1)),X0)
| in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),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) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK87,sK88])],[f975,f976]) ).
fof(f978,plain,
! [X0,X2,X1] :
( ( ( relation_isomorphism(X0,X1,X2)
| ~ sP0(X1,X2,X0) )
& ( sP0(X1,X2,X0)
| ~ relation_isomorphism(X0,X1,X2) ) )
| ~ sP1(X0,X2,X1) ),
inference(nnf_transformation,[],[f755]) ).
fof(f979,plain,
! [X0,X1,X2] :
( ( ( relation_isomorphism(X0,X2,X1)
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| ~ relation_isomorphism(X0,X2,X1) ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f978]) ).
fof(f980,plain,
! [X1,X2,X0] :
( ( sP0(X1,X2,X0)
| ? [X3,X4] :
( ( ~ in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0))
| ~ in(ordered_pair(X3,X4),X0) )
& ( ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) )
| in(ordered_pair(X3,X4),X0) ) )
| ~ one_to_one(X2)
| relation_field(X1) != relation_rng(X2)
| relation_field(X0) != relation_dom(X2) )
& ( ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) )
& ( ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) )
| ~ in(ordered_pair(X3,X4),X0) ) )
& one_to_one(X2)
& relation_field(X1) = relation_rng(X2)
& relation_field(X0) = relation_dom(X2) )
| ~ sP0(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f754]) ).
fof(f981,plain,
! [X1,X2,X0] :
( ( sP0(X1,X2,X0)
| ? [X3,X4] :
( ( ~ in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0))
| ~ in(ordered_pair(X3,X4),X0) )
& ( ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) )
| in(ordered_pair(X3,X4),X0) ) )
| ~ one_to_one(X2)
| relation_field(X1) != relation_rng(X2)
| relation_field(X0) != relation_dom(X2) )
& ( ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) )
& ( ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) )
| ~ in(ordered_pair(X3,X4),X0) ) )
& one_to_one(X2)
& relation_field(X1) = relation_rng(X2)
& relation_field(X0) = relation_dom(X2) )
| ~ sP0(X1,X2,X0) ) ),
inference(flattening,[],[f980]) ).
fof(f982,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(apply(X1,X3),apply(X1,X4)),X0)
| ~ in(X4,relation_field(X2))
| ~ in(X3,relation_field(X2))
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(apply(X1,X3),apply(X1,X4)),X0)
& in(X4,relation_field(X2))
& in(X3,relation_field(X2)) )
| in(ordered_pair(X3,X4),X2) ) )
| ~ one_to_one(X1)
| relation_field(X0) != relation_rng(X1)
| relation_dom(X1) != relation_field(X2) )
& ( ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
| ~ in(X6,relation_field(X2))
| ~ in(X5,relation_field(X2)) )
& ( ( in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
& in(X6,relation_field(X2))
& in(X5,relation_field(X2)) )
| ~ in(ordered_pair(X5,X6),X2) ) )
& one_to_one(X1)
& relation_field(X0) = relation_rng(X1)
& relation_dom(X1) = relation_field(X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f981]) ).
fof(f983,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ~ in(ordered_pair(apply(X1,X3),apply(X1,X4)),X0)
| ~ in(X4,relation_field(X2))
| ~ in(X3,relation_field(X2))
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(apply(X1,X3),apply(X1,X4)),X0)
& in(X4,relation_field(X2))
& in(X3,relation_field(X2)) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ~ in(ordered_pair(apply(X1,sK89(X0,X1,X2)),apply(X1,sK90(X0,X1,X2))),X0)
| ~ in(sK90(X0,X1,X2),relation_field(X2))
| ~ in(sK89(X0,X1,X2),relation_field(X2))
| ~ in(ordered_pair(sK89(X0,X1,X2),sK90(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(apply(X1,sK89(X0,X1,X2)),apply(X1,sK90(X0,X1,X2))),X0)
& in(sK90(X0,X1,X2),relation_field(X2))
& in(sK89(X0,X1,X2),relation_field(X2)) )
| in(ordered_pair(sK89(X0,X1,X2),sK90(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f984,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ~ in(ordered_pair(apply(X1,sK89(X0,X1,X2)),apply(X1,sK90(X0,X1,X2))),X0)
| ~ in(sK90(X0,X1,X2),relation_field(X2))
| ~ in(sK89(X0,X1,X2),relation_field(X2))
| ~ in(ordered_pair(sK89(X0,X1,X2),sK90(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(apply(X1,sK89(X0,X1,X2)),apply(X1,sK90(X0,X1,X2))),X0)
& in(sK90(X0,X1,X2),relation_field(X2))
& in(sK89(X0,X1,X2),relation_field(X2)) )
| in(ordered_pair(sK89(X0,X1,X2),sK90(X0,X1,X2)),X2) ) )
| ~ one_to_one(X1)
| relation_field(X0) != relation_rng(X1)
| relation_dom(X1) != relation_field(X2) )
& ( ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
| ~ in(X6,relation_field(X2))
| ~ in(X5,relation_field(X2)) )
& ( ( in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
& in(X6,relation_field(X2))
& in(X5,relation_field(X2)) )
| ~ in(ordered_pair(X5,X6),X2) ) )
& one_to_one(X1)
& relation_field(X0) = relation_rng(X1)
& relation_dom(X1) = relation_field(X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK89,sK90])],[f982,f983]) ).
fof(f985,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f71]) ).
fof(f986,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( 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)) )
| ~ one_to_one(X0) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f456]) ).
fof(f987,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0)) )
| ~ one_to_one(X0) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f986]) ).
fof(f988,plain,
! [X0] :
( ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> ( sK91(X0) != sK92(X0)
& apply(X0,sK91(X0)) = apply(X0,sK92(X0))
& in(sK92(X0),relation_dom(X0))
& in(sK91(X0),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f989,plain,
! [X0] :
( ( ( one_to_one(X0)
| ( sK91(X0) != sK92(X0)
& apply(X0,sK91(X0)) = apply(X0,sK92(X0))
& in(sK92(X0),relation_dom(X0))
& in(sK91(X0),relation_dom(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0)) )
| ~ one_to_one(X0) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK91,sK92])],[f987,f988]) ).
fof(f990,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( relation_composition(X0,X1) = X2
| ? [X3,X4] :
( ( ! [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) )
| 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) ) )
& ( ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f457]) ).
fof(f991,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( relation_composition(X0,X1) = X2
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| ~ 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) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) ) )
& ( ? [X10] :
( in(ordered_pair(X10,X8),X1)
& in(ordered_pair(X7,X10),X0) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f990]) ).
fof(f992,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| ~ 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,sK94(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK93(X0,X1,X2),X5),X0) )
| ~ in(ordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,sK94(X0,X1,X2)),X1)
& in(ordered_pair(sK93(X0,X1,X2),X6),X0) )
| in(ordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f993,plain,
! [X0,X1,X2] :
( ? [X6] :
( in(ordered_pair(X6,sK94(X0,X1,X2)),X1)
& in(ordered_pair(sK93(X0,X1,X2),X6),X0) )
=> ( in(ordered_pair(sK95(X0,X1,X2),sK94(X0,X1,X2)),X1)
& in(ordered_pair(sK93(X0,X1,X2),sK95(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f994,plain,
! [X0,X1,X7,X8] :
( ? [X10] :
( in(ordered_pair(X10,X8),X1)
& in(ordered_pair(X7,X10),X0) )
=> ( in(ordered_pair(sK96(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK96(X0,X1,X7,X8)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f995,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( relation_composition(X0,X1) = X2
| ( ( ! [X5] :
( ~ in(ordered_pair(X5,sK94(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK93(X0,X1,X2),X5),X0) )
| ~ in(ordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK95(X0,X1,X2),sK94(X0,X1,X2)),X1)
& in(ordered_pair(sK93(X0,X1,X2),sK95(X0,X1,X2)),X0) )
| in(ordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) ) )
& ( ( in(ordered_pair(sK96(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK96(X0,X1,X7,X8)),X0) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK93,sK94,sK95,sK96])],[f991,f994,f993,f992]) ).
fof(f996,plain,
! [X0] :
( ! [X1] :
( ( is_transitive_in(X0,X1)
| ? [X2,X3,X4] :
( ~ in(ordered_pair(X2,X4),X0)
& in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) )
| ~ is_transitive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f459]) ).
fof(f997,plain,
! [X0] :
( ! [X1] :
( ( is_transitive_in(X0,X1)
| ? [X2,X3,X4] :
( ~ in(ordered_pair(X2,X4),X0)
& in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X5,X6,X7] :
( in(ordered_pair(X5,X7),X0)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1) )
| ~ is_transitive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f996]) ).
fof(f998,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ~ in(ordered_pair(X2,X4),X0)
& in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) )
=> ( ~ in(ordered_pair(sK97(X0,X1),sK99(X0,X1)),X0)
& in(ordered_pair(sK98(X0,X1),sK99(X0,X1)),X0)
& in(ordered_pair(sK97(X0,X1),sK98(X0,X1)),X0)
& in(sK99(X0,X1),X1)
& in(sK98(X0,X1),X1)
& in(sK97(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f999,plain,
! [X0] :
( ! [X1] :
( ( is_transitive_in(X0,X1)
| ( ~ in(ordered_pair(sK97(X0,X1),sK99(X0,X1)),X0)
& in(ordered_pair(sK98(X0,X1),sK99(X0,X1)),X0)
& in(ordered_pair(sK97(X0,X1),sK98(X0,X1)),X0)
& in(sK99(X0,X1),X1)
& in(sK98(X0,X1),X1)
& in(sK97(X0,X1),X1) ) )
& ( ! [X5,X6,X7] :
( in(ordered_pair(X5,X7),X0)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1) )
| ~ is_transitive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK97,sK98,sK99])],[f997,f998]) ).
fof(f1000,plain,
! [X0,X1] :
( ! [X2] :
( ( ( complements_of_subsets(X0,X1) = X2
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(nnf_transformation,[],[f460]) ).
fof(f1001,plain,
! [X0,X1] :
( ! [X2] :
( ( ( complements_of_subsets(X0,X1) = X2
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f1000]) ).
fof(f1002,plain,
! [X0,X1] :
( ! [X2] :
( ( ( complements_of_subsets(X0,X1) = X2
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X0,X4),X1) )
& ( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(rectify,[],[f1001]) ).
fof(f1003,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) )
=> ( ( ~ in(subset_complement(X0,sK100(X0,X1,X2)),X1)
| ~ in(sK100(X0,X1,X2),X2) )
& ( in(subset_complement(X0,sK100(X0,X1,X2)),X1)
| in(sK100(X0,X1,X2),X2) )
& element(sK100(X0,X1,X2),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1004,plain,
! [X0,X1] :
( ! [X2] :
( ( ( complements_of_subsets(X0,X1) = X2
| ( ( ~ in(subset_complement(X0,sK100(X0,X1,X2)),X1)
| ~ in(sK100(X0,X1,X2),X2) )
& ( in(subset_complement(X0,sK100(X0,X1,X2)),X1)
| in(sK100(X0,X1,X2),X2) )
& element(sK100(X0,X1,X2),powerset(X0)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X0,X4),X1) )
& ( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK100])],[f1002,f1003]) ).
fof(f1005,plain,
! [X0] :
( ( ( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0)) )
& ( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f465]) ).
fof(f1006,plain,
! [X0,X1] :
( ? [X2] : relation_of2(X2,X0,X1)
=> relation_of2(sK101(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f1007,plain,
! [X0,X1] : relation_of2(sK101(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK101])],[f120,f1006]) ).
fof(f1008,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK102(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f1009,plain,
! [X0] : element(sK102(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK102])],[f121,f1008]) ).
fof(f1010,plain,
! [X0,X1] :
( ? [X2] : relation_of2_as_subset(X2,X0,X1)
=> relation_of2_as_subset(sK103(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f1011,plain,
! [X0,X1] : relation_of2_as_subset(sK103(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK103])],[f122,f1010]) ).
fof(f1012,plain,
! [X0] :
( ( ( reflexive(X0)
| ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) ) )
& ( ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) )
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f519]) ).
fof(f1013,plain,
! [X0] :
( ( ( reflexive(X0)
| ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) ) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f1012]) ).
fof(f1014,plain,
! [X0] :
( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
=> ( ~ in(ordered_pair(sK104(X0),sK104(X0)),X0)
& in(sK104(X0),relation_field(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1015,plain,
! [X0] :
( ( ( reflexive(X0)
| ( ~ in(ordered_pair(sK104(X0),sK104(X0)),X0)
& in(sK104(X0),relation_field(X0)) ) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK104])],[f1013,f1014]) ).
fof(f1016,plain,
! [X0] :
( ( ( transitive(X0)
| ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) )
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f525]) ).
fof(f1017,plain,
! [X0] :
( ( ( transitive(X0)
| ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X4,X5,X6] :
( in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f1016]) ).
fof(f1018,plain,
! [X0] :
( ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> ( ~ in(ordered_pair(sK105(X0),sK107(X0)),X0)
& in(ordered_pair(sK106(X0),sK107(X0)),X0)
& in(ordered_pair(sK105(X0),sK106(X0)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1019,plain,
! [X0] :
( ( ( transitive(X0)
| ( ~ in(ordered_pair(sK105(X0),sK107(X0)),X0)
& in(ordered_pair(sK106(X0),sK107(X0)),X0)
& in(ordered_pair(sK105(X0),sK106(X0)),X0) ) )
& ( ! [X4,X5,X6] :
( in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK105,sK106,sK107])],[f1017,f1018]) ).
fof(f1021,plain,
! [X0] :
( ? [X2] :
( well_orders(X2,X0)
& relation(X2) )
=> ( well_orders(sK108(X0),X0)
& relation(sK108(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1022,plain,
! [X0,X1] :
( ( well_orders(sK108(X0),X0)
& relation(sK108(X0)) )
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK108])],[f527,f1021]) ).
fof(f1024,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0) )
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f530]) ).
fof(f1025,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f1024]) ).
fof(f1026,plain,
! [X0] :
( ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) )
=> ( sK109(X0) != sK110(X0)
& in(ordered_pair(sK110(X0),sK109(X0)),X0)
& in(ordered_pair(sK109(X0),sK110(X0)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1027,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ( sK109(X0) != sK110(X0)
& in(ordered_pair(sK110(X0),sK109(X0)),X0)
& in(ordered_pair(sK109(X0),sK110(X0)),X0) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK109,sK110])],[f1025,f1026]) ).
fof(f1028,plain,
! [X0] :
( ( ( connected(X0)
| ? [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& X1 != X2
& in(X2,relation_field(X0))
& in(X1,relation_field(X0)) ) )
& ( ! [X1,X2] :
( in(ordered_pair(X2,X1),X0)
| in(ordered_pair(X1,X2),X0)
| X1 = X2
| ~ in(X2,relation_field(X0))
| ~ in(X1,relation_field(X0)) )
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f533]) ).
fof(f1029,plain,
! [X0] :
( ( ( connected(X0)
| ? [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& X1 != X2
& in(X2,relation_field(X0))
& in(X1,relation_field(X0)) ) )
& ( ! [X3,X4] :
( in(ordered_pair(X4,X3),X0)
| in(ordered_pair(X3,X4),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) )
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f1028]) ).
fof(f1030,plain,
! [X0] :
( ? [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& X1 != X2
& in(X2,relation_field(X0))
& in(X1,relation_field(X0)) )
=> ( ~ in(ordered_pair(sK112(X0),sK111(X0)),X0)
& ~ in(ordered_pair(sK111(X0),sK112(X0)),X0)
& sK111(X0) != sK112(X0)
& in(sK112(X0),relation_field(X0))
& in(sK111(X0),relation_field(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1031,plain,
! [X0] :
( ( ( connected(X0)
| ( ~ in(ordered_pair(sK112(X0),sK111(X0)),X0)
& ~ in(ordered_pair(sK111(X0),sK112(X0)),X0)
& sK111(X0) != sK112(X0)
& in(sK112(X0),relation_field(X0))
& in(sK111(X0),relation_field(X0)) ) )
& ( ! [X3,X4] :
( in(ordered_pair(X4,X3),X0)
| in(ordered_pair(X3,X4),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) )
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK111,sK112])],[f1029,f1030]) ).
fof(f1034,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,[],[f175]) ).
fof(f1035,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,[],[f1034]) ).
fof(f1036,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK113(X0,X1),X1)
& in(sK113(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1037,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ( ~ in(sK113(X0,X1),X1)
& in(sK113(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK113])],[f535,f1036]) ).
fof(f1040,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK114)
& relation(sK114) ) ),
introduced(choice_axiom,[]) ).
fof(f1041,plain,
( function(sK114)
& relation(sK114) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK114])],[f178,f1040]) ).
fof(f1042,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK115)
& epsilon_connected(sK115)
& epsilon_transitive(sK115) ) ),
introduced(choice_axiom,[]) ).
fof(f1043,plain,
( ordinal(sK115)
& epsilon_connected(sK115)
& epsilon_transitive(sK115) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK115])],[f179,f1042]) ).
fof(f1044,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK116)
& empty(sK116) ) ),
introduced(choice_axiom,[]) ).
fof(f1045,plain,
( relation(sK116)
& empty(sK116) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK116])],[f180,f1044]) ).
fof(f1046,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK117(X0))
& element(sK117(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1047,plain,
! [X0] :
( ( ~ empty(sK117(X0))
& element(sK117(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK117])],[f538,f1046]) ).
fof(f1048,plain,
( ? [X0] : empty(X0)
=> empty(sK118) ),
introduced(choice_axiom,[]) ).
fof(f1049,plain,
empty(sK118),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK118])],[f182,f1048]) ).
fof(f1050,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK119)
& empty(sK119)
& relation(sK119) ) ),
introduced(choice_axiom,[]) ).
fof(f1051,plain,
( function(sK119)
& empty(sK119)
& relation(sK119) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK119])],[f183,f1050]) ).
fof(f1052,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK120)
& epsilon_connected(sK120)
& epsilon_transitive(sK120)
& empty(sK120)
& one_to_one(sK120)
& function(sK120)
& relation(sK120) ) ),
introduced(choice_axiom,[]) ).
fof(f1053,plain,
( ordinal(sK120)
& epsilon_connected(sK120)
& epsilon_transitive(sK120)
& empty(sK120)
& one_to_one(sK120)
& function(sK120)
& relation(sK120) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK120])],[f184,f1052]) ).
fof(f1054,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK121)
& ~ empty(sK121) ) ),
introduced(choice_axiom,[]) ).
fof(f1055,plain,
( relation(sK121)
& ~ empty(sK121) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK121])],[f185,f1054]) ).
fof(f1056,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK122(X0))
& element(sK122(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1057,plain,
! [X0] :
( empty(sK122(X0))
& element(sK122(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK122])],[f186,f1056]) ).
fof(f1058,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK123) ),
introduced(choice_axiom,[]) ).
fof(f1059,plain,
~ empty(sK123),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK123])],[f187,f1058]) ).
fof(f1060,plain,
( ? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( one_to_one(sK124)
& function(sK124)
& relation(sK124) ) ),
introduced(choice_axiom,[]) ).
fof(f1061,plain,
( one_to_one(sK124)
& function(sK124)
& relation(sK124) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK124])],[f188,f1060]) ).
fof(f1062,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK125)
& epsilon_connected(sK125)
& epsilon_transitive(sK125)
& ~ empty(sK125) ) ),
introduced(choice_axiom,[]) ).
fof(f1063,plain,
( ordinal(sK125)
& epsilon_connected(sK125)
& epsilon_transitive(sK125)
& ~ empty(sK125) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK125])],[f189,f1062]) ).
fof(f1064,plain,
( ? [X0] :
( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(sK126)
& relation(sK126) ) ),
introduced(choice_axiom,[]) ).
fof(f1065,plain,
( relation_empty_yielding(sK126)
& relation(sK126) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK126])],[f190,f1064]) ).
fof(f1066,plain,
( ? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) )
=> ( function(sK127)
& relation_empty_yielding(sK127)
& relation(sK127) ) ),
introduced(choice_axiom,[]) ).
fof(f1067,plain,
( function(sK127)
& relation_empty_yielding(sK127)
& relation(sK127) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK127])],[f191,f1066]) ).
fof(f1068,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f197]) ).
fof(f1069,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f546]) ).
fof(f1070,plain,
! [X0,X1] :
( ( equipotent(X0,X1)
| ~ are_equipotent(X0,X1) )
& ( are_equipotent(X0,X1)
| ~ equipotent(X0,X1) ) ),
inference(nnf_transformation,[],[f199]) ).
fof(f1071,plain,
! [X0] :
( ? [X4] :
( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X4)
| singleton(X5) != X6
| ~ in(X5,X0)
| ~ in(X5,X0) )
& ( ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) )
| ~ in(ordered_pair(X5,X6),X4) ) )
& function(X4)
& relation(X4) )
| ~ sP2(X0) ),
inference(nnf_transformation,[],[f757]) ).
fof(f1072,plain,
! [X0] :
( ? [X4] :
( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X4)
| singleton(X5) != X6
| ~ in(X5,X0)
| ~ in(X5,X0) )
& ( ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) )
| ~ in(ordered_pair(X5,X6),X4) ) )
& function(X4)
& relation(X4) )
| ~ sP2(X0) ),
inference(flattening,[],[f1071]) ).
fof(f1073,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| singleton(X2) != X3
| ~ in(X2,X0)
| ~ in(X2,X0) )
& ( ( singleton(X2) = X3
& in(X2,X0)
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),X1) ) )
& function(X1)
& relation(X1) )
| ~ sP2(X0) ),
inference(rectify,[],[f1072]) ).
fof(f1074,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| singleton(X2) != X3
| ~ in(X2,X0)
| ~ in(X2,X0) )
& ( ( singleton(X2) = X3
& in(X2,X0)
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),X1) ) )
& function(X1)
& relation(X1) )
=> ( ! [X3,X2] :
( ( in(ordered_pair(X2,X3),sK128(X0))
| singleton(X2) != X3
| ~ in(X2,X0)
| ~ in(X2,X0) )
& ( ( singleton(X2) = X3
& in(X2,X0)
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),sK128(X0)) ) )
& function(sK128(X0))
& relation(sK128(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1075,plain,
! [X0] :
( ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),sK128(X0))
| singleton(X2) != X3
| ~ in(X2,X0)
| ~ in(X2,X0) )
& ( ( singleton(X2) = X3
& in(X2,X0)
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),sK128(X0)) ) )
& function(sK128(X0))
& relation(sK128(X0)) )
| ~ sP2(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK128])],[f1073,f1074]) ).
fof(f1076,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& singleton(X1) = X3
& in(X1,X0)
& singleton(X1) = X2
& in(X1,X0) )
=> ( sK130(X0) != sK131(X0)
& sK131(X0) = singleton(sK129(X0))
& in(sK129(X0),X0)
& sK130(X0) = singleton(sK129(X0))
& in(sK129(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1077,plain,
! [X0] :
( sP2(X0)
| ( sK130(X0) != sK131(X0)
& sK131(X0) = singleton(sK129(X0))
& in(sK129(X0),X0)
& sK130(X0) = singleton(sK129(X0))
& in(sK129(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK129,sK130,sK131])],[f758,f1076]) ).
fof(f1078,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ordinal_subset(X1,X2)
| ~ in(X2,X0)
| ~ ordinal(X2) )
& in(X1,X0)
& ordinal(X1) )
| ! [X3] :
( ~ in(X3,X0)
| ~ ordinal(X3) ) ),
inference(rectify,[],[f552]) ).
fof(f1079,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ordinal_subset(X1,X2)
| ~ in(X2,X0)
| ~ ordinal(X2) )
& in(X1,X0)
& ordinal(X1) )
=> ( ! [X2] :
( ordinal_subset(sK132(X0),X2)
| ~ in(X2,X0)
| ~ ordinal(X2) )
& in(sK132(X0),X0)
& ordinal(sK132(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1080,plain,
! [X0] :
( ( ! [X2] :
( ordinal_subset(sK132(X0),X2)
| ~ in(X2,X0)
| ~ ordinal(X2) )
& in(sK132(X0),X0)
& ordinal(sK132(X0)) )
| ! [X3] :
( ~ in(X3,X0)
| ~ ordinal(X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK132])],[f1078,f1079]) ).
fof(f1081,plain,
! [X0,X1,X2] :
( ? [X3] :
( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(X5,X0)
| ~ in(X4,X0) )
& ( ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),X3) ) )
& relation(X3) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f554]) ).
fof(f1082,plain,
! [X0,X1,X2] :
( ? [X3] :
( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(X5,X0)
| ~ in(X4,X0) )
& ( ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),X3) ) )
& relation(X3) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(flattening,[],[f1081]) ).
fof(f1083,plain,
! [X0,X1,X2] :
( ? [X3] :
( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X3)
| ~ in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(X5,X0)
| ~ in(X4,X0) )
& ( ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),X3) ) )
& relation(X3) )
=> ( ! [X5,X4] :
( ( in(ordered_pair(X4,X5),sK133(X0,X1,X2))
| ~ in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(X5,X0)
| ~ in(X4,X0) )
& ( ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),sK133(X0,X1,X2)) ) )
& relation(sK133(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1084,plain,
! [X0,X1,X2] :
( ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),sK133(X0,X1,X2))
| ~ in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(X5,X0)
| ~ in(X4,X0) )
& ( ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),sK133(X0,X1,X2)) ) )
& relation(sK133(X0,X1,X2)) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK133])],[f1082,f1083]) ).
fof(f1085,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& singleton(X1) = X3
& in(X1,X0)
& singleton(X1) = X2
& in(X1,X0) )
| ~ sP3(X0) ),
inference(nnf_transformation,[],[f759]) ).
fof(f1086,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& singleton(X1) = X3
& in(X1,X0)
& singleton(X1) = X2
& in(X1,X0) )
=> ( sK135(X0) != sK136(X0)
& sK136(X0) = singleton(sK134(X0))
& in(sK134(X0),X0)
& sK135(X0) = singleton(sK134(X0))
& in(sK134(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1087,plain,
! [X0] :
( ( sK135(X0) != sK136(X0)
& sK136(X0) = singleton(sK134(X0))
& in(sK134(X0),X0)
& sK135(X0) = singleton(sK134(X0))
& in(sK134(X0),X0) )
| ~ sP3(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK134,sK135,sK136])],[f1085,f1086]) ).
fof(f1088,plain,
! [X0] :
( ? [X4] :
! [X5] :
( ( in(X5,X4)
| ! [X6] :
( singleton(X6) != X5
| ~ in(X6,X0)
| ~ in(X6,X0) ) )
& ( ? [X6] :
( singleton(X6) = X5
& in(X6,X0)
& in(X6,X0) )
| ~ in(X5,X4) ) )
| sP3(X0) ),
inference(nnf_transformation,[],[f760]) ).
fof(f1089,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( in(X2,X1)
| ! [X3] :
( singleton(X3) != X2
| ~ in(X3,X0)
| ~ in(X3,X0) ) )
& ( ? [X4] :
( singleton(X4) = X2
& in(X4,X0)
& in(X4,X0) )
| ~ in(X2,X1) ) )
| sP3(X0) ),
inference(rectify,[],[f1088]) ).
fof(f1090,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( in(X2,X1)
| ! [X3] :
( singleton(X3) != X2
| ~ in(X3,X0)
| ~ in(X3,X0) ) )
& ( ? [X4] :
( singleton(X4) = X2
& in(X4,X0)
& in(X4,X0) )
| ~ in(X2,X1) ) )
=> ! [X2] :
( ( in(X2,sK137(X0))
| ! [X3] :
( singleton(X3) != X2
| ~ in(X3,X0)
| ~ in(X3,X0) ) )
& ( ? [X4] :
( singleton(X4) = X2
& in(X4,X0)
& in(X4,X0) )
| ~ in(X2,sK137(X0)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1091,plain,
! [X0,X2] :
( ? [X4] :
( singleton(X4) = X2
& in(X4,X0)
& in(X4,X0) )
=> ( singleton(sK138(X0,X2)) = X2
& in(sK138(X0,X2),X0)
& in(sK138(X0,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1092,plain,
! [X0] :
( ! [X2] :
( ( in(X2,sK137(X0))
| ! [X3] :
( singleton(X3) != X2
| ~ in(X3,X0)
| ~ in(X3,X0) ) )
& ( ( singleton(sK138(X0,X2)) = X2
& in(sK138(X0,X2),X0)
& in(sK138(X0,X2),X0) )
| ~ in(X2,sK137(X0)) ) )
| sP3(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK137,sK138])],[f1089,f1091,f1090]) ).
fof(f1093,plain,
! [X0] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5,X6] :
( singleton(X5) = X6
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& X2 = X4
& sP4(X0,X3)
& X2 = X3 )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f762]) ).
fof(f1094,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& ? [X4,X5] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& X1 = X3
& sP4(X0,X2)
& X1 = X2 )
| ~ sP5(X0) ),
inference(rectify,[],[f1093]) ).
fof(f1095,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& ? [X4,X5] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& X1 = X3
& sP4(X0,X2)
& X1 = X2 )
=> ( sK140(X0) != sK141(X0)
& ? [X5,X4] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = sK141(X0) )
& sK139(X0) = sK141(X0)
& sP4(X0,sK140(X0))
& sK139(X0) = sK140(X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1096,plain,
! [X0] :
( ? [X5,X4] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = sK141(X0) )
=> ( sK143(X0) = singleton(sK142(X0))
& in(sK142(X0),X0)
& sK141(X0) = ordered_pair(sK142(X0),sK143(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1097,plain,
! [X0] :
( ( sK140(X0) != sK141(X0)
& sK143(X0) = singleton(sK142(X0))
& in(sK142(X0),X0)
& sK141(X0) = ordered_pair(sK142(X0),sK143(X0))
& sK139(X0) = sK141(X0)
& sP4(X0,sK140(X0))
& sK139(X0) = sK140(X0) )
| ~ sP5(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK139,sK140,sK141,sK142,sK143])],[f1094,f1096,f1095]) ).
fof(f1098,plain,
! [X0,X3] :
( ? [X7,X8] :
( singleton(X7) = X8
& in(X7,X0)
& ordered_pair(X7,X8) = X3 )
| ~ sP4(X0,X3) ),
inference(nnf_transformation,[],[f761]) ).
fof(f1099,plain,
! [X0,X1] :
( ? [X2,X3] :
( singleton(X2) = X3
& in(X2,X0)
& ordered_pair(X2,X3) = X1 )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f1098]) ).
fof(f1100,plain,
! [X0,X1] :
( ? [X2,X3] :
( singleton(X2) = X3
& in(X2,X0)
& ordered_pair(X2,X3) = X1 )
=> ( sK145(X0,X1) = singleton(sK144(X0,X1))
& in(sK144(X0,X1),X0)
& ordered_pair(sK144(X0,X1),sK145(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f1101,plain,
! [X0,X1] :
( ( sK145(X0,X1) = singleton(sK144(X0,X1))
& in(sK144(X0,X1),X0)
& ordered_pair(sK144(X0,X1),sK145(X0,X1)) = X1 )
| ~ sP4(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK144,sK145])],[f1099,f1100]) ).
fof(f1102,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( ( in(X10,X9)
| ! [X11] :
( ! [X12,X13] :
( singleton(X12) != X13
| ~ in(X12,X0)
| ordered_pair(X12,X13) != X10 )
| X10 != X11
| ~ in(X11,cartesian_product2(X0,X1)) ) )
& ( ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) )
| ~ in(X10,X9) ) )
| sP5(X0) ),
inference(nnf_transformation,[],[f763]) ).
fof(f1103,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ! [X5,X6] :
( singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3 )
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1)) ) )
& ( ? [X7] :
( ? [X8,X9] :
( singleton(X8) = X9
& in(X8,X0)
& ordered_pair(X8,X9) = X3 )
& X3 = X7
& in(X7,cartesian_product2(X0,X1)) )
| ~ in(X3,X2) ) )
| sP5(X0) ),
inference(rectify,[],[f1102]) ).
fof(f1104,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ! [X5,X6] :
( singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3 )
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1)) ) )
& ( ? [X7] :
( ? [X8,X9] :
( singleton(X8) = X9
& in(X8,X0)
& ordered_pair(X8,X9) = X3 )
& X3 = X7
& in(X7,cartesian_product2(X0,X1)) )
| ~ in(X3,X2) ) )
=> ! [X3] :
( ( in(X3,sK146(X0,X1))
| ! [X4] :
( ! [X5,X6] :
( singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3 )
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1)) ) )
& ( ? [X7] :
( ? [X8,X9] :
( singleton(X8) = X9
& in(X8,X0)
& ordered_pair(X8,X9) = X3 )
& X3 = X7
& in(X7,cartesian_product2(X0,X1)) )
| ~ in(X3,sK146(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1105,plain,
! [X0,X1,X3] :
( ? [X7] :
( ? [X8,X9] :
( singleton(X8) = X9
& in(X8,X0)
& ordered_pair(X8,X9) = X3 )
& X3 = X7
& in(X7,cartesian_product2(X0,X1)) )
=> ( ? [X8,X9] :
( singleton(X8) = X9
& in(X8,X0)
& ordered_pair(X8,X9) = X3 )
& sK147(X0,X1,X3) = X3
& in(sK147(X0,X1,X3),cartesian_product2(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1106,plain,
! [X0,X3] :
( ? [X8,X9] :
( singleton(X8) = X9
& in(X8,X0)
& ordered_pair(X8,X9) = X3 )
=> ( sK149(X0,X3) = singleton(sK148(X0,X3))
& in(sK148(X0,X3),X0)
& ordered_pair(sK148(X0,X3),sK149(X0,X3)) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f1107,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK146(X0,X1))
| ! [X4] :
( ! [X5,X6] :
( singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3 )
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1)) ) )
& ( ( sK149(X0,X3) = singleton(sK148(X0,X3))
& in(sK148(X0,X3),X0)
& ordered_pair(sK148(X0,X3),sK149(X0,X3)) = X3
& sK147(X0,X1,X3) = X3
& in(sK147(X0,X1,X3),cartesian_product2(X0,X1)) )
| ~ in(X3,sK146(X0,X1)) ) )
| sP5(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK146,sK147,sK148,sK149])],[f1103,f1106,f1105,f1104]) ).
fof(f1108,plain,
! [X1,X2] :
( ? [X3,X4,X5] :
( X4 != X5
& ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& ordered_pair(X8,X9) = X4 )
& X3 = X4 )
| ~ sP6(X1,X2) ),
inference(nnf_transformation,[],[f764]) ).
fof(f1109,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5,X6] :
( in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
& ordered_pair(X5,X6) = X4 )
& X2 = X4
& ? [X7,X8] :
( in(ordered_pair(apply(X1,X7),apply(X1,X8)),X0)
& ordered_pair(X7,X8) = X3 )
& X2 = X3 )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f1108]) ).
fof(f1110,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5,X6] :
( in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
& ordered_pair(X5,X6) = X4 )
& X2 = X4
& ? [X7,X8] :
( in(ordered_pair(apply(X1,X7),apply(X1,X8)),X0)
& ordered_pair(X7,X8) = X3 )
& X2 = X3 )
=> ( sK151(X0,X1) != sK152(X0,X1)
& ? [X6,X5] :
( in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
& ordered_pair(X5,X6) = sK152(X0,X1) )
& sK150(X0,X1) = sK152(X0,X1)
& ? [X8,X7] :
( in(ordered_pair(apply(X1,X7),apply(X1,X8)),X0)
& ordered_pair(X7,X8) = sK151(X0,X1) )
& sK150(X0,X1) = sK151(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1111,plain,
! [X0,X1] :
( ? [X6,X5] :
( in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
& ordered_pair(X5,X6) = sK152(X0,X1) )
=> ( in(ordered_pair(apply(X1,sK153(X0,X1)),apply(X1,sK154(X0,X1))),X0)
& sK152(X0,X1) = ordered_pair(sK153(X0,X1),sK154(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1112,plain,
! [X0,X1] :
( ? [X8,X7] :
( in(ordered_pair(apply(X1,X7),apply(X1,X8)),X0)
& ordered_pair(X7,X8) = sK151(X0,X1) )
=> ( in(ordered_pair(apply(X1,sK155(X0,X1)),apply(X1,sK156(X0,X1))),X0)
& sK151(X0,X1) = ordered_pair(sK155(X0,X1),sK156(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1113,plain,
! [X0,X1] :
( ( sK151(X0,X1) != sK152(X0,X1)
& in(ordered_pair(apply(X1,sK153(X0,X1)),apply(X1,sK154(X0,X1))),X0)
& sK152(X0,X1) = ordered_pair(sK153(X0,X1),sK154(X0,X1))
& sK150(X0,X1) = sK152(X0,X1)
& in(ordered_pair(apply(X1,sK155(X0,X1)),apply(X1,sK156(X0,X1))),X0)
& sK151(X0,X1) = ordered_pair(sK155(X0,X1),sK156(X0,X1))
& sK150(X0,X1) = sK151(X0,X1) )
| ~ sP6(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK150,sK151,sK152,sK153,sK154,sK155,sK156])],[f1109,f1112,f1111,f1110]) ).
fof(f1114,plain,
! [X0,X1,X2] :
( ? [X10] :
! [X11] :
( ( in(X11,X10)
| ! [X12] :
( ! [X13,X14] :
( ~ in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
| ordered_pair(X13,X14) != X11 )
| X11 != X12
| ~ in(X12,cartesian_product2(X0,X0)) ) )
& ( ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) )
| ~ in(X11,X10) ) )
| sP6(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f765]) ).
fof(f1115,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ! [X6,X7] :
( ~ in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X0,X0)) ) )
& ( ? [X8] :
( ? [X9,X10] :
( in(ordered_pair(apply(X2,X9),apply(X2,X10)),X1)
& ordered_pair(X9,X10) = X4 )
& X4 = X8
& in(X8,cartesian_product2(X0,X0)) )
| ~ in(X4,X3) ) )
| sP6(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rectify,[],[f1114]) ).
fof(f1116,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ! [X6,X7] :
( ~ in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X0,X0)) ) )
& ( ? [X8] :
( ? [X9,X10] :
( in(ordered_pair(apply(X2,X9),apply(X2,X10)),X1)
& ordered_pair(X9,X10) = X4 )
& X4 = X8
& in(X8,cartesian_product2(X0,X0)) )
| ~ in(X4,X3) ) )
=> ! [X4] :
( ( in(X4,sK157(X0,X1,X2))
| ! [X5] :
( ! [X6,X7] :
( ~ in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X0,X0)) ) )
& ( ? [X8] :
( ? [X9,X10] :
( in(ordered_pair(apply(X2,X9),apply(X2,X10)),X1)
& ordered_pair(X9,X10) = X4 )
& X4 = X8
& in(X8,cartesian_product2(X0,X0)) )
| ~ in(X4,sK157(X0,X1,X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1117,plain,
! [X0,X1,X2,X4] :
( ? [X8] :
( ? [X9,X10] :
( in(ordered_pair(apply(X2,X9),apply(X2,X10)),X1)
& ordered_pair(X9,X10) = X4 )
& X4 = X8
& in(X8,cartesian_product2(X0,X0)) )
=> ( ? [X9,X10] :
( in(ordered_pair(apply(X2,X9),apply(X2,X10)),X1)
& ordered_pair(X9,X10) = X4 )
& sK158(X0,X1,X2,X4) = X4
& in(sK158(X0,X1,X2,X4),cartesian_product2(X0,X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1118,plain,
! [X1,X2,X4] :
( ? [X9,X10] :
( in(ordered_pair(apply(X2,X9),apply(X2,X10)),X1)
& ordered_pair(X9,X10) = X4 )
=> ( in(ordered_pair(apply(X2,sK159(X1,X2,X4)),apply(X2,sK160(X1,X2,X4))),X1)
& ordered_pair(sK159(X1,X2,X4),sK160(X1,X2,X4)) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f1119,plain,
! [X0,X1,X2] :
( ! [X4] :
( ( in(X4,sK157(X0,X1,X2))
| ! [X5] :
( ! [X6,X7] :
( ~ in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X0,X0)) ) )
& ( ( in(ordered_pair(apply(X2,sK159(X1,X2,X4)),apply(X2,sK160(X1,X2,X4))),X1)
& ordered_pair(sK159(X1,X2,X4),sK160(X1,X2,X4)) = X4
& sK158(X0,X1,X2,X4) = X4
& in(sK158(X0,X1,X2,X4),cartesian_product2(X0,X0)) )
| ~ in(X4,sK157(X0,X1,X2)) ) )
| sP6(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK157,sK158,sK159,sK160])],[f1115,f1118,f1117,f1116]) ).
fof(f1120,plain,
( ? [X1,X2,X3] :
( X2 != X3
& ordinal(X3)
& X1 = X3
& ordinal(X2)
& X1 = X2 )
| ~ sP7 ),
inference(nnf_transformation,[],[f766]) ).
fof(f1121,plain,
( ? [X0,X1,X2] :
( X1 != X2
& ordinal(X2)
& X0 = X2
& ordinal(X1)
& X0 = X1 )
| ~ sP7 ),
inference(rectify,[],[f1120]) ).
fof(f1122,plain,
( ? [X0,X1,X2] :
( X1 != X2
& ordinal(X2)
& X0 = X2
& ordinal(X1)
& X0 = X1 )
=> ( sK162 != sK163
& ordinal(sK163)
& sK161 = sK163
& ordinal(sK162)
& sK161 = sK162 ) ),
introduced(choice_axiom,[]) ).
fof(f1123,plain,
( ( sK162 != sK163
& ordinal(sK163)
& sK161 = sK163
& ordinal(sK162)
& sK161 = sK162 )
| ~ sP7 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK161,sK162,sK163])],[f1121,f1122]) ).
fof(f1124,plain,
! [X0] :
( ? [X4] :
! [X5] :
( ( in(X5,X4)
| ! [X6] :
( ~ ordinal(X5)
| X5 != X6
| ~ in(X6,X0) ) )
& ( ? [X6] :
( ordinal(X5)
& X5 = X6
& in(X6,X0) )
| ~ in(X5,X4) ) )
| sP7 ),
inference(nnf_transformation,[],[f767]) ).
fof(f1125,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ ordinal(X2)
| X2 != X3
| ~ in(X3,X0) ) )
& ( ? [X4] :
( ordinal(X2)
& X2 = X4
& in(X4,X0) )
| ~ in(X2,X1) ) )
| sP7 ),
inference(rectify,[],[f1124]) ).
fof(f1126,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ ordinal(X2)
| X2 != X3
| ~ in(X3,X0) ) )
& ( ? [X4] :
( ordinal(X2)
& X2 = X4
& in(X4,X0) )
| ~ in(X2,X1) ) )
=> ! [X2] :
( ( in(X2,sK164(X0))
| ! [X3] :
( ~ ordinal(X2)
| X2 != X3
| ~ in(X3,X0) ) )
& ( ? [X4] :
( ordinal(X2)
& X2 = X4
& in(X4,X0) )
| ~ in(X2,sK164(X0)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1127,plain,
! [X0,X2] :
( ? [X4] :
( ordinal(X2)
& X2 = X4
& in(X4,X0) )
=> ( ordinal(X2)
& sK165(X0,X2) = X2
& in(sK165(X0,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1128,plain,
! [X0] :
( ! [X2] :
( ( in(X2,sK164(X0))
| ! [X3] :
( ~ ordinal(X2)
| X2 != X3
| ~ in(X3,X0) ) )
& ( ( ordinal(X2)
& sK165(X0,X2) = X2
& in(sK165(X0,X2),X0) )
| ~ in(X2,sK164(X0)) ) )
| sP7 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK164,sK165])],[f1125,f1127,f1126]) ).
fof(f1129,plain,
! [X0] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( in(X5,X0)
& X4 = X5
& ordinal(X5) )
& X2 = X4
& sP8(X0,X3)
& X2 = X3 )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f769]) ).
fof(f1130,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& ? [X4] :
( in(X4,X0)
& X3 = X4
& ordinal(X4) )
& X1 = X3
& sP8(X0,X2)
& X1 = X2 )
| ~ sP9(X0) ),
inference(rectify,[],[f1129]) ).
fof(f1131,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& ? [X4] :
( in(X4,X0)
& X3 = X4
& ordinal(X4) )
& X1 = X3
& sP8(X0,X2)
& X1 = X2 )
=> ( sK167(X0) != sK168(X0)
& ? [X4] :
( in(X4,X0)
& sK168(X0) = X4
& ordinal(X4) )
& sK166(X0) = sK168(X0)
& sP8(X0,sK167(X0))
& sK166(X0) = sK167(X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1132,plain,
! [X0] :
( ? [X4] :
( in(X4,X0)
& sK168(X0) = X4
& ordinal(X4) )
=> ( in(sK169(X0),X0)
& sK168(X0) = sK169(X0)
& ordinal(sK169(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1133,plain,
! [X0] :
( ( sK167(X0) != sK168(X0)
& in(sK169(X0),X0)
& sK168(X0) = sK169(X0)
& ordinal(sK169(X0))
& sK166(X0) = sK168(X0)
& sP8(X0,sK167(X0))
& sK166(X0) = sK167(X0) )
| ~ sP9(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK166,sK167,sK168,sK169])],[f1130,f1132,f1131]) ).
fof(f1134,plain,
! [X0,X3] :
( ? [X6] :
( in(X6,X0)
& X3 = X6
& ordinal(X6) )
| ~ sP8(X0,X3) ),
inference(nnf_transformation,[],[f768]) ).
fof(f1135,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
& X1 = X2
& ordinal(X2) )
| ~ sP8(X0,X1) ),
inference(rectify,[],[f1134]) ).
fof(f1136,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
& X1 = X2
& ordinal(X2) )
=> ( in(sK170(X0,X1),X0)
& sK170(X0,X1) = X1
& ordinal(sK170(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1137,plain,
! [X0,X1] :
( ( in(sK170(X0,X1),X0)
& sK170(X0,X1) = X1
& ordinal(sK170(X0,X1)) )
| ~ sP8(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK170])],[f1135,f1136]) ).
fof(f1138,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( ( in(X8,X7)
| ! [X9] :
( ! [X10] :
( ~ in(X10,X0)
| X8 != X10
| ~ ordinal(X10) )
| X8 != X9
| ~ in(X9,succ(X1)) ) )
& ( ? [X9] :
( ? [X10] :
( in(X10,X0)
& X8 = X10
& ordinal(X10) )
& X8 = X9
& in(X9,succ(X1)) )
| ~ in(X8,X7) ) )
| sP9(X0)
| ~ ordinal(X1) ),
inference(nnf_transformation,[],[f770]) ).
fof(f1139,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ! [X5] :
( ~ in(X5,X0)
| X3 != X5
| ~ ordinal(X5) )
| X3 != X4
| ~ in(X4,succ(X1)) ) )
& ( ? [X6] :
( ? [X7] :
( in(X7,X0)
& X3 = X7
& ordinal(X7) )
& X3 = X6
& in(X6,succ(X1)) )
| ~ in(X3,X2) ) )
| sP9(X0)
| ~ ordinal(X1) ),
inference(rectify,[],[f1138]) ).
fof(f1140,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ! [X5] :
( ~ in(X5,X0)
| X3 != X5
| ~ ordinal(X5) )
| X3 != X4
| ~ in(X4,succ(X1)) ) )
& ( ? [X6] :
( ? [X7] :
( in(X7,X0)
& X3 = X7
& ordinal(X7) )
& X3 = X6
& in(X6,succ(X1)) )
| ~ in(X3,X2) ) )
=> ! [X3] :
( ( in(X3,sK171(X0,X1))
| ! [X4] :
( ! [X5] :
( ~ in(X5,X0)
| X3 != X5
| ~ ordinal(X5) )
| X3 != X4
| ~ in(X4,succ(X1)) ) )
& ( ? [X6] :
( ? [X7] :
( in(X7,X0)
& X3 = X7
& ordinal(X7) )
& X3 = X6
& in(X6,succ(X1)) )
| ~ in(X3,sK171(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1141,plain,
! [X0,X1,X3] :
( ? [X6] :
( ? [X7] :
( in(X7,X0)
& X3 = X7
& ordinal(X7) )
& X3 = X6
& in(X6,succ(X1)) )
=> ( ? [X7] :
( in(X7,X0)
& X3 = X7
& ordinal(X7) )
& sK172(X0,X1,X3) = X3
& in(sK172(X0,X1,X3),succ(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1142,plain,
! [X0,X3] :
( ? [X7] :
( in(X7,X0)
& X3 = X7
& ordinal(X7) )
=> ( in(sK173(X0,X3),X0)
& sK173(X0,X3) = X3
& ordinal(sK173(X0,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f1143,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK171(X0,X1))
| ! [X4] :
( ! [X5] :
( ~ in(X5,X0)
| X3 != X5
| ~ ordinal(X5) )
| X3 != X4
| ~ in(X4,succ(X1)) ) )
& ( ( in(sK173(X0,X3),X0)
& sK173(X0,X3) = X3
& ordinal(sK173(X0,X3))
& sK172(X0,X1,X3) = X3
& in(sK172(X0,X1,X3),succ(X1)) )
| ~ in(X3,sK171(X0,X1)) ) )
| sP9(X0)
| ~ ordinal(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK171,sK172,sK173])],[f1139,f1142,f1141,f1140]) ).
fof(f1144,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1)) )
& ( ( ? [X4,X5] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) )
| ~ in(X3,X2) ) ),
inference(nnf_transformation,[],[f211]) ).
fof(f1145,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1)) )
& ( ( ? [X4,X5] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) )
| ~ in(X3,X2) ) ),
inference(flattening,[],[f1144]) ).
fof(f1146,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1)) )
& ( ( ? [X6,X7] :
( singleton(X6) = X7
& in(X6,X0)
& ordered_pair(X6,X7) = X3 )
& in(X3,cartesian_product2(X0,X1)) )
| ~ in(X3,X2) ) ),
inference(rectify,[],[f1145]) ).
fof(f1147,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1)) )
& ( ( ? [X6,X7] :
( singleton(X6) = X7
& in(X6,X0)
& ordered_pair(X6,X7) = X3 )
& in(X3,cartesian_product2(X0,X1)) )
| ~ in(X3,X2) ) )
=> ! [X3] :
( ( in(X3,sK174(X0,X1))
| ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1)) )
& ( ( ? [X6,X7] :
( singleton(X6) = X7
& in(X6,X0)
& ordered_pair(X6,X7) = X3 )
& in(X3,cartesian_product2(X0,X1)) )
| ~ in(X3,sK174(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1148,plain,
! [X0,X3] :
( ? [X6,X7] :
( singleton(X6) = X7
& in(X6,X0)
& ordered_pair(X6,X7) = X3 )
=> ( sK176(X0,X3) = singleton(sK175(X0,X3))
& in(sK175(X0,X3),X0)
& ordered_pair(sK175(X0,X3),sK176(X0,X3)) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f1149,plain,
! [X0,X1,X3] :
( ( in(X3,sK174(X0,X1))
| ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1)) )
& ( ( sK176(X0,X3) = singleton(sK175(X0,X3))
& in(sK175(X0,X3),X0)
& ordered_pair(sK175(X0,X3),sK176(X0,X3)) = X3
& in(X3,cartesian_product2(X0,X1)) )
| ~ in(X3,sK174(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK174,sK175,sK176])],[f1146,f1148,f1147]) ).
fof(f1150,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0)) )
& ( ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X0)) )
| ~ in(X4,X3) ) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f566]) ).
fof(f1151,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0)) )
& ( ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X0)) )
| ~ in(X4,X3) ) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(flattening,[],[f1150]) ).
fof(f1152,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0)) )
& ( ( ? [X7,X8] :
( in(ordered_pair(apply(X2,X7),apply(X2,X8)),X1)
& ordered_pair(X7,X8) = X4 )
& in(X4,cartesian_product2(X0,X0)) )
| ~ in(X4,X3) ) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rectify,[],[f1151]) ).
fof(f1153,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0)) )
& ( ( ? [X7,X8] :
( in(ordered_pair(apply(X2,X7),apply(X2,X8)),X1)
& ordered_pair(X7,X8) = X4 )
& in(X4,cartesian_product2(X0,X0)) )
| ~ in(X4,X3) ) )
=> ! [X4] :
( ( in(X4,sK177(X0,X1,X2))
| ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0)) )
& ( ( ? [X7,X8] :
( in(ordered_pair(apply(X2,X7),apply(X2,X8)),X1)
& ordered_pair(X7,X8) = X4 )
& in(X4,cartesian_product2(X0,X0)) )
| ~ in(X4,sK177(X0,X1,X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1154,plain,
! [X1,X2,X4] :
( ? [X7,X8] :
( in(ordered_pair(apply(X2,X7),apply(X2,X8)),X1)
& ordered_pair(X7,X8) = X4 )
=> ( in(ordered_pair(apply(X2,sK178(X1,X2,X4)),apply(X2,sK179(X1,X2,X4))),X1)
& ordered_pair(sK178(X1,X2,X4),sK179(X1,X2,X4)) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f1155,plain,
! [X0,X1,X2] :
( ! [X4] :
( ( in(X4,sK177(X0,X1,X2))
| ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0)) )
& ( ( in(ordered_pair(apply(X2,sK178(X1,X2,X4)),apply(X2,sK179(X1,X2,X4))),X1)
& ordered_pair(sK178(X1,X2,X4),sK179(X1,X2,X4)) = X4
& in(X4,cartesian_product2(X0,X0)) )
| ~ in(X4,sK177(X0,X1,X2)) ) )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK177,sK178,sK179])],[f1152,f1154,f1153]) ).
fof(f1156,plain,
! [X0] :
? [X1] :
! [X2] :
( ( in(X2,X1)
| ~ ordinal(X2)
| ~ in(X2,X0) )
& ( ( ordinal(X2)
& in(X2,X0) )
| ~ in(X2,X1) ) ),
inference(nnf_transformation,[],[f213]) ).
fof(f1157,plain,
! [X0] :
? [X1] :
! [X2] :
( ( in(X2,X1)
| ~ ordinal(X2)
| ~ in(X2,X0) )
& ( ( ordinal(X2)
& in(X2,X0) )
| ~ in(X2,X1) ) ),
inference(flattening,[],[f1156]) ).
fof(f1158,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( in(X2,X1)
| ~ ordinal(X2)
| ~ in(X2,X0) )
& ( ( ordinal(X2)
& in(X2,X0) )
| ~ in(X2,X1) ) )
=> ! [X2] :
( ( in(X2,sK180(X0))
| ~ ordinal(X2)
| ~ in(X2,X0) )
& ( ( ordinal(X2)
& in(X2,X0) )
| ~ in(X2,sK180(X0)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1159,plain,
! [X0,X2] :
( ( in(X2,sK180(X0))
| ~ ordinal(X2)
| ~ in(X2,X0) )
& ( ( ordinal(X2)
& in(X2,X0) )
| ~ in(X2,sK180(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK180])],[f1157,f1158]) ).
fof(f1160,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4) )
| ~ in(X3,succ(X1)) )
& ( ( ? [X4] :
( in(X4,X0)
& X3 = X4
& ordinal(X4) )
& in(X3,succ(X1)) )
| ~ in(X3,X2) ) )
| ~ ordinal(X1) ),
inference(nnf_transformation,[],[f567]) ).
fof(f1161,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4) )
| ~ in(X3,succ(X1)) )
& ( ( ? [X4] :
( in(X4,X0)
& X3 = X4
& ordinal(X4) )
& in(X3,succ(X1)) )
| ~ in(X3,X2) ) )
| ~ ordinal(X1) ),
inference(flattening,[],[f1160]) ).
fof(f1162,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4) )
| ~ in(X3,succ(X1)) )
& ( ( ? [X5] :
( in(X5,X0)
& X3 = X5
& ordinal(X5) )
& in(X3,succ(X1)) )
| ~ in(X3,X2) ) )
| ~ ordinal(X1) ),
inference(rectify,[],[f1161]) ).
fof(f1163,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4) )
| ~ in(X3,succ(X1)) )
& ( ( ? [X5] :
( in(X5,X0)
& X3 = X5
& ordinal(X5) )
& in(X3,succ(X1)) )
| ~ in(X3,X2) ) )
=> ! [X3] :
( ( in(X3,sK181(X0,X1))
| ! [X4] :
( ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4) )
| ~ in(X3,succ(X1)) )
& ( ( ? [X5] :
( in(X5,X0)
& X3 = X5
& ordinal(X5) )
& in(X3,succ(X1)) )
| ~ in(X3,sK181(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1164,plain,
! [X0,X3] :
( ? [X5] :
( in(X5,X0)
& X3 = X5
& ordinal(X5) )
=> ( in(sK182(X0,X3),X0)
& sK182(X0,X3) = X3
& ordinal(sK182(X0,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f1165,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK181(X0,X1))
| ! [X4] :
( ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4) )
| ~ in(X3,succ(X1)) )
& ( ( in(sK182(X0,X3),X0)
& sK182(X0,X3) = X3
& ordinal(sK182(X0,X3))
& in(X3,succ(X1)) )
| ~ in(X3,sK181(X0,X1)) ) )
| ~ ordinal(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK181,sK182])],[f1162,f1164,f1163]) ).
fof(f1166,plain,
! [X0] :
( ? [X3,X4,X5] :
( X4 != X5
& singleton(X3) = X5
& singleton(X3) = X4
& in(X3,X0) )
| ~ sP10(X0) ),
inference(nnf_transformation,[],[f771]) ).
fof(f1167,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& singleton(X1) = X3
& singleton(X1) = X2
& in(X1,X0) )
| ~ sP10(X0) ),
inference(rectify,[],[f1166]) ).
fof(f1168,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& singleton(X1) = X3
& singleton(X1) = X2
& in(X1,X0) )
=> ( sK184(X0) != sK185(X0)
& sK185(X0) = singleton(sK183(X0))
& sK184(X0) = singleton(sK183(X0))
& in(sK183(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1169,plain,
! [X0] :
( ( sK184(X0) != sK185(X0)
& sK185(X0) = singleton(sK183(X0))
& sK184(X0) = singleton(sK183(X0))
& in(sK183(X0),X0) )
| ~ sP10(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK183,sK184,sK185])],[f1167,f1168]) ).
fof(f1170,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( singleton(X2) = apply(X1,X2)
| ~ in(X2,X0) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) )
| ? [X3] :
( ! [X4] : singleton(X3) != X4
& in(X3,X0) )
| sP10(X0) ),
inference(rectify,[],[f772]) ).
fof(f1171,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( singleton(X2) = apply(X1,X2)
| ~ in(X2,X0) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) )
=> ( ! [X2] :
( singleton(X2) = apply(sK186(X0),X2)
| ~ in(X2,X0) )
& relation_dom(sK186(X0)) = X0
& function(sK186(X0))
& relation(sK186(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1172,plain,
! [X0] :
( ? [X3] :
( ! [X4] : singleton(X3) != X4
& in(X3,X0) )
=> ( ! [X4] : singleton(sK187(X0)) != X4
& in(sK187(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1173,plain,
! [X0] :
( ( ! [X2] :
( singleton(X2) = apply(sK186(X0),X2)
| ~ in(X2,X0) )
& relation_dom(sK186(X0)) = X0
& function(sK186(X0))
& relation(sK186(X0)) )
| ( ! [X4] : singleton(sK187(X0)) != X4
& in(sK187(X0),X0) )
| sP10(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK186,sK187])],[f1170,f1172,f1171]) ).
fof(f1174,plain,
( ? [X0] :
! [X1] :
( ? [X2] :
( singleton(X2) != apply(X1,X2)
& in(X2,X0) )
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) )
=> ! [X1] :
( ? [X2] :
( singleton(X2) != apply(X1,X2)
& in(X2,sK188) )
| relation_dom(X1) != sK188
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1175,plain,
! [X1] :
( ? [X2] :
( singleton(X2) != apply(X1,X2)
& in(X2,sK188) )
=> ( singleton(sK189(X1)) != apply(X1,sK189(X1))
& in(sK189(X1),sK188) ) ),
introduced(choice_axiom,[]) ).
fof(f1176,plain,
! [X1] :
( ( singleton(sK189(X1)) != apply(X1,sK189(X1))
& in(sK189(X1),sK188) )
| relation_dom(X1) != sK188
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK188,sK189])],[f570,f1175,f1174]) ).
fof(f1177,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,[],[f220]) ).
fof(f1178,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,[],[f1177]) ).
fof(f1179,plain,
! [X0,X1,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))) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f574]) ).
fof(f1180,plain,
! [X0,X1,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))) ) )
| ~ relation(X2) ),
inference(flattening,[],[f1179]) ).
fof(f1181,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( in(X2,X1)
| are_equipotent(X2,X1)
| ~ subset(X2,X1) )
& ! [X3] :
( in(powerset(X3),X1)
| ~ in(X3,X1) )
& ! [X4,X5] :
( in(X5,X1)
| ~ subset(X5,X4)
| ~ in(X4,X1) )
& in(X0,X1) )
=> ( ! [X2] :
( in(X2,sK190(X0))
| are_equipotent(X2,sK190(X0))
| ~ subset(X2,sK190(X0)) )
& ! [X3] :
( in(powerset(X3),sK190(X0))
| ~ in(X3,sK190(X0)) )
& ! [X5,X4] :
( in(X5,sK190(X0))
| ~ subset(X5,X4)
| ~ in(X4,sK190(X0)) )
& in(X0,sK190(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1182,plain,
! [X0] :
( ! [X2] :
( in(X2,sK190(X0))
| are_equipotent(X2,sK190(X0))
| ~ subset(X2,sK190(X0)) )
& ! [X3] :
( in(powerset(X3),sK190(X0))
| ~ in(X3,sK190(X0)) )
& ! [X4,X5] :
( in(X5,sK190(X0))
| ~ subset(X5,X4)
| ~ in(X4,sK190(X0)) )
& in(X0,sK190(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK190])],[f585,f1181]) ).
fof(f1183,plain,
! [X0,X1,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)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f587]) ).
fof(f1184,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f1183]) ).
fof(f1185,plain,
! [X0,X1,X2] :
( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) )
=> ( in(sK191(X0,X1,X2),X1)
& in(ordered_pair(sK191(X0,X1,X2),X0),X2)
& in(sK191(X0,X1,X2),relation_dom(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1186,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) ) )
& ( ( in(sK191(X0,X1,X2),X1)
& in(ordered_pair(sK191(X0,X1,X2),X0),X2)
& in(sK191(X0,X1,X2),relation_dom(X2)) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK191])],[f1184,f1185]) ).
fof(f1187,plain,
! [X0,X1,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)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f600]) ).
fof(f1188,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f1187]) ).
fof(f1189,plain,
! [X0,X1,X2] :
( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) )
=> ( in(sK192(X0,X1,X2),X1)
& in(ordered_pair(X0,sK192(X0,X1,X2)),X2)
& in(sK192(X0,X1,X2),relation_rng(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1190,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) ) )
& ( ( in(sK192(X0,X1,X2),X1)
& in(ordered_pair(X0,sK192(X0,X1,X2)),X2)
& in(sK192(X0,X1,X2),relation_rng(X2)) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK192])],[f1188,f1189]) ).
fof(f1191,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f604]) ).
fof(f1192,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(flattening,[],[f1191]) ).
fof(f1193,plain,
! [X0,X1] :
( ! [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))) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f622]) ).
fof(f1194,plain,
! [X0,X1] :
( ! [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))) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f1193]) ).
fof(f1195,plain,
! [X0,X1,X2] :
( ( ( ! [X3] :
( ? [X4] : in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1) )
| relation_dom_as_subset(X1,X0,X2) != X1 )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ? [X3] :
( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) ) ) )
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(nnf_transformation,[],[f629]) ).
fof(f1196,plain,
! [X0,X1,X2] :
( ( ( ! [X3] :
( ? [X4] : in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1) )
| relation_dom_as_subset(X1,X0,X2) != X1 )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ? [X5] :
( ! [X6] : ~ in(ordered_pair(X5,X6),X2)
& in(X5,X1) ) ) )
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(rectify,[],[f1195]) ).
fof(f1197,plain,
! [X2,X3] :
( ? [X4] : in(ordered_pair(X3,X4),X2)
=> in(ordered_pair(X3,sK193(X2,X3)),X2) ),
introduced(choice_axiom,[]) ).
fof(f1198,plain,
! [X1,X2] :
( ? [X5] :
( ! [X6] : ~ in(ordered_pair(X5,X6),X2)
& in(X5,X1) )
=> ( ! [X6] : ~ in(ordered_pair(sK194(X1,X2),X6),X2)
& in(sK194(X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1199,plain,
! [X0,X1,X2] :
( ( ( ! [X3] :
( in(ordered_pair(X3,sK193(X2,X3)),X2)
| ~ in(X3,X1) )
| relation_dom_as_subset(X1,X0,X2) != X1 )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ( ! [X6] : ~ in(ordered_pair(sK194(X1,X2),X6),X2)
& in(sK194(X1,X2),X1) ) ) )
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK193,sK194])],[f1196,f1198,f1197]) ).
fof(f1200,plain,
! [X0,X1,X2] :
( ( ( ! [X3] :
( ? [X4] : in(ordered_pair(X4,X3),X2)
| ~ in(X3,X1) )
| relation_rng_as_subset(X0,X1,X2) != X1 )
& ( relation_rng_as_subset(X0,X1,X2) = X1
| ? [X3] :
( ! [X4] : ~ in(ordered_pair(X4,X3),X2)
& in(X3,X1) ) ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(nnf_transformation,[],[f636]) ).
fof(f1201,plain,
! [X0,X1,X2] :
( ( ( ! [X3] :
( ? [X4] : in(ordered_pair(X4,X3),X2)
| ~ in(X3,X1) )
| relation_rng_as_subset(X0,X1,X2) != X1 )
& ( relation_rng_as_subset(X0,X1,X2) = X1
| ? [X5] :
( ! [X6] : ~ in(ordered_pair(X6,X5),X2)
& in(X5,X1) ) ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(rectify,[],[f1200]) ).
fof(f1202,plain,
! [X2,X3] :
( ? [X4] : in(ordered_pair(X4,X3),X2)
=> in(ordered_pair(sK195(X2,X3),X3),X2) ),
introduced(choice_axiom,[]) ).
fof(f1203,plain,
! [X1,X2] :
( ? [X5] :
( ! [X6] : ~ in(ordered_pair(X6,X5),X2)
& in(X5,X1) )
=> ( ! [X6] : ~ in(ordered_pair(X6,sK196(X1,X2)),X2)
& in(sK196(X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1204,plain,
! [X0,X1,X2] :
( ( ( ! [X3] :
( in(ordered_pair(sK195(X2,X3),X3),X2)
| ~ in(X3,X1) )
| relation_rng_as_subset(X0,X1,X2) != X1 )
& ( relation_rng_as_subset(X0,X1,X2) = X1
| ( ! [X6] : ~ in(ordered_pair(X6,sK196(X1,X2)),X2)
& in(sK196(X1,X2),X1) ) ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK195,sK196])],[f1201,f1203,f1202]) ).
fof(f1205,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f653]) ).
fof(f1206,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK197(X0,X1),X1)
| ~ in(sK197(X0,X1),X0) )
& ( in(sK197(X0,X1),X1)
| in(sK197(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1207,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK197(X0,X1),X1)
| ~ in(sK197(X0,X1),X0) )
& ( in(sK197(X0,X1),X1)
| in(sK197(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK197])],[f1205,f1206]) ).
fof(f1208,plain,
! [X0] :
( ? [X1] :
( ( ~ subset(X1,X0)
| ~ ordinal(X1) )
& in(X1,X0) )
=> ( ( ~ subset(sK198(X0),X0)
| ~ ordinal(sK198(X0)) )
& in(sK198(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1209,plain,
! [X0] :
( ordinal(X0)
| ( ( ~ subset(sK198(X0),X0)
| ~ ordinal(sK198(X0)) )
& in(sK198(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK198])],[f656,f1208]) ).
fof(f1210,plain,
! [X0] :
( ? [X2] :
( ! [X3] :
( ordinal_subset(X2,X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(X2,X0)
& ordinal(X2) )
=> ( ! [X3] :
( ordinal_subset(sK199(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(sK199(X0),X0)
& ordinal(sK199(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1211,plain,
! [X0,X1] :
( ( ! [X3] :
( ordinal_subset(sK199(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3) )
& in(sK199(X0),X0)
& ordinal(sK199(X0)) )
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK199])],[f660,f1210]) ).
fof(f1212,plain,
! [X0] :
( ! [X1] :
( ( ( in(X0,X1)
| ~ ordinal_subset(succ(X0),X1) )
& ( ordinal_subset(succ(X0),X1)
| ~ in(X0,X1) ) )
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f663]) ).
fof(f1213,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f667]) ).
fof(f1214,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f1213]) ).
fof(f1215,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f1214]) ).
fof(f1216,plain,
! [X0,X1] :
( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
=> ( sK200(X0,X1) != apply(X1,sK200(X0,X1))
& in(sK200(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1217,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ( sK200(X0,X1) != apply(X1,sK200(X0,X1))
& in(sK200(X0,X1),X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK200])],[f1215,f1216]) ).
fof(f1218,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f295]) ).
fof(f1219,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f296]) ).
fof(f1220,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,[],[f297]) ).
fof(f1221,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,[],[f1220]) ).
fof(f1222,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f300]) ).
fof(f1223,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f1222]) ).
fof(f1224,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f303]) ).
fof(f1225,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
=> ( in(sK201(X0,X1),X1)
& in(sK201(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f1226,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ( in(sK201(X0,X1),X1)
& in(sK201(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK201])],[f673,f1225]) ).
fof(f1227,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) ) )
& ( ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f676]) ).
fof(f1228,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) ) )
& ( ! [X2] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(rectify,[],[f1227]) ).
fof(f1229,plain,
! [X0] :
( ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) )
=> ( ~ in(succ(sK202(X0)),X0)
& in(sK202(X0),X0)
& ordinal(sK202(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1230,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ( ~ in(succ(sK202(X0)),X0)
& in(sK202(X0),X0)
& ordinal(sK202(X0)) ) )
& ( ! [X2] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK202])],[f1228,f1229]) ).
fof(f1231,plain,
! [X0] :
( ? [X2] :
( succ(X2) = X0
& ordinal(X2) )
=> ( succ(sK203(X0)) = X0
& ordinal(sK203(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1232,plain,
! [X0] :
( ( ( ~ being_limit_ordinal(X0)
| ! [X1] :
( succ(X1) != X0
| ~ ordinal(X1) ) )
& ( ( succ(sK203(X0)) = X0
& ordinal(sK203(X0)) )
| being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK203])],[f677,f1231]) ).
fof(f1233,plain,
! [X0,X1] :
( ! [X2] :
( ( ( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2)) )
& ( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2) ) )
| ~ element(X2,powerset(X0)) )
| ~ element(X1,powerset(X0)) ),
inference(nnf_transformation,[],[f678]) ).
fof(f1234,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK204(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f1235,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK204(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK204])],[f698,f1234]) ).
fof(f1236,plain,
! [X2,X3,X0,X1] :
( ( sP11(X2,X3,X0,X1)
| ( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ~ sP11(X2,X3,X0,X1) ) ),
inference(nnf_transformation,[],[f773]) ).
fof(f1237,plain,
! [X2,X3,X0,X1] :
( ( sP11(X2,X3,X0,X1)
| ( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ~ sP11(X2,X3,X0,X1) ) ),
inference(flattening,[],[f1236]) ).
fof(f1238,plain,
! [X0,X1,X2,X3] :
( ( sP11(X0,X1,X2,X3)
| ( ( apply(X2,X1) != X0
| ~ in(X1,relation_dom(X2)) )
& apply(X3,X0) = X1
& in(X0,relation_rng(X2)) ) )
& ( ( apply(X2,X1) = X0
& in(X1,relation_dom(X2)) )
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP11(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1237]) ).
fof(f1239,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP11(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP11(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f774]) ).
fof(f1240,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP11(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP11(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f1239]) ).
fof(f1241,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP11(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X4,X5] :
( ( ( apply(X1,X4) = X5
& in(X4,relation_rng(X0)) )
| apply(X0,X5) != X4
| ~ in(X5,relation_dom(X0)) )
& sP11(X4,X5,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f1240]) ).
fof(f1242,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP11(X2,X3,X0,X1) )
=> ( ( ( sK206(X0,X1) != apply(X1,sK205(X0,X1))
| ~ in(sK205(X0,X1),relation_rng(X0)) )
& sK205(X0,X1) = apply(X0,sK206(X0,X1))
& in(sK206(X0,X1),relation_dom(X0)) )
| ~ sP11(sK205(X0,X1),sK206(X0,X1),X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1243,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ( ( sK206(X0,X1) != apply(X1,sK205(X0,X1))
| ~ in(sK205(X0,X1),relation_rng(X0)) )
& sK205(X0,X1) = apply(X0,sK206(X0,X1))
& in(sK206(X0,X1),relation_dom(X0)) )
| ~ sP11(sK205(X0,X1),sK206(X0,X1),X0,X1)
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X4,X5] :
( ( ( apply(X1,X4) = X5
& in(X4,relation_rng(X0)) )
| apply(X0,X5) != X4
| ~ in(X5,relation_dom(X0)) )
& sP11(X4,X5,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK205,sK206])],[f1241,f1242]) ).
fof(f1244,plain,
! [X0] :
( ? [X1,X2] : in(ordered_pair(X1,X2),X0)
=> in(ordered_pair(sK207(X0),sK208(X0)),X0) ),
introduced(choice_axiom,[]) ).
fof(f1245,plain,
! [X0] :
( empty_set = X0
| in(ordered_pair(sK207(X0),sK208(X0)),X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK207,sK208])],[f712,f1244]) ).
fof(f1246,plain,
! [X0] :
( ( ( well_founded_relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0)) )
& ( is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f716]) ).
fof(f1247,plain,
! [X0] :
( ( ( relation_dom(X0) = empty_set
| empty_set != relation_rng(X0) )
& ( empty_set = relation_rng(X0)
| relation_dom(X0) != empty_set ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f724]) ).
fof(f1248,plain,
! [X0,X1] :
( ( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) )
& ( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ) ),
inference(nnf_transformation,[],[f343]) ).
fof(f1249,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f726]) ).
fof(f1250,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f1249]) ).
fof(f1251,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f1250]) ).
fof(f1252,plain,
! [X1,X2] :
( ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
=> ( apply(X2,sK209(X1,X2)) != apply(X1,sK209(X1,X2))
& in(sK209(X1,X2),relation_dom(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1253,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_dom_restriction(X2,X0) = X1
| ( apply(X2,sK209(X1,X2)) != apply(X1,sK209(X1,X2))
& in(sK209(X1,X2),relation_dom(X1)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
& ( ( ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK209])],[f1251,f1252]) ).
fof(f1254,plain,
! [X0,X1,X2,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)) ) )
| ~ relation(X3) ),
inference(nnf_transformation,[],[f734]) ).
fof(f1255,plain,
! [X0,X1,X2,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)) ) )
| ~ relation(X3) ),
inference(flattening,[],[f1254]) ).
fof(f1256,plain,
! [X1] :
( ? [X2] :
( ! [X3] :
( ~ in(X3,X2)
| ~ in(X3,X1) )
& in(X2,X1) )
=> ( ! [X3] :
( ~ in(X3,sK210(X1))
| ~ in(X3,X1) )
& in(sK210(X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f1257,plain,
! [X0,X1] :
( ( ! [X3] :
( ~ in(X3,sK210(X1))
| ~ in(X3,X1) )
& in(sK210(X1),X1) )
| ~ in(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK210])],[f736,f1256]) ).
fof(f1258,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f358]) ).
fof(f1259,plain,
! [X0,X1,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))) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f738]) ).
fof(f1260,plain,
! [X0,X1,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))) ) )
| ~ relation(X2) ),
inference(flattening,[],[f1259]) ).
fof(f1261,plain,
! [X0,X1,X2] :
( ( ( in(ordered_pair(X0,X1),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2)) )
& ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(nnf_transformation,[],[f742]) ).
fof(f1262,plain,
! [X0,X1,X2] :
( ( ( in(ordered_pair(X0,X1),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2)) )
& ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2) ) )
| ~ function(X2)
| ~ relation(X2) ),
inference(flattening,[],[f1261]) ).
fof(f1263,plain,
! [X0] :
( ( ( well_orders(X0,relation_field(X0))
| ~ well_ordering(X0) )
& ( well_ordering(X0)
| ~ well_orders(X0,relation_field(X0)) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f743]) ).
fof(f1264,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( in(X2,X1)
| are_equipotent(X2,X1)
| ~ subset(X2,X1) )
& ! [X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,X1) )
| ~ in(X3,X1) )
& ! [X6,X7] :
( in(X7,X1)
| ~ subset(X7,X6)
| ~ in(X6,X1) )
& in(X0,X1) )
=> ( ! [X2] :
( in(X2,sK211(X0))
| are_equipotent(X2,sK211(X0))
| ~ subset(X2,sK211(X0)) )
& ! [X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,sK211(X0)) )
| ~ in(X3,sK211(X0)) )
& ! [X7,X6] :
( in(X7,sK211(X0))
| ~ subset(X7,X6)
| ~ in(X6,sK211(X0)) )
& in(X0,sK211(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1265,plain,
! [X0,X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,sK211(X0)) )
=> ( ! [X5] :
( in(X5,sK212(X0,X3))
| ~ subset(X5,X3) )
& in(sK212(X0,X3),sK211(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1266,plain,
! [X0] :
( ! [X2] :
( in(X2,sK211(X0))
| are_equipotent(X2,sK211(X0))
| ~ subset(X2,sK211(X0)) )
& ! [X3] :
( ( ! [X5] :
( in(X5,sK212(X0,X3))
| ~ subset(X5,X3) )
& in(sK212(X0,X3),sK211(X0)) )
| ~ in(X3,sK211(X0)) )
& ! [X6,X7] :
( in(X7,sK211(X0))
| ~ subset(X7,X6)
| ~ in(X6,sK211(X0)) )
& in(X0,sK211(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK211,sK212])],[f752,f1265,f1264]) ).
fof(f1267,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f394]) ).
fof(f1268,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f395]) ).
fof(f1269,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f396]) ).
fof(f1272,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f398]) ).
fof(f1273,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f399]) ).
fof(f1276,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f401]) ).
fof(f1278,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f404]) ).
fof(f1279,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f404]) ).
fof(f1280,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f404]) ).
fof(f1281,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f1282,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f1283,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f12]) ).
fof(f1284,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f406]) ).
fof(f1285,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(ordered_pair(X4,X5),X1)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f779]) ).
fof(f1286,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X4,X5),X1)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f779]) ).
fof(f1287,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f779]) ).
fof(f1288,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| in(sK12(X0,X1),X0)
| in(ordered_pair(sK12(X0,X1),sK13(X0,X1)),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f779]) ).
fof(f1289,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK12(X0,X1) = sK13(X0,X1)
| in(ordered_pair(sK12(X0,X1),sK13(X0,X1)),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f779]) ).
fof(f1290,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK12(X0,X1) != sK13(X0,X1)
| ~ in(sK12(X0,X1),X0)
| ~ in(ordered_pair(sK12(X0,X1),sK13(X0,X1)),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f779]) ).
fof(f1293,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f781]) ).
fof(f1294,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X2)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f786]) ).
fof(f1295,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X5,X6),X2)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f786]) ).
fof(f1296,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f786]) ).
fof(f1297,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| in(sK14(X0,X1,X2),X1)
| in(ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f786]) ).
fof(f1298,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| in(ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),X0)
| in(ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f786]) ).
fof(f1299,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| ~ in(ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),X0)
| ~ in(sK14(X0,X1,X2),X1)
| ~ in(ordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f786]) ).
fof(f1300,plain,
! [X2,X0,X1,X6] :
( in(sK18(X0,X1,X6),relation_dom(X0))
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f792]) ).
fof(f1301,plain,
! [X2,X0,X1,X6] :
( in(sK18(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f792]) ).
fof(f1302,plain,
! [X2,X0,X1,X6] :
( apply(X0,sK18(X0,X1,X6)) = X6
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f792]) ).
fof(f1303,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f792]) ).
fof(f1304,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(sK17(X0,X1,X2),relation_dom(X0))
| in(sK16(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f792]) ).
fof(f1305,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(sK17(X0,X1,X2),X1)
| in(sK16(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f792]) ).
fof(f1306,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| sK16(X0,X1,X2) = apply(X0,sK17(X0,X1,X2))
| in(sK16(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f792]) ).
fof(f1307,plain,
! [X2,X0,X1,X4] :
( relation_image(X0,X1) = X2
| apply(X0,X4) != sK16(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| ~ in(sK16(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f792]) ).
fof(f1308,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,X0)
| ~ in(ordered_pair(X5,X6),X2)
| relation_rng_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f797]) ).
fof(f1309,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X1)
| ~ in(ordered_pair(X5,X6),X2)
| relation_rng_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f797]) ).
fof(f1310,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| relation_rng_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f797]) ).
fof(f1311,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| in(sK20(X0,X1,X2),X0)
| in(ordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f797]) ).
fof(f1312,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| in(ordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),X1)
| in(ordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f797]) ).
fof(f1313,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| ~ in(ordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),X1)
| ~ in(sK20(X0,X1,X2),X0)
| ~ in(ordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f797]) ).
fof(f1314,plain,
! [X0] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f798]) ).
fof(f1315,plain,
! [X0] :
( antisymmetric(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f798]) ).
fof(f1316,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X0))
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f803]) ).
fof(f1317,plain,
! [X2,X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f803]) ).
fof(f1318,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| relation_inverse_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f803]) ).
fof(f1319,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| in(sK21(X0,X1,X2),relation_dom(X0))
| in(sK21(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f803]) ).
fof(f1320,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| in(apply(X0,sK21(X0,X1,X2)),X1)
| in(sK21(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f803]) ).
fof(f1321,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ in(apply(X0,sK21(X0,X1,X2)),X1)
| ~ in(sK21(X0,X1,X2),relation_dom(X0))
| ~ in(sK21(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f803]) ).
fof(f1322,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(sK24(X0,X1,X6),X6),X0)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f809]) ).
fof(f1323,plain,
! [X2,X0,X1,X6] :
( in(sK24(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f809]) ).
fof(f1324,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f809]) ).
fof(f1325,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(ordered_pair(sK23(X0,X1,X2),sK22(X0,X1,X2)),X0)
| in(sK22(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f809]) ).
fof(f1326,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(sK23(X0,X1,X2),X1)
| in(sK22(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f809]) ).
fof(f1327,plain,
! [X2,X0,X1,X4] :
( relation_image(X0,X1) = X2
| ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK22(X0,X1,X2)),X0)
| ~ in(sK22(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f809]) ).
fof(f1328,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(X6,sK27(X0,X1,X6)),X0)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f815]) ).
fof(f1329,plain,
! [X2,X0,X1,X6] :
( in(sK27(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f815]) ).
fof(f1330,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f815]) ).
fof(f1331,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| in(ordered_pair(sK25(X0,X1,X2),sK26(X0,X1,X2)),X0)
| in(sK25(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f815]) ).
fof(f1332,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| in(sK26(X0,X1,X2),X1)
| in(sK25(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f815]) ).
fof(f1333,plain,
! [X2,X0,X1,X4] :
( relation_inverse_image(X0,X1) = X2
| ~ in(X4,X1)
| ~ in(ordered_pair(sK25(X0,X1,X2),X4),X0)
| ~ in(sK25(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f815]) ).
fof(f1334,plain,
! [X0] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f816]) ).
fof(f1335,plain,
! [X0] :
( connected(X0)
| ~ is_connected_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f816]) ).
fof(f1336,plain,
! [X0] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f817]) ).
fof(f1337,plain,
! [X0] :
( transitive(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f817]) ).
fof(f1338,plain,
! [X2,X3,X0,X1,X5] :
( X2 = X5
| X1 = X5
| X0 = X5
| ~ in(X5,X3)
| unordered_triple(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f822]) ).
fof(f1339,plain,
! [X2,X3,X0,X1,X5] :
( in(X5,X3)
| X0 != X5
| unordered_triple(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f822]) ).
fof(f1340,plain,
! [X2,X3,X0,X1,X5] :
( in(X5,X3)
| X1 != X5
| unordered_triple(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f822]) ).
fof(f1341,plain,
! [X2,X3,X0,X1,X5] :
( in(X5,X3)
| X2 != X5
| unordered_triple(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f822]) ).
fof(f1342,plain,
! [X2,X3,X0,X1] :
( unordered_triple(X0,X1,X2) = X3
| sK28(X0,X1,X2,X3) = X2
| sK28(X0,X1,X2,X3) = X1
| sK28(X0,X1,X2,X3) = X0
| in(sK28(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f822]) ).
fof(f1343,plain,
! [X2,X3,X0,X1] :
( unordered_triple(X0,X1,X2) = X3
| sK28(X0,X1,X2,X3) != X0
| ~ in(sK28(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f822]) ).
fof(f1344,plain,
! [X2,X3,X0,X1] :
( unordered_triple(X0,X1,X2) = X3
| sK28(X0,X1,X2,X3) != X1
| ~ in(sK28(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f822]) ).
fof(f1345,plain,
! [X2,X3,X0,X1] :
( unordered_triple(X0,X1,X2) = X3
| sK28(X0,X1,X2,X3) != X2
| ~ in(sK28(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f822]) ).
fof(f1346,plain,
! [X0,X6,X4,X5] :
( X5 = X6
| ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f826]) ).
fof(f1347,plain,
! [X0] :
( function(X0)
| in(ordered_pair(sK29(X0),sK30(X0)),X0) ),
inference(cnf_transformation,[],[f826]) ).
fof(f1348,plain,
! [X0] :
( function(X0)
| in(ordered_pair(sK29(X0),sK31(X0)),X0) ),
inference(cnf_transformation,[],[f826]) ).
fof(f1349,plain,
! [X0] :
( function(X0)
| sK30(X0) != sK31(X0) ),
inference(cnf_transformation,[],[f826]) ).
fof(f1351,plain,
! [X0,X1,X6,X7] :
( pair_first(X0) = X1
| ordered_pair(sK32(X0,X1),sK33(X0,X1)) = X0
| ordered_pair(X6,X7) != X0 ),
inference(cnf_transformation,[],[f830]) ).
fof(f1352,plain,
! [X0,X1,X6,X7] :
( pair_first(X0) = X1
| sK32(X0,X1) != X1
| ordered_pair(X6,X7) != X0 ),
inference(cnf_transformation,[],[f830]) ).
fof(f1353,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f1354,plain,
! [X0,X4] :
( ordered_pair(sK35(X4),sK36(X4)) = X4
| ~ in(X4,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f835]) ).
fof(f1355,plain,
! [X0] :
( relation(X0)
| in(sK34(X0),X0) ),
inference(cnf_transformation,[],[f835]) ).
fof(f1356,plain,
! [X2,X3,X0] :
( relation(X0)
| ordered_pair(X2,X3) != sK34(X0) ),
inference(cnf_transformation,[],[f835]) ).
fof(f1357,plain,
! [X3,X0,X1] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f839]) ).
fof(f1358,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| in(sK37(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f839]) ).
fof(f1359,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(ordered_pair(sK37(X0,X1),sK37(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f839]) ).
fof(f1360,plain,
! [X2,X0,X1] :
( subset(X2,cartesian_product2(X0,X1))
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f840]) ).
fof(f1361,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ subset(X2,cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f840]) ).
fof(f1362,plain,
! [X0,X1,X7,X5] :
( in(X5,X7)
| ~ in(X7,X0)
| ~ in(X5,X1)
| set_meet(X0) != X1
| empty_set = X0 ),
inference(cnf_transformation,[],[f846]) ).
fof(f1363,plain,
! [X0,X1,X5] :
( in(X5,X1)
| in(sK40(X0,X5),X0)
| set_meet(X0) != X1
| empty_set = X0 ),
inference(cnf_transformation,[],[f846]) ).
fof(f1364,plain,
! [X0,X1,X5] :
( in(X5,X1)
| ~ in(X5,sK40(X0,X5))
| set_meet(X0) != X1
| empty_set = X0 ),
inference(cnf_transformation,[],[f846]) ).
fof(f1365,plain,
! [X0,X1,X4] :
( set_meet(X0) = X1
| in(sK38(X0,X1),X4)
| ~ in(X4,X0)
| in(sK38(X0,X1),X1)
| empty_set = X0 ),
inference(cnf_transformation,[],[f846]) ).
fof(f1366,plain,
! [X0,X1] :
( set_meet(X0) = X1
| in(sK39(X0,X1),X0)
| ~ in(sK38(X0,X1),X1)
| empty_set = X0 ),
inference(cnf_transformation,[],[f846]) ).
fof(f1367,plain,
! [X0,X1] :
( set_meet(X0) = X1
| ~ in(sK38(X0,X1),sK39(X0,X1))
| ~ in(sK38(X0,X1),X1)
| empty_set = X0 ),
inference(cnf_transformation,[],[f846]) ).
fof(f1368,plain,
! [X0,X1] :
( empty_set = X1
| set_meet(X0) != X1
| empty_set != X0 ),
inference(cnf_transformation,[],[f846]) ).
fof(f1370,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f850]) ).
fof(f1372,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK41(X0,X1) = X0
| in(sK41(X0,X1),X1) ),
inference(cnf_transformation,[],[f850]) ).
fof(f1373,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK41(X0,X1) != X0
| ~ in(sK41(X0,X1),X1) ),
inference(cnf_transformation,[],[f850]) ).
fof(f1374,plain,
! [X2,X0,X1,X4] :
( X1 != X4
| ~ in(X4,X2)
| fiber(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f855]) ).
fof(f1375,plain,
! [X2,X0,X1,X4] :
( in(ordered_pair(X4,X1),X0)
| ~ in(X4,X2)
| fiber(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f855]) ).
fof(f1376,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(ordered_pair(X4,X1),X0)
| X1 = X4
| fiber(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f855]) ).
fof(f1377,plain,
! [X2,X0,X1] :
( fiber(X0,X1) = X2
| sK42(X0,X1,X2) != X1
| in(sK42(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f855]) ).
fof(f1378,plain,
! [X2,X0,X1] :
( fiber(X0,X1) = X2
| in(ordered_pair(sK42(X0,X1,X2),X1),X0)
| in(sK42(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f855]) ).
fof(f1379,plain,
! [X2,X0,X1] :
( fiber(X0,X1) = X2
| ~ in(ordered_pair(sK42(X0,X1,X2),X1),X0)
| sK42(X0,X1,X2) = X1
| ~ in(sK42(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f855]) ).
fof(f1380,plain,
! [X0,X1] :
( relation_field(X1) = X0
| inclusion_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f860]) ).
fof(f1381,plain,
! [X0,X1,X4,X5] :
( subset(X4,X5)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(X5,X0)
| ~ in(X4,X0)
| inclusion_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f860]) ).
fof(f1382,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5)
| ~ in(X5,X0)
| ~ in(X4,X0)
| inclusion_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f860]) ).
fof(f1383,plain,
! [X0,X1] :
( inclusion_relation(X0) = X1
| in(sK43(X0,X1),X0)
| relation_field(X1) != X0
| ~ relation(X1) ),
inference(cnf_transformation,[],[f860]) ).
fof(f1384,plain,
! [X0,X1] :
( inclusion_relation(X0) = X1
| in(sK44(X0,X1),X0)
| relation_field(X1) != X0
| ~ relation(X1) ),
inference(cnf_transformation,[],[f860]) ).
fof(f1385,plain,
! [X0,X1] :
( inclusion_relation(X0) = X1
| subset(sK43(X0,X1),sK44(X0,X1))
| in(ordered_pair(sK43(X0,X1),sK44(X0,X1)),X1)
| relation_field(X1) != X0
| ~ relation(X1) ),
inference(cnf_transformation,[],[f860]) ).
fof(f1386,plain,
! [X0,X1] :
( inclusion_relation(X0) = X1
| ~ subset(sK43(X0,X1),sK44(X0,X1))
| ~ in(ordered_pair(sK43(X0,X1),sK44(X0,X1)),X1)
| relation_field(X1) != X0
| ~ relation(X1) ),
inference(cnf_transformation,[],[f860]) ).
fof(f1387,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f864]) ).
fof(f1388,plain,
! [X0] :
( empty_set = X0
| in(sK45(X0),X0) ),
inference(cnf_transformation,[],[f864]) ).
fof(f1389,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f868]) ).
fof(f1390,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f868]) ).
fof(f1391,plain,
! [X0,X1] :
( powerset(X0) = X1
| subset(sK46(X0,X1),X0)
| in(sK46(X0,X1),X1) ),
inference(cnf_transformation,[],[f868]) ).
fof(f1392,plain,
! [X0,X1] :
( powerset(X0) = X1
| ~ subset(sK46(X0,X1),X0)
| ~ in(sK46(X0,X1),X1) ),
inference(cnf_transformation,[],[f868]) ).
fof(f1394,plain,
! [X0,X1,X6,X7] :
( pair_second(X0) = X1
| ordered_pair(sK47(X0,X1),sK48(X0,X1)) = X0
| ordered_pair(X6,X7) != X0 ),
inference(cnf_transformation,[],[f872]) ).
fof(f1395,plain,
! [X0,X1,X6,X7] :
( pair_second(X0) = X1
| sK48(X0,X1) != X1
| ordered_pair(X6,X7) != X0 ),
inference(cnf_transformation,[],[f872]) ).
fof(f1396,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f876]) ).
fof(f1397,plain,
! [X0] :
( epsilon_transitive(X0)
| in(sK49(X0),X0) ),
inference(cnf_transformation,[],[f876]) ).
fof(f1398,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK49(X0),X0) ),
inference(cnf_transformation,[],[f876]) ).
fof(f1401,plain,
! [X0,X1] :
( X0 = X1
| in(ordered_pair(sK50(X0,X1),sK51(X0,X1)),X1)
| in(ordered_pair(sK50(X0,X1),sK51(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f880]) ).
fof(f1402,plain,
! [X0,X1] :
( X0 = X1
| ~ in(ordered_pair(sK50(X0,X1),sK51(X0,X1)),X1)
| ~ in(ordered_pair(sK50(X0,X1),sK51(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f880]) ).
fof(f1405,plain,
! [X0,X1] :
( empty(X1)
| ~ element(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f881]) ).
fof(f1406,plain,
! [X0,X1] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f881]) ).
fof(f1407,plain,
! [X2,X0,X1,X4] :
( X1 = X4
| X0 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f886]) ).
fof(f1408,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f886]) ).
fof(f1409,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f886]) ).
fof(f1410,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| sK52(X0,X1,X2) = X1
| sK52(X0,X1,X2) = X0
| in(sK52(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f886]) ).
fof(f1411,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| sK52(X0,X1,X2) != X0
| ~ in(sK52(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f886]) ).
fof(f1412,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| sK52(X0,X1,X2) != X1
| ~ in(sK52(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f886]) ).
fof(f1413,plain,
! [X3,X0] :
( in(sK54(X0,X3),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f891]) ).
fof(f1414,plain,
! [X3,X0] :
( disjoint(fiber(X0,sK54(X0,X3)),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f891]) ).
fof(f1415,plain,
! [X0] :
( well_founded_relation(X0)
| subset(sK53(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f891]) ).
fof(f1416,plain,
! [X0] :
( well_founded_relation(X0)
| empty_set != sK53(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f891]) ).
fof(f1417,plain,
! [X2,X0] :
( well_founded_relation(X0)
| ~ disjoint(fiber(X0,X2),sK53(X0))
| ~ in(X2,sK53(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f891]) ).
fof(f1418,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f896]) ).
fof(f1419,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f896]) ).
fof(f1420,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f896]) ).
fof(f1421,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| in(sK55(X0,X1,X2),X1)
| in(sK55(X0,X1,X2),X0)
| in(sK55(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f896]) ).
fof(f1422,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ in(sK55(X0,X1,X2),X0)
| ~ in(sK55(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f896]) ).
fof(f1423,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ in(sK55(X0,X1,X2),X1)
| ~ in(sK55(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f896]) ).
fof(f1424,plain,
! [X2,X0,X1,X8] :
( in(sK59(X0,X1,X8),X0)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f902]) ).
fof(f1425,plain,
! [X2,X0,X1,X8] :
( in(sK60(X0,X1,X8),X1)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f902]) ).
fof(f1426,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK59(X0,X1,X8),sK60(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f902]) ).
fof(f1428,plain,
! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| in(sK57(X0,X1,X2),X0)
| in(sK56(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f902]) ).
fof(f1429,plain,
! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| in(sK58(X0,X1,X2),X1)
| in(sK56(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f902]) ).
fof(f1430,plain,
! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| sK56(X0,X1,X2) = ordered_pair(sK57(X0,X1,X2),sK58(X0,X1,X2))
| in(sK56(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f902]) ).
fof(f1431,plain,
! [X2,X0,X1,X4,X5] :
( cartesian_product2(X0,X1) = X2
| ordered_pair(X4,X5) != sK56(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0)
| ~ in(sK56(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f902]) ).
fof(f1432,plain,
! [X3,X0,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ epsilon_connected(X0) ),
inference(cnf_transformation,[],[f906]) ).
fof(f1433,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK61(X0),X0) ),
inference(cnf_transformation,[],[f906]) ).
fof(f1434,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK62(X0),X0) ),
inference(cnf_transformation,[],[f906]) ).
fof(f1435,plain,
! [X0] :
( epsilon_connected(X0)
| ~ in(sK61(X0),sK62(X0)) ),
inference(cnf_transformation,[],[f906]) ).
fof(f1436,plain,
! [X0] :
( epsilon_connected(X0)
| sK61(X0) != sK62(X0) ),
inference(cnf_transformation,[],[f906]) ).
fof(f1437,plain,
! [X0] :
( epsilon_connected(X0)
| ~ in(sK62(X0),sK61(X0)) ),
inference(cnf_transformation,[],[f906]) ).
fof(f1439,plain,
! [X0,X1] :
( subset(X0,X1)
| in(ordered_pair(sK63(X0,X1),sK64(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f910]) ).
fof(f1440,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(ordered_pair(sK63(X0,X1),sK64(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f910]) ).
fof(f1441,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f914]) ).
fof(f1442,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK65(X0,X1),X0) ),
inference(cnf_transformation,[],[f914]) ).
fof(f1443,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK65(X0,X1),X1) ),
inference(cnf_transformation,[],[f914]) ).
fof(f1444,plain,
! [X0,X1,X4] :
( in(sK67(X0,X4),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f919]) ).
fof(f1445,plain,
! [X0,X1,X4] :
( disjoint(fiber(X0,sK67(X0,X4)),X4)
| empty_set = X4
| ~ subset(X4,X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f919]) ).
fof(f1446,plain,
! [X0,X1] :
( is_well_founded_in(X0,X1)
| subset(sK66(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f919]) ).
fof(f1447,plain,
! [X0,X1] :
( is_well_founded_in(X0,X1)
| empty_set != sK66(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f919]) ).
fof(f1448,plain,
! [X3,X0,X1] :
( is_well_founded_in(X0,X1)
| ~ disjoint(fiber(X0,X3),sK66(X0,X1))
| ~ in(X3,sK66(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f919]) ).
fof(f1450,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f924]) ).
fof(f1451,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f924]) ).
fof(f1452,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| in(sK68(X0,X1,X2),X0)
| in(sK68(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f924]) ).
fof(f1453,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| in(sK68(X0,X1,X2),X1)
| in(sK68(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f924]) ).
fof(f1454,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ in(sK68(X0,X1,X2),X1)
| ~ in(sK68(X0,X1,X2),X0)
| ~ in(sK68(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f924]) ).
fof(f1458,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| empty_set != X2
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f925]) ).
fof(f1459,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f927]) ).
fof(f1460,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f927]) ).
fof(f1461,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f927]) ).
fof(f1462,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK71(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f933]) ).
fof(f1464,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(ordered_pair(sK69(X0,X1),sK70(X0,X1)),X0)
| in(sK69(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f933]) ).
fof(f1465,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(ordered_pair(sK69(X0,X1),X3),X0)
| ~ in(sK69(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f933]) ).
fof(f1466,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f937]) ).
fof(f1467,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| in(sK72(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f937]) ).
fof(f1468,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| in(sK73(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f937]) ).
fof(f1469,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| in(ordered_pair(sK72(X0,X1),sK73(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f937]) ).
fof(f1470,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| in(ordered_pair(sK73(X0,X1),sK72(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f937]) ).
fof(f1471,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| sK72(X0,X1) != sK73(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f937]) ).
fof(f1472,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f55]) ).
fof(f1473,plain,
! [X0,X1,X5] :
( in(X5,sK76(X0,X5))
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f943]) ).
fof(f1474,plain,
! [X0,X1,X5] :
( in(sK76(X0,X5),X0)
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f943]) ).
fof(f1475,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,X0)
| ~ in(X5,X6)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f943]) ).
fof(f1476,plain,
! [X0,X1] :
( union(X0) = X1
| in(sK74(X0,X1),sK75(X0,X1))
| in(sK74(X0,X1),X1) ),
inference(cnf_transformation,[],[f943]) ).
fof(f1477,plain,
! [X0,X1] :
( union(X0) = X1
| in(sK75(X0,X1),X0)
| in(sK74(X0,X1),X1) ),
inference(cnf_transformation,[],[f943]) ).
fof(f1478,plain,
! [X3,X0,X1] :
( union(X0) = X1
| ~ in(X3,X0)
| ~ in(sK74(X0,X1),X3)
| ~ in(sK74(X0,X1),X1) ),
inference(cnf_transformation,[],[f943]) ).
fof(f1479,plain,
! [X0] :
( reflexive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f945]) ).
fof(f1480,plain,
! [X0] :
( transitive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f945]) ).
fof(f1481,plain,
! [X0] :
( antisymmetric(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f945]) ).
fof(f1482,plain,
! [X0] :
( connected(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f945]) ).
fof(f1483,plain,
! [X0] :
( well_founded_relation(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f945]) ).
fof(f1484,plain,
! [X0] :
( well_ordering(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f945]) ).
fof(f1485,plain,
! [X0,X1] :
( relation(sK77(X0,X1))
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f949]) ).
fof(f1486,plain,
! [X0,X1] :
( function(sK77(X0,X1))
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f949]) ).
fof(f1487,plain,
! [X0,X1] :
( one_to_one(sK77(X0,X1))
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f949]) ).
fof(f1488,plain,
! [X0,X1] :
( relation_dom(sK77(X0,X1)) = X0
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f949]) ).
fof(f1489,plain,
! [X0,X1] :
( relation_rng(sK77(X0,X1)) = X1
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f949]) ).
fof(f1490,plain,
! [X2,X0,X1] :
( equipotent(X0,X1)
| relation_rng(X2) != X1
| relation_dom(X2) != X0
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f949]) ).
fof(f1491,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f954]) ).
fof(f1492,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f954]) ).
fof(f1493,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f954]) ).
fof(f1494,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| in(sK78(X0,X1,X2),X0)
| in(sK78(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f954]) ).
fof(f1495,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ in(sK78(X0,X1,X2),X1)
| in(sK78(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f954]) ).
fof(f1496,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| in(sK78(X0,X1,X2),X1)
| ~ in(sK78(X0,X1,X2),X0)
| ~ in(sK78(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f954]) ).
fof(f1497,plain,
! [X0,X1,X5] :
( in(sK81(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f960]) ).
fof(f1498,plain,
! [X0,X1,X5] :
( apply(X0,sK81(X0,X5)) = X5
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f960]) ).
fof(f1499,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f960]) ).
fof(f1500,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(sK80(X0,X1),relation_dom(X0))
| in(sK79(X0,X1),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f960]) ).
fof(f1501,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| sK79(X0,X1) = apply(X0,sK80(X0,X1))
| in(sK79(X0,X1),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f960]) ).
fof(f1502,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| apply(X0,X3) != sK79(X0,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK79(X0,X1),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f960]) ).
fof(f1503,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK84(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f966]) ).
fof(f1505,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(ordered_pair(sK83(X0,X1),sK82(X0,X1)),X0)
| in(sK82(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f966]) ).
fof(f1506,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(ordered_pair(X3,sK82(X0,X1)),X0)
| ~ in(sK82(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f966]) ).
fof(f1507,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f447]) ).
fof(f1508,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f63]) ).
fof(f1509,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f968]) ).
fof(f1510,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f968]) ).
fof(f1511,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f968]) ).
fof(f1512,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f968]) ).
fof(f1513,plain,
! [X0,X1] :
( is_well_founded_in(X0,X1)
| ~ well_orders(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f968]) ).
fof(f1514,plain,
! [X0,X1] :
( well_orders(X0,X1)
| ~ is_well_founded_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f968]) ).
fof(f1515,plain,
! [X0] :
( union(X0) = X0
| ~ being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f969]) ).
fof(f1516,plain,
! [X0] :
( being_limit_ordinal(X0)
| union(X0) != X0 ),
inference(cnf_transformation,[],[f969]) ).
fof(f1517,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f449]) ).
fof(f1518,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f973]) ).
fof(f1519,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| in(sK85(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f973]) ).
fof(f1520,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| in(sK86(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f973]) ).
fof(f1521,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| sK85(X0,X1) != sK86(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f973]) ).
fof(f1522,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ in(ordered_pair(sK85(X0,X1),sK86(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f973]) ).
fof(f1523,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ in(ordered_pair(sK86(X0,X1),sK85(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f973]) ).
fof(f1524,plain,
! [X0,X1] :
( relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f451]) ).
fof(f1525,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f977]) ).
fof(f1526,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f977]) ).
fof(f1527,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| in(ordered_pair(sK88(X0,X1),sK87(X0,X1)),X0)
| in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f977]) ).
fof(f1528,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(ordered_pair(sK88(X0,X1),sK87(X0,X1)),X0)
| ~ in(ordered_pair(sK87(X0,X1),sK88(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f977]) ).
fof(f1529,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| ~ relation_isomorphism(X0,X2,X1)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f979]) ).
fof(f1530,plain,
! [X2,X0,X1] :
( relation_isomorphism(X0,X2,X1)
| ~ sP0(X2,X1,X0)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f979]) ).
fof(f1531,plain,
! [X2,X0,X1] :
( relation_dom(X1) = relation_field(X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f984]) ).
fof(f1532,plain,
! [X2,X0,X1] :
( relation_field(X0) = relation_rng(X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f984]) ).
fof(f1533,plain,
! [X2,X0,X1] :
( one_to_one(X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f984]) ).
fof(f1534,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,relation_field(X2))
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f984]) ).
fof(f1535,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,relation_field(X2))
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f984]) ).
fof(f1536,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f984]) ).
fof(f1537,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
| ~ in(X6,relation_field(X2))
| ~ in(X5,relation_field(X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f984]) ).
fof(f1538,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK89(X0,X1,X2),relation_field(X2))
| in(ordered_pair(sK89(X0,X1,X2),sK90(X0,X1,X2)),X2)
| ~ one_to_one(X1)
| relation_field(X0) != relation_rng(X1)
| relation_dom(X1) != relation_field(X2) ),
inference(cnf_transformation,[],[f984]) ).
fof(f1539,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK90(X0,X1,X2),relation_field(X2))
| in(ordered_pair(sK89(X0,X1,X2),sK90(X0,X1,X2)),X2)
| ~ one_to_one(X1)
| relation_field(X0) != relation_rng(X1)
| relation_dom(X1) != relation_field(X2) ),
inference(cnf_transformation,[],[f984]) ).
fof(f1540,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(ordered_pair(apply(X1,sK89(X0,X1,X2)),apply(X1,sK90(X0,X1,X2))),X0)
| in(ordered_pair(sK89(X0,X1,X2),sK90(X0,X1,X2)),X2)
| ~ one_to_one(X1)
| relation_field(X0) != relation_rng(X1)
| relation_dom(X1) != relation_field(X2) ),
inference(cnf_transformation,[],[f984]) ).
fof(f1541,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(ordered_pair(apply(X1,sK89(X0,X1,X2)),apply(X1,sK90(X0,X1,X2))),X0)
| ~ in(sK90(X0,X1,X2),relation_field(X2))
| ~ in(sK89(X0,X1,X2),relation_field(X2))
| ~ in(ordered_pair(sK89(X0,X1,X2),sK90(X0,X1,X2)),X2)
| ~ one_to_one(X1)
| relation_field(X0) != relation_rng(X1)
| relation_dom(X1) != relation_field(X2) ),
inference(cnf_transformation,[],[f984]) ).
fof(f1542,plain,
! [X2,X0,X1] :
( sP1(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f756]) ).
fof(f1543,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f985]) ).
fof(f1544,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[],[f985]) ).
fof(f1545,plain,
! [X3,X0,X4] :
( X3 = X4
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f989]) ).
fof(f1546,plain,
! [X0] :
( one_to_one(X0)
| in(sK91(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f989]) ).
fof(f1547,plain,
! [X0] :
( one_to_one(X0)
| in(sK92(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f989]) ).
fof(f1548,plain,
! [X0] :
( one_to_one(X0)
| apply(X0,sK91(X0)) = apply(X0,sK92(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f989]) ).
fof(f1549,plain,
! [X0] :
( one_to_one(X0)
| sK91(X0) != sK92(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f989]) ).
fof(f1550,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK96(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f995]) ).
fof(f1551,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(sK96(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f995]) ).
fof(f1552,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),X2)
| ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f995]) ).
fof(f1553,plain,
! [X2,X0,X1] :
( relation_composition(X0,X1) = X2
| in(ordered_pair(sK93(X0,X1,X2),sK95(X0,X1,X2)),X0)
| in(ordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f995]) ).
fof(f1554,plain,
! [X2,X0,X1] :
( relation_composition(X0,X1) = X2
| in(ordered_pair(sK95(X0,X1,X2),sK94(X0,X1,X2)),X1)
| in(ordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f995]) ).
fof(f1555,plain,
! [X2,X0,X1,X5] :
( relation_composition(X0,X1) = X2
| ~ in(ordered_pair(X5,sK94(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK93(X0,X1,X2),X5),X0)
| ~ in(ordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f995]) ).
fof(f1556,plain,
! [X0,X1,X6,X7,X5] :
( in(ordered_pair(X5,X7),X0)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f999]) ).
fof(f1557,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| in(sK97(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f999]) ).
fof(f1558,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| in(sK98(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f999]) ).
fof(f1559,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| in(sK99(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f999]) ).
fof(f1560,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| in(ordered_pair(sK97(X0,X1),sK98(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f999]) ).
fof(f1561,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| in(ordered_pair(sK98(X0,X1),sK99(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f999]) ).
fof(f1562,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ in(ordered_pair(sK97(X0,X1),sK99(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f999]) ).
fof(f1563,plain,
! [X2,X0,X1,X4] :
( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2)
| ~ element(X4,powerset(X0))
| complements_of_subsets(X0,X1) != X2
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f1004]) ).
fof(f1564,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(subset_complement(X0,X4),X1)
| ~ element(X4,powerset(X0))
| complements_of_subsets(X0,X1) != X2
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f1004]) ).
fof(f1565,plain,
! [X2,X0,X1] :
( complements_of_subsets(X0,X1) = X2
| element(sK100(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f1004]) ).
fof(f1566,plain,
! [X2,X0,X1] :
( complements_of_subsets(X0,X1) = X2
| in(subset_complement(X0,sK100(X0,X1,X2)),X1)
| in(sK100(X0,X1,X2),X2)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f1004]) ).
fof(f1567,plain,
! [X2,X0,X1] :
( complements_of_subsets(X0,X1) = X2
| ~ in(subset_complement(X0,sK100(X0,X1,X2)),X1)
| ~ in(sK100(X0,X1,X2),X2)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f1004]) ).
fof(f1568,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f462]) ).
fof(f1569,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f464]) ).
fof(f1570,plain,
! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1005]) ).
fof(f1571,plain,
! [X0] :
( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1005]) ).
fof(f1572,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f88]) ).
fof(f1573,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f467]) ).
fof(f1574,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f467]) ).
fof(f1575,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f94]) ).
fof(f1576,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f468]) ).
fof(f1577,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f469]) ).
fof(f1578,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f470]) ).
fof(f1579,plain,
! [X2,X0,X1] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f471]) ).
fof(f1580,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f473]) ).
fof(f1581,plain,
! [X2,X0,X1] :
( element(relation_rng_as_subset(X0,X1,X2),powerset(X1))
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f474]) ).
fof(f1582,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f475]) ).
fof(f1583,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f110]) ).
fof(f1584,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f476]) ).
fof(f1585,plain,
! [X2,X0,X1] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f478]) ).
fof(f1586,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f479]) ).
fof(f1587,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f480]) ).
fof(f1588,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f481]) ).
fof(f1589,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f482]) ).
fof(f1590,plain,
! [X0,X1] : relation_of2(sK101(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1007]) ).
fof(f1591,plain,
! [X0] : element(sK102(X0),X0),
inference(cnf_transformation,[],[f1009]) ).
fof(f1592,plain,
! [X0,X1] : relation_of2_as_subset(sK103(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1011]) ).
fof(f1593,plain,
! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f484]) ).
fof(f1594,plain,
! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f484]) ).
fof(f1595,plain,
! [X0] :
( empty(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f485]) ).
fof(f1596,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f485]) ).
fof(f1600,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f487]) ).
fof(f1601,plain,
! [X0,X1] :
( relation_empty_yielding(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f487]) ).
fof(f1602,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f489]) ).
fof(f1603,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f489]) ).
fof(f1604,plain,
! [X0] : ~ empty(succ(X0)),
inference(cnf_transformation,[],[f128]) ).
fof(f1605,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f491]) ).
fof(f1606,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f130]) ).
fof(f1609,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f133]) ).
fof(f1610,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f133]) ).
fof(f1612,plain,
relation_empty_yielding(empty_set),
inference(cnf_transformation,[],[f134]) ).
fof(f1613,plain,
function(empty_set),
inference(cnf_transformation,[],[f134]) ).
fof(f1614,plain,
one_to_one(empty_set),
inference(cnf_transformation,[],[f134]) ).
fof(f1616,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f134]) ).
fof(f1617,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f134]) ).
fof(f1618,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f134]) ).
fof(f1619,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f493]) ).
fof(f1621,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f494]) ).
fof(f1622,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f496]) ).
fof(f1623,plain,
! [X0] :
( function(relation_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f496]) ).
fof(f1625,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f497]) ).
fof(f1626,plain,
! [X0] :
( epsilon_connected(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f497]) ).
fof(f1627,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f497]) ).
fof(f1628,plain,
! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f499]) ).
fof(f1629,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f141]) ).
fof(f1630,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f500]) ).
fof(f1632,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f502]) ).
fof(f1633,plain,
! [X0] :
( epsilon_transitive(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f503]) ).
fof(f1634,plain,
! [X0] :
( epsilon_connected(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f503]) ).
fof(f1635,plain,
! [X0] :
( ordinal(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f503]) ).
fof(f1636,plain,
empty(empty_set),
inference(cnf_transformation,[],[f145]) ).
fof(f1637,plain,
relation(empty_set),
inference(cnf_transformation,[],[f145]) ).
fof(f1638,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f505]) ).
fof(f1639,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f507]) ).
fof(f1640,plain,
! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f507]) ).
fof(f1641,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f509]) ).
fof(f1642,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f511]) ).
fof(f1643,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f512]) ).
fof(f1644,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f512]) ).
fof(f1645,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f513]) ).
fof(f1646,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f513]) ).
fof(f1647,plain,
! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f515]) ).
fof(f1648,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f515]) ).
fof(f1649,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f375]) ).
fof(f1650,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f376]) ).
fof(f1651,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f516]) ).
fof(f1652,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(cnf_transformation,[],[f517]) ).
fof(f1653,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f518]) ).
fof(f1654,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f377]) ).
fof(f1655,plain,
! [X2,X0] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1015]) ).
fof(f1656,plain,
! [X0] :
( reflexive(X0)
| in(sK104(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1015]) ).
fof(f1657,plain,
! [X0] :
( reflexive(X0)
| ~ in(ordered_pair(sK104(X0),sK104(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1015]) ).
fof(f1658,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[],[f160]) ).
fof(f1660,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f521]) ).
fof(f1661,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f522]) ).
fof(f1662,plain,
! [X0,X1] :
( subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f523]) ).
fof(f1663,plain,
! [X0,X6,X4,X5] :
( in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1019]) ).
fof(f1664,plain,
! [X0] :
( transitive(X0)
| in(ordered_pair(sK105(X0),sK106(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1019]) ).
fof(f1665,plain,
! [X0] :
( transitive(X0)
| in(ordered_pair(sK106(X0),sK107(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1019]) ).
fof(f1666,plain,
! [X0] :
( transitive(X0)
| ~ in(ordered_pair(sK105(X0),sK107(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1019]) ).
fof(f1669,plain,
! [X0,X1] :
( relation(sK108(X0))
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1022]) ).
fof(f1670,plain,
! [X0,X1] :
( well_orders(sK108(X0),X0)
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1022]) ).
fof(f1673,plain,
! [X2,X0,X1] :
( in(X2,X0)
| ~ in(X2,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f528]) ).
fof(f1674,plain,
! [X3,X0,X4] :
( X3 = X4
| ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1027]) ).
fof(f1675,plain,
! [X0] :
( antisymmetric(X0)
| in(ordered_pair(sK109(X0),sK110(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1027]) ).
fof(f1676,plain,
! [X0] :
( antisymmetric(X0)
| in(ordered_pair(sK110(X0),sK109(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1027]) ).
fof(f1677,plain,
! [X0] :
( antisymmetric(X0)
| sK109(X0) != sK110(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1027]) ).
fof(f1678,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f532]) ).
fof(f1679,plain,
! [X3,X0,X4] :
( in(ordered_pair(X4,X3),X0)
| in(ordered_pair(X3,X4),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1031]) ).
fof(f1680,plain,
! [X0] :
( connected(X0)
| in(sK111(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1031]) ).
fof(f1681,plain,
! [X0] :
( connected(X0)
| in(sK112(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1031]) ).
fof(f1682,plain,
! [X0] :
( connected(X0)
| sK111(X0) != sK112(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1031]) ).
fof(f1683,plain,
! [X0] :
( connected(X0)
| ~ in(ordered_pair(sK111(X0),sK112(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1031]) ).
fof(f1684,plain,
! [X0] :
( connected(X0)
| ~ in(ordered_pair(sK112(X0),sK111(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1031]) ).
fof(f1689,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f1035]) ).
fof(f1692,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| in(sK113(X0,X1),X0) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f1693,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ in(sK113(X0,X1),X1) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f1697,plain,
relation(sK114),
inference(cnf_transformation,[],[f1041]) ).
fof(f1698,plain,
function(sK114),
inference(cnf_transformation,[],[f1041]) ).
fof(f1699,plain,
epsilon_transitive(sK115),
inference(cnf_transformation,[],[f1043]) ).
fof(f1700,plain,
epsilon_connected(sK115),
inference(cnf_transformation,[],[f1043]) ).
fof(f1701,plain,
ordinal(sK115),
inference(cnf_transformation,[],[f1043]) ).
fof(f1702,plain,
empty(sK116),
inference(cnf_transformation,[],[f1045]) ).
fof(f1703,plain,
relation(sK116),
inference(cnf_transformation,[],[f1045]) ).
fof(f1704,plain,
! [X0] :
( element(sK117(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f1047]) ).
fof(f1705,plain,
! [X0] :
( ~ empty(sK117(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f1047]) ).
fof(f1706,plain,
empty(sK118),
inference(cnf_transformation,[],[f1049]) ).
fof(f1707,plain,
relation(sK119),
inference(cnf_transformation,[],[f1051]) ).
fof(f1708,plain,
empty(sK119),
inference(cnf_transformation,[],[f1051]) ).
fof(f1709,plain,
function(sK119),
inference(cnf_transformation,[],[f1051]) ).
fof(f1710,plain,
relation(sK120),
inference(cnf_transformation,[],[f1053]) ).
fof(f1711,plain,
function(sK120),
inference(cnf_transformation,[],[f1053]) ).
fof(f1712,plain,
one_to_one(sK120),
inference(cnf_transformation,[],[f1053]) ).
fof(f1713,plain,
empty(sK120),
inference(cnf_transformation,[],[f1053]) ).
fof(f1714,plain,
epsilon_transitive(sK120),
inference(cnf_transformation,[],[f1053]) ).
fof(f1715,plain,
epsilon_connected(sK120),
inference(cnf_transformation,[],[f1053]) ).
fof(f1716,plain,
ordinal(sK120),
inference(cnf_transformation,[],[f1053]) ).
fof(f1717,plain,
~ empty(sK121),
inference(cnf_transformation,[],[f1055]) ).
fof(f1718,plain,
relation(sK121),
inference(cnf_transformation,[],[f1055]) ).
fof(f1719,plain,
! [X0] : element(sK122(X0),powerset(X0)),
inference(cnf_transformation,[],[f1057]) ).
fof(f1720,plain,
! [X0] : empty(sK122(X0)),
inference(cnf_transformation,[],[f1057]) ).
fof(f1721,plain,
~ empty(sK123),
inference(cnf_transformation,[],[f1059]) ).
fof(f1722,plain,
relation(sK124),
inference(cnf_transformation,[],[f1061]) ).
fof(f1723,plain,
function(sK124),
inference(cnf_transformation,[],[f1061]) ).
fof(f1724,plain,
one_to_one(sK124),
inference(cnf_transformation,[],[f1061]) ).
fof(f1725,plain,
~ empty(sK125),
inference(cnf_transformation,[],[f1063]) ).
fof(f1726,plain,
epsilon_transitive(sK125),
inference(cnf_transformation,[],[f1063]) ).
fof(f1727,plain,
epsilon_connected(sK125),
inference(cnf_transformation,[],[f1063]) ).
fof(f1728,plain,
ordinal(sK125),
inference(cnf_transformation,[],[f1063]) ).
fof(f1729,plain,
relation(sK126),
inference(cnf_transformation,[],[f1065]) ).
fof(f1730,plain,
relation_empty_yielding(sK126),
inference(cnf_transformation,[],[f1065]) ).
fof(f1731,plain,
relation(sK127),
inference(cnf_transformation,[],[f1067]) ).
fof(f1732,plain,
relation_empty_yielding(sK127),
inference(cnf_transformation,[],[f1067]) ).
fof(f1733,plain,
function(sK127),
inference(cnf_transformation,[],[f1067]) ).
fof(f1734,plain,
! [X2,X0,X1] :
( relation_dom(X2) = relation_dom_as_subset(X0,X1,X2)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f539]) ).
fof(f1735,plain,
! [X2,X0,X1] :
( relation_rng(X2) = relation_rng_as_subset(X0,X1,X2)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f540]) ).
fof(f1736,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f541]) ).
fof(f1737,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f542]) ).
fof(f1738,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f544]) ).
fof(f1739,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f1068]) ).
fof(f1740,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f1068]) ).
fof(f1741,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1069]) ).
fof(f1742,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1069]) ).
fof(f1743,plain,
! [X0,X1] :
( are_equipotent(X0,X1)
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f1070]) ).
fof(f1744,plain,
! [X0,X1] :
( equipotent(X0,X1)
| ~ are_equipotent(X0,X1) ),
inference(cnf_transformation,[],[f1070]) ).
fof(f1745,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f548]) ).
fof(f1746,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f378]) ).
fof(f1747,plain,
! [X0] : equipotent(X0,X0),
inference(cnf_transformation,[],[f379]) ).
fof(f1748,plain,
! [X0] :
( relation(sK128(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f1075]) ).
fof(f1749,plain,
! [X0] :
( function(sK128(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f1075]) ).
fof(f1751,plain,
! [X2,X3,X0] :
( in(X2,X0)
| ~ in(ordered_pair(X2,X3),sK128(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f1075]) ).
fof(f1752,plain,
! [X2,X3,X0] :
( singleton(X2) = X3
| ~ in(ordered_pair(X2,X3),sK128(X0))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f1075]) ).
fof(f1754,plain,
! [X0] :
( sP2(X0)
| in(sK129(X0),X0) ),
inference(cnf_transformation,[],[f1077]) ).
fof(f1755,plain,
! [X0] :
( sP2(X0)
| sK130(X0) = singleton(sK129(X0)) ),
inference(cnf_transformation,[],[f1077]) ).
fof(f1757,plain,
! [X0] :
( sP2(X0)
| sK131(X0) = singleton(sK129(X0)) ),
inference(cnf_transformation,[],[f1077]) ).
fof(f1758,plain,
! [X0] :
( sP2(X0)
| sK130(X0) != sK131(X0) ),
inference(cnf_transformation,[],[f1077]) ).
fof(f1759,plain,
! [X3,X0] :
( ordinal(sK132(X0))
| ~ in(X3,X0)
| ~ ordinal(X3) ),
inference(cnf_transformation,[],[f1080]) ).
fof(f1760,plain,
! [X3,X0] :
( in(sK132(X0),X0)
| ~ in(X3,X0)
| ~ ordinal(X3) ),
inference(cnf_transformation,[],[f1080]) ).
fof(f1761,plain,
! [X2,X3,X0] :
( ordinal_subset(sK132(X0),X2)
| ~ in(X2,X0)
| ~ ordinal(X2)
| ~ in(X3,X0)
| ~ ordinal(X3) ),
inference(cnf_transformation,[],[f1080]) ).
fof(f1762,plain,
! [X2,X0,X1] :
( relation(sK133(X0,X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1084]) ).
fof(f1763,plain,
! [X2,X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(ordered_pair(X4,X5),sK133(X0,X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1084]) ).
fof(f1764,plain,
! [X2,X0,X1,X4,X5] :
( in(X5,X0)
| ~ in(ordered_pair(X4,X5),sK133(X0,X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1084]) ).
fof(f1765,plain,
! [X2,X0,X1,X4,X5] :
( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(ordered_pair(X4,X5),sK133(X0,X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1084]) ).
fof(f1766,plain,
! [X2,X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),sK133(X0,X1,X2))
| ~ in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1084]) ).
fof(f1768,plain,
! [X0] :
( sK135(X0) = singleton(sK134(X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f1087]) ).
fof(f1769,plain,
! [X0] :
( in(sK134(X0),X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f1087]) ).
fof(f1770,plain,
! [X0] :
( sK136(X0) = singleton(sK134(X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f1087]) ).
fof(f1771,plain,
! [X0] :
( sK135(X0) != sK136(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f1087]) ).
fof(f1772,plain,
! [X2,X0] :
( in(sK138(X0,X2),X0)
| ~ in(X2,sK137(X0))
| sP3(X0) ),
inference(cnf_transformation,[],[f1092]) ).
fof(f1774,plain,
! [X2,X0] :
( singleton(sK138(X0,X2)) = X2
| ~ in(X2,sK137(X0))
| sP3(X0) ),
inference(cnf_transformation,[],[f1092]) ).
fof(f1776,plain,
! [X0] :
( sK139(X0) = sK140(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f1097]) ).
fof(f1777,plain,
! [X0] :
( sP4(X0,sK140(X0))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f1097]) ).
fof(f1778,plain,
! [X0] :
( sK139(X0) = sK141(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f1097]) ).
fof(f1779,plain,
! [X0] :
( sK141(X0) = ordered_pair(sK142(X0),sK143(X0))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f1097]) ).
fof(f1780,plain,
! [X0] :
( in(sK142(X0),X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f1097]) ).
fof(f1781,plain,
! [X0] :
( sK143(X0) = singleton(sK142(X0))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f1097]) ).
fof(f1782,plain,
! [X0] :
( sK140(X0) != sK141(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f1097]) ).
fof(f1783,plain,
! [X0,X1] :
( ordered_pair(sK144(X0,X1),sK145(X0,X1)) = X1
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f1101]) ).
fof(f1784,plain,
! [X0,X1] :
( in(sK144(X0,X1),X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f1101]) ).
fof(f1785,plain,
! [X0,X1] :
( sK145(X0,X1) = singleton(sK144(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f1101]) ).
fof(f1786,plain,
! [X3,X0,X1] :
( in(sK147(X0,X1,X3),cartesian_product2(X0,X1))
| ~ in(X3,sK146(X0,X1))
| sP5(X0) ),
inference(cnf_transformation,[],[f1107]) ).
fof(f1787,plain,
! [X3,X0,X1] :
( sK147(X0,X1,X3) = X3
| ~ in(X3,sK146(X0,X1))
| sP5(X0) ),
inference(cnf_transformation,[],[f1107]) ).
fof(f1788,plain,
! [X3,X0,X1] :
( ordered_pair(sK148(X0,X3),sK149(X0,X3)) = X3
| ~ in(X3,sK146(X0,X1))
| sP5(X0) ),
inference(cnf_transformation,[],[f1107]) ).
fof(f1789,plain,
! [X3,X0,X1] :
( in(sK148(X0,X3),X0)
| ~ in(X3,sK146(X0,X1))
| sP5(X0) ),
inference(cnf_transformation,[],[f1107]) ).
fof(f1790,plain,
! [X3,X0,X1] :
( sK149(X0,X3) = singleton(sK148(X0,X3))
| ~ in(X3,sK146(X0,X1))
| sP5(X0) ),
inference(cnf_transformation,[],[f1107]) ).
fof(f1791,plain,
! [X3,X0,X1,X6,X4,X5] :
( in(X3,sK146(X0,X1))
| singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1))
| sP5(X0) ),
inference(cnf_transformation,[],[f1107]) ).
fof(f1792,plain,
! [X0,X1] :
( sK150(X0,X1) = sK151(X0,X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f1113]) ).
fof(f1793,plain,
! [X0,X1] :
( sK151(X0,X1) = ordered_pair(sK155(X0,X1),sK156(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f1113]) ).
fof(f1794,plain,
! [X0,X1] :
( in(ordered_pair(apply(X1,sK155(X0,X1)),apply(X1,sK156(X0,X1))),X0)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f1113]) ).
fof(f1795,plain,
! [X0,X1] :
( sK150(X0,X1) = sK152(X0,X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f1113]) ).
fof(f1796,plain,
! [X0,X1] :
( sK152(X0,X1) = ordered_pair(sK153(X0,X1),sK154(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f1113]) ).
fof(f1797,plain,
! [X0,X1] :
( in(ordered_pair(apply(X1,sK153(X0,X1)),apply(X1,sK154(X0,X1))),X0)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f1113]) ).
fof(f1798,plain,
! [X0,X1] :
( sK151(X0,X1) != sK152(X0,X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f1113]) ).
fof(f1799,plain,
! [X2,X0,X1,X4] :
( in(sK158(X0,X1,X2,X4),cartesian_product2(X0,X0))
| ~ in(X4,sK157(X0,X1,X2))
| sP6(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1119]) ).
fof(f1800,plain,
! [X2,X0,X1,X4] :
( sK158(X0,X1,X2,X4) = X4
| ~ in(X4,sK157(X0,X1,X2))
| sP6(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1119]) ).
fof(f1801,plain,
! [X2,X0,X1,X4] :
( ordered_pair(sK159(X1,X2,X4),sK160(X1,X2,X4)) = X4
| ~ in(X4,sK157(X0,X1,X2))
| sP6(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1119]) ).
fof(f1802,plain,
! [X2,X0,X1,X4] :
( in(ordered_pair(apply(X2,sK159(X1,X2,X4)),apply(X2,sK160(X1,X2,X4))),X1)
| ~ in(X4,sK157(X0,X1,X2))
| sP6(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1119]) ).
fof(f1803,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK157(X0,X1,X2))
| ~ in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
| ordered_pair(X6,X7) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(X0,X0))
| sP6(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1119]) ).
fof(f1804,plain,
( sK161 = sK162
| ~ sP7 ),
inference(cnf_transformation,[],[f1123]) ).
fof(f1805,plain,
( ordinal(sK162)
| ~ sP7 ),
inference(cnf_transformation,[],[f1123]) ).
fof(f1806,plain,
( sK161 = sK163
| ~ sP7 ),
inference(cnf_transformation,[],[f1123]) ).
fof(f1807,plain,
( ordinal(sK163)
| ~ sP7 ),
inference(cnf_transformation,[],[f1123]) ).
fof(f1808,plain,
( sK162 != sK163
| ~ sP7 ),
inference(cnf_transformation,[],[f1123]) ).
fof(f1809,plain,
! [X2,X0] :
( in(sK165(X0,X2),X0)
| ~ in(X2,sK164(X0))
| sP7 ),
inference(cnf_transformation,[],[f1128]) ).
fof(f1810,plain,
! [X2,X0] :
( sK165(X0,X2) = X2
| ~ in(X2,sK164(X0))
| sP7 ),
inference(cnf_transformation,[],[f1128]) ).
fof(f1811,plain,
! [X2,X0] :
( ordinal(X2)
| ~ in(X2,sK164(X0))
| sP7 ),
inference(cnf_transformation,[],[f1128]) ).
fof(f1812,plain,
! [X2,X3,X0] :
( in(X2,sK164(X0))
| ~ ordinal(X2)
| X2 != X3
| ~ in(X3,X0)
| sP7 ),
inference(cnf_transformation,[],[f1128]) ).
fof(f1813,plain,
! [X0] :
( sK166(X0) = sK167(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f1133]) ).
fof(f1814,plain,
! [X0] :
( sP8(X0,sK167(X0))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f1133]) ).
fof(f1815,plain,
! [X0] :
( sK166(X0) = sK168(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f1133]) ).
fof(f1816,plain,
! [X0] :
( ordinal(sK169(X0))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f1133]) ).
fof(f1817,plain,
! [X0] :
( sK168(X0) = sK169(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f1133]) ).
fof(f1818,plain,
! [X0] :
( in(sK169(X0),X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f1133]) ).
fof(f1819,plain,
! [X0] :
( sK167(X0) != sK168(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f1133]) ).
fof(f1820,plain,
! [X0,X1] :
( ordinal(sK170(X0,X1))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f1137]) ).
fof(f1821,plain,
! [X0,X1] :
( sK170(X0,X1) = X1
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f1137]) ).
fof(f1822,plain,
! [X0,X1] :
( in(sK170(X0,X1),X0)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f1137]) ).
fof(f1823,plain,
! [X3,X0,X1] :
( in(sK172(X0,X1,X3),succ(X1))
| ~ in(X3,sK171(X0,X1))
| sP9(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f1143]) ).
fof(f1824,plain,
! [X3,X0,X1] :
( sK172(X0,X1,X3) = X3
| ~ in(X3,sK171(X0,X1))
| sP9(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f1143]) ).
fof(f1825,plain,
! [X3,X0,X1] :
( ordinal(sK173(X0,X3))
| ~ in(X3,sK171(X0,X1))
| sP9(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f1143]) ).
fof(f1826,plain,
! [X3,X0,X1] :
( sK173(X0,X3) = X3
| ~ in(X3,sK171(X0,X1))
| sP9(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f1143]) ).
fof(f1827,plain,
! [X3,X0,X1] :
( in(sK173(X0,X3),X0)
| ~ in(X3,sK171(X0,X1))
| sP9(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f1143]) ).
fof(f1828,plain,
! [X3,X0,X1,X4,X5] :
( in(X3,sK171(X0,X1))
| ~ in(X5,X0)
| X3 != X5
| ~ ordinal(X5)
| X3 != X4
| ~ in(X4,succ(X1))
| sP9(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f1143]) ).
fof(f1829,plain,
! [X3,X0,X1] :
( in(X3,cartesian_product2(X0,X1))
| ~ in(X3,sK174(X0,X1)) ),
inference(cnf_transformation,[],[f1149]) ).
fof(f1830,plain,
! [X3,X0,X1] :
( ordered_pair(sK175(X0,X3),sK176(X0,X3)) = X3
| ~ in(X3,sK174(X0,X1)) ),
inference(cnf_transformation,[],[f1149]) ).
fof(f1831,plain,
! [X3,X0,X1] :
( in(sK175(X0,X3),X0)
| ~ in(X3,sK174(X0,X1)) ),
inference(cnf_transformation,[],[f1149]) ).
fof(f1832,plain,
! [X3,X0,X1] :
( sK176(X0,X3) = singleton(sK175(X0,X3))
| ~ in(X3,sK174(X0,X1)) ),
inference(cnf_transformation,[],[f1149]) ).
fof(f1833,plain,
! [X3,X0,X1,X4,X5] :
( in(X3,sK174(X0,X1))
| singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3
| ~ in(X3,cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f1149]) ).
fof(f1834,plain,
! [X2,X0,X1,X4] :
( in(X4,cartesian_product2(X0,X0))
| ~ in(X4,sK177(X0,X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1155]) ).
fof(f1835,plain,
! [X2,X0,X1,X4] :
( ordered_pair(sK178(X1,X2,X4),sK179(X1,X2,X4)) = X4
| ~ in(X4,sK177(X0,X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1155]) ).
fof(f1836,plain,
! [X2,X0,X1,X4] :
( in(ordered_pair(apply(X2,sK178(X1,X2,X4)),apply(X2,sK179(X1,X2,X4))),X1)
| ~ in(X4,sK177(X0,X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1155]) ).
fof(f1837,plain,
! [X2,X0,X1,X6,X4,X5] :
( in(X4,sK177(X0,X1,X2))
| ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4
| ~ in(X4,cartesian_product2(X0,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1155]) ).
fof(f1838,plain,
! [X2,X0] :
( in(X2,X0)
| ~ in(X2,sK180(X0)) ),
inference(cnf_transformation,[],[f1159]) ).
fof(f1839,plain,
! [X2,X0] :
( ordinal(X2)
| ~ in(X2,sK180(X0)) ),
inference(cnf_transformation,[],[f1159]) ).
fof(f1840,plain,
! [X2,X0] :
( in(X2,sK180(X0))
| ~ ordinal(X2)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f1159]) ).
fof(f1841,plain,
! [X3,X0,X1] :
( in(X3,succ(X1))
| ~ in(X3,sK181(X0,X1))
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f1165]) ).
fof(f1842,plain,
! [X3,X0,X1] :
( ordinal(sK182(X0,X3))
| ~ in(X3,sK181(X0,X1))
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f1165]) ).
fof(f1843,plain,
! [X3,X0,X1] :
( sK182(X0,X3) = X3
| ~ in(X3,sK181(X0,X1))
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f1165]) ).
fof(f1844,plain,
! [X3,X0,X1] :
( in(sK182(X0,X3),X0)
| ~ in(X3,sK181(X0,X1))
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f1165]) ).
fof(f1845,plain,
! [X3,X0,X1,X4] :
( in(X3,sK181(X0,X1))
| ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4)
| ~ in(X3,succ(X1))
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f1165]) ).
fof(f1846,plain,
! [X0] :
( in(sK183(X0),X0)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f1169]) ).
fof(f1847,plain,
! [X0] :
( sK184(X0) = singleton(sK183(X0))
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f1169]) ).
fof(f1848,plain,
! [X0] :
( sK185(X0) = singleton(sK183(X0))
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f1169]) ).
fof(f1849,plain,
! [X0] :
( sK184(X0) != sK185(X0)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f1169]) ).
fof(f1851,plain,
! [X0,X4] :
( relation(sK186(X0))
| singleton(sK187(X0)) != X4
| sP10(X0) ),
inference(cnf_transformation,[],[f1173]) ).
fof(f1853,plain,
! [X0,X4] :
( function(sK186(X0))
| singleton(sK187(X0)) != X4
| sP10(X0) ),
inference(cnf_transformation,[],[f1173]) ).
fof(f1855,plain,
! [X0,X4] :
( relation_dom(sK186(X0)) = X0
| singleton(sK187(X0)) != X4
| sP10(X0) ),
inference(cnf_transformation,[],[f1173]) ).
fof(f1857,plain,
! [X2,X0,X4] :
( singleton(X2) = apply(sK186(X0),X2)
| ~ in(X2,X0)
| singleton(sK187(X0)) != X4
| sP10(X0) ),
inference(cnf_transformation,[],[f1173]) ).
fof(f1858,plain,
! [X1] :
( in(sK189(X1),sK188)
| relation_dom(X1) != sK188
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1176]) ).
fof(f1859,plain,
! [X1] :
( singleton(sK189(X1)) != apply(X1,sK189(X1))
| relation_dom(X1) != sK188
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1176]) ).
fof(f1860,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f571]) ).
fof(f1861,plain,
! [X0,X1] :
( equipotent(X1,X0)
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f572]) ).
fof(f1862,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f1178]) ).
fof(f1863,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f1178]) ).
fof(f1864,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f1178]) ).
fof(f1865,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f221]) ).
fof(f1866,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f573]) ).
fof(f1867,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1180]) ).
fof(f1868,plain,
! [X2,X0,X1] :
( in(X0,relation_rng(X2))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1180]) ).
fof(f1869,plain,
! [X2,X0,X1] :
( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1180]) ).
fof(f1870,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f575]) ).
fof(f1871,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X0,X1),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f576]) ).
fof(f1872,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f577]) ).
fof(f1873,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f578]) ).
fof(f1874,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f578]) ).
fof(f1875,plain,
! [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f579]) ).
fof(f1876,plain,
! [X2,X3,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f581]) ).
fof(f1877,plain,
! [X2,X0,X1] :
( subset(relation_dom(X2),X0)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f582]) ).
fof(f1878,plain,
! [X2,X0,X1] :
( subset(relation_rng(X2),X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f582]) ).
fof(f1879,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f583]) ).
fof(f1880,plain,
! [X0] : in(X0,sK190(X0)),
inference(cnf_transformation,[],[f1182]) ).
fof(f1881,plain,
! [X0,X4,X5] :
( in(X5,sK190(X0))
| ~ subset(X5,X4)
| ~ in(X4,sK190(X0)) ),
inference(cnf_transformation,[],[f1182]) ).
fof(f1882,plain,
! [X3,X0] :
( in(powerset(X3),sK190(X0))
| ~ in(X3,sK190(X0)) ),
inference(cnf_transformation,[],[f1182]) ).
fof(f1883,plain,
! [X2,X0] :
( in(X2,sK190(X0))
| are_equipotent(X2,sK190(X0))
| ~ subset(X2,sK190(X0)) ),
inference(cnf_transformation,[],[f1182]) ).
fof(f1884,plain,
! [X2,X0,X1] :
( relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f586]) ).
fof(f1885,plain,
! [X2,X0,X1] :
( in(sK191(X0,X1,X2),relation_dom(X2))
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1186]) ).
fof(f1886,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK191(X0,X1,X2),X0),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1186]) ).
fof(f1887,plain,
! [X2,X0,X1] :
( in(sK191(X0,X1,X2),X1)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1186]) ).
fof(f1889,plain,
! [X0,X1] :
( subset(relation_image(X1,X0),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f588]) ).
fof(f1890,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f590]) ).
fof(f1891,plain,
! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f591]) ).
fof(f1892,plain,
! [X0,X1] :
( subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
| ~ subset(X0,relation_dom(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f593]) ).
fof(f1893,plain,
! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f594]) ).
fof(f1894,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f596]) ).
fof(f1895,plain,
! [X2,X3,X0,X1] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(relation_rng(X3),X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(cnf_transformation,[],[f598]) ).
fof(f1896,plain,
! [X0,X1] :
( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f599]) ).
fof(f1897,plain,
! [X2,X0,X1] :
( in(sK192(X0,X1,X2),relation_rng(X2))
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1190]) ).
fof(f1898,plain,
! [X2,X0,X1] :
( in(ordered_pair(X0,sK192(X0,X1,X2)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1190]) ).
fof(f1899,plain,
! [X2,X0,X1] :
( in(sK192(X0,X1,X2),X1)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1190]) ).
fof(f1901,plain,
! [X0,X1] :
( subset(relation_inverse_image(X1,X0),relation_dom(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f601]) ).
fof(f1902,plain,
! [X2,X3,X0,X1] :
( relation_of2_as_subset(X3,X2,X1)
| ~ subset(X0,X1)
| ~ relation_of2_as_subset(X3,X2,X0) ),
inference(cnf_transformation,[],[f603]) ).
fof(f1903,plain,
! [X2,X0,X1] :
( in(X0,X2)
| ~ in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1192]) ).
fof(f1904,plain,
! [X2,X0,X1] :
( in(X0,cartesian_product2(X1,X1))
| ~ in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1192]) ).
fof(f1905,plain,
! [X2,X0,X1] :
( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1192]) ).
fof(f1906,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0
| ~ relation(X1) ),
inference(cnf_transformation,[],[f606]) ).
fof(f1907,plain,
! [X2,X0,X1] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f608]) ).
fof(f1908,plain,
! [X0,X1] :
( relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f609]) ).
fof(f1910,plain,
! [X0,X1] :
( relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f610]) ).
fof(f1911,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f612]) ).
fof(f1912,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f612]) ).
fof(f1913,plain,
! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f614]) ).
fof(f1914,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f254]) ).
fof(f1915,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f615]) ).
fof(f1916,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f617]) ).
fof(f1917,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[],[f257]) ).
fof(f1918,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f619]) ).
fof(f1919,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f619]) ).
fof(f1920,plain,
! [X0,X1] :
( subset(relation_field(relation_restriction(X1,X0)),relation_field(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f620]) ).
fof(f1921,plain,
! [X0,X1] :
( subset(relation_field(relation_restriction(X1,X0)),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f620]) ).
fof(f1922,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1194]) ).
fof(f1923,plain,
! [X2,X0,X1] :
( in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1194]) ).
fof(f1924,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1194]) ).
fof(f1925,plain,
! [X0,X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f624]) ).
fof(f1926,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f625]) ).
fof(f1927,plain,
! [X2,X0,X1] :
( subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f626]) ).
fof(f1928,plain,
! [X2,X0,X1] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f628]) ).
fof(f1929,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X1,X0,X2) = X1
| in(sK194(X1,X2),X1)
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(cnf_transformation,[],[f1199]) ).
fof(f1930,plain,
! [X2,X0,X1,X6] :
( relation_dom_as_subset(X1,X0,X2) = X1
| ~ in(ordered_pair(sK194(X1,X2),X6),X2)
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(cnf_transformation,[],[f1199]) ).
fof(f1931,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X3,sK193(X2,X3)),X2)
| ~ in(X3,X1)
| relation_dom_as_subset(X1,X0,X2) != X1
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(cnf_transformation,[],[f1199]) ).
fof(f1932,plain,
! [X0,X1] :
( reflexive(relation_restriction(X1,X0))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f631]) ).
fof(f1933,plain,
! [X2,X0,X1] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f633]) ).
fof(f1934,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f635]) ).
fof(f1935,plain,
! [X2,X0,X1] :
( relation_rng_as_subset(X0,X1,X2) = X1
| in(sK196(X1,X2),X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f1204]) ).
fof(f1936,plain,
! [X2,X0,X1,X6] :
( relation_rng_as_subset(X0,X1,X2) = X1
| ~ in(ordered_pair(X6,sK196(X1,X2)),X2)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f1204]) ).
fof(f1937,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(sK195(X2,X3),X3),X2)
| ~ in(X3,X1)
| relation_rng_as_subset(X0,X1,X2) != X1
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f1204]) ).
fof(f1938,plain,
! [X0,X1] :
( connected(relation_restriction(X1,X0))
| ~ connected(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f638]) ).
fof(f1939,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f640]) ).
fof(f1940,plain,
! [X0,X1] :
( transitive(relation_restriction(X1,X0))
| ~ transitive(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f642]) ).
fof(f1941,plain,
! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f644]) ).
fof(f1942,plain,
! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f644]) ).
fof(f1943,plain,
! [X0,X1] :
( antisymmetric(relation_restriction(X1,X0))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f646]) ).
fof(f1944,plain,
! [X0,X1] :
( relation_field(relation_restriction(X1,X0)) = X0
| ~ well_orders(X1,X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f648]) ).
fof(f1945,plain,
! [X0,X1] :
( well_ordering(relation_restriction(X1,X0))
| ~ well_orders(X1,X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f648]) ).
fof(f1946,plain,
! [X2,X0,X1] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f649]) ).
fof(f1947,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f650]) ).
fof(f1948,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f278]) ).
fof(f1949,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f652]) ).
fof(f1950,plain,
! [X0,X1] :
( X0 = X1
| in(sK197(X0,X1),X1)
| in(sK197(X0,X1),X0) ),
inference(cnf_transformation,[],[f1207]) ).
fof(f1951,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK197(X0,X1),X1)
| ~ in(sK197(X0,X1),X0) ),
inference(cnf_transformation,[],[f1207]) ).
fof(f1952,plain,
! [X0] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f281]) ).
fof(f1953,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f282]) ).
fof(f1954,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f655]) ).
fof(f1955,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f655]) ).
fof(f1956,plain,
! [X0] :
( ordinal(X0)
| in(sK198(X0),X0) ),
inference(cnf_transformation,[],[f1209]) ).
fof(f1957,plain,
! [X0] :
( ordinal(X0)
| ~ subset(sK198(X0),X0)
| ~ ordinal(sK198(X0)) ),
inference(cnf_transformation,[],[f1209]) ).
fof(f1958,plain,
! [X0,X1] :
( well_founded_relation(relation_restriction(X1,X0))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f658]) ).
fof(f1959,plain,
! [X0,X1] :
( ordinal(sK199(X0))
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f1211]) ).
fof(f1960,plain,
! [X0,X1] :
( in(sK199(X0),X0)
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f1211]) ).
fof(f1961,plain,
! [X3,X0,X1] :
( ordinal_subset(sK199(X0),X3)
| ~ in(X3,X0)
| ~ ordinal(X3)
| empty_set = X0
| ~ subset(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f1211]) ).
fof(f1962,plain,
! [X0,X1] :
( well_ordering(relation_restriction(X1,X0))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f662]) ).
fof(f1963,plain,
! [X0,X1] :
( ordinal_subset(succ(X0),X1)
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1212]) ).
fof(f1964,plain,
! [X0,X1] :
( in(X0,X1)
| ~ ordinal_subset(succ(X0),X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1212]) ).
fof(f1965,plain,
! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f664]) ).
fof(f1966,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(cnf_transformation,[],[f665]) ).
fof(f1967,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(cnf_transformation,[],[f665]) ).
fof(f1970,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| in(sK200(X0,X1),X0)
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1217]) ).
fof(f1971,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK200(X0,X1) != apply(X1,sK200(X0,X1))
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1217]) ).
fof(f1972,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f668]) ).
fof(f1973,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f293]) ).
fof(f1974,plain,
! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f669]) ).
fof(f1975,plain,
! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f669]) ).
fof(f1976,plain,
! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ),
inference(cnf_transformation,[],[f1218]) ).
fof(f1977,plain,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1218]) ).
fof(f1979,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1219]) ).
fof(f1980,plain,
! [X2,X0,X1] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f1221]) ).
fof(f1981,plain,
! [X2,X0,X1] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f1221]) ).
fof(f1982,plain,
! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f1221]) ).
fof(f1983,plain,
! [X0,X1] :
( relation_field(relation_restriction(X1,X0)) = X0
| ~ subset(X0,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f671]) ).
fof(f1984,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f299]) ).
fof(f1985,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f1223]) ).
fof(f1988,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f301]) ).
fof(f1989,plain,
! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f672]) ).
fof(f1990,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1224]) ).
fof(f1991,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1224]) ).
fof(f1992,plain,
! [X0] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f304]) ).
fof(f1993,plain,
! [X0,X1] :
( in(sK201(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1226]) ).
fof(f1994,plain,
! [X0,X1] :
( in(sK201(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1226]) ).
fof(f1995,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f1226]) ).
fof(f1996,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f674]) ).
fof(f1997,plain,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(cnf_transformation,[],[f307]) ).
fof(f1998,plain,
! [X2,X0] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1230]) ).
fof(f1999,plain,
! [X0] :
( being_limit_ordinal(X0)
| ordinal(sK202(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1230]) ).
fof(f2000,plain,
! [X0] :
( being_limit_ordinal(X0)
| in(sK202(X0),X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1230]) ).
fof(f2001,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ in(succ(sK202(X0)),X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1230]) ).
fof(f2002,plain,
! [X0] :
( ordinal(sK203(X0))
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1232]) ).
fof(f2003,plain,
! [X0] :
( succ(sK203(X0)) = X0
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1232]) ).
fof(f2004,plain,
! [X0,X1] :
( ~ being_limit_ordinal(X0)
| succ(X1) != X0
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1232]) ).
fof(f2005,plain,
! [X2,X0,X1] :
( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f1233]) ).
fof(f2006,plain,
! [X2,X0,X1] :
( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f1233]) ).
fof(f2007,plain,
! [X0,X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f679]) ).
fof(f2008,plain,
! [X0,X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f680]) ).
fof(f2009,plain,
! [X0,X1] :
( set_union2(X0,set_difference(X1,X0)) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f681]) ).
fof(f2010,plain,
! [X0,X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f683]) ).
fof(f2011,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f685]) ).
fof(f2012,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f686]) ).
fof(f2013,plain,
! [X0,X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f688]) ).
fof(f2014,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f690]) ).
fof(f2015,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f692]) ).
fof(f2016,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f320]) ).
fof(f2017,plain,
! [X2,X0,X1] :
( relation_isomorphism(X1,X0,function_inverse(X2))
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f694]) ).
fof(f2018,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f322]) ).
fof(f2019,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f696]) ).
fof(f2020,plain,
! [X0] :
( connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f697]) ).
fof(f2021,plain,
! [X0,X1] :
( in(sK204(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1235]) ).
fof(f2022,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f1235]) ).
fof(f2023,plain,
! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| empty_set = X0 ),
inference(cnf_transformation,[],[f700]) ).
fof(f2024,plain,
! [X2,X0,X1] :
( reflexive(X1)
| ~ reflexive(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f702]) ).
fof(f2025,plain,
! [X2,X0,X1] :
( transitive(X1)
| ~ transitive(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f702]) ).
fof(f2026,plain,
! [X2,X0,X1] :
( connected(X1)
| ~ connected(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f702]) ).
fof(f2027,plain,
! [X2,X0,X1] :
( antisymmetric(X1)
| ~ antisymmetric(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f702]) ).
fof(f2028,plain,
! [X2,X0,X1] :
( well_founded_relation(X1)
| ~ well_founded_relation(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f702]) ).
fof(f2029,plain,
! [X2,X3,X0,X1] :
( in(X1,relation_dom(X2))
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1238]) ).
fof(f2030,plain,
! [X2,X3,X0,X1] :
( apply(X2,X1) = X0
| apply(X3,X0) != X1
| ~ in(X0,relation_rng(X2))
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1238]) ).
fof(f2031,plain,
! [X2,X3,X0,X1] :
( sP11(X0,X1,X2,X3)
| in(X0,relation_rng(X2)) ),
inference(cnf_transformation,[],[f1238]) ).
fof(f2032,plain,
! [X2,X3,X0,X1] :
( sP11(X0,X1,X2,X3)
| apply(X3,X0) = X1 ),
inference(cnf_transformation,[],[f1238]) ).
fof(f2033,plain,
! [X2,X3,X0,X1] :
( sP11(X0,X1,X2,X3)
| apply(X2,X1) != X0
| ~ in(X1,relation_dom(X2)) ),
inference(cnf_transformation,[],[f1238]) ).
fof(f2035,plain,
! [X0,X1,X4,X5] :
( sP11(X4,X5,X0,X1)
| function_inverse(X0) != X1
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1243]) ).
fof(f2037,plain,
! [X0,X1,X4,X5] :
( apply(X1,X4) = X5
| apply(X0,X5) != X4
| ~ in(X5,relation_dom(X0))
| function_inverse(X0) != X1
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1243]) ).
fof(f2038,plain,
! [X0,X1] :
( function_inverse(X0) = X1
| in(sK206(X0,X1),relation_dom(X0))
| ~ sP11(sK205(X0,X1),sK206(X0,X1),X0,X1)
| relation_rng(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1243]) ).
fof(f2039,plain,
! [X0,X1] :
( function_inverse(X0) = X1
| sK205(X0,X1) = apply(X0,sK206(X0,X1))
| ~ sP11(sK205(X0,X1),sK206(X0,X1),X0,X1)
| relation_rng(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1243]) ).
fof(f2040,plain,
! [X0,X1] :
( function_inverse(X0) = X1
| sK206(X0,X1) != apply(X1,sK205(X0,X1))
| ~ in(sK205(X0,X1),relation_rng(X0))
| ~ sP11(sK205(X0,X1),sK206(X0,X1),X0,X1)
| relation_rng(X0) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1243]) ).
fof(f2041,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f706]) ).
fof(f2042,plain,
! [X2,X0,X1] :
( well_ordering(X1)
| ~ relation_isomorphism(X0,X1,X2)
| ~ well_ordering(X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f708]) ).
fof(f2043,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f710]) ).
fof(f2044,plain,
! [X0] :
( relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f710]) ).
fof(f2045,plain,
! [X0] :
( empty_set = X0
| in(ordered_pair(sK207(X0),sK208(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1245]) ).
fof(f2046,plain,
! [X0,X1] :
( apply(X1,apply(function_inverse(X1),X0)) = X0
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f714]) ).
fof(f2047,plain,
! [X0,X1] :
( apply(relation_composition(function_inverse(X1),X1),X0) = X0
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f714]) ).
fof(f2048,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f715]) ).
fof(f2049,plain,
! [X0] :
( is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1246]) ).
fof(f2050,plain,
! [X0] :
( well_founded_relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1246]) ).
fof(f2051,plain,
! [X0] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[],[f336]) ).
fof(f2052,plain,
empty_set = relation_dom(empty_set),
inference(cnf_transformation,[],[f337]) ).
fof(f2053,plain,
empty_set = relation_rng(empty_set),
inference(cnf_transformation,[],[f337]) ).
fof(f2054,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f717]) ).
fof(f2055,plain,
! [X0] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f719]) ).
fof(f2056,plain,
! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f721]) ).
fof(f2057,plain,
! [X0] :
( empty_set = X0
| relation_dom(X0) != empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[],[f723]) ).
fof(f2058,plain,
! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f723]) ).
fof(f2059,plain,
! [X0] :
( empty_set = relation_rng(X0)
| relation_dom(X0) != empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1247]) ).
fof(f2060,plain,
! [X0] :
( relation_dom(X0) = empty_set
| empty_set != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1247]) ).
fof(f2061,plain,
! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ),
inference(cnf_transformation,[],[f1248]) ).
fof(f2062,plain,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) ),
inference(cnf_transformation,[],[f1248]) ).
fof(f2065,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| in(sK209(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1253]) ).
fof(f2066,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| apply(X2,sK209(X1,X2)) != apply(X1,sK209(X1,X2))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f1253]) ).
fof(f2067,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f345]) ).
fof(f2068,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f727]) ).
fof(f2069,plain,
! [X0] :
( well_founded_relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f728]) ).
fof(f2070,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[],[f729]) ).
fof(f2071,plain,
! [X2,X0,X1] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f731]) ).
fof(f2072,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f350]) ).
fof(f2073,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f350]) ).
fof(f2074,plain,
! [X2,X0,X1] :
( apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1)
| ~ in(X1,X0)
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f733]) ).
fof(f2075,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(cnf_transformation,[],[f1255]) ).
fof(f2076,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(cnf_transformation,[],[f1255]) ).
fof(f2077,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2)
| ~ relation(X3) ),
inference(cnf_transformation,[],[f1255]) ).
fof(f2078,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f735]) ).
fof(f2079,plain,
! [X0,X1] : pair_first(ordered_pair(X0,X1)) = X0,
inference(cnf_transformation,[],[f354]) ).
fof(f2080,plain,
! [X0,X1] : pair_second(ordered_pair(X0,X1)) = X1,
inference(cnf_transformation,[],[f354]) ).
fof(f2081,plain,
! [X0,X1] :
( in(sK210(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1257]) ).
fof(f2082,plain,
! [X3,X0,X1] :
( ~ in(X3,sK210(X1))
| ~ in(X3,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1257]) ).
fof(f2083,plain,
! [X0] :
( well_ordering(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f737]) ).
fof(f2084,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f357]) ).
fof(f2085,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1258]) ).
fof(f2086,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ),
inference(cnf_transformation,[],[f1258]) ).
fof(f2087,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1260]) ).
fof(f2088,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1260]) ).
fof(f2089,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1260]) ).
fof(f2090,plain,
! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f739]) ).
fof(f2091,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f740]) ).
fof(f2093,plain,
! [X2,X0,X1] :
( apply(X2,X0) = X1
| ~ in(ordered_pair(X0,X1),X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1262]) ).
fof(f2094,plain,
! [X2,X0,X1] :
( in(ordered_pair(X0,X1),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f1262]) ).
fof(f2095,plain,
! [X0] :
( well_ordering(X0)
| ~ well_orders(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1263]) ).
fof(f2096,plain,
! [X0] :
( well_orders(X0,relation_field(X0))
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1263]) ).
fof(f2097,plain,
! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f745]) ).
fof(f2098,plain,
! [X2,X0,X1] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[],[f746]) ).
fof(f2099,plain,
! [X0,X1] :
( set_intersection2(relation_dom(X1),X0) = relation_dom(relation_dom_restriction(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f747]) ).
fof(f2100,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f748]) ).
fof(f2101,plain,
! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f749]) ).
fof(f2102,plain,
! [X0,X1] :
( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f750]) ).
fof(f2103,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f370]) ).
fof(f2104,plain,
! [X0] : in(X0,sK211(X0)),
inference(cnf_transformation,[],[f1266]) ).
fof(f2105,plain,
! [X0,X6,X7] :
( in(X7,sK211(X0))
| ~ subset(X7,X6)
| ~ in(X6,sK211(X0)) ),
inference(cnf_transformation,[],[f1266]) ).
fof(f2106,plain,
! [X3,X0] :
( in(sK212(X0,X3),sK211(X0))
| ~ in(X3,sK211(X0)) ),
inference(cnf_transformation,[],[f1266]) ).
fof(f2107,plain,
! [X3,X0,X5] :
( in(X5,sK212(X0,X3))
| ~ subset(X5,X3)
| ~ in(X3,sK211(X0)) ),
inference(cnf_transformation,[],[f1266]) ).
fof(f2108,plain,
! [X2,X0] :
( in(X2,sK211(X0))
| are_equipotent(X2,sK211(X0))
| ~ subset(X2,sK211(X0)) ),
inference(cnf_transformation,[],[f1266]) ).
fof(f2109,plain,
! [X2,X0,X1] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[],[f753]) ).
fof(f2110,plain,
! [X0] : succ(X0) = set_union2(X0,unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1353,f2067]) ).
fof(f2111,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1508,f2067]) ).
fof(f2112,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f1283,f2016,f2016]) ).
fof(f2113,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK12(X0,X1) != sK13(X0,X1)
| ~ in(sK12(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK12(X0,X1),sK13(X0,X1)),unordered_pair(sK12(X0,X1),sK12(X0,X1))),X1)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1290,f2111]) ).
fof(f2114,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK12(X0,X1) = sK13(X0,X1)
| in(unordered_pair(unordered_pair(sK12(X0,X1),sK13(X0,X1)),unordered_pair(sK12(X0,X1),sK12(X0,X1))),X1)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1289,f2111]) ).
fof(f2115,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| in(sK12(X0,X1),X0)
| in(unordered_pair(unordered_pair(sK12(X0,X1),sK13(X0,X1)),unordered_pair(sK12(X0,X1),sK12(X0,X1))),X1)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1288,f2111]) ).
fof(f2116,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| X4 != X5
| ~ in(X4,X0)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1287,f2111]) ).
fof(f2117,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1286,f2111]) ).
fof(f2118,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1285,f2111]) ).
fof(f2119,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),unordered_pair(sK14(X0,X1,X2),sK14(X0,X1,X2))),X0)
| ~ in(sK14(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),unordered_pair(sK14(X0,X1,X2),sK14(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1299,f2111,f2111]) ).
fof(f2120,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),unordered_pair(sK14(X0,X1,X2),sK14(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),unordered_pair(sK14(X0,X1,X2),sK14(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1298,f2111,f2111]) ).
fof(f2121,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X0,X1) = X2
| in(sK14(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),unordered_pair(sK14(X0,X1,X2),sK14(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1297,f2111]) ).
fof(f2122,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1296,f2111,f2111]) ).
fof(f2123,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1295,f2111,f2111]) ).
fof(f2124,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| relation_dom_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1294,f2111]) ).
fof(f2125,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),unordered_pair(sK19(X0,X1,X2),sK19(X0,X1,X2))),X1)
| ~ in(sK20(X0,X1,X2),X0)
| ~ in(unordered_pair(unordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),unordered_pair(sK19(X0,X1,X2),sK19(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1313,f2111,f2111]) ).
fof(f2126,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),unordered_pair(sK19(X0,X1,X2),sK19(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),unordered_pair(sK19(X0,X1,X2),sK19(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1312,f2111,f2111]) ).
fof(f2127,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X1) = X2
| in(sK20(X0,X1,X2),X0)
| in(unordered_pair(unordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),unordered_pair(sK19(X0,X1,X2),sK19(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1311,f2111]) ).
fof(f2128,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1)
| ~ in(X6,X0)
| relation_rng_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1310,f2111,f2111]) ).
fof(f2129,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| relation_rng_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1309,f2111,f2111]) ).
fof(f2130,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| relation_rng_restriction(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1308,f2111]) ).
fof(f2131,plain,
! [X2,X0,X1,X4] :
( relation_image(X0,X1) = X2
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(X4,sK22(X0,X1,X2)),unordered_pair(X4,X4)),X0)
| ~ in(sK22(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1327,f2111]) ).
fof(f2132,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK23(X0,X1,X2),sK22(X0,X1,X2)),unordered_pair(sK23(X0,X1,X2),sK23(X0,X1,X2))),X0)
| in(sK22(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1325,f2111]) ).
fof(f2133,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X0)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1324,f2111]) ).
fof(f2134,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(sK24(X0,X1,X6),X6),unordered_pair(sK24(X0,X1,X6),sK24(X0,X1,X6))),X0)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1322,f2111]) ).
fof(f2135,plain,
! [X2,X0,X1,X4] :
( relation_inverse_image(X0,X1) = X2
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(sK25(X0,X1,X2),X4),unordered_pair(sK25(X0,X1,X2),sK25(X0,X1,X2))),X0)
| ~ in(sK25(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1333,f2111]) ).
fof(f2136,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK25(X0,X1,X2),sK26(X0,X1,X2)),unordered_pair(sK25(X0,X1,X2),sK25(X0,X1,X2))),X0)
| in(sK25(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1331,f2111]) ).
fof(f2137,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X0)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1330,f2111]) ).
fof(f2138,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK27(X0,X1,X6)),unordered_pair(X6,X6)),X0)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1328,f2111]) ).
fof(f2139,plain,
! [X0] :
( function(X0)
| in(unordered_pair(unordered_pair(sK29(X0),sK31(X0)),unordered_pair(sK29(X0),sK29(X0))),X0) ),
inference(definition_unfolding,[],[f1348,f2111]) ).
fof(f2140,plain,
! [X0] :
( function(X0)
| in(unordered_pair(unordered_pair(sK29(X0),sK30(X0)),unordered_pair(sK29(X0),sK29(X0))),X0) ),
inference(definition_unfolding,[],[f1347,f2111]) ).
fof(f2141,plain,
! [X0,X6,X4,X5] :
( X5 = X6
| ~ in(unordered_pair(unordered_pair(X4,X6),unordered_pair(X4,X4)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| ~ function(X0) ),
inference(definition_unfolding,[],[f1346,f2111,f2111]) ).
fof(f2142,plain,
! [X0,X1,X6,X7] :
( pair_first(X0) = X1
| sK32(X0,X1) != X1
| unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0 ),
inference(definition_unfolding,[],[f1352,f2111]) ).
fof(f2143,plain,
! [X0,X1,X6,X7] :
( pair_first(X0) = X1
| unordered_pair(unordered_pair(sK32(X0,X1),sK33(X0,X1)),unordered_pair(sK32(X0,X1),sK32(X0,X1))) = X0
| unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0 ),
inference(definition_unfolding,[],[f1351,f2111,f2111]) ).
fof(f2145,plain,
! [X2,X3,X0] :
( relation(X0)
| sK34(X0) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f1356,f2111]) ).
fof(f2146,plain,
! [X0,X4] :
( unordered_pair(unordered_pair(sK35(X4),sK36(X4)),unordered_pair(sK35(X4),sK35(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1354,f2111]) ).
fof(f2147,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK37(X0,X1),sK37(X0,X1)),unordered_pair(sK37(X0,X1),sK37(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1359,f2111]) ).
fof(f2148,plain,
! [X3,X0,X1] :
( in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X3)),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1357,f2111]) ).
fof(f2149,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK41(X0,X1) != X0
| ~ in(sK41(X0,X1),X1) ),
inference(definition_unfolding,[],[f1373,f2067]) ).
fof(f2150,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK41(X0,X1) = X0
| in(sK41(X0,X1),X1) ),
inference(definition_unfolding,[],[f1372,f2067]) ).
fof(f2152,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f1370,f2067]) ).
fof(f2153,plain,
! [X2,X0,X1] :
( fiber(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(sK42(X0,X1,X2),X1),unordered_pair(sK42(X0,X1,X2),sK42(X0,X1,X2))),X0)
| sK42(X0,X1,X2) = X1
| ~ in(sK42(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1379,f2111]) ).
fof(f2154,plain,
! [X2,X0,X1] :
( fiber(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK42(X0,X1,X2),X1),unordered_pair(sK42(X0,X1,X2),sK42(X0,X1,X2))),X0)
| in(sK42(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1378,f2111]) ).
fof(f2155,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X0)
| X1 = X4
| fiber(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1376,f2111]) ).
fof(f2156,plain,
! [X2,X0,X1,X4] :
( in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X0)
| ~ in(X4,X2)
| fiber(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1375,f2111]) ).
fof(f2157,plain,
! [X0,X1] :
( inclusion_relation(X0) = X1
| ~ subset(sK43(X0,X1),sK44(X0,X1))
| ~ in(unordered_pair(unordered_pair(sK43(X0,X1),sK44(X0,X1)),unordered_pair(sK43(X0,X1),sK43(X0,X1))),X1)
| relation_field(X1) != X0
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1386,f2111]) ).
fof(f2158,plain,
! [X0,X1] :
( inclusion_relation(X0) = X1
| subset(sK43(X0,X1),sK44(X0,X1))
| in(unordered_pair(unordered_pair(sK43(X0,X1),sK44(X0,X1)),unordered_pair(sK43(X0,X1),sK43(X0,X1))),X1)
| relation_field(X1) != X0
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1385,f2111]) ).
fof(f2159,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ subset(X4,X5)
| ~ in(X5,X0)
| ~ in(X4,X0)
| inclusion_relation(X0) != X1
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1382,f2111]) ).
fof(f2160,plain,
! [X0,X1,X4,X5] :
( subset(X4,X5)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ in(X5,X0)
| ~ in(X4,X0)
| inclusion_relation(X0) != X1
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1381,f2111]) ).
fof(f2161,plain,
! [X0,X1,X6,X7] :
( pair_second(X0) = X1
| sK48(X0,X1) != X1
| unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0 ),
inference(definition_unfolding,[],[f1395,f2111]) ).
fof(f2162,plain,
! [X0,X1,X6,X7] :
( pair_second(X0) = X1
| unordered_pair(unordered_pair(sK47(X0,X1),sK48(X0,X1)),unordered_pair(sK47(X0,X1),sK47(X0,X1))) = X0
| unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0 ),
inference(definition_unfolding,[],[f1394,f2111,f2111]) ).
fof(f2164,plain,
! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK50(X0,X1),sK51(X0,X1)),unordered_pair(sK50(X0,X1),sK50(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK50(X0,X1),sK51(X0,X1)),unordered_pair(sK50(X0,X1),sK50(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1402,f2111,f2111]) ).
fof(f2165,plain,
! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK50(X0,X1),sK51(X0,X1)),unordered_pair(sK50(X0,X1),sK50(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK50(X0,X1),sK51(X0,X1)),unordered_pair(sK50(X0,X1),sK50(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1401,f2111,f2111]) ).
fof(f2168,plain,
! [X2,X0,X1,X4,X5] :
( cartesian_product2(X0,X1) = X2
| sK56(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X1)
| ~ in(X4,X0)
| ~ in(sK56(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1431,f2111]) ).
fof(f2169,plain,
! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| sK56(X0,X1,X2) = unordered_pair(unordered_pair(sK57(X0,X1,X2),sK58(X0,X1,X2)),unordered_pair(sK57(X0,X1,X2),sK57(X0,X1,X2)))
| in(sK56(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1430,f2111]) ).
fof(f2171,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK59(X0,X1,X8),sK60(X0,X1,X8)),unordered_pair(sK59(X0,X1,X8),sK59(X0,X1,X8))) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f1426,f2111]) ).
fof(f2172,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK63(X0,X1),sK64(X0,X1)),unordered_pair(sK63(X0,X1),sK63(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1440,f2111]) ).
fof(f2173,plain,
! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK63(X0,X1),sK64(X0,X1)),unordered_pair(sK63(X0,X1),sK63(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1439,f2111]) ).
fof(f2175,plain,
! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| ~ in(sK68(X0,X1,X2),X1)
| ~ in(sK68(X0,X1,X2),X0)
| ~ in(sK68(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1454,f2016]) ).
fof(f2176,plain,
! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| in(sK68(X0,X1,X2),X1)
| in(sK68(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1453,f2016]) ).
fof(f2177,plain,
! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| in(sK68(X0,X1,X2),X0)
| in(sK68(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f1452,f2016]) ).
fof(f2178,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,set_difference(X0,X1)) != X2 ),
inference(definition_unfolding,[],[f1451,f2016]) ).
fof(f2179,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,set_difference(X0,X1)) != X2 ),
inference(definition_unfolding,[],[f1450,f2016]) ).
fof(f2183,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK69(X0,X1),X3),unordered_pair(sK69(X0,X1),sK69(X0,X1))),X0)
| ~ in(sK69(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1465,f2111]) ).
fof(f2184,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK69(X0,X1),sK70(X0,X1)),unordered_pair(sK69(X0,X1),sK69(X0,X1))),X0)
| in(sK69(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1464,f2111]) ).
fof(f2186,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK71(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1462,f2111]) ).
fof(f2187,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK73(X0,X1),sK72(X0,X1)),unordered_pair(sK73(X0,X1),sK73(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1470,f2111]) ).
fof(f2188,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK72(X0,X1),sK73(X0,X1)),unordered_pair(sK72(X0,X1),sK72(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1469,f2111]) ).
fof(f2189,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1466,f2111,f2111]) ).
fof(f2190,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK82(X0,X1)),unordered_pair(X3,X3)),X0)
| ~ in(sK82(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1506,f2111]) ).
fof(f2191,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK83(X0,X1),sK82(X0,X1)),unordered_pair(sK83(X0,X1),sK83(X0,X1))),X0)
| in(sK82(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1505,f2111]) ).
fof(f2193,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK84(X0,X5),X5),unordered_pair(sK84(X0,X5),sK84(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1503,f2111]) ).
fof(f2194,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK86(X0,X1),sK85(X0,X1)),unordered_pair(sK86(X0,X1),sK86(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1523,f2111]) ).
fof(f2195,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK85(X0,X1),sK86(X0,X1)),unordered_pair(sK85(X0,X1),sK85(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1522,f2111]) ).
fof(f2196,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1518,f2111,f2111]) ).
fof(f2197,plain,
! [X0,X1] :
( relation_restriction(X0,X1) = set_difference(X0,set_difference(X0,cartesian_product2(X1,X1)))
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1524,f2016]) ).
fof(f2198,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK88(X0,X1),sK87(X0,X1)),unordered_pair(sK88(X0,X1),sK88(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1528,f2111,f2111]) ).
fof(f2199,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK88(X0,X1),sK87(X0,X1)),unordered_pair(sK88(X0,X1),sK88(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1527,f2111,f2111]) ).
fof(f2200,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1526,f2111,f2111]) ).
fof(f2201,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1525,f2111,f2111]) ).
fof(f2202,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(apply(X1,sK89(X0,X1,X2)),apply(X1,sK90(X0,X1,X2))),unordered_pair(apply(X1,sK89(X0,X1,X2)),apply(X1,sK89(X0,X1,X2)))),X0)
| ~ in(sK90(X0,X1,X2),relation_field(X2))
| ~ in(sK89(X0,X1,X2),relation_field(X2))
| ~ in(unordered_pair(unordered_pair(sK89(X0,X1,X2),sK90(X0,X1,X2)),unordered_pair(sK89(X0,X1,X2),sK89(X0,X1,X2))),X2)
| ~ one_to_one(X1)
| relation_field(X0) != relation_rng(X1)
| relation_dom(X1) != relation_field(X2) ),
inference(definition_unfolding,[],[f1541,f2111,f2111]) ).
fof(f2203,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(apply(X1,sK89(X0,X1,X2)),apply(X1,sK90(X0,X1,X2))),unordered_pair(apply(X1,sK89(X0,X1,X2)),apply(X1,sK89(X0,X1,X2)))),X0)
| in(unordered_pair(unordered_pair(sK89(X0,X1,X2),sK90(X0,X1,X2)),unordered_pair(sK89(X0,X1,X2),sK89(X0,X1,X2))),X2)
| ~ one_to_one(X1)
| relation_field(X0) != relation_rng(X1)
| relation_dom(X1) != relation_field(X2) ),
inference(definition_unfolding,[],[f1540,f2111,f2111]) ).
fof(f2204,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK90(X0,X1,X2),relation_field(X2))
| in(unordered_pair(unordered_pair(sK89(X0,X1,X2),sK90(X0,X1,X2)),unordered_pair(sK89(X0,X1,X2),sK89(X0,X1,X2))),X2)
| ~ one_to_one(X1)
| relation_field(X0) != relation_rng(X1)
| relation_dom(X1) != relation_field(X2) ),
inference(definition_unfolding,[],[f1539,f2111]) ).
fof(f2205,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK89(X0,X1,X2),relation_field(X2))
| in(unordered_pair(unordered_pair(sK89(X0,X1,X2),sK90(X0,X1,X2)),unordered_pair(sK89(X0,X1,X2),sK89(X0,X1,X2))),X2)
| ~ one_to_one(X1)
| relation_field(X0) != relation_rng(X1)
| relation_dom(X1) != relation_field(X2) ),
inference(definition_unfolding,[],[f1538,f2111]) ).
fof(f2206,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(apply(X1,X5),apply(X1,X6)),unordered_pair(apply(X1,X5),apply(X1,X5))),X0)
| ~ in(X6,relation_field(X2))
| ~ in(X5,relation_field(X2))
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f1537,f2111,f2111]) ).
fof(f2207,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(apply(X1,X5),apply(X1,X6)),unordered_pair(apply(X1,X5),apply(X1,X5))),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f1536,f2111,f2111]) ).
fof(f2208,plain,
! [X2,X0,X1,X6,X5] :
( in(X6,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f1535,f2111]) ).
fof(f2209,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f1534,f2111]) ).
fof(f2210,plain,
! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) ),
inference(definition_unfolding,[],[f1544,f2016]) ).
fof(f2211,plain,
! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) ),
inference(definition_unfolding,[],[f1543,f2016]) ).
fof(f2212,plain,
! [X2,X0,X1,X5] :
( relation_composition(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(X5,sK94(X0,X1,X2)),unordered_pair(X5,X5)),X1)
| ~ in(unordered_pair(unordered_pair(sK93(X0,X1,X2),X5),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X0)
| ~ in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1555,f2111,f2111,f2111]) ).
fof(f2213,plain,
! [X2,X0,X1] :
( relation_composition(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK95(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK95(X0,X1,X2),sK95(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1554,f2111,f2111]) ).
fof(f2214,plain,
! [X2,X0,X1] :
( relation_composition(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK95(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1553,f2111,f2111]) ).
fof(f2215,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),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)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1552,f2111,f2111,f2111]) ).
fof(f2216,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK96(X0,X1,X7,X8),X8),unordered_pair(sK96(X0,X1,X7,X8),sK96(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1551,f2111,f2111]) ).
fof(f2217,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK96(X0,X1,X7,X8)),unordered_pair(X7,X7)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1550,f2111,f2111]) ).
fof(f2218,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK97(X0,X1),sK99(X0,X1)),unordered_pair(sK97(X0,X1),sK97(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1562,f2111]) ).
fof(f2219,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK98(X0,X1),sK99(X0,X1)),unordered_pair(sK98(X0,X1),sK98(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1561,f2111]) ).
fof(f2220,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK97(X0,X1),sK98(X0,X1)),unordered_pair(sK97(X0,X1),sK97(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1560,f2111]) ).
fof(f2221,plain,
! [X0,X1,X6,X7,X5] :
( in(unordered_pair(unordered_pair(X5,X7),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1556,f2111,f2111,f2111]) ).
fof(f2222,plain,
! [X0] : ~ empty(set_union2(X0,unordered_pair(X0,X0))),
inference(definition_unfolding,[],[f1604,f2110]) ).
fof(f2223,plain,
! [X0,X1] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1605,f2016]) ).
fof(f2226,plain,
! [X0] :
( ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1627,f2110]) ).
fof(f2227,plain,
! [X0] :
( epsilon_connected(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1626,f2110]) ).
fof(f2228,plain,
! [X0] :
( epsilon_transitive(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1625,f2110]) ).
fof(f2230,plain,
! [X0] : set_difference(X0,set_difference(X0,X0)) = X0,
inference(definition_unfolding,[],[f1650,f2016]) ).
fof(f2231,plain,
! [X0] :
( reflexive(X0)
| ~ in(unordered_pair(unordered_pair(sK104(X0),sK104(X0)),unordered_pair(sK104(X0),sK104(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1657,f2111]) ).
fof(f2232,plain,
! [X2,X0] :
( in(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,X2)),X0)
| ~ in(X2,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1655,f2111]) ).
fof(f2233,plain,
! [X0] : empty_set != unordered_pair(X0,X0),
inference(definition_unfolding,[],[f1658,f2067]) ).
fof(f2235,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f1660,f2067]) ).
fof(f2236,plain,
! [X0,X1] :
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,X1) ),
inference(definition_unfolding,[],[f1661,f2067]) ).
fof(f2237,plain,
! [X0] :
( transitive(X0)
| ~ in(unordered_pair(unordered_pair(sK105(X0),sK107(X0)),unordered_pair(sK105(X0),sK105(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1666,f2111]) ).
fof(f2238,plain,
! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK106(X0),sK107(X0)),unordered_pair(sK106(X0),sK106(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1665,f2111]) ).
fof(f2239,plain,
! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK105(X0),sK106(X0)),unordered_pair(sK105(X0),sK105(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1664,f2111]) ).
fof(f2240,plain,
! [X0,X6,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X6),unordered_pair(X4,X4)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| ~ transitive(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1663,f2111,f2111,f2111]) ).
fof(f2243,plain,
! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK110(X0),sK109(X0)),unordered_pair(sK110(X0),sK110(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1676,f2111]) ).
fof(f2244,plain,
! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK109(X0),sK110(X0)),unordered_pair(sK109(X0),sK109(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1675,f2111]) ).
fof(f2245,plain,
! [X3,X0,X4] :
( X3 = X4
| ~ in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X0)
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1674,f2111,f2111]) ).
fof(f2246,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f1678,f2067]) ).
fof(f2247,plain,
! [X0] :
( connected(X0)
| ~ in(unordered_pair(unordered_pair(sK112(X0),sK111(X0)),unordered_pair(sK112(X0),sK112(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1684,f2111]) ).
fof(f2248,plain,
! [X0] :
( connected(X0)
| ~ in(unordered_pair(unordered_pair(sK111(X0),sK112(X0)),unordered_pair(sK111(X0),sK111(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1683,f2111]) ).
fof(f2249,plain,
! [X3,X0,X4] :
( in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X0)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1679,f2111,f2111]) ).
fof(f2255,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f1689,f2111]) ).
fof(f2257,plain,
! [X2,X3,X0] :
( unordered_pair(X2,X2) = X3
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),sK128(X0))
| ~ sP2(X0) ),
inference(definition_unfolding,[],[f1752,f2067,f2111]) ).
fof(f2258,plain,
! [X2,X3,X0] :
( in(X2,X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),sK128(X0))
| ~ sP2(X0) ),
inference(definition_unfolding,[],[f1751,f2111]) ).
fof(f2260,plain,
! [X0] :
( sP2(X0)
| sK131(X0) = unordered_pair(sK129(X0),sK129(X0)) ),
inference(definition_unfolding,[],[f1757,f2067]) ).
fof(f2261,plain,
! [X0] :
( sP2(X0)
| sK130(X0) = unordered_pair(sK129(X0),sK129(X0)) ),
inference(definition_unfolding,[],[f1755,f2067]) ).
fof(f2262,plain,
! [X2,X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),sK133(X0,X1,X2))
| ~ in(unordered_pair(unordered_pair(apply(X2,X4),apply(X2,X5)),unordered_pair(apply(X2,X4),apply(X2,X4))),X1)
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1766,f2111,f2111]) ).
fof(f2263,plain,
! [X2,X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(apply(X2,X4),apply(X2,X5)),unordered_pair(apply(X2,X4),apply(X2,X4))),X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),sK133(X0,X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1765,f2111,f2111]) ).
fof(f2264,plain,
! [X2,X0,X1,X4,X5] :
( in(X5,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),sK133(X0,X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1764,f2111]) ).
fof(f2265,plain,
! [X2,X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),sK133(X0,X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1763,f2111]) ).
fof(f2266,plain,
! [X0] :
( sK136(X0) = unordered_pair(sK134(X0),sK134(X0))
| ~ sP3(X0) ),
inference(definition_unfolding,[],[f1770,f2067]) ).
fof(f2267,plain,
! [X0] :
( sK135(X0) = unordered_pair(sK134(X0),sK134(X0))
| ~ sP3(X0) ),
inference(definition_unfolding,[],[f1768,f2067]) ).
fof(f2269,plain,
! [X2,X0] :
( unordered_pair(sK138(X0,X2),sK138(X0,X2)) = X2
| ~ in(X2,sK137(X0))
| sP3(X0) ),
inference(definition_unfolding,[],[f1774,f2067]) ).
fof(f2270,plain,
! [X0] :
( sK143(X0) = unordered_pair(sK142(X0),sK142(X0))
| ~ sP5(X0) ),
inference(definition_unfolding,[],[f1781,f2067]) ).
fof(f2271,plain,
! [X0] :
( sK141(X0) = unordered_pair(unordered_pair(sK142(X0),sK143(X0)),unordered_pair(sK142(X0),sK142(X0)))
| ~ sP5(X0) ),
inference(definition_unfolding,[],[f1779,f2111]) ).
fof(f2272,plain,
! [X0,X1] :
( sK145(X0,X1) = unordered_pair(sK144(X0,X1),sK144(X0,X1))
| ~ sP4(X0,X1) ),
inference(definition_unfolding,[],[f1785,f2067]) ).
fof(f2273,plain,
! [X0,X1] :
( unordered_pair(unordered_pair(sK144(X0,X1),sK145(X0,X1)),unordered_pair(sK144(X0,X1),sK144(X0,X1))) = X1
| ~ sP4(X0,X1) ),
inference(definition_unfolding,[],[f1783,f2111]) ).
fof(f2274,plain,
! [X3,X0,X1,X6,X4,X5] :
( in(X3,sK146(X0,X1))
| unordered_pair(X5,X5) != X6
| ~ in(X5,X0)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X3
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1))
| sP5(X0) ),
inference(definition_unfolding,[],[f1791,f2067,f2111]) ).
fof(f2275,plain,
! [X3,X0,X1] :
( sK149(X0,X3) = unordered_pair(sK148(X0,X3),sK148(X0,X3))
| ~ in(X3,sK146(X0,X1))
| sP5(X0) ),
inference(definition_unfolding,[],[f1790,f2067]) ).
fof(f2276,plain,
! [X3,X0,X1] :
( unordered_pair(unordered_pair(sK148(X0,X3),sK149(X0,X3)),unordered_pair(sK148(X0,X3),sK148(X0,X3))) = X3
| ~ in(X3,sK146(X0,X1))
| sP5(X0) ),
inference(definition_unfolding,[],[f1788,f2111]) ).
fof(f2277,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(apply(X1,sK153(X0,X1)),apply(X1,sK154(X0,X1))),unordered_pair(apply(X1,sK153(X0,X1)),apply(X1,sK153(X0,X1)))),X0)
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f1797,f2111]) ).
fof(f2278,plain,
! [X0,X1] :
( sK152(X0,X1) = unordered_pair(unordered_pair(sK153(X0,X1),sK154(X0,X1)),unordered_pair(sK153(X0,X1),sK153(X0,X1)))
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f1796,f2111]) ).
fof(f2279,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(apply(X1,sK155(X0,X1)),apply(X1,sK156(X0,X1))),unordered_pair(apply(X1,sK155(X0,X1)),apply(X1,sK155(X0,X1)))),X0)
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f1794,f2111]) ).
fof(f2280,plain,
! [X0,X1] :
( sK151(X0,X1) = unordered_pair(unordered_pair(sK155(X0,X1),sK156(X0,X1)),unordered_pair(sK155(X0,X1),sK155(X0,X1)))
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f1793,f2111]) ).
fof(f2281,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK157(X0,X1,X2))
| ~ in(unordered_pair(unordered_pair(apply(X2,X6),apply(X2,X7)),unordered_pair(apply(X2,X6),apply(X2,X6))),X1)
| unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(X0,X0))
| sP6(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1803,f2111,f2111]) ).
fof(f2282,plain,
! [X2,X0,X1,X4] :
( in(unordered_pair(unordered_pair(apply(X2,sK159(X1,X2,X4)),apply(X2,sK160(X1,X2,X4))),unordered_pair(apply(X2,sK159(X1,X2,X4)),apply(X2,sK159(X1,X2,X4)))),X1)
| ~ in(X4,sK157(X0,X1,X2))
| sP6(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1802,f2111]) ).
fof(f2283,plain,
! [X2,X0,X1,X4] :
( unordered_pair(unordered_pair(sK159(X1,X2,X4),sK160(X1,X2,X4)),unordered_pair(sK159(X1,X2,X4),sK159(X1,X2,X4))) = X4
| ~ in(X4,sK157(X0,X1,X2))
| sP6(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1801,f2111]) ).
fof(f2284,plain,
! [X3,X0,X1,X4,X5] :
( in(X3,sK171(X0,X1))
| ~ in(X5,X0)
| X3 != X5
| ~ ordinal(X5)
| X3 != X4
| ~ in(X4,set_union2(X1,unordered_pair(X1,X1)))
| sP9(X0)
| ~ ordinal(X1) ),
inference(definition_unfolding,[],[f1828,f2110]) ).
fof(f2285,plain,
! [X3,X0,X1] :
( in(sK172(X0,X1,X3),set_union2(X1,unordered_pair(X1,X1)))
| ~ in(X3,sK171(X0,X1))
| sP9(X0)
| ~ ordinal(X1) ),
inference(definition_unfolding,[],[f1823,f2110]) ).
fof(f2286,plain,
! [X3,X0,X1,X4,X5] :
( in(X3,sK174(X0,X1))
| unordered_pair(X4,X4) != X5
| ~ in(X4,X0)
| unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != X3
| ~ in(X3,cartesian_product2(X0,X1)) ),
inference(definition_unfolding,[],[f1833,f2067,f2111]) ).
fof(f2287,plain,
! [X3,X0,X1] :
( sK176(X0,X3) = unordered_pair(sK175(X0,X3),sK175(X0,X3))
| ~ in(X3,sK174(X0,X1)) ),
inference(definition_unfolding,[],[f1832,f2067]) ).
fof(f2288,plain,
! [X3,X0,X1] :
( unordered_pair(unordered_pair(sK175(X0,X3),sK176(X0,X3)),unordered_pair(sK175(X0,X3),sK175(X0,X3))) = X3
| ~ in(X3,sK174(X0,X1)) ),
inference(definition_unfolding,[],[f1830,f2111]) ).
fof(f2289,plain,
! [X2,X0,X1,X6,X4,X5] :
( in(X4,sK177(X0,X1,X2))
| ~ in(unordered_pair(unordered_pair(apply(X2,X5),apply(X2,X6)),unordered_pair(apply(X2,X5),apply(X2,X5))),X1)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X4,cartesian_product2(X0,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1837,f2111,f2111]) ).
fof(f2290,plain,
! [X2,X0,X1,X4] :
( in(unordered_pair(unordered_pair(apply(X2,sK178(X1,X2,X4)),apply(X2,sK179(X1,X2,X4))),unordered_pair(apply(X2,sK178(X1,X2,X4)),apply(X2,sK178(X1,X2,X4)))),X1)
| ~ in(X4,sK177(X0,X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1836,f2111]) ).
fof(f2291,plain,
! [X2,X0,X1,X4] :
( unordered_pair(unordered_pair(sK178(X1,X2,X4),sK179(X1,X2,X4)),unordered_pair(sK178(X1,X2,X4),sK178(X1,X2,X4))) = X4
| ~ in(X4,sK177(X0,X1,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1835,f2111]) ).
fof(f2292,plain,
! [X3,X0,X1,X4] :
( in(X3,sK181(X0,X1))
| ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4)
| ~ in(X3,set_union2(X1,unordered_pair(X1,X1)))
| ~ ordinal(X1) ),
inference(definition_unfolding,[],[f1845,f2110]) ).
fof(f2293,plain,
! [X3,X0,X1] :
( in(X3,set_union2(X1,unordered_pair(X1,X1)))
| ~ in(X3,sK181(X0,X1))
| ~ ordinal(X1) ),
inference(definition_unfolding,[],[f1841,f2110]) ).
fof(f2294,plain,
! [X0] :
( sK185(X0) = unordered_pair(sK183(X0),sK183(X0))
| ~ sP10(X0) ),
inference(definition_unfolding,[],[f1848,f2067]) ).
fof(f2295,plain,
! [X0] :
( sK184(X0) = unordered_pair(sK183(X0),sK183(X0))
| ~ sP10(X0) ),
inference(definition_unfolding,[],[f1847,f2067]) ).
fof(f2296,plain,
! [X2,X0,X4] :
( apply(sK186(X0),X2) = unordered_pair(X2,X2)
| ~ in(X2,X0)
| unordered_pair(sK187(X0),sK187(X0)) != X4
| sP10(X0) ),
inference(definition_unfolding,[],[f1857,f2067,f2067]) ).
fof(f2298,plain,
! [X0,X4] :
( relation_dom(sK186(X0)) = X0
| unordered_pair(sK187(X0),sK187(X0)) != X4
| sP10(X0) ),
inference(definition_unfolding,[],[f1855,f2067]) ).
fof(f2299,plain,
! [X0,X4] :
( function(sK186(X0))
| unordered_pair(sK187(X0),sK187(X0)) != X4
| sP10(X0) ),
inference(definition_unfolding,[],[f1853,f2067]) ).
fof(f2300,plain,
! [X0,X4] :
( relation(sK186(X0))
| unordered_pair(sK187(X0),sK187(X0)) != X4
| sP10(X0) ),
inference(definition_unfolding,[],[f1851,f2067]) ).
fof(f2301,plain,
! [X1] :
( apply(X1,sK189(X1)) != unordered_pair(sK189(X1),sK189(X1))
| relation_dom(X1) != sK188
| ~ function(X1)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1859,f2067]) ).
fof(f2302,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(definition_unfolding,[],[f1864,f2111]) ).
fof(f2303,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f1863,f2111]) ).
fof(f2304,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f1862,f2111]) ).
fof(f2305,plain,
! [X0] : in(X0,set_union2(X0,unordered_pair(X0,X0))),
inference(definition_unfolding,[],[f1865,f2110]) ).
fof(f2306,plain,
! [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) = set_difference(relation_rng(X1),set_difference(relation_rng(X1),X0))
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1875,f2016]) ).
fof(f2308,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK191(X0,X1,X2),X0),unordered_pair(sK191(X0,X1,X2),sK191(X0,X1,X2))),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1886,f2111]) ).
fof(f2309,plain,
! [X0,X1] :
( relation_image(X1,X0) = relation_image(X1,set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0)))
| ~ relation(X1) ),
inference(definition_unfolding,[],[f1891,f2016]) ).
fof(f2311,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK192(X0,X1,X2)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1898,f2111]) ).
fof(f2313,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f1913,f2016]) ).
fof(f2314,plain,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(definition_unfolding,[],[f1917,f2067]) ).
fof(f2315,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1919,f2111]) ).
fof(f2316,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1918,f2111]) ).
fof(f2317,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X3,sK193(X2,X3)),unordered_pair(X3,X3)),X2)
| ~ in(X3,X1)
| relation_dom_as_subset(X1,X0,X2) != X1
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(definition_unfolding,[],[f1931,f2111]) ).
fof(f2318,plain,
! [X2,X0,X1,X6] :
( relation_dom_as_subset(X1,X0,X2) = X1
| ~ in(unordered_pair(unordered_pair(sK194(X1,X2),X6),unordered_pair(sK194(X1,X2),sK194(X1,X2))),X2)
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(definition_unfolding,[],[f1930,f2111]) ).
fof(f2319,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(sK195(X2,X3),X3),unordered_pair(sK195(X2,X3),sK195(X2,X3))),X2)
| ~ in(X3,X1)
| relation_rng_as_subset(X0,X1,X2) != X1
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(definition_unfolding,[],[f1937,f2111]) ).
fof(f2320,plain,
! [X2,X0,X1,X6] :
( relation_rng_as_subset(X0,X1,X2) = X1
| ~ in(unordered_pair(unordered_pair(X6,sK196(X1,X2)),unordered_pair(X6,X6)),X2)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(definition_unfolding,[],[f1936,f2111]) ).
fof(f2321,plain,
! [X2,X0,X1] :
( subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f1946,f2016,f2016]) ).
fof(f2322,plain,
! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X0
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f1947,f2016]) ).
fof(f2323,plain,
! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)),
inference(definition_unfolding,[],[f1948,f2016]) ).
fof(f2324,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1955,f2111]) ).
fof(f2325,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1954,f2111]) ).
fof(f2326,plain,
! [X0,X1] :
( in(X0,X1)
| ~ ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1964,f2110]) ).
fof(f2327,plain,
! [X0,X1] :
( ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1)
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1963,f2110]) ).
fof(f2328,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f1967,f2111,f2111]) ).
fof(f2329,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f1966,f2111,f2111]) ).
fof(f2330,plain,
! [X0,X1] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f1979,f2067]) ).
fof(f2334,plain,
! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f1985,f2067,f2067]) ).
fof(f2335,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ in(set_union2(sK202(X0),unordered_pair(sK202(X0),sK202(X0))),X0)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f2001,f2110]) ).
fof(f2336,plain,
! [X2,X0] :
( in(set_union2(X2,unordered_pair(X2,X2)),X0)
| ~ in(X2,X0)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f1998,f2110]) ).
fof(f2337,plain,
! [X0,X1] :
( ~ being_limit_ordinal(X0)
| set_union2(X1,unordered_pair(X1,X1)) != X0
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f2004,f2110]) ).
fof(f2338,plain,
! [X0] :
( set_union2(sK203(X0),unordered_pair(sK203(X0),sK203(X0))) = X0
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f2003,f2110]) ).
fof(f2339,plain,
! [X0,X1] :
( set_union2(unordered_pair(X0,X0),X1) = X1
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f2012,f2067]) ).
fof(f2340,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f2022,f2016]) ).
fof(f2341,plain,
! [X0,X1] :
( in(sK204(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f2021,f2016]) ).
fof(f2342,plain,
! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK207(X0),sK208(X0)),unordered_pair(sK207(X0),sK207(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f2045,f2111]) ).
fof(f2343,plain,
! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) = X0
| in(X1,X0) ),
inference(definition_unfolding,[],[f2062,f2067]) ).
fof(f2344,plain,
! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) != X0 ),
inference(definition_unfolding,[],[f2061,f2067]) ).
fof(f2345,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| apply(X2,sK209(X1,X2)) != apply(X1,sK209(X1,X2))
| relation_dom(X1) != set_difference(relation_dom(X2),set_difference(relation_dom(X2),X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f2066,f2016]) ).
fof(f2346,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X0) = X1
| in(sK209(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_difference(relation_dom(X2),set_difference(relation_dom(X2),X0))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f2065,f2016]) ).
fof(f2348,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f2070,f2067,f2067]) ).
fof(f2349,plain,
! [X2,X3,X0,X1] :
( 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)
| ~ in(X0,X2)
| ~ relation(X3) ),
inference(definition_unfolding,[],[f2077,f2111,f2111]) ).
fof(f2350,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(definition_unfolding,[],[f2076,f2111,f2111]) ).
fof(f2351,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(definition_unfolding,[],[f2075,f2111]) ).
fof(f2352,plain,
! [X0,X1] : pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X1,
inference(definition_unfolding,[],[f2080,f2111]) ).
fof(f2353,plain,
! [X0,X1] : pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X0,
inference(definition_unfolding,[],[f2079,f2111]) ).
fof(f2354,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f2094,f2111]) ).
fof(f2355,plain,
! [X2,X0,X1] :
( apply(X2,X0) = X1
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f2093,f2111]) ).
fof(f2357,plain,
! [X2,X0,X1] :
( X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ),
inference(definition_unfolding,[],[f2098,f2067]) ).
fof(f2358,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0))
| ~ relation(X1) ),
inference(definition_unfolding,[],[f2099,f2016]) ).
fof(f2359,plain,
! [X2,X0,X1] :
( X1 = X2
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ),
inference(definition_unfolding,[],[f2109,f2067]) ).
fof(f2360,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),X1)
| ~ in(X5,X0)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(equality_resolution,[],[f2116]) ).
fof(f2361,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),identity_relation(X0))
| ~ in(X5,X0)
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f2360]) ).
fof(f2362,plain,
! [X0,X4,X5] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f2117]) ).
fof(f2363,plain,
! [X0,X4,X5] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f2118]) ).
fof(f2366,plain,
! [X0,X1,X6,X5] :
( 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)
| ~ in(X5,X1)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f2122]) ).
fof(f2367,plain,
! [X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f2123]) ).
fof(f2368,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f2124]) ).
fof(f2369,plain,
! [X2,X0,X1,X7] :
( in(apply(X0,X7),X2)
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| relation_image(X0,X1) != X2
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1303]) ).
fof(f2370,plain,
! [X0,X1,X7] :
( in(apply(X0,X7),relation_image(X0,X1))
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f2369]) ).
fof(f2371,plain,
! [X0,X1,X6] :
( apply(X0,sK18(X0,X1,X6)) = X6
| ~ in(X6,relation_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1302]) ).
fof(f2372,plain,
! [X0,X1,X6] :
( in(sK18(X0,X1,X6),X1)
| ~ in(X6,relation_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1301]) ).
fof(f2373,plain,
! [X0,X1,X6] :
( in(sK18(X0,X1,X6),relation_dom(X0))
| ~ in(X6,relation_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1300]) ).
fof(f2374,plain,
! [X0,X1,X6,X5] :
( 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)
| ~ in(X6,X0)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(equality_resolution,[],[f2128]) ).
fof(f2375,plain,
! [X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(equality_resolution,[],[f2129]) ).
fof(f2376,plain,
! [X0,X1,X6,X5] :
( in(X6,X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(equality_resolution,[],[f2130]) ).
fof(f2377,plain,
! [X0,X1,X4] :
( in(X4,relation_inverse_image(X0,X1))
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1318]) ).
fof(f2378,plain,
! [X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ in(X4,relation_inverse_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1317]) ).
fof(f2379,plain,
! [X0,X1,X4] :
( in(X4,relation_dom(X0))
| ~ in(X4,relation_inverse_image(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1316]) ).
fof(f2380,plain,
! [X0,X1,X6,X7] :
( in(X6,relation_image(X0,X1))
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f2133]) ).
fof(f2381,plain,
! [X0,X1,X6] :
( in(sK24(X0,X1,X6),X1)
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f1323]) ).
fof(f2382,plain,
! [X0,X1,X6] :
( in(unordered_pair(unordered_pair(sK24(X0,X1,X6),X6),unordered_pair(sK24(X0,X1,X6),sK24(X0,X1,X6))),X0)
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f2134]) ).
fof(f2383,plain,
! [X0,X1,X6,X7] :
( in(X6,relation_inverse_image(X0,X1))
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f2137]) ).
fof(f2384,plain,
! [X0,X1,X6] :
( in(sK27(X0,X1,X6),X1)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f1329]) ).
fof(f2385,plain,
! [X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK27(X0,X1,X6)),unordered_pair(X6,X6)),X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f2138]) ).
fof(f2386,plain,
! [X3,X0,X1,X5] :
( in(X5,X3)
| unordered_triple(X0,X1,X5) != X3 ),
inference(equality_resolution,[],[f1341]) ).
fof(f2387,plain,
! [X0,X1,X5] : in(X5,unordered_triple(X0,X1,X5)),
inference(equality_resolution,[],[f2386]) ).
fof(f2388,plain,
! [X2,X3,X0,X5] :
( in(X5,X3)
| unordered_triple(X0,X5,X2) != X3 ),
inference(equality_resolution,[],[f1340]) ).
fof(f2389,plain,
! [X2,X0,X5] : in(X5,unordered_triple(X0,X5,X2)),
inference(equality_resolution,[],[f2388]) ).
fof(f2390,plain,
! [X2,X3,X1,X5] :
( in(X5,X3)
| unordered_triple(X5,X1,X2) != X3 ),
inference(equality_resolution,[],[f1339]) ).
fof(f2391,plain,
! [X2,X1,X5] : in(X5,unordered_triple(X5,X1,X2)),
inference(equality_resolution,[],[f2390]) ).
fof(f2392,plain,
! [X2,X0,X1,X5] :
( X2 = X5
| X1 = X5
| X0 = X5
| ~ in(X5,unordered_triple(X0,X1,X2)) ),
inference(equality_resolution,[],[f1338]) ).
fof(f2393,plain,
! [X1,X6,X7] :
( pair_first(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))) = X1
| sK32(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1) != X1 ),
inference(equality_resolution,[],[f2142]) ).
fof(f2394,plain,
! [X1,X6,X7] :
( pair_first(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))) = X1
| unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) = unordered_pair(unordered_pair(sK32(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1),sK33(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1)),unordered_pair(sK32(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1),sK32(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1))) ),
inference(equality_resolution,[],[f2143]) ).
fof(f2399,plain,
! [X0] :
( empty_set = set_meet(X0)
| empty_set != X0 ),
inference(equality_resolution,[],[f1368]) ).
fof(f2400,plain,
empty_set = set_meet(empty_set),
inference(equality_resolution,[],[f2399]) ).
fof(f2401,plain,
! [X0,X5] :
( in(X5,set_meet(X0))
| ~ in(X5,sK40(X0,X5))
| empty_set = X0 ),
inference(equality_resolution,[],[f1364]) ).
fof(f2402,plain,
! [X0,X5] :
( in(X5,set_meet(X0))
| in(sK40(X0,X5),X0)
| empty_set = X0 ),
inference(equality_resolution,[],[f1363]) ).
fof(f2403,plain,
! [X0,X7,X5] :
( in(X5,X7)
| ~ in(X7,X0)
| ~ in(X5,set_meet(X0))
| empty_set = X0 ),
inference(equality_resolution,[],[f1362]) ).
fof(f2406,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,unordered_pair(X0,X0)) ),
inference(equality_resolution,[],[f2152]) ).
fof(f2407,plain,
! [X0,X1,X4] :
( in(X4,fiber(X0,X1))
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X0)
| X1 = X4
| ~ relation(X0) ),
inference(equality_resolution,[],[f2155]) ).
fof(f2408,plain,
! [X0,X1,X4] :
( in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X0)
| ~ in(X4,fiber(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f2156]) ).
fof(f2409,plain,
! [X2,X0,X4] :
( ~ in(X4,X2)
| fiber(X0,X4) != X2
| ~ relation(X0) ),
inference(equality_resolution,[],[f1374]) ).
fof(f2410,plain,
! [X0,X4] :
( ~ in(X4,fiber(X0,X4))
| ~ relation(X0) ),
inference(equality_resolution,[],[f2409]) ).
fof(f2411,plain,
! [X1] :
( inclusion_relation(relation_field(X1)) = X1
| ~ subset(sK43(relation_field(X1),X1),sK44(relation_field(X1),X1))
| ~ in(unordered_pair(unordered_pair(sK43(relation_field(X1),X1),sK44(relation_field(X1),X1)),unordered_pair(sK43(relation_field(X1),X1),sK43(relation_field(X1),X1))),X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f2157]) ).
fof(f2412,plain,
! [X1] :
( inclusion_relation(relation_field(X1)) = X1
| subset(sK43(relation_field(X1),X1),sK44(relation_field(X1),X1))
| in(unordered_pair(unordered_pair(sK43(relation_field(X1),X1),sK44(relation_field(X1),X1)),unordered_pair(sK43(relation_field(X1),X1),sK43(relation_field(X1),X1))),X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f2158]) ).
fof(f2413,plain,
! [X1] :
( inclusion_relation(relation_field(X1)) = X1
| in(sK44(relation_field(X1),X1),relation_field(X1))
| ~ relation(X1) ),
inference(equality_resolution,[],[f1384]) ).
fof(f2414,plain,
! [X1] :
( inclusion_relation(relation_field(X1)) = X1
| in(sK43(relation_field(X1),X1),relation_field(X1))
| ~ relation(X1) ),
inference(equality_resolution,[],[f1383]) ).
fof(f2415,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),inclusion_relation(X0))
| ~ subset(X4,X5)
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ relation(inclusion_relation(X0)) ),
inference(equality_resolution,[],[f2159]) ).
fof(f2416,plain,
! [X0,X4,X5] :
( subset(X4,X5)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),inclusion_relation(X0))
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ relation(inclusion_relation(X0)) ),
inference(equality_resolution,[],[f2160]) ).
fof(f2417,plain,
! [X0] :
( relation_field(inclusion_relation(X0)) = X0
| ~ relation(inclusion_relation(X0)) ),
inference(equality_resolution,[],[f1380]) ).
fof(f2418,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f1387]) ).
fof(f2419,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f1390]) ).
fof(f2420,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f1389]) ).
fof(f2421,plain,
! [X1,X6,X7] :
( pair_second(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))) = X1
| sK48(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1) != X1 ),
inference(equality_resolution,[],[f2161]) ).
fof(f2422,plain,
! [X1,X6,X7] :
( pair_second(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))) = X1
| unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) = unordered_pair(unordered_pair(sK47(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1),sK48(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1)),unordered_pair(sK47(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1),sK47(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1))) ),
inference(equality_resolution,[],[f2162]) ).
fof(f2427,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f1409]) ).
fof(f2428,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f2427]) ).
fof(f2429,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f1408]) ).
fof(f2430,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f2429]) ).
fof(f2431,plain,
! [X0,X1,X4] :
( X1 = X4
| X0 = X4
| ~ in(X4,unordered_pair(X0,X1)) ),
inference(equality_resolution,[],[f1407]) ).
fof(f2432,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f1420]) ).
fof(f2433,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f1419]) ).
fof(f2434,plain,
! [X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f1418]) ).
fof(f2437,plain,
! [X0,X1,X8] :
( unordered_pair(unordered_pair(sK59(X0,X1,X8),sK60(X0,X1,X8)),unordered_pair(sK59(X0,X1,X8),sK59(X0,X1,X8))) = X8
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f2171]) ).
fof(f2438,plain,
! [X0,X1,X8] :
( in(sK60(X0,X1,X8),X1)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f1425]) ).
fof(f2439,plain,
! [X0,X1,X8] :
( in(sK59(X0,X1,X8),X0)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f1424]) ).
fof(f2440,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,set_difference(X0,X1)))
| ~ in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f2178]) ).
fof(f2441,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,set_difference(X0,set_difference(X0,X1))) ),
inference(equality_resolution,[],[f2179]) ).
fof(f2443,plain,
! [X0,X1] :
( empty_set = apply(X0,X1)
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1458]) ).
fof(f2447,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK71(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f2186]) ).
fof(f2448,plain,
! [X0,X6,X5] :
( in(X5,union(X0))
| ~ in(X6,X0)
| ~ in(X5,X6) ),
inference(equality_resolution,[],[f1475]) ).
fof(f2449,plain,
! [X0,X5] :
( in(sK76(X0,X5),X0)
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f1474]) ).
fof(f2450,plain,
! [X0,X5] :
( in(X5,sK76(X0,X5))
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f1473]) ).
fof(f2451,plain,
! [X2,X0] :
( equipotent(X0,relation_rng(X2))
| relation_dom(X2) != X0
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(equality_resolution,[],[f1490]) ).
fof(f2452,plain,
! [X2] :
( equipotent(relation_dom(X2),relation_rng(X2))
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2) ),
inference(equality_resolution,[],[f2451]) ).
fof(f2453,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f1493]) ).
fof(f2454,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f1492]) ).
fof(f2455,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f1491]) ).
fof(f2456,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1499]) ).
fof(f2457,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f2456]) ).
fof(f2458,plain,
! [X0,X5] :
( apply(X0,sK81(X0,X5)) = X5
| ~ in(X5,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1498]) ).
fof(f2459,plain,
! [X0,X5] :
( in(sK81(X0,X5),relation_dom(X0))
| ~ in(X5,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1497]) ).
fof(f2461,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK84(X0,X5),X5),unordered_pair(sK84(X0,X5),sK84(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f2193]) ).
fof(f2462,plain,
! [X0,X4,X5] :
( 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)
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f2200]) ).
fof(f2463,plain,
! [X0,X4,X5] :
( 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))
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f2201]) ).
fof(f2464,plain,
! [X0,X1,X8,X9,X7] :
( in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),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)
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f2215]) ).
fof(f2465,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK96(X0,X1,X7,X8),X8),unordered_pair(sK96(X0,X1,X7,X8),sK96(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f2216]) ).
fof(f2466,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK96(X0,X1,X7,X8)),unordered_pair(X7,X7)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f2217]) ).
fof(f2467,plain,
! [X0,X1,X4] :
( in(X4,complements_of_subsets(X0,X1))
| ~ in(subset_complement(X0,X4),X1)
| ~ element(X4,powerset(X0))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(equality_resolution,[],[f1564]) ).
fof(f2468,plain,
! [X0,X1,X4] :
( in(subset_complement(X0,X4),X1)
| ~ in(X4,complements_of_subsets(X0,X1))
| ~ element(X4,powerset(X0))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(equality_resolution,[],[f1563]) ).
fof(f2473,plain,
! [X3,X0,X1,X4,X5] :
( in(X3,sK146(X0,X1))
| ~ in(X5,X0)
| unordered_pair(unordered_pair(X5,unordered_pair(X5,X5)),unordered_pair(X5,X5)) != X3
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1))
| sP5(X0) ),
inference(equality_resolution,[],[f2274]) ).
fof(f2474,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X5,unordered_pair(X5,X5)),unordered_pair(X5,X5)),sK146(X0,X1))
| ~ in(X5,X0)
| unordered_pair(unordered_pair(X5,unordered_pair(X5,X5)),unordered_pair(X5,X5)) != X4
| ~ in(X4,cartesian_product2(X0,X1))
| sP5(X0) ),
inference(equality_resolution,[],[f2473]) ).
fof(f2475,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,unordered_pair(X5,X5)),unordered_pair(X5,X5)),sK146(X0,X1))
| ~ in(X5,X0)
| ~ in(unordered_pair(unordered_pair(X5,unordered_pair(X5,X5)),unordered_pair(X5,X5)),cartesian_product2(X0,X1))
| sP5(X0) ),
inference(equality_resolution,[],[f2474]) ).
fof(f2476,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),sK157(X0,X1,X2))
| ~ in(unordered_pair(unordered_pair(apply(X2,X6),apply(X2,X7)),unordered_pair(apply(X2,X6),apply(X2,X6))),X1)
| unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X5
| ~ in(X5,cartesian_product2(X0,X0))
| sP6(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(equality_resolution,[],[f2281]) ).
fof(f2477,plain,
! [X2,X0,X1,X6,X7] :
( in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),sK157(X0,X1,X2))
| ~ in(unordered_pair(unordered_pair(apply(X2,X6),apply(X2,X7)),unordered_pair(apply(X2,X6),apply(X2,X6))),X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),cartesian_product2(X0,X0))
| sP6(X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(equality_resolution,[],[f2476]) ).
fof(f2478,plain,
! [X3,X0] :
( in(X3,sK164(X0))
| ~ ordinal(X3)
| ~ in(X3,X0)
| sP7 ),
inference(equality_resolution,[],[f1812]) ).
fof(f2479,plain,
! [X0,X1,X4,X5] :
( in(X5,sK171(X0,X1))
| ~ in(X5,X0)
| ~ ordinal(X5)
| X4 != X5
| ~ in(X4,set_union2(X1,unordered_pair(X1,X1)))
| sP9(X0)
| ~ ordinal(X1) ),
inference(equality_resolution,[],[f2284]) ).
fof(f2480,plain,
! [X0,X1,X5] :
( in(X5,sK171(X0,X1))
| ~ in(X5,X0)
| ~ ordinal(X5)
| ~ in(X5,set_union2(X1,unordered_pair(X1,X1)))
| sP9(X0)
| ~ ordinal(X1) ),
inference(equality_resolution,[],[f2479]) ).
fof(f2481,plain,
! [X3,X0,X1,X4] :
( in(X3,sK174(X0,X1))
| ~ in(X4,X0)
| unordered_pair(unordered_pair(X4,unordered_pair(X4,X4)),unordered_pair(X4,X4)) != X3
| ~ in(X3,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f2286]) ).
fof(f2482,plain,
! [X0,X1,X4] :
( in(unordered_pair(unordered_pair(X4,unordered_pair(X4,X4)),unordered_pair(X4,X4)),sK174(X0,X1))
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,unordered_pair(X4,X4)),unordered_pair(X4,X4)),cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f2481]) ).
fof(f2483,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),sK177(X0,X1,X2))
| ~ in(unordered_pair(unordered_pair(apply(X2,X5),apply(X2,X6)),unordered_pair(apply(X2,X5),apply(X2,X5))),X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),cartesian_product2(X0,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(equality_resolution,[],[f2289]) ).
fof(f2484,plain,
! [X0,X1,X4] :
( in(X4,sK181(X0,X1))
| ~ in(X4,X0)
| ~ ordinal(X4)
| ~ in(X4,set_union2(X1,unordered_pair(X1,X1)))
| ~ ordinal(X1) ),
inference(equality_resolution,[],[f2292]) ).
fof(f2485,plain,
! [X2,X0] :
( apply(sK186(X0),X2) = unordered_pair(X2,X2)
| ~ in(X2,X0)
| sP10(X0) ),
inference(equality_resolution,[],[f2296]) ).
fof(f2486,plain,
! [X0] :
( relation_dom(sK186(X0)) = X0
| sP10(X0) ),
inference(equality_resolution,[],[f2298]) ).
fof(f2487,plain,
! [X0] :
( function(sK186(X0))
| sP10(X0) ),
inference(equality_resolution,[],[f2299]) ).
fof(f2488,plain,
! [X0] :
( relation(sK186(X0))
| sP10(X0) ),
inference(equality_resolution,[],[f2300]) ).
fof(f2489,plain,
! [X1] :
( identity_relation(relation_dom(X1)) = X1
| sK200(relation_dom(X1),X1) != apply(X1,sK200(relation_dom(X1),X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f1971]) ).
fof(f2490,plain,
! [X1] :
( identity_relation(relation_dom(X1)) = X1
| in(sK200(relation_dom(X1),X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f1970]) ).
fof(f2495,plain,
! [X1] :
( ~ being_limit_ordinal(set_union2(X1,unordered_pair(X1,X1)))
| ~ ordinal(X1)
| ~ ordinal(set_union2(X1,unordered_pair(X1,X1))) ),
inference(equality_resolution,[],[f2337]) ).
fof(f2496,plain,
! [X2,X3,X1] :
( sP11(apply(X2,X1),X1,X2,X3)
| ~ in(X1,relation_dom(X2)) ),
inference(equality_resolution,[],[f2033]) ).
fof(f2497,plain,
! [X2,X3,X0] :
( apply(X2,apply(X3,X0)) = X0
| ~ in(X0,relation_rng(X2))
| ~ sP11(X0,apply(X3,X0),X2,X3) ),
inference(equality_resolution,[],[f2030]) ).
fof(f2498,plain,
! [X2,X3,X0] :
( in(apply(X3,X0),relation_dom(X2))
| ~ in(X0,relation_rng(X2))
| ~ sP11(X0,apply(X3,X0),X2,X3) ),
inference(equality_resolution,[],[f2029]) ).
fof(f2499,plain,
! [X0,X1,X5] :
( apply(X1,apply(X0,X5)) = X5
| ~ in(X5,relation_dom(X0))
| function_inverse(X0) != X1
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f2037]) ).
fof(f2500,plain,
! [X0,X5] :
( apply(function_inverse(X0),apply(X0,X5)) = X5
| ~ in(X5,relation_dom(X0))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f2499]) ).
fof(f2503,plain,
! [X0,X4,X5] :
( sP11(X4,X5,X0,function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f2035]) ).
fof(f2507,plain,
! [X2,X0] :
( in(unordered_pair(unordered_pair(X0,apply(X2,X0)),unordered_pair(X0,X0)),X2)
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ),
inference(equality_resolution,[],[f2354]) ).
cnf(c_49,plain,
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f1267]) ).
cnf(c_50,plain,
( ~ proper_subset(X0,X1)
| ~ proper_subset(X1,X0) ),
inference(cnf_transformation,[],[f1268]) ).
cnf(c_51,plain,
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f1269]) ).
cnf(c_54,plain,
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f1272]) ).
cnf(c_55,plain,
( ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation(X0) ),
inference(cnf_transformation,[],[f1273]) ).
cnf(c_56,plain,
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1276]) ).
cnf(c_58,plain,
( ~ empty(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f1280]) ).
cnf(c_59,plain,
( ~ empty(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1279]) ).
cnf(c_60,plain,
( ~ empty(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f1278]) ).
cnf(c_61,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f1281]) ).
cnf(c_62,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f1282]) ).
cnf(c_63,plain,
set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(cnf_transformation,[],[f2112]) ).
cnf(c_64,plain,
( ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X0,X1)
| ordinal_subset(X1,X0) ),
inference(cnf_transformation,[],[f1284]) ).
cnf(c_65,plain,
( sK12(X0,X1) != sK13(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK12(X0,X1),sK13(X0,X1)),unordered_pair(sK12(X0,X1),sK12(X0,X1))),X1)
| ~ in(sK12(X0,X1),X0)
| ~ relation(X1)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f2113]) ).
cnf(c_66,plain,
( ~ relation(X0)
| sK12(X1,X0) = sK13(X1,X0)
| identity_relation(X1) = X0
| in(unordered_pair(unordered_pair(sK12(X1,X0),sK13(X1,X0)),unordered_pair(sK12(X1,X0),sK12(X1,X0))),X0) ),
inference(cnf_transformation,[],[f2114]) ).
cnf(c_67,plain,
( ~ relation(X0)
| identity_relation(X1) = X0
| in(unordered_pair(unordered_pair(sK12(X1,X0),sK13(X1,X0)),unordered_pair(sK12(X1,X0),sK12(X1,X0))),X0)
| in(sK12(X1,X0),X1) ),
inference(cnf_transformation,[],[f2115]) ).
cnf(c_68,plain,
( ~ in(X0,X1)
| ~ relation(identity_relation(X1))
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),identity_relation(X1)) ),
inference(cnf_transformation,[],[f2361]) ).
cnf(c_69,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2))
| ~ relation(identity_relation(X2))
| X0 = X1 ),
inference(cnf_transformation,[],[f2362]) ).
cnf(c_70,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2))
| ~ relation(identity_relation(X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f2363]) ).
cnf(c_71,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f1293]) ).
cnf(c_74,plain,
( ~ in(unordered_pair(unordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),unordered_pair(sK14(X0,X1,X2),sK14(X0,X1,X2))),X0)
| ~ in(unordered_pair(unordered_pair(sK14(X0,X1,X2),sK15(X0,X1,X2)),unordered_pair(sK14(X0,X1,X2),sK14(X0,X1,X2))),X2)
| ~ in(sK14(X0,X1,X2),X1)
| ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f2119]) ).
cnf(c_75,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation_dom_restriction(X0,X2) = X1
| in(unordered_pair(unordered_pair(sK14(X0,X2,X1),sK15(X0,X2,X1)),unordered_pair(sK14(X0,X2,X1),sK14(X0,X2,X1))),X0)
| in(unordered_pair(unordered_pair(sK14(X0,X2,X1),sK15(X0,X2,X1)),unordered_pair(sK14(X0,X2,X1),sK14(X0,X2,X1))),X1) ),
inference(cnf_transformation,[],[f2120]) ).
cnf(c_76,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation_dom_restriction(X0,X2) = X1
| in(unordered_pair(unordered_pair(sK14(X0,X2,X1),sK15(X0,X2,X1)),unordered_pair(sK14(X0,X2,X1),sK14(X0,X2,X1))),X1)
| in(sK14(X0,X2,X1),X2) ),
inference(cnf_transformation,[],[f2121]) ).
cnf(c_77,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(X0,X3)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f2366]) ).
cnf(c_78,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f2367]) ).
cnf(c_79,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3))
| ~ relation(relation_dom_restriction(X2,X3))
| ~ relation(X2)
| in(X0,X3) ),
inference(cnf_transformation,[],[f2368]) ).
cnf(c_80,plain,
( sK16(X0,X1,X2) != apply(X0,X3)
| ~ in(sK16(X0,X1,X2),X2)
| ~ in(X3,relation_dom(X0))
| ~ in(X3,X1)
| ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1307]) ).
cnf(c_81,plain,
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK17(X0,X1,X2)) = sK16(X0,X1,X2)
| relation_image(X0,X1) = X2
| in(sK16(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1306]) ).
cnf(c_82,plain,
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) = X2
| in(sK16(X0,X1,X2),X2)
| in(sK17(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1305]) ).
cnf(c_83,plain,
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) = X2
| in(sK17(X0,X1,X2),relation_dom(X0))
| in(sK16(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1304]) ).
cnf(c_84,plain,
( ~ in(X0,relation_dom(X1))
| ~ in(X0,X2)
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X0),relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f2370]) ).
cnf(c_85,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| apply(X1,sK18(X1,X2,X0)) = X0 ),
inference(cnf_transformation,[],[f2371]) ).
cnf(c_86,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| in(sK18(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f2372]) ).
cnf(c_87,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| in(sK18(X1,X2,X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f2373]) ).
cnf(c_88,plain,
( ~ in(unordered_pair(unordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),unordered_pair(sK19(X0,X1,X2),sK19(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK19(X0,X1,X2),sK20(X0,X1,X2)),unordered_pair(sK19(X0,X1,X2),sK19(X0,X1,X2))),X2)
| ~ in(sK20(X0,X1,X2),X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f2125]) ).
cnf(c_89,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation_rng_restriction(X2,X0) = X1
| in(unordered_pair(unordered_pair(sK19(X2,X0,X1),sK20(X2,X0,X1)),unordered_pair(sK19(X2,X0,X1),sK19(X2,X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK19(X2,X0,X1),sK20(X2,X0,X1)),unordered_pair(sK19(X2,X0,X1),sK19(X2,X0,X1))),X1) ),
inference(cnf_transformation,[],[f2126]) ).
cnf(c_90,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation_rng_restriction(X2,X0) = X1
| in(unordered_pair(unordered_pair(sK19(X2,X0,X1),sK20(X2,X0,X1)),unordered_pair(sK19(X2,X0,X1),sK19(X2,X0,X1))),X1)
| in(sK20(X2,X0,X1),X2) ),
inference(cnf_transformation,[],[f2127]) ).
cnf(c_91,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(relation_rng_restriction(X3,X2))
| ~ in(X1,X3)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X3,X2)) ),
inference(cnf_transformation,[],[f2374]) ).
cnf(c_92,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3) ),
inference(cnf_transformation,[],[f2375]) ).
cnf(c_93,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3))
| ~ relation(relation_rng_restriction(X2,X3))
| ~ relation(X3)
| in(X1,X2) ),
inference(cnf_transformation,[],[f2376]) ).
cnf(c_94,plain,
( ~ is_antisymmetric_in(X0,relation_field(X0))
| ~ relation(X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1315]) ).
cnf(c_95,plain,
( ~ relation(X0)
| ~ antisymmetric(X0)
| is_antisymmetric_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1314]) ).
cnf(c_96,plain,
( ~ in(apply(X0,sK21(X0,X1,X2)),X1)
| ~ in(sK21(X0,X1,X2),relation_dom(X0))
| ~ in(sK21(X0,X1,X2),X2)
| ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1321]) ).
cnf(c_97,plain,
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) = X2
| in(apply(X0,sK21(X0,X1,X2)),X1)
| in(sK21(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1320]) ).
cnf(c_98,plain,
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) = X2
| in(sK21(X0,X1,X2),relation_dom(X0))
| in(sK21(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1319]) ).
cnf(c_99,plain,
( ~ in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| in(X1,relation_inverse_image(X0,X2)) ),
inference(cnf_transformation,[],[f2377]) ).
cnf(c_100,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X0),X2) ),
inference(cnf_transformation,[],[f2378]) ).
cnf(c_101,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f2379]) ).
cnf(c_102,plain,
( ~ in(unordered_pair(unordered_pair(X0,sK22(X1,X2,X3)),unordered_pair(X0,X0)),X1)
| ~ in(sK22(X1,X2,X3),X3)
| ~ in(X0,X2)
| ~ relation(X1)
| relation_image(X1,X2) = X3 ),
inference(cnf_transformation,[],[f2131]) ).
cnf(c_103,plain,
( ~ relation(X0)
| relation_image(X0,X1) = X2
| in(sK22(X0,X1,X2),X2)
| in(sK23(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1326]) ).
cnf(c_104,plain,
( ~ relation(X0)
| relation_image(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK23(X0,X1,X2),sK22(X0,X1,X2)),unordered_pair(sK23(X0,X1,X2),sK23(X0,X1,X2))),X0)
| in(sK22(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f2132]) ).
cnf(c_105,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ in(X0,X3)
| ~ relation(X2)
| in(X1,relation_image(X2,X3)) ),
inference(cnf_transformation,[],[f2380]) ).
cnf(c_106,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ relation(X1)
| in(sK24(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f2381]) ).
cnf(c_107,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK24(X1,X2,X0),X0),unordered_pair(sK24(X1,X2,X0),sK24(X1,X2,X0))),X1) ),
inference(cnf_transformation,[],[f2382]) ).
cnf(c_108,plain,
( ~ in(unordered_pair(unordered_pair(sK25(X0,X1,X2),X3),unordered_pair(sK25(X0,X1,X2),sK25(X0,X1,X2))),X0)
| ~ in(sK25(X0,X1,X2),X2)
| ~ in(X3,X1)
| ~ relation(X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f2135]) ).
cnf(c_109,plain,
( ~ relation(X0)
| relation_inverse_image(X0,X1) = X2
| in(sK25(X0,X1,X2),X2)
| in(sK26(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1332]) ).
cnf(c_110,plain,
( ~ relation(X0)
| relation_inverse_image(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK25(X0,X1,X2),sK26(X0,X1,X2)),unordered_pair(sK25(X0,X1,X2),sK25(X0,X1,X2))),X0)
| in(sK25(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f2136]) ).
cnf(c_111,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ in(X1,X3)
| ~ relation(X2)
| in(X0,relation_inverse_image(X2,X3)) ),
inference(cnf_transformation,[],[f2383]) ).
cnf(c_112,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| in(sK27(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f2384]) ).
cnf(c_113,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,sK27(X1,X2,X0)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f2385]) ).
cnf(c_114,plain,
( ~ is_connected_in(X0,relation_field(X0))
| ~ relation(X0)
| connected(X0) ),
inference(cnf_transformation,[],[f1335]) ).
cnf(c_115,plain,
( ~ relation(X0)
| ~ connected(X0)
| is_connected_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1334]) ).
cnf(c_116,plain,
( ~ is_transitive_in(X0,relation_field(X0))
| ~ relation(X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f1337]) ).
cnf(c_117,plain,
( ~ relation(X0)
| ~ transitive(X0)
| is_transitive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1336]) ).
cnf(c_118,plain,
( sK28(X0,X1,X2,X3) != X2
| ~ in(sK28(X0,X1,X2,X3),X3)
| unordered_triple(X0,X1,X2) = X3 ),
inference(cnf_transformation,[],[f1345]) ).
cnf(c_119,plain,
( sK28(X0,X1,X2,X3) != X1
| ~ in(sK28(X0,X1,X2,X3),X3)
| unordered_triple(X0,X1,X2) = X3 ),
inference(cnf_transformation,[],[f1344]) ).
cnf(c_120,plain,
( sK28(X0,X1,X2,X3) != X0
| ~ in(sK28(X0,X1,X2,X3),X3)
| unordered_triple(X0,X1,X2) = X3 ),
inference(cnf_transformation,[],[f1343]) ).
cnf(c_121,plain,
( sK28(X0,X1,X2,X3) = X0
| sK28(X0,X1,X2,X3) = X1
| sK28(X0,X1,X2,X3) = X2
| unordered_triple(X0,X1,X2) = X3
| in(sK28(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f1342]) ).
cnf(c_122,plain,
in(X0,unordered_triple(X1,X2,X0)),
inference(cnf_transformation,[],[f2387]) ).
cnf(c_123,plain,
in(X0,unordered_triple(X1,X0,X2)),
inference(cnf_transformation,[],[f2389]) ).
cnf(c_124,plain,
in(X0,unordered_triple(X0,X1,X2)),
inference(cnf_transformation,[],[f2391]) ).
cnf(c_125,plain,
( ~ in(X0,unordered_triple(X1,X2,X3))
| X0 = X1
| X0 = X2
| X0 = X3 ),
inference(cnf_transformation,[],[f2392]) ).
cnf(c_126,plain,
( sK30(X0) != sK31(X0)
| function(X0) ),
inference(cnf_transformation,[],[f1349]) ).
cnf(c_127,plain,
( in(unordered_pair(unordered_pair(sK29(X0),sK31(X0)),unordered_pair(sK29(X0),sK29(X0))),X0)
| function(X0) ),
inference(cnf_transformation,[],[f2139]) ).
cnf(c_128,plain,
( in(unordered_pair(unordered_pair(sK29(X0),sK30(X0)),unordered_pair(sK29(X0),sK29(X0))),X0)
| function(X0) ),
inference(cnf_transformation,[],[f2140]) ).
cnf(c_129,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ in(unordered_pair(unordered_pair(X0,X3),unordered_pair(X0,X0)),X2)
| ~ function(X2)
| X1 = X3 ),
inference(cnf_transformation,[],[f2141]) ).
cnf(c_130,plain,
( sK32(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2
| pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 ),
inference(cnf_transformation,[],[f2393]) ).
cnf(c_131,plain,
( unordered_pair(unordered_pair(sK32(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK33(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK32(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK32(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))
| pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 ),
inference(cnf_transformation,[],[f2394]) ).
cnf(c_133,plain,
( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != sK34(X2)
| relation(X2) ),
inference(cnf_transformation,[],[f2145]) ).
cnf(c_134,plain,
( in(sK34(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[],[f1355]) ).
cnf(c_135,plain,
( ~ in(X0,X1)
| ~ relation(X1)
| unordered_pair(unordered_pair(sK35(X0),sK36(X0)),unordered_pair(sK35(X0),sK35(X0))) = X0 ),
inference(cnf_transformation,[],[f2146]) ).
cnf(c_136,plain,
( ~ in(unordered_pair(unordered_pair(sK37(X0,X1),sK37(X0,X1)),unordered_pair(sK37(X0,X1),sK37(X0,X1))),X0)
| ~ relation(X0)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f2147]) ).
cnf(c_137,plain,
( ~ relation(X0)
| in(sK37(X0,X1),X1)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f1358]) ).
cnf(c_138,plain,
( ~ in(X0,X1)
| ~ is_reflexive_in(X2,X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f2148]) ).
cnf(c_139,plain,
( ~ subset(X0,cartesian_product2(X1,X2))
| relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f1361]) ).
cnf(c_140,plain,
( ~ relation_of2(X0,X1,X2)
| subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f1360]) ).
cnf(c_142,plain,
set_meet(empty_set) = empty_set,
inference(cnf_transformation,[],[f2400]) ).
cnf(c_143,plain,
( ~ in(sK38(X0,X1),sK39(X0,X1))
| ~ in(sK38(X0,X1),X1)
| set_meet(X0) = X1
| X0 = empty_set ),
inference(cnf_transformation,[],[f1367]) ).
cnf(c_144,plain,
( ~ in(sK38(X0,X1),X1)
| set_meet(X0) = X1
| X0 = empty_set
| in(sK39(X0,X1),X0) ),
inference(cnf_transformation,[],[f1366]) ).
cnf(c_145,plain,
( ~ in(X0,X1)
| set_meet(X1) = X2
| X1 = empty_set
| in(sK38(X1,X2),X0)
| in(sK38(X1,X2),X2) ),
inference(cnf_transformation,[],[f1365]) ).
cnf(c_146,plain,
( ~ in(X0,sK40(X1,X0))
| X1 = empty_set
| in(X0,set_meet(X1)) ),
inference(cnf_transformation,[],[f2401]) ).
cnf(c_147,plain,
( X0 = empty_set
| in(sK40(X0,X1),X0)
| in(X1,set_meet(X0)) ),
inference(cnf_transformation,[],[f2402]) ).
cnf(c_148,plain,
( ~ in(X0,set_meet(X1))
| ~ in(X2,X1)
| X1 = empty_set
| in(X0,X2) ),
inference(cnf_transformation,[],[f2403]) ).
cnf(c_149,plain,
( sK41(X0,X1) != X0
| ~ in(sK41(X0,X1),X1)
| unordered_pair(X0,X0) = X1 ),
inference(cnf_transformation,[],[f2149]) ).
cnf(c_150,plain,
( unordered_pair(X0,X0) = X1
| sK41(X0,X1) = X0
| in(sK41(X0,X1),X1) ),
inference(cnf_transformation,[],[f2150]) ).
cnf(c_152,plain,
( ~ in(X0,unordered_pair(X1,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f2406]) ).
cnf(c_153,plain,
( ~ in(unordered_pair(unordered_pair(sK42(X0,X1,X2),X1),unordered_pair(sK42(X0,X1,X2),sK42(X0,X1,X2))),X0)
| ~ in(sK42(X0,X1,X2),X2)
| ~ relation(X0)
| sK42(X0,X1,X2) = X1
| fiber(X0,X1) = X2 ),
inference(cnf_transformation,[],[f2153]) ).
cnf(c_154,plain,
( ~ relation(X0)
| fiber(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK42(X0,X1,X2),X1),unordered_pair(sK42(X0,X1,X2),sK42(X0,X1,X2))),X0)
| in(sK42(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f2154]) ).
cnf(c_155,plain,
( sK42(X0,X1,X2) != X1
| ~ relation(X0)
| fiber(X0,X1) = X2
| in(sK42(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1377]) ).
cnf(c_156,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| X0 = X1
| in(X0,fiber(X2,X1)) ),
inference(cnf_transformation,[],[f2407]) ).
cnf(c_157,plain,
( ~ in(X0,fiber(X1,X2))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f2408]) ).
cnf(c_158,plain,
( ~ in(X0,fiber(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f2410]) ).
cnf(c_159,plain,
( ~ in(unordered_pair(unordered_pair(sK43(relation_field(X0),X0),sK44(relation_field(X0),X0)),unordered_pair(sK43(relation_field(X0),X0),sK43(relation_field(X0),X0))),X0)
| ~ subset(sK43(relation_field(X0),X0),sK44(relation_field(X0),X0))
| ~ relation(X0)
| inclusion_relation(relation_field(X0)) = X0 ),
inference(cnf_transformation,[],[f2411]) ).
cnf(c_160,plain,
( ~ relation(X0)
| inclusion_relation(relation_field(X0)) = X0
| in(unordered_pair(unordered_pair(sK43(relation_field(X0),X0),sK44(relation_field(X0),X0)),unordered_pair(sK43(relation_field(X0),X0),sK43(relation_field(X0),X0))),X0)
| subset(sK43(relation_field(X0),X0),sK44(relation_field(X0),X0)) ),
inference(cnf_transformation,[],[f2412]) ).
cnf(c_161,plain,
( ~ relation(X0)
| inclusion_relation(relation_field(X0)) = X0
| in(sK44(relation_field(X0),X0),relation_field(X0)) ),
inference(cnf_transformation,[],[f2413]) ).
cnf(c_162,plain,
( ~ relation(X0)
| inclusion_relation(relation_field(X0)) = X0
| in(sK43(relation_field(X0),X0),relation_field(X0)) ),
inference(cnf_transformation,[],[f2414]) ).
cnf(c_163,plain,
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ subset(X2,X0)
| ~ relation(inclusion_relation(X1))
| in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),inclusion_relation(X1)) ),
inference(cnf_transformation,[],[f2415]) ).
cnf(c_164,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),inclusion_relation(X2))
| ~ in(X0,X2)
| ~ in(X1,X2)
| ~ relation(inclusion_relation(X2))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f2416]) ).
cnf(c_165,plain,
( ~ relation(inclusion_relation(X0))
| relation_field(inclusion_relation(X0)) = X0 ),
inference(cnf_transformation,[],[f2417]) ).
cnf(c_166,plain,
( X0 = empty_set
| in(sK45(X0),X0) ),
inference(cnf_transformation,[],[f1388]) ).
cnf(c_167,plain,
~ in(X0,empty_set),
inference(cnf_transformation,[],[f2418]) ).
cnf(c_168,plain,
( ~ in(sK46(X0,X1),X1)
| ~ subset(sK46(X0,X1),X0)
| powerset(X0) = X1 ),
inference(cnf_transformation,[],[f1392]) ).
cnf(c_169,plain,
( powerset(X0) = X1
| in(sK46(X0,X1),X1)
| subset(sK46(X0,X1),X0) ),
inference(cnf_transformation,[],[f1391]) ).
cnf(c_170,plain,
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2419]) ).
cnf(c_171,plain,
( ~ in(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f2420]) ).
cnf(c_172,plain,
( sK48(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2
| pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 ),
inference(cnf_transformation,[],[f2421]) ).
cnf(c_173,plain,
( unordered_pair(unordered_pair(sK47(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK48(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK47(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK47(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))
| pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 ),
inference(cnf_transformation,[],[f2422]) ).
cnf(c_175,plain,
( ~ subset(sK49(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f1398]) ).
cnf(c_176,plain,
( in(sK49(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f1397]) ).
cnf(c_177,plain,
( ~ in(X0,X1)
| ~ epsilon_transitive(X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1396]) ).
cnf(c_178,plain,
( ~ in(unordered_pair(unordered_pair(sK50(X0,X1),sK51(X0,X1)),unordered_pair(sK50(X0,X1),sK50(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK50(X0,X1),sK51(X0,X1)),unordered_pair(sK50(X0,X1),sK50(X0,X1))),X1)
| ~ relation(X0)
| ~ relation(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f2164]) ).
cnf(c_179,plain,
( ~ relation(X0)
| ~ relation(X1)
| X0 = X1
| in(unordered_pair(unordered_pair(sK50(X1,X0),sK51(X1,X0)),unordered_pair(sK50(X1,X0),sK50(X1,X0))),X0)
| in(unordered_pair(unordered_pair(sK50(X1,X0),sK51(X1,X0)),unordered_pair(sK50(X1,X0),sK50(X1,X0))),X1) ),
inference(cnf_transformation,[],[f2165]) ).
cnf(c_182,plain,
( ~ empty(X0)
| ~ empty(X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f1406]) ).
cnf(c_183,plain,
( ~ element(X0,X1)
| ~ empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f1405]) ).
cnf(c_186,plain,
( sK52(X0,X1,X2) != X1
| ~ in(sK52(X0,X1,X2),X2)
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1412]) ).
cnf(c_187,plain,
( sK52(X0,X1,X2) != X0
| ~ in(sK52(X0,X1,X2),X2)
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1411]) ).
cnf(c_188,plain,
( sK52(X0,X1,X2) = X0
| sK52(X0,X1,X2) = X1
| unordered_pair(X0,X1) = X2
| in(sK52(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1410]) ).
cnf(c_189,plain,
in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f2428]) ).
cnf(c_190,plain,
in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f2430]) ).
cnf(c_191,plain,
( ~ in(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f2431]) ).
cnf(c_192,plain,
( ~ disjoint(fiber(X0,X1),sK53(X0))
| ~ in(X1,sK53(X0))
| ~ relation(X0)
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f1417]) ).
cnf(c_193,plain,
( sK53(X0) != empty_set
| ~ relation(X0)
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f1416]) ).
cnf(c_194,plain,
( ~ relation(X0)
| subset(sK53(X0),relation_field(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f1415]) ).
cnf(c_195,plain,
( ~ subset(X0,relation_field(X1))
| ~ relation(X1)
| ~ well_founded_relation(X1)
| X0 = empty_set
| disjoint(fiber(X1,sK54(X1,X0)),X0) ),
inference(cnf_transformation,[],[f1414]) ).
cnf(c_196,plain,
( ~ subset(X0,relation_field(X1))
| ~ relation(X1)
| ~ well_founded_relation(X1)
| X0 = empty_set
| in(sK54(X1,X0),X0) ),
inference(cnf_transformation,[],[f1413]) ).
cnf(c_197,plain,
( ~ in(sK55(X0,X1,X2),X1)
| ~ in(sK55(X0,X1,X2),X2)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1423]) ).
cnf(c_198,plain,
( ~ in(sK55(X0,X1,X2),X0)
| ~ in(sK55(X0,X1,X2),X2)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1422]) ).
cnf(c_199,plain,
( set_union2(X0,X1) = X2
| in(sK55(X0,X1,X2),X0)
| in(sK55(X0,X1,X2),X1)
| in(sK55(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1421]) ).
cnf(c_200,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) ),
inference(cnf_transformation,[],[f2432]) ).
cnf(c_201,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f2433]) ).
cnf(c_202,plain,
( ~ in(X0,set_union2(X1,X2))
| in(X0,X1)
| in(X0,X2) ),
inference(cnf_transformation,[],[f2434]) ).
cnf(c_203,plain,
( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != sK56(X2,X3,X4)
| ~ in(sK56(X2,X3,X4),X4)
| ~ in(X0,X2)
| ~ in(X1,X3)
| cartesian_product2(X2,X3) = X4 ),
inference(cnf_transformation,[],[f2168]) ).
cnf(c_204,plain,
( unordered_pair(unordered_pair(sK57(X0,X1,X2),sK58(X0,X1,X2)),unordered_pair(sK57(X0,X1,X2),sK57(X0,X1,X2))) = sK56(X0,X1,X2)
| cartesian_product2(X0,X1) = X2
| in(sK56(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f2169]) ).
cnf(c_205,plain,
( cartesian_product2(X0,X1) = X2
| in(sK56(X0,X1,X2),X2)
| in(sK58(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1429]) ).
cnf(c_206,plain,
( cartesian_product2(X0,X1) = X2
| in(sK56(X0,X1,X2),X2)
| in(sK57(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f1428]) ).
cnf(c_208,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| unordered_pair(unordered_pair(sK59(X1,X2,X0),sK60(X1,X2,X0)),unordered_pair(sK59(X1,X2,X0),sK59(X1,X2,X0))) = X0 ),
inference(cnf_transformation,[],[f2437]) ).
cnf(c_209,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| in(sK60(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f2438]) ).
cnf(c_210,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| in(sK59(X1,X2,X0),X1) ),
inference(cnf_transformation,[],[f2439]) ).
cnf(c_211,plain,
( ~ in(sK62(X0),sK61(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1437]) ).
cnf(c_212,plain,
( sK62(X0) != sK61(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1436]) ).
cnf(c_213,plain,
( ~ in(sK61(X0),sK62(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1435]) ).
cnf(c_214,plain,
( in(sK62(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1434]) ).
cnf(c_215,plain,
( in(sK61(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1433]) ).
cnf(c_216,plain,
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ epsilon_connected(X1)
| X0 = X2
| in(X0,X2)
| in(X2,X0) ),
inference(cnf_transformation,[],[f1432]) ).
cnf(c_217,plain,
( ~ in(unordered_pair(unordered_pair(sK63(X0,X1),sK64(X0,X1)),unordered_pair(sK63(X0,X1),sK63(X0,X1))),X1)
| ~ relation(X0)
| ~ relation(X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f2172]) ).
cnf(c_218,plain,
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK63(X1,X0),sK64(X1,X0)),unordered_pair(sK63(X1,X0),sK63(X1,X0))),X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f2173]) ).
cnf(c_220,plain,
( ~ in(sK65(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1443]) ).
cnf(c_221,plain,
( in(sK65(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1442]) ).
cnf(c_222,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f1441]) ).
cnf(c_223,plain,
( ~ disjoint(fiber(X0,X1),sK66(X0,X2))
| ~ in(X1,sK66(X0,X2))
| ~ relation(X0)
| is_well_founded_in(X0,X2) ),
inference(cnf_transformation,[],[f1448]) ).
cnf(c_224,plain,
( sK66(X0,X1) != empty_set
| ~ relation(X0)
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f1447]) ).
cnf(c_225,plain,
( ~ relation(X0)
| subset(sK66(X0,X1),X1)
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f1446]) ).
cnf(c_226,plain,
( ~ subset(X0,X1)
| ~ is_well_founded_in(X2,X1)
| ~ relation(X2)
| X0 = empty_set
| disjoint(fiber(X2,sK67(X2,X0)),X0) ),
inference(cnf_transformation,[],[f1445]) ).
cnf(c_227,plain,
( ~ subset(X0,X1)
| ~ is_well_founded_in(X2,X1)
| ~ relation(X2)
| X0 = empty_set
| in(sK67(X2,X0),X0) ),
inference(cnf_transformation,[],[f1444]) ).
cnf(c_228,plain,
( ~ in(sK68(X0,X1,X2),X0)
| ~ in(sK68(X0,X1,X2),X1)
| ~ in(sK68(X0,X1,X2),X2)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(cnf_transformation,[],[f2175]) ).
cnf(c_229,plain,
( set_difference(X0,set_difference(X0,X1)) = X2
| in(sK68(X0,X1,X2),X1)
| in(sK68(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f2176]) ).
cnf(c_230,plain,
( set_difference(X0,set_difference(X0,X1)) = X2
| in(sK68(X0,X1,X2),X0)
| in(sK68(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f2177]) ).
cnf(c_231,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_difference(X2,set_difference(X2,X1))) ),
inference(cnf_transformation,[],[f2440]) ).
cnf(c_232,plain,
( ~ in(X0,set_difference(X1,set_difference(X1,X2)))
| in(X0,X2) ),
inference(cnf_transformation,[],[f2441]) ).
cnf(c_234,plain,
( ~ function(X0)
| ~ relation(X0)
| apply(X0,X1) = empty_set
| in(X1,relation_dom(X0)) ),
inference(cnf_transformation,[],[f2443]) ).
cnf(c_238,plain,
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f1461]) ).
cnf(c_239,plain,
( ~ ordinal(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1460]) ).
cnf(c_240,plain,
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f1459]) ).
cnf(c_241,plain,
( ~ in(unordered_pair(unordered_pair(sK69(X0,X1),X2),unordered_pair(sK69(X0,X1),sK69(X0,X1))),X0)
| ~ in(sK69(X0,X1),X1)
| ~ relation(X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f2183]) ).
cnf(c_242,plain,
( ~ relation(X0)
| relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK69(X0,X1),sK70(X0,X1)),unordered_pair(sK69(X0,X1),sK69(X0,X1))),X0)
| in(sK69(X0,X1),X1) ),
inference(cnf_transformation,[],[f2184]) ).
cnf(c_244,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,sK71(X1,X0)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f2447]) ).
cnf(c_245,plain,
( sK72(X0,X1) != sK73(X0,X1)
| ~ relation(X0)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1471]) ).
cnf(c_246,plain,
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK73(X0,X1),sK72(X0,X1)),unordered_pair(sK73(X0,X1),sK73(X0,X1))),X0)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f2187]) ).
cnf(c_247,plain,
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK72(X0,X1),sK73(X0,X1)),unordered_pair(sK72(X0,X1),sK72(X0,X1))),X0)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f2188]) ).
cnf(c_248,plain,
( ~ relation(X0)
| in(sK73(X0,X1),X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1468]) ).
cnf(c_249,plain,
( ~ relation(X0)
| in(sK72(X0,X1),X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1467]) ).
cnf(c_250,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2)
| ~ in(X0,X3)
| ~ in(X1,X3)
| ~ is_antisymmetric_in(X2,X3)
| ~ relation(X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f2189]) ).
cnf(c_251,plain,
cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f1472]) ).
cnf(c_252,plain,
( ~ in(sK74(X0,X1),X1)
| ~ in(sK74(X0,X1),X2)
| ~ in(X2,X0)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f1478]) ).
cnf(c_253,plain,
( union(X0) = X1
| in(sK74(X0,X1),X1)
| in(sK75(X0,X1),X0) ),
inference(cnf_transformation,[],[f1477]) ).
cnf(c_254,plain,
( union(X0) = X1
| in(sK74(X0,X1),sK75(X0,X1))
| in(sK74(X0,X1),X1) ),
inference(cnf_transformation,[],[f1476]) ).
cnf(c_255,plain,
( ~ in(X0,X1)
| ~ in(X1,X2)
| in(X0,union(X2)) ),
inference(cnf_transformation,[],[f2448]) ).
cnf(c_256,plain,
( ~ in(X0,union(X1))
| in(sK76(X1,X0),X1) ),
inference(cnf_transformation,[],[f2449]) ).
cnf(c_257,plain,
( ~ in(X0,union(X1))
| in(X0,sK76(X1,X0)) ),
inference(cnf_transformation,[],[f2450]) ).
cnf(c_258,plain,
( ~ relation(X0)
| ~ antisymmetric(X0)
| ~ connected(X0)
| ~ transitive(X0)
| ~ well_founded_relation(X0)
| ~ reflexive(X0)
| well_ordering(X0) ),
inference(cnf_transformation,[],[f1484]) ).
cnf(c_259,plain,
( ~ relation(X0)
| ~ well_ordering(X0)
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f1483]) ).
cnf(c_260,plain,
( ~ relation(X0)
| ~ well_ordering(X0)
| connected(X0) ),
inference(cnf_transformation,[],[f1482]) ).
cnf(c_261,plain,
( ~ relation(X0)
| ~ well_ordering(X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1481]) ).
cnf(c_262,plain,
( ~ relation(X0)
| ~ well_ordering(X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f1480]) ).
cnf(c_263,plain,
( ~ relation(X0)
| ~ well_ordering(X0)
| reflexive(X0) ),
inference(cnf_transformation,[],[f1479]) ).
cnf(c_264,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| equipotent(relation_dom(X0),relation_rng(X0)) ),
inference(cnf_transformation,[],[f2452]) ).
cnf(c_265,plain,
( ~ equipotent(X0,X1)
| relation_rng(sK77(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f1489]) ).
cnf(c_266,plain,
( ~ equipotent(X0,X1)
| relation_dom(sK77(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f1488]) ).
cnf(c_267,plain,
( ~ equipotent(X0,X1)
| one_to_one(sK77(X0,X1)) ),
inference(cnf_transformation,[],[f1487]) ).
cnf(c_268,plain,
( ~ equipotent(X0,X1)
| function(sK77(X0,X1)) ),
inference(cnf_transformation,[],[f1486]) ).
cnf(c_269,plain,
( ~ equipotent(X0,X1)
| relation(sK77(X0,X1)) ),
inference(cnf_transformation,[],[f1485]) ).
cnf(c_270,plain,
( ~ in(sK78(X0,X1,X2),X0)
| ~ in(sK78(X0,X1,X2),X2)
| set_difference(X0,X1) = X2
| in(sK78(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1496]) ).
cnf(c_271,plain,
( ~ in(sK78(X0,X1,X2),X1)
| set_difference(X0,X1) = X2
| in(sK78(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1495]) ).
cnf(c_272,plain,
( set_difference(X0,X1) = X2
| in(sK78(X0,X1,X2),X0)
| in(sK78(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f1494]) ).
cnf(c_273,plain,
( ~ in(X0,X1)
| in(X0,set_difference(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f2453]) ).
cnf(c_274,plain,
( ~ in(X0,set_difference(X1,X2))
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f2454]) ).
cnf(c_275,plain,
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ),
inference(cnf_transformation,[],[f2455]) ).
cnf(c_276,plain,
( apply(X0,X1) != sK79(X0,X2)
| ~ in(sK79(X0,X2),X2)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) = X2 ),
inference(cnf_transformation,[],[f1502]) ).
cnf(c_277,plain,
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK80(X0,X1)) = sK79(X0,X1)
| relation_rng(X0) = X1
| in(sK79(X0,X1),X1) ),
inference(cnf_transformation,[],[f1501]) ).
cnf(c_278,plain,
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) = X1
| in(sK80(X0,X1),relation_dom(X0))
| in(sK79(X0,X1),X1) ),
inference(cnf_transformation,[],[f1500]) ).
cnf(c_279,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X0),relation_rng(X1)) ),
inference(cnf_transformation,[],[f2457]) ).
cnf(c_280,plain,
( ~ in(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| apply(X1,sK81(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f2458]) ).
cnf(c_281,plain,
( ~ in(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| in(sK81(X1,X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f2459]) ).
cnf(c_282,plain,
( ~ in(unordered_pair(unordered_pair(X0,sK82(X1,X2)),unordered_pair(X0,X0)),X1)
| ~ in(sK82(X1,X2),X2)
| ~ relation(X1)
| relation_rng(X1) = X2 ),
inference(cnf_transformation,[],[f2190]) ).
cnf(c_283,plain,
( ~ relation(X0)
| relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK83(X0,X1),sK82(X0,X1)),unordered_pair(sK83(X0,X1),sK83(X0,X1))),X0)
| in(sK82(X0,X1),X1) ),
inference(cnf_transformation,[],[f2191]) ).
cnf(c_285,plain,
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK84(X1,X0),X0),unordered_pair(sK84(X1,X0),sK84(X1,X0))),X1) ),
inference(cnf_transformation,[],[f2461]) ).
cnf(c_286,plain,
( ~ element(X0,powerset(X1))
| set_difference(X1,X0) = subset_complement(X1,X0) ),
inference(cnf_transformation,[],[f1507]) ).
cnf(c_287,plain,
( ~ is_antisymmetric_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_reflexive_in(X0,X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0)
| well_orders(X0,X1) ),
inference(cnf_transformation,[],[f1514]) ).
cnf(c_288,plain,
( ~ well_orders(X0,X1)
| ~ relation(X0)
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f1513]) ).
cnf(c_289,plain,
( ~ well_orders(X0,X1)
| ~ relation(X0)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1512]) ).
cnf(c_290,plain,
( ~ well_orders(X0,X1)
| ~ relation(X0)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1511]) ).
cnf(c_291,plain,
( ~ well_orders(X0,X1)
| ~ relation(X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1510]) ).
cnf(c_292,plain,
( ~ well_orders(X0,X1)
| ~ relation(X0)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f1509]) ).
cnf(c_293,plain,
( union(X0) != X0
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1516]) ).
cnf(c_294,plain,
( ~ being_limit_ordinal(X0)
| union(X0) = X0 ),
inference(cnf_transformation,[],[f1515]) ).
cnf(c_295,plain,
( ~ relation(X0)
| set_union2(relation_dom(X0),relation_rng(X0)) = relation_field(X0) ),
inference(cnf_transformation,[],[f1517]) ).
cnf(c_296,plain,
( ~ in(unordered_pair(unordered_pair(sK86(X0,X1),sK85(X0,X1)),unordered_pair(sK86(X0,X1),sK86(X0,X1))),X0)
| ~ relation(X0)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f2194]) ).
cnf(c_297,plain,
( ~ in(unordered_pair(unordered_pair(sK85(X0,X1),sK86(X0,X1)),unordered_pair(sK85(X0,X1),sK85(X0,X1))),X0)
| ~ relation(X0)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f2195]) ).
cnf(c_298,plain,
( sK86(X0,X1) != sK85(X0,X1)
| ~ relation(X0)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1521]) ).
cnf(c_299,plain,
( ~ relation(X0)
| in(sK86(X0,X1),X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1520]) ).
cnf(c_300,plain,
( ~ relation(X0)
| in(sK85(X0,X1),X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1519]) ).
cnf(c_301,plain,
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ is_connected_in(X3,X1)
| ~ relation(X3)
| X0 = X2
| in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X3)
| in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X3) ),
inference(cnf_transformation,[],[f2196]) ).
cnf(c_302,plain,
( ~ relation(X0)
| set_difference(X0,set_difference(X0,cartesian_product2(X1,X1))) = relation_restriction(X0,X1) ),
inference(cnf_transformation,[],[f2197]) ).
cnf(c_303,plain,
( ~ in(unordered_pair(unordered_pair(sK88(X0,X1),sK87(X0,X1)),unordered_pair(sK88(X0,X1),sK88(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK87(X0,X1),sK88(X0,X1)),unordered_pair(sK87(X0,X1),sK87(X0,X1))),X1)
| ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f2198]) ).
cnf(c_304,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X1) = X0
| in(unordered_pair(unordered_pair(sK88(X1,X0),sK87(X1,X0)),unordered_pair(sK88(X1,X0),sK88(X1,X0))),X1)
| in(unordered_pair(unordered_pair(sK87(X1,X0),sK88(X1,X0)),unordered_pair(sK87(X1,X0),sK87(X1,X0))),X0) ),
inference(cnf_transformation,[],[f2199]) ).
cnf(c_305,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(relation_inverse(X2))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),relation_inverse(X2)) ),
inference(cnf_transformation,[],[f2462]) ).
cnf(c_306,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_inverse(X2))
| ~ relation(relation_inverse(X2))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2) ),
inference(cnf_transformation,[],[f2463]) ).
cnf(c_307,plain,
( ~ sP0(X0,X1,X2)
| ~ sP1(X2,X1,X0)
| relation_isomorphism(X2,X0,X1) ),
inference(cnf_transformation,[],[f1530]) ).
cnf(c_308,plain,
( ~ relation_isomorphism(X0,X1,X2)
| ~ sP1(X0,X2,X1)
| sP0(X1,X2,X0) ),
inference(cnf_transformation,[],[f1529]) ).
cnf(c_309,plain,
( relation_dom(X0) != relation_field(X1)
| relation_field(X2) != relation_rng(X0)
| ~ in(unordered_pair(unordered_pair(apply(X0,sK89(X2,X0,X1)),apply(X0,sK90(X2,X0,X1))),unordered_pair(apply(X0,sK89(X2,X0,X1)),apply(X0,sK89(X2,X0,X1)))),X2)
| ~ in(unordered_pair(unordered_pair(sK89(X2,X0,X1),sK90(X2,X0,X1)),unordered_pair(sK89(X2,X0,X1),sK89(X2,X0,X1))),X1)
| ~ in(sK89(X2,X0,X1),relation_field(X1))
| ~ in(sK90(X2,X0,X1),relation_field(X1))
| ~ one_to_one(X0)
| sP0(X2,X0,X1) ),
inference(cnf_transformation,[],[f2202]) ).
cnf(c_310,plain,
( relation_dom(X0) != relation_field(X1)
| relation_field(X2) != relation_rng(X0)
| ~ one_to_one(X0)
| in(unordered_pair(unordered_pair(apply(X0,sK89(X2,X0,X1)),apply(X0,sK90(X2,X0,X1))),unordered_pair(apply(X0,sK89(X2,X0,X1)),apply(X0,sK89(X2,X0,X1)))),X2)
| in(unordered_pair(unordered_pair(sK89(X2,X0,X1),sK90(X2,X0,X1)),unordered_pair(sK89(X2,X0,X1),sK89(X2,X0,X1))),X1)
| sP0(X2,X0,X1) ),
inference(cnf_transformation,[],[f2203]) ).
cnf(c_311,plain,
( relation_dom(X0) != relation_field(X1)
| relation_field(X2) != relation_rng(X0)
| ~ one_to_one(X0)
| in(unordered_pair(unordered_pair(sK89(X2,X0,X1),sK90(X2,X0,X1)),unordered_pair(sK89(X2,X0,X1),sK89(X2,X0,X1))),X1)
| in(sK90(X2,X0,X1),relation_field(X1))
| sP0(X2,X0,X1) ),
inference(cnf_transformation,[],[f2204]) ).
cnf(c_312,plain,
( relation_dom(X0) != relation_field(X1)
| relation_field(X2) != relation_rng(X0)
| ~ one_to_one(X0)
| in(unordered_pair(unordered_pair(sK89(X2,X0,X1),sK90(X2,X0,X1)),unordered_pair(sK89(X2,X0,X1),sK89(X2,X0,X1))),X1)
| in(sK89(X2,X0,X1),relation_field(X1))
| sP0(X2,X0,X1) ),
inference(cnf_transformation,[],[f2205]) ).
cnf(c_313,plain,
( ~ in(unordered_pair(unordered_pair(apply(X0,X1),apply(X0,X2)),unordered_pair(apply(X0,X1),apply(X0,X1))),X3)
| ~ sP0(X3,X0,X4)
| ~ in(X1,relation_field(X4))
| ~ in(X2,relation_field(X4))
| in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X4) ),
inference(cnf_transformation,[],[f2206]) ).
cnf(c_314,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ sP0(X3,X4,X2)
| in(unordered_pair(unordered_pair(apply(X4,X0),apply(X4,X1)),unordered_pair(apply(X4,X0),apply(X4,X0))),X3) ),
inference(cnf_transformation,[],[f2207]) ).
cnf(c_315,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ sP0(X3,X4,X2)
| in(X1,relation_field(X2)) ),
inference(cnf_transformation,[],[f2208]) ).
cnf(c_316,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ sP0(X3,X4,X2)
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f2209]) ).
cnf(c_317,plain,
( ~ sP0(X0,X1,X2)
| one_to_one(X1) ),
inference(cnf_transformation,[],[f1533]) ).
cnf(c_318,plain,
( ~ sP0(X0,X1,X2)
| relation_field(X0) = relation_rng(X1) ),
inference(cnf_transformation,[],[f1532]) ).
cnf(c_319,plain,
( ~ sP0(X0,X1,X2)
| relation_dom(X1) = relation_field(X2) ),
inference(cnf_transformation,[],[f1531]) ).
cnf(c_320,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| sP1(X2,X0,X1) ),
inference(cnf_transformation,[],[f1542]) ).
cnf(c_321,plain,
( set_difference(X0,set_difference(X0,X1)) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f2210]) ).
cnf(c_322,plain,
( ~ disjoint(X0,X1)
| set_difference(X0,set_difference(X0,X1)) = empty_set ),
inference(cnf_transformation,[],[f2211]) ).
cnf(c_323,plain,
( sK91(X0) != sK92(X0)
| ~ function(X0)
| ~ relation(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1549]) ).
cnf(c_324,plain,
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK91(X0)) = apply(X0,sK92(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1548]) ).
cnf(c_325,plain,
( ~ function(X0)
| ~ relation(X0)
| in(sK92(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1547]) ).
cnf(c_326,plain,
( ~ function(X0)
| ~ relation(X0)
| in(sK91(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1546]) ).
cnf(c_327,plain,
( apply(X0,X1) != apply(X0,X2)
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f1545]) ).
cnf(c_328,plain,
( ~ in(unordered_pair(unordered_pair(sK93(X0,X1,X2),sK94(X0,X1,X2)),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK93(X0,X1,X2),X3),unordered_pair(sK93(X0,X1,X2),sK93(X0,X1,X2))),X0)
| ~ in(unordered_pair(unordered_pair(X3,sK94(X0,X1,X2)),unordered_pair(X3,X3)),X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) = X2 ),
inference(cnf_transformation,[],[f2212]) ).
cnf(c_329,plain,
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X1,X0) = X2
| in(unordered_pair(unordered_pair(sK93(X1,X0,X2),sK94(X1,X0,X2)),unordered_pair(sK93(X1,X0,X2),sK93(X1,X0,X2))),X2)
| in(unordered_pair(unordered_pair(sK95(X1,X0,X2),sK94(X1,X0,X2)),unordered_pair(sK95(X1,X0,X2),sK95(X1,X0,X2))),X0) ),
inference(cnf_transformation,[],[f2213]) ).
cnf(c_330,plain,
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X1,X0) = X2
| in(unordered_pair(unordered_pair(sK93(X1,X0,X2),sK94(X1,X0,X2)),unordered_pair(sK93(X1,X0,X2),sK93(X1,X0,X2))),X2)
| in(unordered_pair(unordered_pair(sK93(X1,X0,X2),sK95(X1,X0,X2)),unordered_pair(sK93(X1,X0,X2),sK93(X1,X0,X2))),X1) ),
inference(cnf_transformation,[],[f2214]) ).
cnf(c_331,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4)
| ~ relation(relation_composition(X2,X4))
| ~ relation(X2)
| ~ relation(X4)
| in(unordered_pair(unordered_pair(X0,X3),unordered_pair(X0,X0)),relation_composition(X2,X4)) ),
inference(cnf_transformation,[],[f2464]) ).
cnf(c_332,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3))
| ~ relation(relation_composition(X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(sK96(X2,X3,X0,X1),X1),unordered_pair(sK96(X2,X3,X0,X1),sK96(X2,X3,X0,X1))),X3) ),
inference(cnf_transformation,[],[f2465]) ).
cnf(c_333,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3))
| ~ relation(relation_composition(X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X0,sK96(X2,X3,X0,X1)),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f2466]) ).
cnf(c_334,plain,
( ~ in(unordered_pair(unordered_pair(sK97(X0,X1),sK99(X0,X1)),unordered_pair(sK97(X0,X1),sK97(X0,X1))),X0)
| ~ relation(X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f2218]) ).
cnf(c_335,plain,
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK98(X0,X1),sK99(X0,X1)),unordered_pair(sK98(X0,X1),sK98(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f2219]) ).
cnf(c_336,plain,
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK97(X0,X1),sK98(X0,X1)),unordered_pair(sK97(X0,X1),sK97(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f2220]) ).
cnf(c_337,plain,
( ~ relation(X0)
| in(sK99(X0,X1),X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1559]) ).
cnf(c_338,plain,
( ~ relation(X0)
| in(sK98(X0,X1),X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1558]) ).
cnf(c_339,plain,
( ~ relation(X0)
| in(sK97(X0,X1),X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1557]) ).
cnf(c_340,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2)
| ~ in(X0,X4)
| ~ in(X1,X4)
| ~ in(X3,X4)
| ~ is_transitive_in(X2,X4)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X0,X3),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f2221]) ).
cnf(c_341,plain,
( ~ in(subset_complement(X0,sK100(X0,X1,X2)),X1)
| ~ in(sK100(X0,X1,X2),X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| complements_of_subsets(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1567]) ).
cnf(c_342,plain,
( ~ element(X0,powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1)))
| complements_of_subsets(X1,X0) = X2
| in(subset_complement(X1,sK100(X1,X0,X2)),X0)
| in(sK100(X1,X0,X2),X2) ),
inference(cnf_transformation,[],[f1566]) ).
cnf(c_343,plain,
( ~ element(X0,powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1)))
| complements_of_subsets(X1,X0) = X2
| element(sK100(X1,X0,X2),powerset(X1)) ),
inference(cnf_transformation,[],[f1565]) ).
cnf(c_344,plain,
( ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ in(subset_complement(X0,X2),X1)
| ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(X0))
| in(X2,complements_of_subsets(X0,X1)) ),
inference(cnf_transformation,[],[f2467]) ).
cnf(c_345,plain,
( ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ in(X2,complements_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(X0))
| in(subset_complement(X0,X2),X1) ),
inference(cnf_transformation,[],[f2468]) ).
cnf(c_346,plain,
( ~ subset(X0,X1)
| X0 = X1
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f1568]) ).
cnf(c_347,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_inverse(X0) = function_inverse(X0) ),
inference(cnf_transformation,[],[f1569]) ).
cnf(c_348,plain,
( ~ is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0)
| reflexive(X0) ),
inference(cnf_transformation,[],[f1571]) ).
cnf(c_349,plain,
( ~ relation(X0)
| ~ reflexive(X0)
| is_reflexive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1570]) ).
cnf(c_350,plain,
relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f1572]) ).
cnf(c_351,plain,
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f1574]) ).
cnf(c_352,plain,
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f1573]) ).
cnf(c_353,plain,
element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f1575]) ).
cnf(c_354,plain,
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f1576]) ).
cnf(c_355,plain,
( ~ element(X0,powerset(X1))
| element(subset_complement(X1,X0),powerset(X1)) ),
inference(cnf_transformation,[],[f1577]) ).
cnf(c_356,plain,
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f1578]) ).
cnf(c_357,plain,
( ~ relation_of2(X0,X1,X2)
| element(relation_dom_as_subset(X1,X2,X0),powerset(X1)) ),
inference(cnf_transformation,[],[f1579]) ).
cnf(c_358,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f1580]) ).
cnf(c_359,plain,
( ~ relation_of2(X0,X1,X2)
| element(relation_rng_as_subset(X1,X2,X0),powerset(X2)) ),
inference(cnf_transformation,[],[f1581]) ).
cnf(c_360,plain,
( ~ element(X0,powerset(powerset(X1)))
| element(union_of_subsets(X1,X0),powerset(X1)) ),
inference(cnf_transformation,[],[f1582]) ).
cnf(c_361,plain,
relation(identity_relation(X0)),
inference(cnf_transformation,[],[f1583]) ).
cnf(c_362,plain,
( ~ element(X0,powerset(powerset(X1)))
| element(meet_of_subsets(X1,X0),powerset(X1)) ),
inference(cnf_transformation,[],[f1584]) ).
cnf(c_363,plain,
( ~ element(X0,powerset(X1))
| ~ element(X2,powerset(X1))
| element(subset_difference(X1,X0,X2),powerset(X1)) ),
inference(cnf_transformation,[],[f1585]) ).
cnf(c_364,plain,
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f1586]) ).
cnf(c_365,plain,
( ~ element(X0,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X0),powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1587]) ).
cnf(c_366,plain,
( ~ relation(X0)
| relation(relation_rng_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f1588]) ).
cnf(c_367,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f1589]) ).
cnf(c_368,plain,
relation_of2(sK101(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1590]) ).
cnf(c_369,plain,
element(sK102(X0),X0),
inference(cnf_transformation,[],[f1591]) ).
cnf(c_370,plain,
relation_of2_as_subset(sK103(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1592]) ).
cnf(c_371,plain,
( ~ empty(X0)
| ~ relation(X1)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f1594]) ).
cnf(c_372,plain,
( ~ empty(X0)
| ~ relation(X1)
| empty(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f1593]) ).
cnf(c_373,plain,
( ~ empty(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f1596]) ).
cnf(c_374,plain,
( ~ empty(X0)
| empty(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f1595]) ).
cnf(c_378,plain,
( ~ relation(X0)
| ~ relation_empty_yielding(X0)
| relation_empty_yielding(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f1601]) ).
cnf(c_379,plain,
( ~ relation(X0)
| ~ relation_empty_yielding(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f1600]) ).
cnf(c_380,plain,
( ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| function(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f1603]) ).
cnf(c_381,plain,
( ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f1602]) ).
cnf(c_382,plain,
~ empty(set_union2(X0,unordered_pair(X0,X0))),
inference(cnf_transformation,[],[f2222]) ).
cnf(c_383,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation(set_difference(X1,set_difference(X1,X0))) ),
inference(cnf_transformation,[],[f2223]) ).
cnf(c_384,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[],[f1606]) ).
cnf(c_387,plain,
function(identity_relation(X0)),
inference(cnf_transformation,[],[f1610]) ).
cnf(c_388,plain,
relation(identity_relation(X0)),
inference(cnf_transformation,[],[f1609]) ).
cnf(c_389,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f1618]) ).
cnf(c_390,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f1617]) ).
cnf(c_391,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f1616]) ).
cnf(c_393,plain,
one_to_one(empty_set),
inference(cnf_transformation,[],[f1614]) ).
cnf(c_394,plain,
function(empty_set),
inference(cnf_transformation,[],[f1613]) ).
cnf(c_395,plain,
relation_empty_yielding(empty_set),
inference(cnf_transformation,[],[f1612]) ).
cnf(c_397,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation(set_union2(X1,X0)) ),
inference(cnf_transformation,[],[f1619]) ).
cnf(c_399,plain,
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f1621]) ).
cnf(c_400,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| function(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f1623]) ).
cnf(c_401,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f1622]) ).
cnf(c_402,plain,
( ~ ordinal(X0)
| ordinal(set_union2(X0,unordered_pair(X0,X0))) ),
inference(cnf_transformation,[],[f2226]) ).
cnf(c_403,plain,
( ~ ordinal(X0)
| epsilon_connected(set_union2(X0,unordered_pair(X0,X0))) ),
inference(cnf_transformation,[],[f2227]) ).
cnf(c_404,plain,
( ~ ordinal(X0)
| epsilon_transitive(set_union2(X0,unordered_pair(X0,X0))) ),
inference(cnf_transformation,[],[f2228]) ).
cnf(c_406,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation(set_difference(X1,X0)) ),
inference(cnf_transformation,[],[f1628]) ).
cnf(c_407,plain,
~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f1629]) ).
cnf(c_408,plain,
( ~ empty(set_union2(X0,X1))
| empty(X1) ),
inference(cnf_transformation,[],[f1630]) ).
cnf(c_409,plain,
( ~ function(X0)
| ~ relation(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f1632]) ).
cnf(c_411,plain,
( ~ ordinal(X0)
| ordinal(union(X0)) ),
inference(cnf_transformation,[],[f1635]) ).
cnf(c_412,plain,
( ~ ordinal(X0)
| epsilon_connected(union(X0)) ),
inference(cnf_transformation,[],[f1634]) ).
cnf(c_413,plain,
( ~ ordinal(X0)
| epsilon_transitive(union(X0)) ),
inference(cnf_transformation,[],[f1633]) ).
cnf(c_414,plain,
relation(empty_set),
inference(cnf_transformation,[],[f1637]) ).
cnf(c_415,plain,
empty(empty_set),
inference(cnf_transformation,[],[f1636]) ).
cnf(c_416,plain,
( ~ empty(cartesian_product2(X0,X1))
| empty(X0)
| empty(X1) ),
inference(cnf_transformation,[],[f1638]) ).
cnf(c_417,plain,
( ~ function(X0)
| ~ relation(X0)
| function(relation_rng_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f1640]) ).
cnf(c_418,plain,
( ~ function(X0)
| ~ relation(X0)
| relation(relation_rng_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f1639]) ).
cnf(c_419,plain,
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f1641]) ).
cnf(c_420,plain,
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f1642]) ).
cnf(c_421,plain,
( ~ empty(X0)
| relation(relation_dom(X0)) ),
inference(cnf_transformation,[],[f1644]) ).
cnf(c_422,plain,
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f1643]) ).
cnf(c_423,plain,
( ~ empty(X0)
| relation(relation_rng(X0)) ),
inference(cnf_transformation,[],[f1646]) ).
cnf(c_424,plain,
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f1645]) ).
cnf(c_425,plain,
( ~ empty(X0)
| ~ relation(X1)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f1648]) ).
cnf(c_426,plain,
( ~ empty(X0)
| ~ relation(X1)
| empty(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f1647]) ).
cnf(c_427,plain,
set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f1649]) ).
cnf(c_428,plain,
set_difference(X0,set_difference(X0,X0)) = X0,
inference(cnf_transformation,[],[f2230]) ).
cnf(c_429,plain,
( ~ element(X0,powerset(X1))
| subset_complement(X1,subset_complement(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f1651]) ).
cnf(c_430,plain,
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(cnf_transformation,[],[f1652]) ).
cnf(c_431,plain,
( ~ element(X0,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f1653]) ).
cnf(c_432,plain,
~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f1654]) ).
cnf(c_433,plain,
( ~ in(unordered_pair(unordered_pair(sK104(X0),sK104(X0)),unordered_pair(sK104(X0),sK104(X0))),X0)
| ~ relation(X0)
| reflexive(X0) ),
inference(cnf_transformation,[],[f2231]) ).
cnf(c_434,plain,
( ~ relation(X0)
| in(sK104(X0),relation_field(X0))
| reflexive(X0) ),
inference(cnf_transformation,[],[f1656]) ).
cnf(c_435,plain,
( ~ in(X0,relation_field(X1))
| ~ relation(X1)
| ~ reflexive(X1)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f2232]) ).
cnf(c_436,plain,
unordered_pair(X0,X0) != empty_set,
inference(cnf_transformation,[],[f2233]) ).
cnf(c_438,plain,
( ~ disjoint(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2235]) ).
cnf(c_439,plain,
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f2236]) ).
cnf(c_440,plain,
( ~ relation(X0)
| subset(relation_dom(relation_rng_restriction(X1,X0)),relation_dom(X0)) ),
inference(cnf_transformation,[],[f1662]) ).
cnf(c_441,plain,
( ~ in(unordered_pair(unordered_pair(sK105(X0),sK107(X0)),unordered_pair(sK105(X0),sK105(X0))),X0)
| ~ relation(X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f2237]) ).
cnf(c_442,plain,
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK106(X0),sK107(X0)),unordered_pair(sK106(X0),sK106(X0))),X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f2238]) ).
cnf(c_443,plain,
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK105(X0),sK106(X0)),unordered_pair(sK105(X0),sK105(X0))),X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f2239]) ).
cnf(c_444,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ in(unordered_pair(unordered_pair(X3,X0),unordered_pair(X3,X3)),X2)
| ~ relation(X2)
| ~ transitive(X2)
| in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2) ),
inference(cnf_transformation,[],[f2240]) ).
cnf(c_447,plain,
( ~ equipotent(X0,relation_field(X1))
| ~ relation(X1)
| ~ well_ordering(X1)
| well_orders(sK108(X0),X0) ),
inference(cnf_transformation,[],[f1670]) ).
cnf(c_448,plain,
( ~ equipotent(X0,relation_field(X1))
| ~ relation(X1)
| ~ well_ordering(X1)
| relation(sK108(X0)) ),
inference(cnf_transformation,[],[f1669]) ).
cnf(c_451,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[],[f1673]) ).
cnf(c_452,plain,
( sK109(X0) != sK110(X0)
| ~ relation(X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1677]) ).
cnf(c_453,plain,
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK110(X0),sK109(X0)),unordered_pair(sK110(X0),sK110(X0))),X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f2243]) ).
cnf(c_454,plain,
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK109(X0),sK110(X0)),unordered_pair(sK109(X0),sK109(X0))),X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f2244]) ).
cnf(c_455,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2)
| ~ relation(X2)
| ~ antisymmetric(X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f2245]) ).
cnf(c_456,plain,
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0) ),
inference(cnf_transformation,[],[f2246]) ).
cnf(c_457,plain,
( ~ in(unordered_pair(unordered_pair(sK112(X0),sK111(X0)),unordered_pair(sK112(X0),sK112(X0))),X0)
| ~ relation(X0)
| connected(X0) ),
inference(cnf_transformation,[],[f2247]) ).
cnf(c_458,plain,
( ~ in(unordered_pair(unordered_pair(sK111(X0),sK112(X0)),unordered_pair(sK111(X0),sK111(X0))),X0)
| ~ relation(X0)
| connected(X0) ),
inference(cnf_transformation,[],[f2248]) ).
cnf(c_459,plain,
( sK112(X0) != sK111(X0)
| ~ relation(X0)
| connected(X0) ),
inference(cnf_transformation,[],[f1682]) ).
cnf(c_460,plain,
( ~ relation(X0)
| in(sK112(X0),relation_field(X0))
| connected(X0) ),
inference(cnf_transformation,[],[f1681]) ).
cnf(c_461,plain,
( ~ relation(X0)
| in(sK111(X0),relation_field(X0))
| connected(X0) ),
inference(cnf_transformation,[],[f1680]) ).
cnf(c_462,plain,
( ~ in(X0,relation_field(X1))
| ~ in(X2,relation_field(X1))
| ~ relation(X1)
| ~ connected(X1)
| X0 = X2
| in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X1)
| in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X1) ),
inference(cnf_transformation,[],[f2249]) ).
cnf(c_469,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f2255]) ).
cnf(c_470,plain,
( ~ in(sK113(X0,X1),X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1693]) ).
cnf(c_471,plain,
( in(sK113(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1692]) ).
cnf(c_475,plain,
function(sK114),
inference(cnf_transformation,[],[f1698]) ).
cnf(c_476,plain,
relation(sK114),
inference(cnf_transformation,[],[f1697]) ).
cnf(c_477,plain,
ordinal(sK115),
inference(cnf_transformation,[],[f1701]) ).
cnf(c_478,plain,
epsilon_connected(sK115),
inference(cnf_transformation,[],[f1700]) ).
cnf(c_479,plain,
epsilon_transitive(sK115),
inference(cnf_transformation,[],[f1699]) ).
cnf(c_480,plain,
relation(sK116),
inference(cnf_transformation,[],[f1703]) ).
cnf(c_481,plain,
empty(sK116),
inference(cnf_transformation,[],[f1702]) ).
cnf(c_482,plain,
( ~ empty(sK117(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f1705]) ).
cnf(c_483,plain,
( element(sK117(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f1704]) ).
cnf(c_484,plain,
empty(sK118),
inference(cnf_transformation,[],[f1706]) ).
cnf(c_485,plain,
function(sK119),
inference(cnf_transformation,[],[f1709]) ).
cnf(c_486,plain,
empty(sK119),
inference(cnf_transformation,[],[f1708]) ).
cnf(c_487,plain,
relation(sK119),
inference(cnf_transformation,[],[f1707]) ).
cnf(c_488,plain,
ordinal(sK120),
inference(cnf_transformation,[],[f1716]) ).
cnf(c_489,plain,
epsilon_connected(sK120),
inference(cnf_transformation,[],[f1715]) ).
cnf(c_490,plain,
epsilon_transitive(sK120),
inference(cnf_transformation,[],[f1714]) ).
cnf(c_491,plain,
empty(sK120),
inference(cnf_transformation,[],[f1713]) ).
cnf(c_492,plain,
one_to_one(sK120),
inference(cnf_transformation,[],[f1712]) ).
cnf(c_493,plain,
function(sK120),
inference(cnf_transformation,[],[f1711]) ).
cnf(c_494,plain,
relation(sK120),
inference(cnf_transformation,[],[f1710]) ).
cnf(c_495,plain,
relation(sK121),
inference(cnf_transformation,[],[f1718]) ).
cnf(c_496,plain,
~ empty(sK121),
inference(cnf_transformation,[],[f1717]) ).
cnf(c_497,plain,
empty(sK122(X0)),
inference(cnf_transformation,[],[f1720]) ).
cnf(c_498,plain,
element(sK122(X0),powerset(X0)),
inference(cnf_transformation,[],[f1719]) ).
cnf(c_499,plain,
~ empty(sK123),
inference(cnf_transformation,[],[f1721]) ).
cnf(c_500,plain,
one_to_one(sK124),
inference(cnf_transformation,[],[f1724]) ).
cnf(c_501,plain,
function(sK124),
inference(cnf_transformation,[],[f1723]) ).
cnf(c_502,plain,
relation(sK124),
inference(cnf_transformation,[],[f1722]) ).
cnf(c_503,plain,
ordinal(sK125),
inference(cnf_transformation,[],[f1728]) ).
cnf(c_504,plain,
epsilon_connected(sK125),
inference(cnf_transformation,[],[f1727]) ).
cnf(c_505,plain,
epsilon_transitive(sK125),
inference(cnf_transformation,[],[f1726]) ).
cnf(c_506,plain,
~ empty(sK125),
inference(cnf_transformation,[],[f1725]) ).
cnf(c_507,plain,
relation_empty_yielding(sK126),
inference(cnf_transformation,[],[f1730]) ).
cnf(c_508,plain,
relation(sK126),
inference(cnf_transformation,[],[f1729]) ).
cnf(c_509,plain,
function(sK127),
inference(cnf_transformation,[],[f1733]) ).
cnf(c_510,plain,
relation_empty_yielding(sK127),
inference(cnf_transformation,[],[f1732]) ).
cnf(c_511,plain,
relation(sK127),
inference(cnf_transformation,[],[f1731]) ).
cnf(c_512,plain,
( ~ relation_of2(X0,X1,X2)
| relation_dom_as_subset(X1,X2,X0) = relation_dom(X0) ),
inference(cnf_transformation,[],[f1734]) ).
cnf(c_513,plain,
( ~ relation_of2(X0,X1,X2)
| relation_rng_as_subset(X1,X2,X0) = relation_rng(X0) ),
inference(cnf_transformation,[],[f1735]) ).
cnf(c_514,plain,
( ~ element(X0,powerset(powerset(X1)))
| union_of_subsets(X1,X0) = union(X0) ),
inference(cnf_transformation,[],[f1736]) ).
cnf(c_515,plain,
( ~ element(X0,powerset(powerset(X1)))
| meet_of_subsets(X1,X0) = set_meet(X0) ),
inference(cnf_transformation,[],[f1737]) ).
cnf(c_516,plain,
( ~ element(X0,powerset(X1))
| ~ element(X2,powerset(X1))
| subset_difference(X1,X0,X2) = set_difference(X0,X2) ),
inference(cnf_transformation,[],[f1738]) ).
cnf(c_517,plain,
( ~ relation_of2(X0,X1,X2)
| relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1740]) ).
cnf(c_518,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f1739]) ).
cnf(c_519,plain,
( ~ subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f1742]) ).
cnf(c_520,plain,
( ~ ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1741]) ).
cnf(c_521,plain,
( ~ are_equipotent(X0,X1)
| equipotent(X0,X1) ),
inference(cnf_transformation,[],[f1744]) ).
cnf(c_522,plain,
( ~ equipotent(X0,X1)
| are_equipotent(X0,X1) ),
inference(cnf_transformation,[],[f1743]) ).
cnf(c_523,plain,
( ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X1,X1) ),
inference(cnf_transformation,[],[f1745]) ).
cnf(c_524,plain,
subset(X0,X0),
inference(cnf_transformation,[],[f1746]) ).
cnf(c_525,plain,
equipotent(X0,X0),
inference(cnf_transformation,[],[f1747]) ).
cnf(c_526,plain,
( ~ in(X0,X1)
| ~ sP2(X1)
| in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK128(X1)) ),
inference(cnf_transformation,[],[f2510]) ).
cnf(c_527,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK128(X2))
| ~ sP2(X2)
| unordered_pair(X0,X0) = X1 ),
inference(cnf_transformation,[],[f2257]) ).
cnf(c_528,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK128(X2))
| ~ sP2(X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f2258]) ).
cnf(c_530,plain,
( ~ sP2(X0)
| function(sK128(X0)) ),
inference(cnf_transformation,[],[f1749]) ).
cnf(c_531,plain,
( ~ sP2(X0)
| relation(sK128(X0)) ),
inference(cnf_transformation,[],[f1748]) ).
cnf(c_532,plain,
( sK130(X0) != sK131(X0)
| sP2(X0) ),
inference(cnf_transformation,[],[f1758]) ).
cnf(c_533,plain,
( unordered_pair(sK129(X0),sK129(X0)) = sK131(X0)
| sP2(X0) ),
inference(cnf_transformation,[],[f2260]) ).
cnf(c_535,plain,
( unordered_pair(sK129(X0),sK129(X0)) = sK130(X0)
| sP2(X0) ),
inference(cnf_transformation,[],[f2261]) ).
cnf(c_536,plain,
( in(sK129(X0),X0)
| sP2(X0) ),
inference(cnf_transformation,[],[f1754]) ).
cnf(c_537,plain,
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ ordinal(X0)
| ~ ordinal(X2)
| ordinal_subset(sK132(X1),X0) ),
inference(cnf_transformation,[],[f1761]) ).
cnf(c_538,plain,
( ~ in(X0,X1)
| ~ ordinal(X0)
| in(sK132(X1),X1) ),
inference(cnf_transformation,[],[f1760]) ).
cnf(c_539,plain,
( ~ in(X0,X1)
| ~ ordinal(X0)
| ordinal(sK132(X1)) ),
inference(cnf_transformation,[],[f1759]) ).
cnf(c_540,plain,
( ~ in(unordered_pair(unordered_pair(apply(X0,X1),apply(X0,X2)),unordered_pair(apply(X0,X1),apply(X0,X1))),X3)
| ~ in(X1,X4)
| ~ in(X2,X4)
| ~ function(X0)
| ~ relation(X0)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),sK133(X4,X3,X0)) ),
inference(cnf_transformation,[],[f2262]) ).
cnf(c_541,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK133(X2,X3,X4))
| ~ function(X4)
| ~ relation(X3)
| ~ relation(X4)
| in(unordered_pair(unordered_pair(apply(X4,X0),apply(X4,X1)),unordered_pair(apply(X4,X0),apply(X4,X0))),X3) ),
inference(cnf_transformation,[],[f2263]) ).
cnf(c_542,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK133(X2,X3,X4))
| ~ function(X4)
| ~ relation(X3)
| ~ relation(X4)
| in(X1,X2) ),
inference(cnf_transformation,[],[f2264]) ).
cnf(c_543,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK133(X2,X3,X4))
| ~ function(X4)
| ~ relation(X3)
| ~ relation(X4)
| in(X0,X2) ),
inference(cnf_transformation,[],[f2265]) ).
cnf(c_544,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ relation(X1)
| relation(sK133(X2,X1,X0)) ),
inference(cnf_transformation,[],[f1762]) ).
cnf(c_545,plain,
( sK135(X0) != sK136(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f1771]) ).
cnf(c_546,plain,
( ~ sP3(X0)
| unordered_pair(sK134(X0),sK134(X0)) = sK136(X0) ),
inference(cnf_transformation,[],[f2266]) ).
cnf(c_547,plain,
( ~ sP3(X0)
| in(sK134(X0),X0) ),
inference(cnf_transformation,[],[f1769]) ).
cnf(c_548,plain,
( ~ sP3(X0)
| unordered_pair(sK134(X0),sK134(X0)) = sK135(X0) ),
inference(cnf_transformation,[],[f2267]) ).
cnf(c_550,plain,
( ~ in(X0,X1)
| in(unordered_pair(X0,X0),sK137(X1))
| sP3(X1) ),
inference(cnf_transformation,[],[f2511]) ).
cnf(c_551,plain,
( ~ in(X0,sK137(X1))
| unordered_pair(sK138(X1,X0),sK138(X1,X0)) = X0
| sP3(X1) ),
inference(cnf_transformation,[],[f2269]) ).
cnf(c_553,plain,
( ~ in(X0,sK137(X1))
| in(sK138(X1,X0),X1)
| sP3(X1) ),
inference(cnf_transformation,[],[f1772]) ).
cnf(c_554,plain,
( sK140(X0) != sK141(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f1782]) ).
cnf(c_555,plain,
( ~ sP5(X0)
| unordered_pair(sK142(X0),sK142(X0)) = sK143(X0) ),
inference(cnf_transformation,[],[f2270]) ).
cnf(c_556,plain,
( ~ sP5(X0)
| in(sK142(X0),X0) ),
inference(cnf_transformation,[],[f1780]) ).
cnf(c_557,plain,
( ~ sP5(X0)
| unordered_pair(unordered_pair(sK142(X0),sK143(X0)),unordered_pair(sK142(X0),sK142(X0))) = sK141(X0) ),
inference(cnf_transformation,[],[f2271]) ).
cnf(c_558,plain,
( ~ sP5(X0)
| sK141(X0) = sK139(X0) ),
inference(cnf_transformation,[],[f1778]) ).
cnf(c_559,plain,
( ~ sP5(X0)
| sP4(X0,sK140(X0)) ),
inference(cnf_transformation,[],[f1777]) ).
cnf(c_560,plain,
( ~ sP5(X0)
| sK140(X0) = sK139(X0) ),
inference(cnf_transformation,[],[f1776]) ).
cnf(c_561,plain,
( ~ sP4(X0,X1)
| unordered_pair(sK144(X0,X1),sK144(X0,X1)) = sK145(X0,X1) ),
inference(cnf_transformation,[],[f2272]) ).
cnf(c_562,plain,
( ~ sP4(X0,X1)
| in(sK144(X0,X1),X0) ),
inference(cnf_transformation,[],[f1784]) ).
cnf(c_563,plain,
( ~ sP4(X0,X1)
| unordered_pair(unordered_pair(sK144(X0,X1),sK145(X0,X1)),unordered_pair(sK144(X0,X1),sK144(X0,X1))) = X1 ),
inference(cnf_transformation,[],[f2273]) ).
cnf(c_564,plain,
( ~ in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),cartesian_product2(X1,X2))
| ~ in(X0,X1)
| in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK146(X1,X2))
| sP5(X1) ),
inference(cnf_transformation,[],[f2475]) ).
cnf(c_565,plain,
( ~ in(X0,sK146(X1,X2))
| unordered_pair(sK148(X1,X0),sK148(X1,X0)) = sK149(X1,X0)
| sP5(X1) ),
inference(cnf_transformation,[],[f2275]) ).
cnf(c_566,plain,
( ~ in(X0,sK146(X1,X2))
| in(sK148(X1,X0),X1)
| sP5(X1) ),
inference(cnf_transformation,[],[f1789]) ).
cnf(c_567,plain,
( ~ in(X0,sK146(X1,X2))
| unordered_pair(unordered_pair(sK148(X1,X0),sK149(X1,X0)),unordered_pair(sK148(X1,X0),sK148(X1,X0))) = X0
| sP5(X1) ),
inference(cnf_transformation,[],[f2276]) ).
cnf(c_568,plain,
( ~ in(X0,sK146(X1,X2))
| sK147(X1,X2,X0) = X0
| sP5(X1) ),
inference(cnf_transformation,[],[f1787]) ).
cnf(c_569,plain,
( ~ in(X0,sK146(X1,X2))
| in(sK147(X1,X2,X0),cartesian_product2(X1,X2))
| sP5(X1) ),
inference(cnf_transformation,[],[f1786]) ).
cnf(c_570,plain,
( sK151(X0,X1) != sK152(X0,X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f1798]) ).
cnf(c_571,plain,
( ~ sP6(X0,X1)
| in(unordered_pair(unordered_pair(apply(X1,sK153(X0,X1)),apply(X1,sK154(X0,X1))),unordered_pair(apply(X1,sK153(X0,X1)),apply(X1,sK153(X0,X1)))),X0) ),
inference(cnf_transformation,[],[f2277]) ).
cnf(c_572,plain,
( ~ sP6(X0,X1)
| unordered_pair(unordered_pair(sK153(X0,X1),sK154(X0,X1)),unordered_pair(sK153(X0,X1),sK153(X0,X1))) = sK152(X0,X1) ),
inference(cnf_transformation,[],[f2278]) ).
cnf(c_573,plain,
( ~ sP6(X0,X1)
| sK152(X0,X1) = sK150(X0,X1) ),
inference(cnf_transformation,[],[f1795]) ).
cnf(c_574,plain,
( ~ sP6(X0,X1)
| in(unordered_pair(unordered_pair(apply(X1,sK155(X0,X1)),apply(X1,sK156(X0,X1))),unordered_pair(apply(X1,sK155(X0,X1)),apply(X1,sK155(X0,X1)))),X0) ),
inference(cnf_transformation,[],[f2279]) ).
cnf(c_575,plain,
( ~ sP6(X0,X1)
| unordered_pair(unordered_pair(sK155(X0,X1),sK156(X0,X1)),unordered_pair(sK155(X0,X1),sK155(X0,X1))) = sK151(X0,X1) ),
inference(cnf_transformation,[],[f2280]) ).
cnf(c_576,plain,
( ~ sP6(X0,X1)
| sK151(X0,X1) = sK150(X0,X1) ),
inference(cnf_transformation,[],[f1792]) ).
cnf(c_577,plain,
( ~ in(unordered_pair(unordered_pair(apply(X0,X1),apply(X0,X2)),unordered_pair(apply(X0,X1),apply(X0,X1))),X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),cartesian_product2(X4,X4))
| ~ function(X0)
| ~ relation(X0)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),sK157(X4,X3,X0))
| sP6(X3,X0) ),
inference(cnf_transformation,[],[f2477]) ).
cnf(c_578,plain,
( ~ in(X0,sK157(X1,X2,X3))
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(apply(X3,sK159(X2,X3,X0)),apply(X3,sK160(X2,X3,X0))),unordered_pair(apply(X3,sK159(X2,X3,X0)),apply(X3,sK159(X2,X3,X0)))),X2)
| sP6(X2,X3) ),
inference(cnf_transformation,[],[f2282]) ).
cnf(c_579,plain,
( ~ in(X0,sK157(X1,X2,X3))
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X3)
| unordered_pair(unordered_pair(sK159(X2,X3,X0),sK160(X2,X3,X0)),unordered_pair(sK159(X2,X3,X0),sK159(X2,X3,X0))) = X0
| sP6(X2,X3) ),
inference(cnf_transformation,[],[f2283]) ).
cnf(c_580,plain,
( ~ in(X0,sK157(X1,X2,X3))
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X3)
| sK158(X1,X2,X3,X0) = X0
| sP6(X2,X3) ),
inference(cnf_transformation,[],[f1800]) ).
cnf(c_581,plain,
( ~ in(X0,sK157(X1,X2,X3))
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X3)
| in(sK158(X1,X2,X3,X0),cartesian_product2(X1,X1))
| sP6(X2,X3) ),
inference(cnf_transformation,[],[f1799]) ).
cnf(c_582,plain,
( sK162 != sK163
| ~ sP7 ),
inference(cnf_transformation,[],[f1808]) ).
cnf(c_583,plain,
( ~ sP7
| ordinal(sK163) ),
inference(cnf_transformation,[],[f1807]) ).
cnf(c_584,plain,
( ~ sP7
| sK163 = sK161 ),
inference(cnf_transformation,[],[f1806]) ).
cnf(c_585,plain,
( ~ sP7
| ordinal(sK162) ),
inference(cnf_transformation,[],[f1805]) ).
cnf(c_586,plain,
( ~ sP7
| sK162 = sK161 ),
inference(cnf_transformation,[],[f1804]) ).
cnf(c_587,plain,
( ~ in(X0,X1)
| ~ ordinal(X0)
| in(X0,sK164(X1))
| sP7 ),
inference(cnf_transformation,[],[f2478]) ).
cnf(c_588,plain,
( ~ in(X0,sK164(X1))
| ordinal(X0)
| sP7 ),
inference(cnf_transformation,[],[f1811]) ).
cnf(c_589,plain,
( ~ in(X0,sK164(X1))
| sK165(X1,X0) = X0
| sP7 ),
inference(cnf_transformation,[],[f1810]) ).
cnf(c_590,plain,
( ~ in(X0,sK164(X1))
| in(sK165(X1,X0),X1)
| sP7 ),
inference(cnf_transformation,[],[f1809]) ).
cnf(c_591,plain,
( sK167(X0) != sK168(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f1819]) ).
cnf(c_592,plain,
( ~ sP9(X0)
| in(sK169(X0),X0) ),
inference(cnf_transformation,[],[f1818]) ).
cnf(c_593,plain,
( ~ sP9(X0)
| sK168(X0) = sK169(X0) ),
inference(cnf_transformation,[],[f1817]) ).
cnf(c_594,plain,
( ~ sP9(X0)
| ordinal(sK169(X0)) ),
inference(cnf_transformation,[],[f1816]) ).
cnf(c_595,plain,
( ~ sP9(X0)
| sK168(X0) = sK166(X0) ),
inference(cnf_transformation,[],[f1815]) ).
cnf(c_596,plain,
( ~ sP9(X0)
| sP8(X0,sK167(X0)) ),
inference(cnf_transformation,[],[f1814]) ).
cnf(c_597,plain,
( ~ sP9(X0)
| sK167(X0) = sK166(X0) ),
inference(cnf_transformation,[],[f1813]) ).
cnf(c_598,plain,
( ~ sP8(X0,X1)
| in(sK170(X0,X1),X0) ),
inference(cnf_transformation,[],[f1822]) ).
cnf(c_599,plain,
( ~ sP8(X0,X1)
| sK170(X0,X1) = X1 ),
inference(cnf_transformation,[],[f1821]) ).
cnf(c_600,plain,
( ~ sP8(X0,X1)
| ordinal(sK170(X0,X1)) ),
inference(cnf_transformation,[],[f1820]) ).
cnf(c_601,plain,
( ~ in(X0,set_union2(X1,unordered_pair(X1,X1)))
| ~ in(X0,X2)
| ~ ordinal(X0)
| ~ ordinal(X1)
| in(X0,sK171(X2,X1))
| sP9(X2) ),
inference(cnf_transformation,[],[f2480]) ).
cnf(c_602,plain,
( ~ in(X0,sK171(X1,X2))
| ~ ordinal(X2)
| in(sK173(X1,X0),X1)
| sP9(X1) ),
inference(cnf_transformation,[],[f1827]) ).
cnf(c_603,plain,
( ~ in(X0,sK171(X1,X2))
| ~ ordinal(X2)
| sK173(X1,X0) = X0
| sP9(X1) ),
inference(cnf_transformation,[],[f1826]) ).
cnf(c_604,plain,
( ~ in(X0,sK171(X1,X2))
| ~ ordinal(X2)
| ordinal(sK173(X1,X0))
| sP9(X1) ),
inference(cnf_transformation,[],[f1825]) ).
cnf(c_605,plain,
( ~ in(X0,sK171(X1,X2))
| ~ ordinal(X2)
| sK172(X1,X2,X0) = X0
| sP9(X1) ),
inference(cnf_transformation,[],[f1824]) ).
cnf(c_606,plain,
( ~ in(X0,sK171(X1,X2))
| ~ ordinal(X2)
| in(sK172(X1,X2,X0),set_union2(X2,unordered_pair(X2,X2)))
| sP9(X1) ),
inference(cnf_transformation,[],[f2285]) ).
cnf(c_607,plain,
( ~ in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),cartesian_product2(X1,X2))
| ~ in(X0,X1)
| in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK174(X1,X2)) ),
inference(cnf_transformation,[],[f2482]) ).
cnf(c_608,plain,
( ~ in(X0,sK174(X1,X2))
| unordered_pair(sK175(X1,X0),sK175(X1,X0)) = sK176(X1,X0) ),
inference(cnf_transformation,[],[f2287]) ).
cnf(c_609,plain,
( ~ in(X0,sK174(X1,X2))
| in(sK175(X1,X0),X1) ),
inference(cnf_transformation,[],[f1831]) ).
cnf(c_610,plain,
( ~ in(X0,sK174(X1,X2))
| unordered_pair(unordered_pair(sK175(X1,X0),sK176(X1,X0)),unordered_pair(sK175(X1,X0),sK175(X1,X0))) = X0 ),
inference(cnf_transformation,[],[f2288]) ).
cnf(c_611,plain,
( ~ in(X0,sK174(X1,X2))
| in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f1829]) ).
cnf(c_612,plain,
( ~ in(unordered_pair(unordered_pair(apply(X0,X1),apply(X0,X2)),unordered_pair(apply(X0,X1),apply(X0,X1))),X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),cartesian_product2(X4,X4))
| ~ function(X0)
| ~ relation(X0)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),sK177(X4,X3,X0)) ),
inference(cnf_transformation,[],[f2483]) ).
cnf(c_613,plain,
( ~ in(X0,sK177(X1,X2,X3))
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(apply(X3,sK178(X2,X3,X0)),apply(X3,sK179(X2,X3,X0))),unordered_pair(apply(X3,sK178(X2,X3,X0)),apply(X3,sK178(X2,X3,X0)))),X2) ),
inference(cnf_transformation,[],[f2290]) ).
cnf(c_614,plain,
( ~ in(X0,sK177(X1,X2,X3))
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X3)
| unordered_pair(unordered_pair(sK178(X2,X3,X0),sK179(X2,X3,X0)),unordered_pair(sK178(X2,X3,X0),sK178(X2,X3,X0))) = X0 ),
inference(cnf_transformation,[],[f2291]) ).
cnf(c_615,plain,
( ~ in(X0,sK177(X1,X2,X3))
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X3)
| in(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f1834]) ).
cnf(c_616,plain,
( ~ in(X0,X1)
| ~ ordinal(X0)
| in(X0,sK180(X1)) ),
inference(cnf_transformation,[],[f1840]) ).
cnf(c_617,plain,
( ~ in(X0,sK180(X1))
| ordinal(X0) ),
inference(cnf_transformation,[],[f1839]) ).
cnf(c_618,plain,
( ~ in(X0,sK180(X1))
| in(X0,X1) ),
inference(cnf_transformation,[],[f1838]) ).
cnf(c_619,plain,
( ~ in(X0,set_union2(X1,unordered_pair(X1,X1)))
| ~ in(X0,X2)
| ~ ordinal(X0)
| ~ ordinal(X1)
| in(X0,sK181(X2,X1)) ),
inference(cnf_transformation,[],[f2484]) ).
cnf(c_620,plain,
( ~ in(X0,sK181(X1,X2))
| ~ ordinal(X2)
| in(sK182(X1,X0),X1) ),
inference(cnf_transformation,[],[f1844]) ).
cnf(c_621,plain,
( ~ in(X0,sK181(X1,X2))
| ~ ordinal(X2)
| sK182(X1,X0) = X0 ),
inference(cnf_transformation,[],[f1843]) ).
cnf(c_622,plain,
( ~ in(X0,sK181(X1,X2))
| ~ ordinal(X2)
| ordinal(sK182(X1,X0)) ),
inference(cnf_transformation,[],[f1842]) ).
cnf(c_623,plain,
( ~ in(X0,sK181(X1,X2))
| ~ ordinal(X2)
| in(X0,set_union2(X2,unordered_pair(X2,X2))) ),
inference(cnf_transformation,[],[f2293]) ).
cnf(c_624,plain,
( sK184(X0) != sK185(X0)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f1849]) ).
cnf(c_625,plain,
( ~ sP10(X0)
| unordered_pair(sK183(X0),sK183(X0)) = sK185(X0) ),
inference(cnf_transformation,[],[f2294]) ).
cnf(c_626,plain,
( ~ sP10(X0)
| unordered_pair(sK183(X0),sK183(X0)) = sK184(X0) ),
inference(cnf_transformation,[],[f2295]) ).
cnf(c_627,plain,
( ~ sP10(X0)
| in(sK183(X0),X0) ),
inference(cnf_transformation,[],[f1846]) ).
cnf(c_628,plain,
( ~ in(X0,X1)
| apply(sK186(X1),X0) = unordered_pair(X0,X0)
| sP10(X1) ),
inference(cnf_transformation,[],[f2485]) ).
cnf(c_630,plain,
( relation_dom(sK186(X0)) = X0
| sP10(X0) ),
inference(cnf_transformation,[],[f2486]) ).
cnf(c_632,plain,
( function(sK186(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f2487]) ).
cnf(c_634,plain,
( relation(sK186(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f2488]) ).
cnf(c_636,negated_conjecture,
( unordered_pair(sK189(X0),sK189(X0)) != apply(X0,sK189(X0))
| relation_dom(X0) != sK188
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2301]) ).
cnf(c_637,negated_conjecture,
( relation_dom(X0) != sK188
| ~ function(X0)
| ~ relation(X0)
| in(sK189(X0),sK188) ),
inference(cnf_transformation,[],[f1858]) ).
cnf(c_638,plain,
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f1860]) ).
cnf(c_639,plain,
( ~ equipotent(X0,X1)
| equipotent(X1,X0) ),
inference(cnf_transformation,[],[f1861]) ).
cnf(c_640,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),cartesian_product2(X3,X1)) ),
inference(cnf_transformation,[],[f2302]) ).
cnf(c_641,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f2303]) ).
cnf(c_642,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f2304]) ).
cnf(c_643,plain,
in(X0,set_union2(X0,unordered_pair(X0,X0))),
inference(cnf_transformation,[],[f2305]) ).
cnf(c_644,plain,
( unordered_pair(X0,X1) != unordered_pair(X2,X3)
| X0 = X2
| X0 = X3 ),
inference(cnf_transformation,[],[f1866]) ).
cnf(c_645,plain,
( ~ in(X0,relation_rng(X1))
| ~ in(X0,X2)
| ~ relation(X1)
| in(X0,relation_rng(relation_rng_restriction(X2,X1))) ),
inference(cnf_transformation,[],[f1869]) ).
cnf(c_646,plain,
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2)
| in(X0,relation_rng(X2)) ),
inference(cnf_transformation,[],[f1868]) ).
cnf(c_647,plain,
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2)
| in(X0,X1) ),
inference(cnf_transformation,[],[f1867]) ).
cnf(c_648,plain,
( ~ relation(X0)
| subset(relation_rng(relation_rng_restriction(X1,X0)),X1) ),
inference(cnf_transformation,[],[f1870]) ).
cnf(c_649,plain,
( ~ relation(X0)
| subset(relation_rng_restriction(X1,X0),X0) ),
inference(cnf_transformation,[],[f1871]) ).
cnf(c_650,plain,
( ~ relation(X0)
| subset(relation_rng(relation_rng_restriction(X1,X0)),relation_rng(X0)) ),
inference(cnf_transformation,[],[f1872]) ).
cnf(c_651,plain,
( ~ subset(X0,X1)
| subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
inference(cnf_transformation,[],[f1874]) ).
cnf(c_652,plain,
( ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f1873]) ).
cnf(c_653,plain,
( ~ relation(X0)
| set_difference(relation_rng(X0),set_difference(relation_rng(X0),X1)) = relation_rng(relation_rng_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f2306]) ).
cnf(c_654,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X3)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(cnf_transformation,[],[f1876]) ).
cnf(c_655,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| subset(relation_rng(X0),X2) ),
inference(cnf_transformation,[],[f1878]) ).
cnf(c_656,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| subset(relation_dom(X0),X1) ),
inference(cnf_transformation,[],[f1877]) ).
cnf(c_657,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f1879]) ).
cnf(c_658,plain,
( ~ subset(X0,sK190(X1))
| in(X0,sK190(X1))
| are_equipotent(X0,sK190(X1)) ),
inference(cnf_transformation,[],[f1883]) ).
cnf(c_659,plain,
( ~ in(X0,sK190(X1))
| in(powerset(X0),sK190(X1)) ),
inference(cnf_transformation,[],[f1882]) ).
cnf(c_660,plain,
( ~ in(X0,sK190(X1))
| ~ subset(X2,X0)
| in(X2,sK190(X1)) ),
inference(cnf_transformation,[],[f1881]) ).
cnf(c_661,plain,
in(X0,sK190(X0)),
inference(cnf_transformation,[],[f1880]) ).
cnf(c_662,plain,
( ~ relation(X0)
| relation_dom_restriction(relation_rng_restriction(X1,X0),X2) = relation_rng_restriction(X1,relation_dom_restriction(X0,X2)) ),
inference(cnf_transformation,[],[f1884]) ).
cnf(c_664,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ relation(X1)
| in(sK191(X0,X2,X1),X2) ),
inference(cnf_transformation,[],[f1887]) ).
cnf(c_665,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK191(X0,X2,X1),X0),unordered_pair(sK191(X0,X2,X1),sK191(X0,X2,X1))),X1) ),
inference(cnf_transformation,[],[f2308]) ).
cnf(c_666,plain,
( ~ in(X0,relation_image(X1,X2))
| ~ relation(X1)
| in(sK191(X0,X2,X1),relation_dom(X1)) ),
inference(cnf_transformation,[],[f1885]) ).
cnf(c_667,plain,
( ~ relation(X0)
| subset(relation_image(X0,X1),relation_rng(X0)) ),
inference(cnf_transformation,[],[f1889]) ).
cnf(c_668,plain,
( ~ function(X0)
| ~ relation(X0)
| subset(relation_image(X0,relation_inverse_image(X0,X1)),X1) ),
inference(cnf_transformation,[],[f1890]) ).
cnf(c_669,plain,
( ~ relation(X0)
| relation_image(X0,set_difference(relation_dom(X0),set_difference(relation_dom(X0),X1))) = relation_image(X0,X1) ),
inference(cnf_transformation,[],[f2309]) ).
cnf(c_670,plain,
( ~ subset(X0,relation_dom(X1))
| ~ relation(X1)
| subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ),
inference(cnf_transformation,[],[f1892]) ).
cnf(c_671,plain,
( ~ relation(X0)
| relation_image(X0,relation_dom(X0)) = relation_rng(X0) ),
inference(cnf_transformation,[],[f1893]) ).
cnf(c_672,plain,
( ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| relation_image(X1,relation_inverse_image(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f1894]) ).
cnf(c_673,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ subset(relation_rng(X0),X3)
| relation_of2_as_subset(X0,X1,X3) ),
inference(cnf_transformation,[],[f1895]) ).
cnf(c_674,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation_image(X0,relation_rng(X1)) = relation_rng(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f1896]) ).
cnf(c_676,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| in(sK192(X0,X2,X1),X2) ),
inference(cnf_transformation,[],[f1899]) ).
cnf(c_677,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,sK192(X0,X2,X1)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f2311]) ).
cnf(c_678,plain,
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| in(sK192(X0,X2,X1),relation_rng(X1)) ),
inference(cnf_transformation,[],[f1897]) ).
cnf(c_679,plain,
( ~ relation(X0)
| subset(relation_inverse_image(X0,X1),relation_dom(X0)) ),
inference(cnf_transformation,[],[f1901]) ).
cnf(c_680,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ subset(X2,X3)
| relation_of2_as_subset(X0,X1,X3) ),
inference(cnf_transformation,[],[f1902]) ).
cnf(c_681,plain,
( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| ~ relation(X2)
| in(X0,relation_restriction(X2,X1)) ),
inference(cnf_transformation,[],[f1905]) ).
cnf(c_682,plain,
( ~ in(X0,relation_restriction(X1,X2))
| ~ relation(X1)
| in(X0,cartesian_product2(X2,X2)) ),
inference(cnf_transformation,[],[f1904]) ).
cnf(c_683,plain,
( ~ in(X0,relation_restriction(X1,X2))
| ~ relation(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f1903]) ).
cnf(c_684,plain,
( relation_inverse_image(X0,X1) != empty_set
| ~ subset(X1,relation_rng(X0))
| ~ relation(X0)
| X1 = empty_set ),
inference(cnf_transformation,[],[f1906]) ).
cnf(c_685,plain,
( ~ subset(X0,X1)
| ~ relation(X2)
| subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(cnf_transformation,[],[f1907]) ).
cnf(c_686,plain,
( ~ relation(X0)
| relation_dom_restriction(relation_rng_restriction(X1,X0),X1) = relation_restriction(X0,X1) ),
inference(cnf_transformation,[],[f1908]) ).
cnf(c_688,plain,
( ~ relation(X0)
| relation_rng_restriction(X1,relation_dom_restriction(X0,X1)) = relation_restriction(X0,X1) ),
inference(cnf_transformation,[],[f1910]) ).
cnf(c_689,plain,
( ~ in(X0,relation_field(relation_restriction(X1,X2)))
| ~ relation(X1)
| in(X0,X2) ),
inference(cnf_transformation,[],[f1912]) ).
cnf(c_690,plain,
( ~ in(X0,relation_field(relation_restriction(X1,X2)))
| ~ relation(X1)
| in(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f1911]) ).
cnf(c_691,plain,
( ~ subset(X0,X1)
| ~ subset(X0,X2)
| subset(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(cnf_transformation,[],[f2313]) ).
cnf(c_692,plain,
set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f1914]) ).
cnf(c_693,plain,
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f1915]) ).
cnf(c_694,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X0)
| subset(X2,X1) ),
inference(cnf_transformation,[],[f1916]) ).
cnf(c_695,plain,
unordered_pair(empty_set,empty_set) = powerset(empty_set),
inference(cnf_transformation,[],[f2314]) ).
cnf(c_696,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(cnf_transformation,[],[f2315]) ).
cnf(c_697,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f2316]) ).
cnf(c_698,plain,
( ~ relation(X0)
| subset(relation_field(relation_restriction(X0,X1)),X1) ),
inference(cnf_transformation,[],[f1921]) ).
cnf(c_699,plain,
( ~ relation(X0)
| subset(relation_field(relation_restriction(X0,X1)),relation_field(X0)) ),
inference(cnf_transformation,[],[f1920]) ).
cnf(c_700,plain,
( ~ in(apply(X0,X1),relation_dom(X2))
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ function(X2)
| ~ relation(X0)
| ~ relation(X2)
| in(X1,relation_dom(relation_composition(X0,X2))) ),
inference(cnf_transformation,[],[f1924]) ).
cnf(c_701,plain,
( ~ in(X0,relation_dom(relation_composition(X1,X2)))
| ~ function(X1)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X2)
| in(apply(X1,X0),relation_dom(X2)) ),
inference(cnf_transformation,[],[f1923]) ).
cnf(c_702,plain,
( ~ in(X0,relation_dom(relation_composition(X1,X2)))
| ~ function(X1)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X2)
| in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f1922]) ).
cnf(c_703,plain,
( ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0)
| in(X0,X1) ),
inference(cnf_transformation,[],[f1925]) ).
cnf(c_704,plain,
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(cnf_transformation,[],[f1926]) ).
cnf(c_705,plain,
( ~ relation(X0)
| subset(fiber(relation_restriction(X0,X1),X2),fiber(X0,X2)) ),
inference(cnf_transformation,[],[f1927]) ).
cnf(c_706,plain,
( ~ in(X0,relation_dom(relation_composition(X1,X2)))
| ~ function(X1)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X2)
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf_transformation,[],[f1928]) ).
cnf(c_707,plain,
( relation_dom_as_subset(X0,X1,X2) != X0
| ~ relation_of2_as_subset(X2,X0,X1)
| ~ in(X3,X0)
| in(unordered_pair(unordered_pair(X3,sK193(X2,X3)),unordered_pair(X3,X3)),X2) ),
inference(cnf_transformation,[],[f2317]) ).
cnf(c_708,plain,
( ~ in(unordered_pair(unordered_pair(sK194(X0,X1),X2),unordered_pair(sK194(X0,X1),sK194(X0,X1))),X1)
| ~ relation_of2_as_subset(X1,X0,X3)
| relation_dom_as_subset(X0,X3,X1) = X0 ),
inference(cnf_transformation,[],[f2318]) ).
cnf(c_709,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_dom_as_subset(X1,X2,X0) = X1
| in(sK194(X1,X0),X1) ),
inference(cnf_transformation,[],[f1929]) ).
cnf(c_710,plain,
( ~ relation(X0)
| ~ reflexive(X0)
| reflexive(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f1932]) ).
cnf(c_711,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X2)
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf_transformation,[],[f1933]) ).
cnf(c_712,plain,
( ~ in(X0,X1)
| ~ ordinal(X1)
| ordinal(X0) ),
inference(cnf_transformation,[],[f1934]) ).
cnf(c_713,plain,
( relation_rng_as_subset(X0,X1,X2) != X1
| ~ relation_of2_as_subset(X2,X0,X1)
| ~ in(X3,X1)
| in(unordered_pair(unordered_pair(sK195(X2,X3),X3),unordered_pair(sK195(X2,X3),sK195(X2,X3))),X2) ),
inference(cnf_transformation,[],[f2319]) ).
cnf(c_714,plain,
( ~ in(unordered_pair(unordered_pair(X0,sK196(X1,X2)),unordered_pair(X0,X0)),X2)
| ~ relation_of2_as_subset(X2,X3,X1)
| relation_rng_as_subset(X3,X1,X2) = X1 ),
inference(cnf_transformation,[],[f2320]) ).
cnf(c_715,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_rng_as_subset(X1,X2,X0) = X2
| in(sK196(X2,X0),X2) ),
inference(cnf_transformation,[],[f1935]) ).
cnf(c_716,plain,
( ~ relation(X0)
| ~ connected(X0)
| connected(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f1938]) ).
cnf(c_717,plain,
( ~ ordinal(X0)
| ~ ordinal(X1)
| X0 = X1
| in(X0,X1)
| in(X1,X0) ),
inference(cnf_transformation,[],[f1939]) ).
cnf(c_718,plain,
( ~ relation(X0)
| ~ transitive(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f1940]) ).
cnf(c_719,plain,
( ~ subset(X0,X1)
| ~ relation(X0)
| ~ relation(X1)
| subset(relation_rng(X0),relation_rng(X1)) ),
inference(cnf_transformation,[],[f1942]) ).
cnf(c_720,plain,
( ~ subset(X0,X1)
| ~ relation(X0)
| ~ relation(X1)
| subset(relation_dom(X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f1941]) ).
cnf(c_721,plain,
( ~ relation(X0)
| ~ antisymmetric(X0)
| antisymmetric(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f1943]) ).
cnf(c_722,plain,
( ~ well_orders(X0,X1)
| ~ relation(X0)
| well_ordering(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f1945]) ).
cnf(c_723,plain,
( ~ well_orders(X0,X1)
| ~ relation(X0)
| relation_field(relation_restriction(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f1944]) ).
cnf(c_724,plain,
( ~ subset(X0,X1)
| subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2))) ),
inference(cnf_transformation,[],[f2321]) ).
cnf(c_725,plain,
( ~ subset(X0,X1)
| set_difference(X0,set_difference(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f2322]) ).
cnf(c_726,plain,
set_difference(X0,set_difference(X0,empty_set)) = empty_set,
inference(cnf_transformation,[],[f2323]) ).
cnf(c_727,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f1949]) ).
cnf(c_728,plain,
( ~ in(sK197(X0,X1),X0)
| ~ in(sK197(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1951]) ).
cnf(c_729,plain,
( X0 = X1
| in(sK197(X0,X1),X0)
| in(sK197(X0,X1),X1) ),
inference(cnf_transformation,[],[f1950]) ).
cnf(c_730,plain,
reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f1952]) ).
cnf(c_731,plain,
subset(empty_set,X0),
inference(cnf_transformation,[],[f1953]) ).
cnf(c_732,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| in(X1,relation_field(X2)) ),
inference(cnf_transformation,[],[f2324]) ).
cnf(c_733,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f2325]) ).
cnf(c_734,plain,
( ~ subset(sK198(X0),X0)
| ~ ordinal(sK198(X0))
| ordinal(X0) ),
inference(cnf_transformation,[],[f1957]) ).
cnf(c_735,plain,
( in(sK198(X0),X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f1956]) ).
cnf(c_736,plain,
( ~ relation(X0)
| ~ well_founded_relation(X0)
| well_founded_relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f1958]) ).
cnf(c_737,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| ~ ordinal(X0)
| ~ ordinal(X2)
| X1 = empty_set
| ordinal_subset(sK199(X1),X0) ),
inference(cnf_transformation,[],[f1961]) ).
cnf(c_738,plain,
( ~ subset(X0,X1)
| ~ ordinal(X1)
| X0 = empty_set
| in(sK199(X0),X0) ),
inference(cnf_transformation,[],[f1960]) ).
cnf(c_739,plain,
( ~ subset(X0,X1)
| ~ ordinal(X1)
| X0 = empty_set
| ordinal(sK199(X0)) ),
inference(cnf_transformation,[],[f1959]) ).
cnf(c_740,plain,
( ~ relation(X0)
| ~ well_ordering(X0)
| well_ordering(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f1962]) ).
cnf(c_741,plain,
( ~ ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f2326]) ).
cnf(c_742,plain,
( ~ in(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f2327]) ).
cnf(c_743,plain,
( ~ subset(X0,X1)
| subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f1965]) ).
cnf(c_744,plain,
( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| X1 = X3 ),
inference(cnf_transformation,[],[f2328]) ).
cnf(c_745,plain,
( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| X0 = X2 ),
inference(cnf_transformation,[],[f2329]) ).
cnf(c_746,plain,
( apply(X0,sK200(relation_dom(X0),X0)) != sK200(relation_dom(X0),X0)
| ~ function(X0)
| ~ relation(X0)
| identity_relation(relation_dom(X0)) = X0 ),
inference(cnf_transformation,[],[f2489]) ).
cnf(c_747,plain,
( ~ function(X0)
| ~ relation(X0)
| identity_relation(relation_dom(X0)) = X0
| in(sK200(relation_dom(X0),X0),relation_dom(X0)) ),
inference(cnf_transformation,[],[f2490]) ).
cnf(c_750,plain,
( ~ in(X0,X1)
| apply(identity_relation(X1),X0) = X0 ),
inference(cnf_transformation,[],[f1972]) ).
cnf(c_751,plain,
subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f1973]) ).
cnf(c_752,plain,
( ~ relation(X0)
| relation_rng(relation_inverse(X0)) = relation_dom(X0) ),
inference(cnf_transformation,[],[f1975]) ).
cnf(c_753,plain,
( ~ relation(X0)
| relation_dom(relation_inverse(X0)) = relation_rng(X0) ),
inference(cnf_transformation,[],[f1974]) ).
cnf(c_754,plain,
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f1977]) ).
cnf(c_755,plain,
( set_difference(X0,X1) != empty_set
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1976]) ).
cnf(c_756,plain,
( ~ in(X0,X1)
| subset(unordered_pair(X0,X0),X1) ),
inference(cnf_transformation,[],[f2330]) ).
cnf(c_758,plain,
( ~ in(X0,X1)
| ~ in(X2,X1)
| subset(unordered_pair(X2,X0),X1) ),
inference(cnf_transformation,[],[f1982]) ).
cnf(c_759,plain,
( ~ subset(unordered_pair(X0,X1),X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f1981]) ).
cnf(c_760,plain,
( ~ subset(unordered_pair(X0,X1),X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f1980]) ).
cnf(c_761,plain,
( ~ subset(X0,relation_field(X1))
| ~ relation(X1)
| ~ well_ordering(X1)
| relation_field(relation_restriction(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f1983]) ).
cnf(c_762,plain,
set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
inference(cnf_transformation,[],[f1984]) ).
cnf(c_765,plain,
( ~ subset(X0,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = X0
| X0 = empty_set ),
inference(cnf_transformation,[],[f2334]) ).
cnf(c_766,plain,
set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f1988]) ).
cnf(c_767,plain,
( ~ in(X0,X1)
| ~ in(X1,X2)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f1989]) ).
cnf(c_768,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1991]) ).
cnf(c_769,plain,
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1990]) ).
cnf(c_770,plain,
transitive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f1992]) ).
cnf(c_771,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ disjoint(X2,X1) ),
inference(cnf_transformation,[],[f1995]) ).
cnf(c_772,plain,
( in(sK201(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1994]) ).
cnf(c_773,plain,
( in(sK201(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1993]) ).
cnf(c_774,plain,
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(cnf_transformation,[],[f1996]) ).
cnf(c_775,plain,
set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[],[f1997]) ).
cnf(c_776,plain,
( ~ in(set_union2(sK202(X0),unordered_pair(sK202(X0),sK202(X0))),X0)
| ~ ordinal(X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f2335]) ).
cnf(c_777,plain,
( ~ ordinal(X0)
| in(sK202(X0),X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f2000]) ).
cnf(c_778,plain,
( ~ ordinal(X0)
| ordinal(sK202(X0))
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1999]) ).
cnf(c_779,plain,
( ~ in(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| in(set_union2(X0,unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f2336]) ).
cnf(c_780,plain,
( ~ ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ being_limit_ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2495]) ).
cnf(c_781,plain,
( ~ ordinal(X0)
| set_union2(sK203(X0),unordered_pair(sK203(X0),sK203(X0))) = X0
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f2338]) ).
cnf(c_782,plain,
( ~ ordinal(X0)
| ordinal(sK203(X0))
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f2002]) ).
cnf(c_783,plain,
( ~ subset(X0,subset_complement(X1,X2))
| ~ element(X0,powerset(X1))
| ~ element(X2,powerset(X1))
| disjoint(X0,X2) ),
inference(cnf_transformation,[],[f2006]) ).
cnf(c_784,plain,
( ~ element(X0,powerset(X1))
| ~ element(X2,powerset(X1))
| ~ disjoint(X0,X2)
| subset(X0,subset_complement(X1,X2)) ),
inference(cnf_transformation,[],[f2005]) ).
cnf(c_785,plain,
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_dom(relation_composition(X1,X0)),relation_dom(X1)) ),
inference(cnf_transformation,[],[f2007]) ).
cnf(c_786,plain,
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_rng(relation_composition(X1,X0)),relation_rng(X0)) ),
inference(cnf_transformation,[],[f2008]) ).
cnf(c_787,plain,
( ~ subset(X0,X1)
| set_union2(X0,set_difference(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f2009]) ).
cnf(c_788,plain,
( ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X0)
| ~ relation(X1)
| relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ),
inference(cnf_transformation,[],[f2010]) ).
cnf(c_789,plain,
( complements_of_subsets(X0,X1) != empty_set
| ~ element(X1,powerset(powerset(X0)))
| X1 = empty_set ),
inference(cnf_transformation,[],[f2011]) ).
cnf(c_790,plain,
( ~ in(X0,X1)
| set_union2(unordered_pair(X0,X0),X1) = X1 ),
inference(cnf_transformation,[],[f2339]) ).
cnf(c_791,plain,
( ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X0)
| ~ relation(X1)
| relation_rng(relation_composition(X1,X0)) = relation_rng(X0) ),
inference(cnf_transformation,[],[f2013]) ).
cnf(c_792,plain,
( ~ element(X0,powerset(powerset(X1)))
| subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X0)) = meet_of_subsets(X1,complements_of_subsets(X1,X0))
| X0 = empty_set ),
inference(cnf_transformation,[],[f2014]) ).
cnf(c_793,plain,
( ~ element(X0,powerset(powerset(X1)))
| subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X0)) = union_of_subsets(X1,complements_of_subsets(X1,X0))
| X0 = empty_set ),
inference(cnf_transformation,[],[f2015]) ).
cnf(c_794,plain,
( ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_isomorphism(X1,X0,function_inverse(X2)) ),
inference(cnf_transformation,[],[f2017]) ).
cnf(c_795,plain,
set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[],[f2018]) ).
cnf(c_796,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| element(X2,X1) ),
inference(cnf_transformation,[],[f2019]) ).
cnf(c_797,plain,
( ~ ordinal(X0)
| connected(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f2020]) ).
cnf(c_798,plain,
( ~ in(X0,set_difference(X1,set_difference(X1,X2)))
| ~ disjoint(X1,X2) ),
inference(cnf_transformation,[],[f2340]) ).
cnf(c_799,plain,
( in(sK204(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f2341]) ).
cnf(c_800,plain,
( ~ element(X0,powerset(X1))
| ~ element(X2,X1)
| X1 = empty_set
| in(X2,subset_complement(X1,X0))
| in(X2,X0) ),
inference(cnf_transformation,[],[f2023]) ).
cnf(c_801,plain,
( ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ well_founded_relation(X0)
| well_founded_relation(X1) ),
inference(cnf_transformation,[],[f2028]) ).
cnf(c_802,plain,
( ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ antisymmetric(X0)
| antisymmetric(X1) ),
inference(cnf_transformation,[],[f2027]) ).
cnf(c_803,plain,
( ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ connected(X0)
| connected(X1) ),
inference(cnf_transformation,[],[f2026]) ).
cnf(c_804,plain,
( ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ transitive(X0)
| transitive(X1) ),
inference(cnf_transformation,[],[f2025]) ).
cnf(c_805,plain,
( ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ reflexive(X0)
| reflexive(X1) ),
inference(cnf_transformation,[],[f2024]) ).
cnf(c_806,plain,
( ~ in(X0,relation_dom(X1))
| sP11(apply(X1,X0),X0,X1,X2) ),
inference(cnf_transformation,[],[f2496]) ).
cnf(c_807,plain,
( apply(X0,X1) = X2
| sP11(X1,X2,X3,X0) ),
inference(cnf_transformation,[],[f2032]) ).
cnf(c_808,plain,
( sP11(X0,X1,X2,X3)
| in(X0,relation_rng(X2)) ),
inference(cnf_transformation,[],[f2031]) ).
cnf(c_809,plain,
( ~ sP11(X0,apply(X1,X0),X2,X1)
| ~ in(X0,relation_rng(X2))
| apply(X2,apply(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f2497]) ).
cnf(c_810,plain,
( ~ sP11(X0,apply(X1,X0),X2,X1)
| ~ in(X0,relation_rng(X2))
| in(apply(X1,X0),relation_dom(X2)) ),
inference(cnf_transformation,[],[f2498]) ).
cnf(c_811,plain,
( apply(X0,sK205(X1,X0)) != sK206(X1,X0)
| relation_dom(X0) != relation_rng(X1)
| ~ sP11(sK205(X1,X0),sK206(X1,X0),X1,X0)
| ~ in(sK205(X1,X0),relation_rng(X1))
| ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ one_to_one(X1)
| function_inverse(X1) = X0 ),
inference(cnf_transformation,[],[f2040]) ).
cnf(c_812,plain,
( relation_dom(X0) != relation_rng(X1)
| ~ sP11(sK205(X1,X0),sK206(X1,X0),X1,X0)
| ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ one_to_one(X1)
| apply(X1,sK206(X1,X0)) = sK205(X1,X0)
| function_inverse(X1) = X0 ),
inference(cnf_transformation,[],[f2039]) ).
cnf(c_813,plain,
( relation_dom(X0) != relation_rng(X1)
| ~ sP11(sK205(X1,X0),sK206(X1,X0),X1,X0)
| ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ one_to_one(X1)
| function_inverse(X1) = X0
| in(sK206(X1,X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f2038]) ).
cnf(c_814,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(function_inverse(X1))
| ~ relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| apply(function_inverse(X1),apply(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f2500]) ).
cnf(c_816,plain,
( ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| sP11(X1,X2,X0,function_inverse(X0)) ),
inference(cnf_transformation,[],[f2503]) ).
cnf(c_818,plain,
( ~ in(X0,subset_complement(X1,X2))
| ~ element(X2,powerset(X1))
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f2041]) ).
cnf(c_819,plain,
( ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ well_ordering(X0)
| well_ordering(X1) ),
inference(cnf_transformation,[],[f2042]) ).
cnf(c_820,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_rng(function_inverse(X0)) = relation_dom(X0) ),
inference(cnf_transformation,[],[f2044]) ).
cnf(c_821,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_dom(function_inverse(X0)) = relation_rng(X0) ),
inference(cnf_transformation,[],[f2043]) ).
cnf(c_822,plain,
( ~ relation(X0)
| X0 = empty_set
| in(unordered_pair(unordered_pair(sK207(X0),sK208(X0)),unordered_pair(sK207(X0),sK207(X0))),X0) ),
inference(cnf_transformation,[],[f2342]) ).
cnf(c_823,plain,
( ~ in(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| apply(relation_composition(function_inverse(X1),X1),X0) = X0 ),
inference(cnf_transformation,[],[f2047]) ).
cnf(c_824,plain,
( ~ in(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| apply(X1,apply(function_inverse(X1),X0)) = X0 ),
inference(cnf_transformation,[],[f2046]) ).
cnf(c_825,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f2048]) ).
cnf(c_826,plain,
( ~ is_well_founded_in(X0,relation_field(X0))
| ~ relation(X0)
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f2050]) ).
cnf(c_827,plain,
( ~ relation(X0)
| ~ well_founded_relation(X0)
| is_well_founded_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f2049]) ).
cnf(c_828,plain,
antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[],[f2051]) ).
cnf(c_829,plain,
relation_rng(empty_set) = empty_set,
inference(cnf_transformation,[],[f2053]) ).
cnf(c_830,plain,
relation_dom(empty_set) = empty_set,
inference(cnf_transformation,[],[f2052]) ).
cnf(c_831,plain,
( ~ proper_subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f2054]) ).
cnf(c_832,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| one_to_one(function_inverse(X0)) ),
inference(cnf_transformation,[],[f2055]) ).
cnf(c_833,plain,
( ~ subset(X0,X1)
| ~ disjoint(X1,X2)
| disjoint(X0,X2) ),
inference(cnf_transformation,[],[f2056]) ).
cnf(c_834,plain,
( relation_rng(X0) != empty_set
| ~ relation(X0)
| X0 = empty_set ),
inference(cnf_transformation,[],[f2058]) ).
cnf(c_835,plain,
( relation_dom(X0) != empty_set
| ~ relation(X0)
| X0 = empty_set ),
inference(cnf_transformation,[],[f2057]) ).
cnf(c_836,plain,
( relation_rng(X0) != empty_set
| ~ relation(X0)
| relation_dom(X0) = empty_set ),
inference(cnf_transformation,[],[f2060]) ).
cnf(c_837,plain,
( relation_dom(X0) != empty_set
| ~ relation(X0)
| relation_rng(X0) = empty_set ),
inference(cnf_transformation,[],[f2059]) ).
cnf(c_838,plain,
( set_difference(X0,unordered_pair(X1,X1)) = X0
| in(X1,X0) ),
inference(cnf_transformation,[],[f2343]) ).
cnf(c_839,plain,
( set_difference(X0,unordered_pair(X1,X1)) != X0
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f2344]) ).
cnf(c_840,plain,
( set_difference(relation_dom(X1),set_difference(relation_dom(X1),X2)) != relation_dom(X0)
| apply(X0,sK209(X0,X1)) != apply(X1,sK209(X0,X1))
| ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| relation_dom_restriction(X1,X2) = X0 ),
inference(cnf_transformation,[],[f2345]) ).
cnf(c_841,plain,
( set_difference(relation_dom(X0),set_difference(relation_dom(X0),X1)) != relation_dom(X2)
| ~ function(X0)
| ~ function(X2)
| ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) = X2
| in(sK209(X2,X0),relation_dom(X2)) ),
inference(cnf_transformation,[],[f2346]) ).
cnf(c_844,plain,
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[],[f2068]) ).
cnf(c_845,plain,
( ~ ordinal(X0)
| well_founded_relation(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f2069]) ).
cnf(c_846,plain,
( ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f2348]) ).
cnf(c_847,plain,
( ~ in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) ),
inference(cnf_transformation,[],[f2071]) ).
cnf(c_848,plain,
relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f2073]) ).
cnf(c_849,plain,
relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f2072]) ).
cnf(c_850,plain,
( ~ in(X0,X1)
| ~ function(X2)
| ~ relation(X2)
| apply(relation_dom_restriction(X2,X1),X0) = apply(X2,X0) ),
inference(cnf_transformation,[],[f2074]) ).
cnf(c_851,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ in(X0,X3)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X3),X2)) ),
inference(cnf_transformation,[],[f2349]) ).
cnf(c_852,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3) ),
inference(cnf_transformation,[],[f2350]) ).
cnf(c_853,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3)
| in(X0,X2) ),
inference(cnf_transformation,[],[f2351]) ).
cnf(c_854,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f2078]) ).
cnf(c_855,plain,
pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X1,
inference(cnf_transformation,[],[f2352]) ).
cnf(c_856,plain,
pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X0,
inference(cnf_transformation,[],[f2353]) ).
cnf(c_857,plain,
( ~ in(X0,sK210(X1))
| ~ in(X0,X1)
| ~ in(X2,X1) ),
inference(cnf_transformation,[],[f2082]) ).
cnf(c_858,plain,
( ~ in(X0,X1)
| in(sK210(X1),X1) ),
inference(cnf_transformation,[],[f2081]) ).
cnf(c_859,plain,
( ~ ordinal(X0)
| well_ordering(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f2083]) ).
cnf(c_860,plain,
subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f2084]) ).
cnf(c_861,plain,
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f2086]) ).
cnf(c_862,plain,
( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 ),
inference(cnf_transformation,[],[f2085]) ).
cnf(c_863,plain,
( ~ in(X0,relation_dom(X1))
| ~ in(X0,X2)
| ~ relation(X1)
| in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f2089]) ).
cnf(c_864,plain,
( ~ in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ relation(X1)
| in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f2088]) ).
cnf(c_865,plain,
( ~ in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ relation(X1)
| in(X0,X2) ),
inference(cnf_transformation,[],[f2087]) ).
cnf(c_866,plain,
( ~ relation(X0)
| subset(relation_dom_restriction(X0,X1),X0) ),
inference(cnf_transformation,[],[f2090]) ).
cnf(c_867,plain,
( ~ empty(X0)
| ~ empty(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f2091]) ).
cnf(c_868,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,apply(X1,X0)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f2507]) ).
cnf(c_869,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) = X1 ),
inference(cnf_transformation,[],[f2355]) ).
cnf(c_871,plain,
( ~ relation(X0)
| ~ well_ordering(X0)
| well_orders(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f2096]) ).
cnf(c_872,plain,
( ~ well_orders(X0,relation_field(X0))
| ~ relation(X0)
| well_ordering(X0) ),
inference(cnf_transformation,[],[f2095]) ).
cnf(c_873,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| subset(set_union2(X0,X2),X1) ),
inference(cnf_transformation,[],[f2097]) ).
cnf(c_874,plain,
( unordered_pair(X0,X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f2357]) ).
cnf(c_875,plain,
( ~ relation(X0)
| set_difference(relation_dom(X0),set_difference(relation_dom(X0),X1)) = relation_dom(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f2358]) ).
cnf(c_876,plain,
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(cnf_transformation,[],[f2100]) ).
cnf(c_877,plain,
( ~ relation(X0)
| relation_composition(identity_relation(X1),X0) = relation_dom_restriction(X0,X1) ),
inference(cnf_transformation,[],[f2101]) ).
cnf(c_878,plain,
( ~ relation(X0)
| subset(relation_rng(relation_dom_restriction(X0,X1)),relation_rng(X0)) ),
inference(cnf_transformation,[],[f2102]) ).
cnf(c_879,plain,
union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f2103]) ).
cnf(c_880,plain,
( ~ subset(X0,sK211(X1))
| in(X0,sK211(X1))
| are_equipotent(X0,sK211(X1)) ),
inference(cnf_transformation,[],[f2108]) ).
cnf(c_881,plain,
( ~ in(X0,sK211(X1))
| ~ subset(X2,X0)
| in(X2,sK212(X1,X0)) ),
inference(cnf_transformation,[],[f2107]) ).
cnf(c_882,plain,
( ~ in(X0,sK211(X1))
| in(sK212(X1,X0),sK211(X1)) ),
inference(cnf_transformation,[],[f2106]) ).
cnf(c_883,plain,
( ~ in(X0,sK211(X1))
| ~ subset(X2,X0)
| in(X2,sK211(X1)) ),
inference(cnf_transformation,[],[f2105]) ).
cnf(c_884,plain,
in(X0,sK211(X0)),
inference(cnf_transformation,[],[f2104]) ).
cnf(c_885,plain,
( unordered_pair(X0,X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f2359]) ).
cnf(c_1420,plain,
( ~ relation(X0)
| relation(relation_rng_restriction(X1,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_418,c_366]) ).
cnf(c_1426,plain,
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_379,c_364]) ).
cnf(c_1428,plain,
relation_field(inclusion_relation(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_165,c_350,c_165]) ).
cnf(c_1431,plain,
( ~ empty(X0)
| one_to_one(X0) ),
inference(global_subsumption_just,[status(thm)],[c_56,c_54,c_51,c_56]) ).
cnf(c_1435,plain,
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_401,c_356]) ).
cnf(c_1441,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X1,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_381,c_358]) ).
cnf(c_1443,plain,
( ~ being_limit_ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(global_subsumption_just,[status(thm)],[c_780,c_402,c_780]) ).
cnf(c_1446,plain,
( ~ in(X0,X1)
| ~ ordinal(X1)
| ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1) ),
inference(global_subsumption_just,[status(thm)],[c_742,c_712,c_742]) ).
cnf(c_1456,plain,
( ~ in(X0,X1)
| ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| in(set_union2(X0,unordered_pair(X0,X0)),X1) ),
inference(global_subsumption_just,[status(thm)],[c_779,c_712,c_779]) ).
cnf(c_1460,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| sP11(X1,X2,X0,function_inverse(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_816,c_352,c_351,c_816]) ).
cnf(c_1561,plain,
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ subset(X2,X0)
| in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),inclusion_relation(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_163,c_350]) ).
cnf(c_1562,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),inclusion_relation(X2))
| ~ in(X0,X2)
| ~ in(X1,X2)
| subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_164,c_350]) ).
cnf(c_1565,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2))
| X0 = X1 ),
inference(backward_subsumption_resolution,[status(thm)],[c_69,c_361]) ).
cnf(c_1566,plain,
( ~ in(X0,X1)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),identity_relation(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_68,c_361]) ).
cnf(c_1567,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2))
| in(X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_70,c_361]) ).
cnf(c_1824,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_inverse(X2))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_306,c_1435]) ).
cnf(c_1825,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),relation_inverse(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_305,c_1435]) ).
cnf(c_1916,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3))
| ~ relation(X3)
| in(X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_93,c_1420]) ).
cnf(c_1917,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3))
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_92,c_1420]) ).
cnf(c_1918,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ in(X1,X3)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X3,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_91,c_1420]) ).
cnf(c_1925,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| in(X0,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_79,c_1426]) ).
cnf(c_1926,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_78,c_1426]) ).
cnf(c_1927,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ 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_77,c_1426]) ).
cnf(c_2462,plain,
( ~ in(subset_complement(X0,X1),X2)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(X0))
| in(X1,complements_of_subsets(X0,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_344,c_365]) ).
cnf(c_2463,plain,
( ~ in(X0,complements_of_subsets(X1,X2))
| ~ element(X2,powerset(powerset(X1)))
| ~ element(X0,powerset(X1))
| in(subset_complement(X1,X0),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_345,c_365]) ).
cnf(c_2546,plain,
( ~ in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),cartesian_product2(X1,X2))
| in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK146(X1,X2))
| sP5(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_564,c_469]) ).
cnf(c_2547,plain,
( ~ in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),cartesian_product2(X1,X2))
| in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK174(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_607,c_469]) ).
cnf(c_2720,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| apply(function_inverse(X1),apply(X1,X0)) = X0 ),
inference(backward_subsumption_resolution,[status(thm)],[c_814,c_351]) ).
cnf(c_2728,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| apply(function_inverse(X1),apply(X1,X0)) = X0 ),
inference(backward_subsumption_resolution,[status(thm)],[c_2720,c_352]) ).
cnf(c_3006,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X0,sK96(X2,X3,X0,X1)),unordered_pair(X0,X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_333,c_1441]) ).
cnf(c_3007,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(sK96(X2,X3,X0,X1),X1),unordered_pair(sK96(X2,X3,X0,X1),sK96(X2,X3,X0,X1))),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_332,c_1441]) ).
cnf(c_3008,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4)
| ~ relation(X2)
| ~ relation(X4)
| in(unordered_pair(unordered_pair(X0,X3),unordered_pair(X0,X0)),relation_composition(X2,X4)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_331,c_1441]) ).
cnf(c_10488,negated_conjecture,
( relation_dom(X0) != sK188
| ~ function(X0)
| ~ relation(X0)
| in(sK189(X0),sK188) ),
inference(demodulation,[status(thm)],[c_637]) ).
cnf(c_10489,negated_conjecture,
( unordered_pair(sK189(X0),sK189(X0)) != apply(X0,sK189(X0))
| relation_dom(X0) != sK188
| ~ function(X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_636]) ).
cnf(c_49518,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_3008,c_3007,c_3006,c_2728,c_2547,c_2546,c_2463,c_2462,c_1927,c_1926,c_1925,c_1918,c_1917,c_1916,c_1825,c_1824,c_1567,c_1566,c_1565,c_1562,c_1561,c_1460,c_1456,c_1446,c_1443,c_1431,c_1428,c_885,c_884,c_883,c_882,c_881,c_880,c_879,c_878,c_877,c_875,c_874,c_873,c_872,c_871,c_869,c_867,c_866,c_865,c_864,c_863,c_862,c_861,c_860,c_859,c_858,c_857,c_856,c_855,c_854,c_853,c_852,c_851,c_850,c_849,c_848,c_847,c_846,c_845,c_844,c_841,c_840,c_839,c_838,c_837,c_836,c_835,c_834,c_833,c_832,c_831,c_830,c_829,c_828,c_827,c_826,c_825,c_824,c_823,c_822,c_821,c_820,c_819,c_818,c_813,c_812,c_811,c_810,c_809,c_808,c_807,c_806,c_805,c_804,c_803,c_802,c_801,c_800,c_799,c_798,c_797,c_796,c_795,c_794,c_793,c_792,c_791,c_789,c_788,c_787,c_786,c_785,c_784,c_783,c_782,c_781,c_778,c_777,c_776,c_775,c_774,c_773,c_772,c_771,c_770,c_769,c_768,c_767,c_766,c_762,c_761,c_760,c_759,c_758,c_753,c_752,c_751,c_750,c_747,c_746,c_745,c_744,c_743,c_741,c_740,c_739,c_738,c_737,c_736,c_735,c_734,c_733,c_732,c_731,c_730,c_729,c_728,c_726,c_725,c_724,c_723,c_722,c_721,c_720,c_719,c_718,c_717,c_716,c_715,c_714,c_713,c_712,c_711,c_710,c_709,c_708,c_707,c_706,c_705,c_704,c_703,c_702,c_701,c_700,c_699,c_698,c_695,c_694,c_693,c_692,c_691,c_690,c_689,c_688,c_686,c_685,c_684,c_683,c_682,c_681,c_680,c_679,c_678,c_677,c_676,c_674,c_673,c_672,c_671,c_670,c_669,c_668,c_667,c_666,c_665,c_664,c_662,c_661,c_660,c_659,c_658,c_657,c_656,c_655,c_654,c_653,c_652,c_651,c_650,c_649,c_648,c_647,c_646,c_645,c_644,c_643,c_639,c_638,c_10488,c_10489,c_634,c_632,c_630,c_628,c_627,c_626,c_625,c_624,c_623,c_622,c_621,c_620,c_619,c_618,c_617,c_616,c_615,c_614,c_613,c_612,c_611,c_610,c_609,c_608,c_606,c_605,c_604,c_603,c_602,c_601,c_600,c_599,c_598,c_597,c_596,c_595,c_594,c_593,c_592,c_591,c_590,c_589,c_588,c_587,c_586,c_585,c_584,c_583,c_582,c_581,c_580,c_579,c_578,c_577,c_576,c_575,c_574,c_573,c_572,c_571,c_570,c_569,c_568,c_567,c_566,c_565,c_563,c_562,c_561,c_560,c_559,c_558,c_557,c_556,c_555,c_554,c_553,c_551,c_550,c_548,c_547,c_546,c_545,c_544,c_543,c_542,c_541,c_540,c_539,c_538,c_537,c_535,c_536,c_533,c_532,c_531,c_530,c_528,c_527,c_526,c_525,c_523,c_522,c_521,c_520,c_519,c_518,c_517,c_516,c_515,c_514,c_513,c_512,c_511,c_510,c_509,c_508,c_507,c_506,c_505,c_504,c_503,c_502,c_501,c_500,c_499,c_498,c_497,c_496,c_495,c_494,c_493,c_492,c_491,c_490,c_489,c_488,c_487,c_486,c_485,c_484,c_483,c_482,c_481,c_480,c_479,c_478,c_477,c_476,c_475,c_471,c_470,c_642,c_641,c_640,c_876,c_765,c_462,c_461,c_460,c_459,c_458,c_457,c_456,c_455,c_454,c_453,c_452,c_451,c_755,c_754,c_448,c_447,c_756,c_444,c_443,c_442,c_441,c_440,c_439,c_438,c_790,c_436,c_435,c_434,c_433,c_432,c_431,c_430,c_429,c_428,c_427,c_426,c_425,c_424,c_423,c_422,c_421,c_420,c_419,c_417,c_416,c_413,c_412,c_411,c_409,c_408,c_407,c_406,c_404,c_403,c_402,c_400,c_399,c_397,c_394,c_393,c_391,c_390,c_389,c_387,c_384,c_383,c_382,c_380,c_378,c_415,c_414,c_395,c_374,c_373,c_372,c_371,c_370,c_369,c_368,c_367,c_366,c_365,c_364,c_363,c_362,c_388,c_360,c_359,c_358,c_357,c_356,c_355,c_354,c_353,c_352,c_351,c_350,c_349,c_348,c_347,c_346,c_343,c_342,c_341,c_340,c_339,c_338,c_337,c_336,c_335,c_334,c_330,c_329,c_328,c_327,c_326,c_325,c_324,c_323,c_322,c_321,c_320,c_319,c_318,c_317,c_316,c_315,c_314,c_313,c_312,c_311,c_310,c_309,c_308,c_307,c_304,c_303,c_302,c_301,c_300,c_299,c_298,c_297,c_296,c_295,c_294,c_293,c_292,c_291,c_290,c_289,c_288,c_287,c_286,c_285,c_696,c_283,c_282,c_281,c_280,c_279,c_278,c_277,c_276,c_275,c_274,c_273,c_272,c_271,c_270,c_269,c_268,c_267,c_266,c_265,c_264,c_263,c_262,c_261,c_260,c_259,c_258,c_257,c_256,c_255,c_254,c_253,c_252,c_251,c_250,c_249,c_248,c_247,c_246,c_245,c_244,c_697,c_242,c_241,c_868,c_234,c_232,c_231,c_230,c_229,c_228,c_227,c_226,c_225,c_224,c_223,c_222,c_221,c_220,c_218,c_217,c_216,c_215,c_214,c_213,c_212,c_211,c_210,c_209,c_208,c_206,c_205,c_204,c_203,c_202,c_201,c_200,c_199,c_198,c_197,c_196,c_195,c_194,c_193,c_192,c_191,c_190,c_189,c_188,c_187,c_186,c_727,c_183,c_182,c_179,c_178,c_177,c_176,c_175,c_173,c_172,c_171,c_170,c_169,c_168,c_167,c_166,c_162,c_161,c_160,c_159,c_158,c_157,c_156,c_155,c_154,c_153,c_152,c_150,c_149,c_148,c_147,c_146,c_145,c_144,c_143,c_142,c_140,c_139,c_138,c_137,c_136,c_135,c_134,c_133,c_131,c_130,c_129,c_128,c_127,c_126,c_125,c_124,c_123,c_122,c_121,c_120,c_119,c_118,c_117,c_116,c_115,c_114,c_113,c_112,c_111,c_110,c_109,c_108,c_107,c_106,c_105,c_104,c_103,c_102,c_101,c_100,c_99,c_98,c_97,c_96,c_95,c_94,c_90,c_89,c_88,c_87,c_86,c_85,c_84,c_83,c_82,c_81,c_80,c_76,c_75,c_74,c_524,c_71,c_67,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_58,c_238,c_55,c_54,c_240,c_239,c_51,c_50,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU284+2 : TPTP v8.2.0. Released v3.3.0.
% 0.04/0.13 % Command : run_iprover %s %d THM
% 0.12/0.35 % Computer : n027.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Jun 21 13:06:54 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 82.59/11.89 % SZS status Started for theBenchmark.p
% 82.59/11.89 % SZS status Theorem for theBenchmark.p
% 82.59/11.89
% 82.59/11.89 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 82.59/11.89
% 82.59/11.89 ------ iProver source info
% 82.59/11.89
% 82.59/11.89 git: date: 2024-06-12 09:56:46 +0000
% 82.59/11.89 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 82.59/11.89 git: non_committed_changes: false
% 82.59/11.89
% 82.59/11.89 ------ Parsing...
% 82.59/11.89 ------ Clausification by vclausify_rel & Parsing by iProver...
% 82.59/11.89
% 82.59/11.89 ------ Preprocessing...
% 82.59/11.89
% 82.59/11.89 ------ Preprocessing...
% 82.59/11.89
% 82.59/11.89 ------ Preprocessing...
% 82.59/11.89 ------ Proving...
% 82.59/11.89 ------ Problem Properties
% 82.59/11.89
% 82.59/11.89
% 82.59/11.89 clauses 765
% 82.59/11.89 conjectures 2
% 82.59/11.89 EPR 116
% 82.59/11.89 Horn 593
% 82.59/11.89 unary 94
% 82.59/11.89 binary 236
% 82.59/11.89 lits 2242
% 82.59/11.89 lits eq 353
% 82.59/11.89 fd_pure 0
% 82.59/11.89 fd_pseudo 0
% 82.59/11.89 fd_cond 21
% 82.59/11.89 fd_pseudo_cond 105
% 82.59/11.89 AC symbols 0
% 82.59/11.89
% 82.59/11.89 ------ Input Options Time Limit: Unbounded
% 82.59/11.89
% 82.59/11.89
% 82.59/11.89 ------
% 82.59/11.89 Current options:
% 82.59/11.89 ------
% 82.59/11.89
% 82.59/11.89
% 82.59/11.89
% 82.59/11.89
% 82.59/11.89 ------ Proving...
% 82.59/11.89
% 82.59/11.89
% 82.59/11.89 % SZS status Theorem for theBenchmark.p
% 82.59/11.89
% 82.59/11.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 82.59/11.92
% 82.59/11.92
%------------------------------------------------------------------------------